Method and device for generating a reference frequency

专利摘要:
The invention provides for the use of a first optical resonator (3a, 24) and a second optical resonator (25), wherein the first resonator (3a, 24) has a first resonator mode with a first frequency f1, and the second resonator (25) has a second resonator mode with a second frequency f2, the frequencies of the two resonator modes being functions of an operating parameter BP and assuming the values f1 and f2 at a predetermined value BP0 of the operating parameter such that f1 (BP0) = f1 and f2 (BP0) = f2, the resonators (3a; 24,25) being designed so that the first derivative of the frequencies f1 (BP), f2 (BP) after BP or at least a difference quotient around BP0 except for a deviation of maximum ± 0.1% coincide, wherein light of the first frequency f1 is stabilized by means of the first resonator to the first frequency f1 and light of the second frequency f2 by means of the second resonator a to the second frequency f2, and the difference between the stabilized frequencies f1 and f2, Df = | f1 - f2 |, is determined to obtain the stabilized reference frequency Df.
公开号:AT518549A4
申请号:T50282/2016
申请日:2016-04-06
公开日:2017-11-15
发明作者:Trupke Michael
申请人:Technische Universität Wien；
IPC主号:

专利说明:

METHOD AND DEVICE FOR GENERATING A REFERENCE FREQUENCY
FIELD OF THE INVENTION
The present invention relates to a method for generating a reference frequency
The present invention also relates to a device for generating a reference frequency.
STATE OF THE ART
Frequency references or their generation are known in different forms. Examples are quartz oscillators, microwave transitions in atomic ground states (rubidium furnace, cesium reference,
Hydrogen maser) and optical transitions in atoms (strontium) or ions (aluminum). In everyday use, quartz oscillators are mainly used for cost reasons, while atomic references are used where higher accuracies are required, for example in the scientific, military or telecommunications field. Important applications besides timekeeping itself are navigation via satellite signals (e.g., GPS) or direct navigation by means of acceleration measurement, as well as network synchronization and frequency allocation for communication channels in radio, satellite, or cellular networks.
Quartz oscillators are inexpensive and compact and can have thermal stabilization, time delays of less than 100 milliseconds per year, and short time stabilities of less than 1 picosecond per second. Favorable quartz references, as used in commercial navigation systems, have accuracies in the range of 10 ~ 6, while military systems with fine temperature compensation have accuracies in the range of 10 ~ 8 to 10 ~ 10. This accuracy allows a more precise localization, since the position relative to the positioning satellites is expressed in units of time by means of the speed of light. Atomic references are much more expensive, but offer much higher accuracy. Cesium clocks are the international standard on the basis of which the second is defined, and are thus by definition absolutely exact. However, they nevertheless show short time fluctuations, for example because of the finite interaction time of the atoms with the oscillating field. Strontium clocks and aluminum ion clocks are the most accurate known references, but require highly complex laser systems and traps to cool, hold, and measure their resonant frequency. In addition, the reference frequencies provided thereby can not or only insufficiently selected or varied. For more information on quartz references and atom-based frequency references, refer to Ref. 1 ["Quartz Crystal Resonators and Oscillators for Frequency Control and Timing Applications - A Tutorial"; JR Vig; Rev. 8.5.6.2, available at http: //www.ieee-uffc .org / frequency-control].
Optical resonators have also long been used as frequency references, mainly to stabilize the optical frequency of a laser, as described in Ref. 2, "Laser-Based Measurements for Time and Frequency Domain Applications: A Handbook," P. Maddaloni, M. Bellini An advantage of such references is the uninterrupted interaction of the light with the resonator Disadvantages are the vibration dependence, frequency shifts due to change in length and frequency shift due to deposits on or material changes in the mirror surfaces Contrary to quartz-based references, optical references do not require moving parts, unlike atom-based references, optical references do not have intrinsic magnetic field dependence, and optical references are much less expensive than atomic references, but do not achieve accuracy.
On the other hand, in view of the increasing shift from electronic methods to optical methods in telecommunications and data processing, it would be desirable to have highly accurate optical references that can be seamlessly integrated into modern data distribution and data processing structures.
Finally, in addition to the aforementioned application problems, there is the fundamental theoretical problem that the current atomic time standards depend on physical quantities such as the fine-structure constant. In this respect, a long-term stable, purely optical reference, which is determined only by geometry and speed of light, would have a fundamental appeal, but currently the required accuracy to compete with atomic references, is not attainable by optical references.
OBJECT OF THE INVENTION
It is therefore an object of the present invention to provide a method and a device for generating a reference frequency available, which avoid the disadvantages mentioned above. In particular, the reference frequency should at the same time be highly stable and comparatively inexpensive.
Preferably, the reference frequency should be in a frequency range between about 100 MHz and several terahertz and be as freely selectable as possible. Particularly preferably, the method according to the invention or the device according to the invention is intended to permit the integration of the generation of the reference frequency into photonic structures, as they are increasingly used in communications and data processing technology.
PRESENTATION OF THE INVENTION
The core of the invention is the realization that optical resonators can be designed such that in the range of the desired operating parameters (such as a pressure or a temperature, in principle, however, magnetic or electric field strengths are conceivable) two different optical modes each have a dependency of their Frequency of changes in the operating parameters, in particular the length or the temperature of the respective resonator, this dependence for the two modes but has almost the same sensitivity. Consequently, the difference Δf between the frequency f1 of the first mode and the frequency f2 of the second mode, i. Äf = | fl - f2 |, stable to parameter changes, so that Äf can serve as a stable reference frequency. Calculations have shown that for an approximately equal behavior of the modes as a function of an operating parameter, in particular the resonator length or the temperature, a slight deviation of the sensitivities of fl and f2 is tolerable, which can typically be up to ± 0.1%. It should be noted here that under optical modes generally not necessarily visible light is to be understood, but it can also be long-wave or short-wave modes.
Accordingly, the invention provides a method for generating a reference frequency Af using a first optical resonator and a second optical resonator, the first resonator having a first resonator mode having a first frequency fl and the second resonator having a second resonator mode having a second frequency f2 the frequencies of the two resonator modes are functions of an operating parameter BP, in particular a temperature, and assume the values fl and f2 at a predetermined value BP0 of the operating parameter, so that fl (BP0) = fl and f2 (BP0) = f2, the resonators thus be designed such that the first derivative of the frequencies fl (BP), f2 (BP) to BP or at least a difference quotient around BP0 to a maximum deviation of ± 0.1% match, wherein light of the first frequency fl by means of the first resonator is stabilized to the first frequency fl and light of the second frequency f2 by means of the second Resonat ors to the second frequency f2, and where the difference between the stabilized frequencies
, is determined to obtain the stabilized reference frequency Af.
The percentage deviation can be related to fl or f2.
By way of explanation, it should be noted that said deviation fundamentally depends on the fluctuation range of the operating parameter BP. For example, if the temperature can be stabilized to ± 1 mK as the operating parameter, then a difference between the thermal coefficients of 0.1% will result in a stability of 10 ~ 6, which corresponds to a favorable quartz oscillator.
Lasers are commonly used to generate the light of the resonator modes, but other light sources may be used. The latter applies in particular because the principle of the invention is basically not limited to the optical wavelength range, i. In principle, it is also possible to proceed analogously at shorter or longer wavelengths, e.g. with radio, microwave or terahertz systems.
In this case, a single laser can be used, which basically generates light of frequency fl and at the same time in a conventional manner, e.g. by means of an acousto-optical frequency shifter, can also be used to produce light of frequency f2. Analogously, therefore, the invention provides a device for generating a reference frequency Af, wherein a first optical resonator is provided, which has a first resonator having a first frequency fl, and a second optical resonator having a second resonator having a second frequency f2, wherein the frequencies of the two resonator modes are functions of an operating parameter BP, in particular of a temperature, and assume the values fl and f2 at a predetermined value BP0 of the operating parameter, so that fl (BP0) = f1 and f2 (BP0) = f2, the resonators thus are designed so that the first derivative of the frequencies fl (BP), f2 (BP) after BP or at least a difference quotient around BP0 to a maximum deviation of ± 0.1% match, the device further comprising first light generating means for generating light the first frequency fl and second light generating means for generating light of the second frequency f2, wherein the first light-generating means and the second light-generating means preferably comprise a total of at least one laser, the apparatus further comprising first stabilizing means for stabilizing the first frequency fl, and second
Stabilizing means for stabilizing the second frequency f2; and determining means being provided for determining the difference between the stabilized frequencies fl and
, to determine and to obtain the stabilized reference frequency Af.
The essential influencing variable or the essential operating parameter is in practice the temperature, since this causes a change in the dimensions, in particular the resonator length of the respective resonator. The frequency fl of the first mode of a first resonator of a resonator length Li is in the case of a Fabry-Perot resonator given by the condition fl = c * mi / (2 * ni * Li), where c is the speed of light, ni is the refractive index for the first resonator mode in the first resonator and irq an integer. This applies to a certain temperature, an operating point temperature at which the resonator length Li is present. Taking into account the temperature dependence of the resonator length Li by means of a linear temperature coefficient ßi of the first resonator so the temperature-dependent frequency fl results
where T indicates the temperature difference to the operating point temperature. Approximately thus results
Similarly, for the temperature-dependent frequency f2 of a second resonator, the resonator length L2 is approximately obtained
, where m2 is an integer, n2 is the refractive index of the second resonator mode in the second resonator, and β2 is the linear temperature coefficient of the second resonator. If one now forms the difference f1 (T) -f2 (T) and sets its derivative to T zero, one obtains the following condition, which must be satisfied in order to achieve exactly the same temperature behavior of the two modes:
Exactly the same condition also arises when one assumes ring resonators, also referred to as whispering gallery mode resonators, in which case the resonator lengths Li, L2 are given by the perimeters of the resonators and approximately
applies. The integer numbers m2, m2 can therefore be understood as the number of wavelengths of the first and second resonator modes in the first and second resonators, respectively.
Using the above condition, the design of the resonators can thus be carried out by the person skilled in the art so that known geometries and the linear temperature coefficients-in particular by suitable choice of material-are adapted accordingly. In particular, in the case of a known material, a corresponding dimensioning can be carried out or a corresponding choice of material can be made for a given dimensioning.
Typically, this involves first a numerical treatment and, based on this, the manufacture of the resonator. There may be a slight deviation from the above equation at a certain operating point temperature T2 due to manufacturing tolerances. That the equation would only be satisfied in this case if m2.2 are not integers. In practice, however, it turns out that on the one hand a specific temperature change or
Adjusting the temperature, the properties of the optical resonators can be changed so that the equation at a further operating temperature T2 ^ Ti is finally satisfied.
On the other hand, complex calculations and tests have shown that for an approximately equal behavior of the modes depending on a parameter, in particular the resonator length or the temperature, the above equation does not need to be fulfilled identically, but a slight deviation is tolerable, typically up to zero , 1%. Only with larger deviations, the achievable stability of the reference frequency is so low that other methods such. the generation of a reference frequency by means of quartz oscillators are more interesting in practice, especially for cost reasons. That is the design condition to be satisfied for the design of the resonators
or in words:
except for a maximum deviation
The percentage deviation can be on the left side
or on the right side of the tree
Be related equation.
Alternatively, a stable mode pair, that is to say a first resonator mode and a second resonator mode whose frequencies have approximately the same temperature behavior, can be generated by coupling two modes. The coupling, which can be done by appropriate design of the resonators in a conventional manner, causes a split mode spectrum, wherein the strength of the coupling, 2 * g, the reference frequency Äf. Accordingly, two successive modes can be found in the split-mode spectrum, which form the first resonator mode with frequency fl and the second resonator mode f2, wherein
applies. The two coupled
Resonator modes are also referred to below as a coupled mode pair.
Therefore, it is provided in a preferred embodiment of the method according to the invention that the first optical resonator has a resonator length Li and a linear temperature coefficient ßi and the second optical
Resonator a resonator L2 and a linear temperature coefficient ß2, wherein the resonators are designed so that
* n2 except for a maximum deviation of ± 0.1% with m2, m2 integers corresponding to the number of wavelengths of the first and second resonator modes in the first and second resonators, respectively, and n2, n2 the refractive indices for the first resonator mode in the first resonator and the second resonator mode in the second resonator, or in that coupled modes are present in the first and second resonators, and a mode spectrum split due to the coupling includes the first resonator mode and the second resonator mode.
Analogously to the above, it is provided in a preferred embodiment of the device according to the invention that the first optical resonator has a resonator length L2 and a linear temperature coefficient β2 and the second optical resonator has a resonator length L2 and a linear temperature coefficient β2, wherein the resonators are designed that
except one
Deviation of ± 0.1% maximum applies to m2, m2 integers corresponding to the number of wavelengths of the first and second resonator modes in the first and second resonators, and n2, n2 to the refractive indices for the first resonator mode in the first resonator and second resonator mode in the second resonator or that coupled modes are present in the first and second resonator and a mode spectrum split due to the coupling includes the first resonator mode and the second resonator mode.
In order to stabilize the frequencies f1, f2, fundamentally different means or methods known from the prior art can be used. A well-established method is the Pound-Drever-Hall method. Accordingly, it is in a preferred embodiment of the invention
Device provided in that the first stabilizing means comprise first modulation means to aufzumodulieren the light of first frequency fl sidebands, and first demodulation means having a first detector for generating a first error signal by means of the first detector reflected back or transmitted modulated light of the first frequency fl, and first control means for using the first error signal to regulate the first light generating means to stabilize the first frequency fl, and the second stabilizing means to comprise second modulating means for modulating sidebands to the second frequency light f2 and second demodulating means to a second detector to generate a second error signal by means of the modulated light of the second frequency f2 reflected or transmitted back to the second detector, and second control means to use the second error signal to generate the second error signal
To regulate light generating means so that the second frequency f2 is stabilized. That it is determined with the demodulation of the symmetry of the intensity of the sidebands around the central frequency and the light as long as finely adjusted until a possible symmetrical distribution exists.
To produce the stable pair of modes, the first and second optical resonators need not necessarily be separate resonators, so that the above condition is met. Rather, the first and second optical resonators can be simultaneously formed by a single resonator in which both modes are present. This is not limited to a specific type of resonator, in particular, in this case as a resonator, a Fabry-Perot interferometer or resonator or a ring resonator can be used. It is therefore provided in a preferred embodiment of the method according to the invention that the first resonator simultaneously also the second
Resonator forms and is identical to this. Analogously, it is provided in a preferred embodiment of the device according to the invention that the first resonator simultaneously forms the second resonator and is identical to this.
Of course, such a first resonator, which also simultaneously forms the second resonator and is identical to it, is also suitable for producing coupled modes. For example, a mode-locking can be done in a simple manner by placing a partially reflecting element in the beam path, thereby producing counter-rotating coupled modes. That the reflective element preferably reflects only a portion of the light and is transparent to a portion of the light. In particular, in the case of ring resonators, a stable mode pair can be generated in this way, in which the
Propagation direction of a resonator clockwise and the propagation direction of the other resonator counterclockwise. Therefore, it is provided in a preferred embodiment of the method according to the invention that the mode coupling is generated by means of an at least partially reflective element. Analogously, it is provided in a preferred embodiment of the device according to the invention that an at least partially reflective element is provided to produce the mode coupling.
If the first and second resonators are separate resonators, one way to create coupled modes is to couple the resonators, where the coupling may be evanescent, for example. Ring resonators are particularly suitable for such an evanescent, since the coupling of light into such resonators is usually evanescent. It is therefore provided in a preferred embodiment of the method according to the invention that the mode coupling is generated by evanescent coupling of the first resonator to the second resonator. Analogously, it is provided in a preferred embodiment of the device according to the invention that the first resonator is evanescently coupled to the second resonator in order to generate the mode coupling.
Elaborate analyzes of optical resonators of the Fabry-Perot type have shown that with skillful design of the resonator different spatial modes can be used to produce a stable pair of modes. In this case, for modes with the same longitudinal index but different transverse indices, the frequency difference of the modes,
be made extremely stable. The choice of the basis for describing the modes with longitudinal and transversal indices does not matter. For example, the Hermite-Gauss base can be used. It is therefore provided in a preferred embodiment of the method according to the invention that the two resonator modes can be described by one longitudinal index and two transverse indices, the first resonator mode and the second resonator mode having the same longitudinal index and at least one different transverse index. Analogously, it is provided in a preferred embodiment of the device according to the invention that the two resonator modes are each characterized by a longitudinal index and two transverse indices, wherein the first resonator and the second resonator have the same longitudinal index and at least one different transverse index. It should be noted that in optical resonators of the Fabry-Perot type, in addition to the resonator length, it is also possible to vary the radii of curvature of mirrors, with skillful design of these radii of curvature further improving the stability of the reference frequency.
In principle, by controlling the respective operating parameter, in particular by controlling the temperature, the respective resonator length of the optical resonators can be controlled and thus the stability of the reference frequency λ f can be improved. It turns out, however, that the long-term stability can be dramatically improved by producing light of a third frequency f3, which has a greater dependence on the operating parameter, in particular a greater temperature dependence, than λf, and the difference of this third frequency f3 with one of the other two Frequencies fl or f2 is used as the comparison frequency f4. The larger dependency can be given mathematically in general as an absolutely larger first derivative (according to the respective operating parameter, in particular the temperature) or at least as an absolutely larger difference quotient around BP0.
By once determining the ratio or the difference between f4 and λf at the operating point (ie at BP0), an error signal can be generated by the subsequent, continuous comparison of f4 and λf that for controlling the operating parameter, in particular the temperature, for example by means of a Heizstromquelle and / or a Peltier element, can be exploited. Due to the higher sensitivity of f3, this can be used to control Äf much more sensitively than would be possible on the basis of Äf or fl and f2 alone. Therefore, in a preferred embodiment of the method according to the invention, light of a third frequency f3 is generated and stabilized by means of a resonator, where f3 has a greater dependence on the operating parameter, in particular on the temperature than λf, that a comparison frequency f4
or f4 = | f3 - f2 | is given and that the ratio
or the difference f4-Äf determined and to
Control of operating parameter control means, in particular temperature control means, which are provided for controlling the operating parameter, in particular the temperature, of the first resonator and / or second resonator, is used. Analogously, it is provided in a preferred embodiment of the device according to the invention that third light generating means for generating light of a third frequency f3 are provided and a resonator for stabilization, wherein f3 has a greater dependence on the operating parameter, in particular of the temperature, as Af that a Comparison frequency f4 by f4 = | f3 - fl | or f4 = | f3 - f2 | is provided, wherein further determining means are provided to determine the ratio f4 / Af or the difference f4-Af, and that operating parameter control means, in particular temperature control means are provided to the operating parameters, in particular the temperature of the first resonator and / or the second Resonator depending on the ratio f4 / Af or the difference f4-Af to control.
It should be noted that the light of the frequency f3 does not necessarily have to be visible light, but it may also be longer-wave or shorter-wave light. Overall, in this way the reference frequency can be stabilized for a long time without the need for an external, atomic or otherwise generated reference.
To stabilize the light of the frequency f3, the existing resonator or the existing resonators or an additional resonator can be used, so that all conceivable constructive or manufacturing cost requirements can be met. It is therefore provided in a preferred embodiment of the method according to the invention that for stabilizing the light of the third frequency f3, the first resonator and / or the second
Resonator or a third resonator can be used. Analogously, it is provided in a preferred embodiment of the device according to the invention that the resonator for stabilizing the light of the third frequency f3, the first resonator and / or the second resonator or a third resonator.
In a particularly preferred embodiment of the method according to the invention, it is provided that the light of the third frequency f3 is formed by a comb mode of a frequency comb. Analogously, it is provided in a particularly preferred embodiment of the device according to the invention that the third light generating means comprise a frequency comb to form the light of the third frequency f3 as a comb mode of the frequency comb or by means of a tooth spacing of the comb modes of the frequency comb. The stabilization of f3 can in this case be effected by the first and / or second resonator by setting a tooth spacing of the frequency comb by the λf obtained, if necessary multiplied by a factor. This stabilization therefore takes place before the feedback loop is performed by comparing f4 with λf. The use of a frequency comb has the advantage that f3 can be selected to be so large that in any case a significantly greater temperature dependence for f3 or f4 than for Äf is given, which is used for a correspondingly precise long-term stabilization of Äf by means of the temperature control already described above can. Typically, in practice, f3 is selected in the range of 100 to 1000 THz.
As already noted, different types of resonators can be used, in particular Fabry-Perot resonators or interferometers or ring resonators (also referred to as whisper-gullet mode resonators). Accordingly, it is in a preferred embodiment of the invention
Provided method that a Fabry-Perot resonator is used as the first resonator and / or as a second resonator. Analogously, it is provided in a particularly preferred embodiment of the device according to the invention that the first resonator and / or the second resonator is a Fabry-Perot resonator. Furthermore, in a preferred embodiment of the method according to the invention, it is provided that an optical ring resonator is used as the first resonator and / or as the second resonator. Analogously, it is provided in a particularly preferred embodiment of the device according to the invention that the first resonator and / or the second resonator is an optical ring resonator.
The optical resonators mentioned in particular have the advantage of miniaturization, so that they can be easily integrated into photonic structures on optical chips or in mass production-capable microsystems. Fabry-Perot resonators can be realized, for example, as waveguides with integrated Bragg mirrors. To form ring resonators, closed waveguides may be used, which may be circular, elliptical, or stadium shaped, for example, but may in principle take any closed form. Accordingly, in a preferred embodiment of the method according to the invention, it is provided that an optical resonator embodied as a waveguide on an optical chip is used as the first resonator and / or as the second resonator. Analogously, it is provided in a particularly preferred embodiment of the device according to the invention, that the first resonator and / or the second resonator is formed as a waveguide on an optical chip.
BRIEF DESCRIPTION OF THE FIGURES
The invention will now be explained in more detail with reference to exemplary embodiments. The drawings are exemplary and should be the
Although set out the idea of the invention, it does not restrict or even reproduce it in any way.
Showing:
1 shows a schematic representation of a Fabry-Perot type optical resonator (also referred to as "cavity").
FIG. 2 a shows the variation of the frequency dependencies with the length L of the resonator from FIG. 1
2b shows an enlarged detail view of a portion of Fig. 2a
Fig. 3 is a schematic representation of an embodiment of a device according to the invention for generating a reference frequency, wherein the frequency of an oscillator is stabilized to the reference frequency
Fig. 4 is a schematic representation of another
Embodiment of the device according to the invention, wherein the length of the resonator is stabilized by means of the temperature to the ratio of two frequency differences between three optical modes
Fig. 5 is a schematic representation of another
Embodiment of the device according to the invention, in which the length of the resonator is stabilized by the temperature on the difference between the optical frequency of a mode of the resonator and a mode of a frequency comb, wherein the tooth spacing in the frequency comb is determined by the reference frequency
6 a) to d) are schematic representations of the relevant frequencies for the application of FIG. 5
Fig. 7 a) to d) the effect of deviations from
Resonator properties of their ideals
Fig. 8 shows a further embodiment of the device according to the invention, wherein three ring resonators are used
Fig. 9 shows a further embodiment of the invention
Device analogous to FIG. 8, wherein, however, the first and the second ring resonator are coupled
10a is a diagrammatic illustration of the frequencies of the modes of the individual ring resonators of FIG. 8 and of the coupled ring resonators of FIG. 9 as a function of temperature (relative to an operating point temperature). FIG.
10b is a diagrammatic illustration of the reference frequency in the case of the coupled ring resonators of FIG. 9 as a function of the temperature (relative to an operating point temperature).
WAYS FOR CARRYING OUT THE INVENTION
Fig. 1 shows a schematic representation of a Fabry-Perot resonator 3a, which can be used according to the invention for generating a stable reference frequency. In such an optical resonator 3a, the frequency of an optical mode is determined by radii of curvature RI, R2 of a first mirror 1 and a second mirror 2 and by a length L of the resonator 3a. The frequency f of a mode of the resonator 3a in vacuum is
The length L of the resonator is determined by the dimension of a holder 3 of the mirror 1, 2. The speed of light c determines the circulation time of a light particle or photon in the resonator 3a. This cycle time is further conditioned by the transversal mode indices m and n, which are part of the set of integer, positive integers including 0. For the above formula, the Hermite-Gauss base was chosen for the resonator modes. The principle presented here is, however, independent of the base and can also be described in every other complete basis.
The longitudinal mode index is given by 1, also part of the whole positive numbers. The frequency difference between two modes with longitudinal indices 11 and 12 and transversal indices ml = m2 = nl = n2 = 0 is given by
and thus is always dependent on the length L of the resonator 3a. According to the invention, the frequency difference λ f between two modes with the same longitudinal index 1, but different transverse indices, for example ml = 0, nl = 0 and m2 = 1, n 2 = 0, can be used as reference frequency, since this proves to be extremely stable, as will be further explained below. The resulting frequency difference is λf
The nonmonotonic behavior of the arccos function makes it possible to find combinations of L, RI and R2 for which the length dependence of the frequency has reversal points and even deviates from the reference value in the third order.
This fact can be seen in Fig. 2a. Here, the first derivative of the frequency difference or the reference frequency λ f after the resonator length L is shown for different combinations of R 1 and R 2. The resonator length L is normalized in Fig. 2a for all functions to the maximum length Lmax = Rl + R2. The derivative is in turn normalized to the local frequency difference or the local reference frequency λf at the length L / Lmax. The functions shown in Fig. 2a correspond to the following configurations of the resonator 3a: mirror 1 flat, mirror 2 curved ("plano-concave", dashed line);
Mirror 1 and mirror 2 with the same radius of curvature ("symmetrical", dotted line), mirror 1 with radius of curvature RI, mirror 2 with radius of curvature R2 = <J> * R1 ("optimal", solid line). The factor Φ will be explained later.
For comparison, the behavior of the normalized derivative for the frequency of a single optical mode with m = n = 0 is also shown in FIG. 2a (dot-dash line).
In Fig. 2b the region around L / Lmax ~ 0.8 is shown in detail.
Here it is clearly visible that the derivatives have a zero crossing both for the symmetrical and for the plano-concave geometry, while the derivative for the optimal case even has quadratic behavior.
The optimum case can be achieved by setting the ratio of the radii of curvature Φ ~ 1.7048. The most stable point is then at an optimal resonator length of Lopt ~ 2.0428 * R1. The size Lopt can be solved by solving the transcendental equation
being found. The optimum ratio Φ of the radii of curvature RI, R2 can thus be considered
be expressed. The zero-crossing length for symmetric and plano-concave resonators 3a can thus be solved by solving the equation
with Lx = L / Lmax, and is ~ 0, 8446 * Lmax.
It should be noted here that all the resonators 3a with R2 / R1 << J> have at least one zero crossing in the first derivative. With favorable combinations of radii RI, R2 and length L, therefore, a stable frequency difference λf between selected modes can be measured. Such a resonator 3a can thus serve as a frequency reference, which is insensitive to changes in length caused by vibrations, for example.
Factors affecting both the length L and the radii of curvature RI, R2 of the mirrors 1, 2 have a more marked effect on the reference frequency λ f. Especially in a vacuum, the most important factor is the temperature. This can be done by extending the expression for the frequency difference,
With and
(with q = 1 or q = 2). Here only linear and quadratic terms of temperature dependence were quoted, which are dominant in virtually all cases. Here, <* s, l and <* S, 2 are the linear and quadratic expansion coefficients of the holder, while (X-Rq> i and (X-Rq> 2)
Expansion coefficients of the mirrors are. T denotes the temperature difference to an operating point temperature at which the length L is present.
Hereinafter, it is assumed for the sake of simplicity that the two mirrors 1, 2 are made of the same material, so that
applies. It is this
Note that the temperature dependence is determined by a suitable choice of different coefficients - e.g. by choosing different materials - for the two mirrors 1, 2 can be further reduced.
Since, as explained above, small changes in length are negligible, the reference frequency λ f (T) changes mainly due to the thermal expansion of the mirrors 1, 2. The mirrors 1, 2 may consist of a material which at a certain temperature, preferably the operating point temperature , has a zero crossing of the linear temperature coefficient, ie
so that only a quadratic temperature dependence exists. These
Materials are routinely used in optics, such as ULE® glass at room temperature or silicon at 124K.
But if the holder 3 consists of a material with non-vanishing linear thermal coefficient, the frequency difference between transverse fundamental modes Δί (Τ, Ο, Ο) and their optical frequencies will have a corresponding thermal dependence.
This sensitivity is used in the embodiments of FIGS. 4 and 5 described below for the self-stabilization of the resonator.
In the above description, it has been assumed throughout that the optical resonator 3a is in an evacuated container. However, the invention can also be rendered functional in a light-transmitting medium such as air. For this purpose, the dependence of the speed of light on the refractive index and its dependence on pressure P, temperature T and other environmental influences X, in all formulas by means of the substitution c ^ c / n (T, P, X) must be introduced. In this extension, environmental influences, which depend on the temperature, such as the pressure P in an airtight resonator 3a, can be compensated for by slightly changing the parameters. Temperature independent parameters, e.g. Contamination of the medium can not be compensated and leads to a frequency surge.
Fig. 3 shows schematically an embodiment of a device according to the invention for generating the reference frequency Af, wherein the frequency of a controllable oscillator 7 is stabilized to the reference frequency Af. A laser 4 generates a linearly polarized optical wave with a small frequency width. This is passed to an electro-optical modulator 4a, which generates sidebands on the optical wave. The modulated optical wave is conducted via a polarizing beam splitter 4b and a quarter wave retardation optical system 4c to the optical resonator. The latter is shown again in FIG. 3 - and also in FIGS. 4 and 5 - as a Fabry-Perot resonator 3 a, but in principle it would also be possible to use another type of resonator, in particular also a ring resonator.
The polarization optics 4b and 4c ensure that the light reflected by the resonator 3a leaves the beam splitter 4b in the direction of a demodulator 4d. The sidebands make it possible to generate an error signal by means of the demodulator 4d, by means of which the laser frequency is at the frequency f1 of a first resonator mode, which is a transverse fundamental mode M1 (with mode indices 11, ml = 0, nl = 0) of the optical resonator 3a, can be stabilized, which is indicated by the dashed, pointing to the laser 4 arrow in Fig. 3. This stabilization method is known as the Pound-Drever-Hall method, cf. Ref. 6 [Drever, R.W.P., Hall, J.L., Kowalski, F.V., Hough, J., Ford, G.M., Munley, A.J., &amp; Ward, H .; "Laser phase and frequency stabilization using an optical resonator"; Applied Physics B, 31 (2), 97-105 (1983)].
A part of the laser beam of the laser 4 is now guided by means of a beam splitter 5 to an acousto-optical frequency shifter 6. This beam is passed through a second electro-optical modulator 6a and is passed through a second polarizing beam splitter 6b and a second quarter wave retardation optical system 6c to the optical resonator 3a. The aim of this second beam path is to excite a second resonator mode in the form of a higher transverse mode M2 with the same longitudinal index 12 = 11 (for example, with indices m2 = 1, n2 = 0) and the frequency f2. For this, the beam profile must be matched to that of the desired second resonator mode. This can be achieved, for example, by a structured phase plate 6e, as often happens in optics and quantum optics.
Also this beam is after its re-emergence or reflection by the resonator 3a through the
Polarization optics 6b, 6c led to a second demodulator 6d. The second electro-optic modulator 6a may be operated at a different frequency than the electro-optic modulator 4a to allow clean demodulation at the second demodulator 6d. The error signal is determined here directly by the Pound-Drever-Hall method: The frequency f2 is given by fl + Af. However, the laser beam has the frequency fl + f (7), where f (7) is the frequency of the oscillator 7. If f (7) Φ Af, then the Pound Drever Hall measurement will output an error signal. The error signal thus arises from the difference between fl + f (7) and f2. Expressed in shorter terms, it can therefore be said that the resulting error signal corresponds to the difference between the oscillator frequency f (7) and Af and the frequency f (7) of the oscillator 7 to the frequency difference between the two excited modes of the resonator 3a, ie to the reference frequency Af , is stabilized.
A temperature controller 8 can further minimize the already low sensitivity of the structure. Such regulators are commercially available for stabilization to fluctuations around 1CT3K.
The resonator 3a itself can be used to achieve an even higher frequency accuracy or stability of the reference frequency Af. An example of such a system is shown in the embodiment of FIG. Here, a further partial beam is guided by the beam splitter 5 to a further acousto-optic modulator 10. This is operated with a frequency that by means of a suitable, fixed
Frequency multiplier 9, which multiplies the incoming frequency by a factor af, is generated directly from the oscillator 7. The acousto-optic modulator 10 thereby generates a beam which is exactly resonant at the desired operating point with another longitudinal, third resonator mode M3 (with indices 13-11, n = 0, m = 0) with a frequency f3. By means of a further electro-optical modulator 10a, which is connected downstream of the acousto-optic modulator 10, sidebands are generated on the optical wave - analogous to the above-described function of the electrooptical modulator 4a.
Since the frequency distance f4 between the frequency f3 of this third resonator mode and the laser frequency or the frequency fl of the first resonator mode has a much greater temperature dependence than the frequency spacing λf of the second frequency f2 of the higher transverse mode M2 from the laser frequency f1, a temperature deviation will result in that the resonance condition for f3 is no longer satisfied.
This deviation is detected by a third demodulator 10d. Similar to the above, the error signal can be detected as a difference between fl + λf * af and f3. Here, f3 is the frequency of the resonator mode M3 at the temperature setpoint. In short, the error signal corresponds to the difference between f4 and λf * af. The error signal can now be passed to a Heizstromquelle 12 to control these.
In the example shown, optical circulators 11 and another polarization optics 13 are used to guide the various beams to the desired demodulators 4d, 10d. The absolute frequency deviation f4 is proportional to the difference of the longitudinal indices 13-11. This difference is limited in the example given by the modulation frequency of the acousto-optic modulator 10 to about 1 GHz, but can in other embodiments
Orders of magnitude higher. The latter can be achieved, for example, by generating the different frequencies of light fl, f3 and optionally f2 from different laser sources.
In practice, the mode index 11 may be a number in the range of about 101 to 105, since the optical wavelength is on the order of ~ 1 pm. The frequency fl is thereby a few 100 THz. This frequency fl is significantly larger than Äf and f4. In order to also choose f4 to be so large and thus enable a much more accurate self-stabilization of the resonator 3a, an optical frequency comb 15 can be used, cf. Fig. 5.
In this embodiment, the modes of the frequency comb 15 are directly integral with the frequency supplied by a suitable fixed frequency divider 14. Such a frequency comb 15 is commercially available. In the embodiment of FIG. 5, the frequency of the oscillator 7 is passed via the frequency divider 14 to the frequency comb 15 and sets there the tooth spacing between the comb modes. Part of the laser light is now guided by the beam splitter optics 5 to a photodiode 16, which also hits light from the frequency comb 15. Here beat frequencies are created by mixing the optical frequencies of frequency comb 15 and laser 4. One of these beats can be isolated using a suitable filter. At a frequency comparator 17a (usually a phase-locked loop), this beat frequency can be compared with that of the stabilized oscillator 7. For this purpose, the frequency of the stabilized oscillator 7 must be adjusted in general again by a fixed further frequency multiplier 17 to the beat frequency at the desired operating point. The resulting deviation signal can - as in the previous embodiment of FIG. 4 - to a
Heizstromquelle 12 are led to stabilize the length of the resonator 3a with high accuracy.
The effect of a temperature change is shown in FIG. Here, lines a) and b) show the modes of the optical resonator 3a at the target temperature, while the effect of the temperature change in lines c) and d) is shown. A change in temperature changes the optical frequency fl of the transversal fundamental mode, f (11,0,0) - »· f (11,0,0) (T), the frequency difference from this mode to the next transverse fundamental mode,
as well as the
reference frequency
However, the relative change of the reference frequency 8 is much smaller than the relative change of the other two frequencies mentioned. For the application of Fig. 4, this means that while the temperature hardly affects the reference frequency λ f, it has a clearly measurable effect on the ratio of the two frequencies, in other words
In the application of FIG. 5, the change of the reference frequency is transmitted multiplicatively to the tooth spacing of the frequency comb 15. The original comparison mode of the frequency comb 15 with comb mode index ΊΠ ^ and mode spacing
has a frequency
and becomes a frequency due to a temperature or length change
postponed.
The original distance of the selected transverse fundamental mode of the resonator 3a to the nearest combode
changes as a result
Again, the remains
Reference frequency close to its original value, while a measurable boost of frequency spacing
can arise. That fl is given by the frequency of the mode ml to which the laser 4 is equalized; f2 is given by the frequency of a higher transverse mode m2 to which the frequency of the laser 4 plus the frequency of the acousto-optic frequency shifter 6 is equalized; f3 is the frequency of
Comb fashion near fl, given by
f4 is the
Frequency difference f3-f1.
The self-regulation strategies will now be further explained by means of a numerical example.
The accuracy of the stabilization depends on the frequency resolution capability of the system. In general, the resonant frequency of a mode in an optical resonator 3a with an accuracy of
be determined. Here, t is the measurement time, h is the reduced Planck constant, λ is the wavelength, and P is the optical power. F indicates the finesse of the resonator given by the quality of the mirrors.
Realistic values of these parameters are P = 100 pW and F = 100000. Although a higher optical power can improve the frequency resolution, but leads to excessive levels to heat the mirror by absorption. This effect is negligible at 100 pW. For the following numerical examples λ = 1.55 pm is chosen as this is a common wavelength in optical telecommunications. It is also believed that the resonator, as described in ref. 3 [Hagemann, C., et al; Optics Letters (39) 17, 5102-5105 (2014)] - has a length of L = 21 cm For a measuring time of one second, "Ultrastable laser with average fractional frequency drift rate below 5 * 10- 19 / s" The resolution for the difference between two frequencies can then be estimated as 5f (min) = of (min) xV2 = 0.09 mHz.
In the embodiment of FIG. 5, the holder 3, for example, made of aluminum, with a linear expansion coefficient of 23 ppm / K, while the mirrors 1, 2 are for example made of ULE® glass. The resonator 3a is located at the zero crossing temperature of the linear expansion coefficient of the mirrors (~ 22 ° C) and in vacuum.
The mirrors 1, 2 have the above-described radii of curvature R2 = OR1 and R1 = L / Lopt. When the method of Fig. 4 is used and 12-11 = 1, there is a frequency difference of Af (0,0) = 714 MHz between two adjacent fundamental longitudinal modes, while the difference between the first longitudinal fundamental mode and the first transverse fundamental mode Mode Af = 464MHz. This corresponds to the combined frequency resolution of a temperature change of about 10 nK. This in turn corresponds to a relative frequency change of the reference frequency of 2x10 ~ 25 per second, which is below the current record of Ref. 3 by 6 orders of magnitude. The relative change in length of the resonator 3a in this example is 2.3 × 10 -13, and this value is 3 orders of magnitude higher than the currently smallest thermal-length fluctuations from Ref. 3.
If the value of 10 ~ 16 from Ref. 3 is assumed to be the smallest possible value for thermal length fluctuations, then the frequency shift corresponding to such a change in length, which is determined by means of the method from FIG
Frequency comb stabilization is still measured, 19.5 mHz. The change would thus be resolvable with the assumed values and thus controllable. In this case, the relative change in the reference frequency would be less than 1CT31. It should also be underlined at this point that long-term shifts, as described in ref. 3, are largely prevented by the presented self-correction.
The above calculations are based on optimal values. The illustrations in Fig. 7 show the effect of deviations from the optimum parameters. Large variations of 1 μΚ in temperature and 1 μm in length of the resonator 3a are assumed to illustrate their effects. The contours show the magnitude of the absolute value of the mean relative deviation of λf resulting from these variations in length and temperature. Not all contours are shown. Fig. 7 a) shows the effect of deviations of the temperature (ΔΤ) and the length (AL) from their ideal values around the operating point. Here it can be seen that the assumed fluctuations in the ideal values have a very small effect. In the case of deviations from the ideal values, the effect increases, but the significance of length deviations becomes increasingly smaller for increasing temperature deviations.
Fig. 7b), c) and d) show the effect of deviations in length and radius of curvature of a mirror for three different temperature deviations. Here again it can be seen that small length deviations have a small effect, but the system is relatively sensitive to deviations in the radius of curvature. Nevertheless, by adjusting the temperature, a non-ideal resonator 3a can also be made resistant to fluctuation. For comparison, the frequency of the optical mode of a resonator 3a, which consists entirely of ULE® glass, would be at the said fluctuation ranges.
Have values in the order of 10 21 by temperature variation and 1CT13 by variations in length.
The methods for self-stabilization can of course also be used for non-ideal optical resonators, although the reference frequency Af will not have the best possible stability.
Finally, embodiments are presented that can be easily integrated into mass production capable microsystems. Modern communication and data processing systems increasingly include photonic components consisting of optical waveguides on chips. An optical waveguide is generally a structure which consists of a core with a higher refractive index than the surrounding media. This has light propagating modes in the waveguide, which can be roughly understood by a picture of total internal reflection. Meanwhile, a variety of chip-integrated laser sources, modulators and detectors have been developed. With these components, chip-based optical resonators can be used in a fully integrated photonic system as frequency references or can thus be generated according to the invention a stable reference frequency Af.
There are different types of chip-based resonators. For example, it is also possible to modify the methods described above for waveguide geometries with integrated Bragg mirrors, which ultimately produces a resonator corresponding to the Fabry-Perot type. Another possible kind of
Waveguide resonator is the whispering gallery mode resonator, also called ring resonator, which is very attractive for the application because it can have very high grades, cf. e.g. Ref. 4 [D. Spencer, J.F. Bauters, M.J.R. Heck, and J.E.
Bowers; "Integrated waveguide-coupled Si3N4 resonators in the ultrahigh-Q regime"; Optica, Vol. 1, No. 3, p. 153, September 20, (2014)]. This type of resonator generally consists of a closed waveguide, which is used for For example, in the following embodiments, circular resonators are assumed for the sake of simplicity, but the description is applicable to any desired geometry by substituting the resonator length for the purpose of circularity, ellipticity, or stadiums.
Light is introduced and executed by means of evanescent coupling in the ring resonators. The resonant frequencies can be calculated by the scope and the effective refractive index of the propagating mode. For these systems, however, no analytical methods are available to calculate the mode spectrum. Therefore, numerical minimization methods must be used. Nevertheless, areas can be found here for which the frequency difference between two modes minimally depends on the temperature.
The light modes of a waveguide have a share in the media surrounding the core, and this fraction is mode-dependent. The fact that stable pairs of modes can exist here, too, is due to the fact that different modes thereby have different effective refractive indices, which also have different temperature dependencies. Therefore, also here mode pairs can be generated for which the change of the resonance frequencies for small operating parameter fluctuations, in particular temperature fluctuations, is almost identical.
The mode pairs can be generated in multiple waveguide arrangements. For example, all three required modes can be generated in a single ring resonator (not shown). Alternatively, the modes may reside in three different resonators 24, 25, 26, giving greater freedom in determining the mode properties, cf. Fig. 8. Another variant is the generation of a pair of ring resonators 35, which are coupled together, see. Fig. 9. The coupling produces a mode pair whose frequency spacing can be finely tuned by the fabrication parameters (radii and spacing between the rings), cf. Ref. 5 [Zhang, Z., Dainese, M., Wosinski, L., &amp; Qiu, M .; "Resonance splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling"; Optics Express, 16 (7), 4621-4630 (2008)].
The resonant frequency in a circular resonator is given by
Here m is the number of wavelengths in the resonator, n is the refractive index and ß is the linear temperature coefficient. The value T again indicates the deviation of the temperature from the desired setpoint or the operating point temperature. Small temperature changes are assumed so that square deviations can be neglected. The temperature coefficient β then describes all effects that influence the propagation of the mode. These are, for example, the thermal expansion, which influences the radius r of the ring and the dimensions of the waveguide, and the thermal dependence of the refractive indices n of the core and cladding. In general, the dimensional dependence will be the same for all modes, but the change in refractive indices n of each mode will be different. This results in a slightly different coefficient β for each mode. The frequency difference between two modes is then given by
wherein the indices 1 and 2 represent the respective mode. By the above expression, the zero crossing of the first derivative becomes the condition
found. These two expressions can be used to find the necessary relationship between mode indices, radii and refractive indices, as well as their thermal dependencies. Extensive research has shown that this condition can be relaxed somewhat to achieve satisfactory results, namely the design condition
The ratio between mode indices and radii is limited by the frequency of light, which is around 195THz for telecommunications applications, for example.
In addition, for a given waveguide technology, the dependence of the losses on the resonator radius must be taken into account, so that the choice of radii can be restricted. This is because the waveguides have finite transmission. The longer the waveguide, the more light is lost. Conversely, however, that smaller ring radii lead to losses because of the greater curvature. This results in a range of particularly useful radii.
Furthermore, both the refractive indices ni, n2 as well as the thermal coefficients ßi, ß2 depend on the
Waveguide dimensions, and therefore must be optimized together to the target value. In principle, therefore, a desired frequency difference and a meaningful size restriction for the radii r2, r2 can be selected. Together with the achievable range of the refractive indices n2, n2, this results in limits for the selectable mode indices. Thereafter, the refractive indices n2, n2 and temperature coefficient ßm ß2 can be selected for the desired frequency difference λf. From Ref. 4 it can be seen, for example, that differences in the refractive index between -0% and -0.15% can be achieved by dimensioning the waveguide. The biggest difference between them
Temperature dependencies of two modes can be calculated to -0.8%. For modes in a single ring (Γ- ^ = 1 ^) this results in stable pairs of modes with a smallest frequency difference of -11 GHz at a radius of 5mm. The frequency difference can be finely tuned by the radius. With two different rings, the frequency difference can be tuned finer and freer by the different radii. The stable frequency is extremely sensitive to the radii of the rings for one as well as for two rings. For example, a deviation in the radius of 0.02 percent may cause a deviation of up to two percent in frequency. In practice, therefore, the manufacturing process must be set very accurately to an output frequency. In the electronic domain, however, the frequency conversion is routine, so a known frequency deviation can be corrected at least here and the stability still be used. For many applications, a stable, well-known frequency is sufficient.
Because the mode indices are integers, the design condition described above will not be met in practice because the dimensions, refractive indices, and thermal dependencies will be subject to certain fabrication variations. Two effects heretofore neglected can be used to nonetheless produce a zero crossing of the temperature dependence: First, the modes are generally subject to different dispersion relations, so that the indices of refraction (at constant temperature) are fine, albeit in stages, by the choice of mode indices irq and m2. can be changed. Second, the modes are also subject to higher-order thermal coefficients, so that the values βi and β2 can be finely adjusted by changing the operating point temperature.
Another variant to create a stable mode pair is the coupling of two modes. This coupling can be generated in a single ring by a reflective element, or can be generated by evanescent coupling of two rings (see Ref.
In a single ring thereby the variants of a spatial mode, which propagate clockwise and counterclockwise in the ring coupled. Since the spatial modes are nominally identical, their thermal coefficients will also be nearly the same, so that a high stability can be expected. The strength of the coupling, which in this case represents exactly the reference frequency λ f, can be determined by the reflectivity. However, a simple reflective element (as used in Ref. 5) will generally result in leakage because it causes a non-adiabatic change in the mode parameters and thereby a dispersion into free modes in the cladding.
By using two rings, these losses can be largely avoided, since the coupling can occur by means of evanescence between the modes of the rings, whereby the propagation parameters change only slowly along the rings. This variant of the application is well suited for stable frequencies λf in the range around 250 MHz. This value results from the fact that the line widths of good ring resonators with diameters are around 1 cm in the range of 10 MHz, while the distance between two modes in this dimensioning is 6.5 GHz (Ref. 4). The stable frequency difference λf is thus significantly larger than the line width, whereby the modes can be well resolved. On the other hand, it is significantly smaller than the mode spacing in a ring, whereby the overlap with the next mode is vanishingly small. The coupling strength between the rings depends exponentially on the minimum distance of the rings (which need not be concentric), and can thereby be chosen. The coupling creates where the
Modes of the two individual rings have the same frequency / 0, two modes which are split by the coupling 2g.
The frequency spacing AfK (T) between the two modes for rings with thermal coefficients β2 and β2 is given by
which is therefore insensitive to temperature to first-order resonance. Here several minor corrections were neglected, for example a small push of the temperature
which is much smaller than 1 Kelvin for the parameters used here, as well as another push by the finite width and asymmetry of the resonance lines, and a push by a small temperature dependence of the coupling strength. In practice, these thrusts must be determined by measurement. Furthermore, in general, the resonant frequencies of the two rings will not be identical at the desired operating point temperature. Due to the difference in the thermal coefficients ßi and ß2, however, the rings can be brought into resonance. However, since the quadratic term of the temperature dependence also depends on this difference, it is necessary to adjust the sensitivity to the tunability. For example, with a temperature coefficient difference of 0.2%, a thermal tuning of about ± 15K is necessary to achieve the resonance condition. Nevertheless, this variant can then be used to generate a stable reference frequency, wherein a further mode of the system or a third ring can serve as a temperature-dependent element for long-term stabilization according to the invention. It should be noted at this point that the same effect can also be achieved with coupled Fabry-Perot resonators.
A variant with three different resonators is shown in FIG. Here, the light is made of three different modulated laser light sources - a first laser light source 18 for generating light of frequency f, a second laser light source 19 for generating light of frequency f2 and a third laser light source 20 for generating light of frequency f3 - in three waveguides - a first waveguide 21, a second waveguide 22 and a third waveguide 23 - out. The modes of these waveguides slightly overlap those of three ring resonators - a first ring resonator 24, a second ring resonator 25 and a third ring resonator 26 - thereby evanescently couple light into their selected resonant modes. The transmitted light is collected by respective detectors - a first detector 27, a second detector 28 and a third detector 29. Again, by means of the sidebands produced by the modulation, the frequency of each laser 18, 19, 20 is maintained at the desired resonance in the respective ring 24, 25, 26, so that the frequencies fl, f2, f3 are stabilized. Again, the Pound-Drever-Hall method (Ref 6) is used. The modulation of the lasers 18, 19, 20, the demodulation of the detector signals and the regulation of the laser current are performed on the integrated electronic modules 37. There, the apparent from the demodulation deviation of the laser frequency of the resonator mode frequency by a correction of the laser current for each laser light source 18, 19, 20 made individually.
Furthermore, the light from the laser light sources 18 and 19 by means of integrated beam splitter - a first
Beam splitter 30 and a second beam splitter 31 - led to another, fourth detector 32, at which the beat frequency Äf between the two mode frequencies fl, f2 in the rings 24 and 25 is measured. The same method can be used for the laser light sources 19 and 20 via the second beam splitter 31 and a third beam splitter 33 to measure on a fifth detector 34 the beat f4 between the mode frequencies f2 and f3 of the rings 25 and 26.
Due to the described design of the resonators 24, 25, the beat frequency λ f on the fourth detector 32 is highly stable, while the beat frequency f 4 on the detector 34 is susceptible to interference. A part of the light which carries the stable beat frequency λ f can now be led away from the chip at an optical output 36 as an optical signal and can be distributed via optical fibers or as a free jet to other devices.
Furthermore, the determined beat frequencies may serve as the self-stabilization of the device or the reference frequency λf, as in the previous description. The beats frequencies λf and f4 from the detectors 32 and 34 can be compared again at electronics 38, and changes from the preset reference value for the control a Heizstromquelle be used. This allows the temperature of the chip, and thus the clock frequency, to be precisely stabilized.
Preferably, this must be done much slower than the correction of the laser currents. In practice, this condition is easily met, since thermal regulation can at best be done on a millisecond scale, while the laser currents can be corrected in less than a microsecond.
A variant with coupled resonators is finally shown in FIG. All elements retain their function as in FIG. 8, except for the rings 25 and 26, which are replaced by the coupled ring resonator pair 35. In this figure, the laser modulation and control loops, and the temperature control, have been omitted for the sake of clarity, but here also perform the same functions as in Fig. 8. The modes from the sources 18 and 19 couple here via the wave initiators 21 and 22 to a respective mode of the stable pair of modes in the ring resonator pair 35. To illustrate this serve Fig. 10a and Fig. 10b.
In Fig. 10a, the intersection between two modes of the paired ring resonator pair 35 is shown. The dashed lines represent the frequencies of the modes of the individual resonators of the ring resonator pair 35, while the solid lines show the frequencies of the modes of the coupled system. Due to the different thermal coefficients, the frequencies of the individual rings intersect. The coupling is about the resonance to the nearly parallel course of the frequencies of the coupled system.
In Fig. 10b, the course of the frequency difference
shown for a difference of 0.2% between the thermal coefficients and a coupling frequency of 2g = 250 MHz. It should be noted here that the chip-integrated resonators are, of course, also suitable for the frequency comb-based stabilization (described with reference to FIGS. 5 and 6) and thus can be used for the integrated stabilization of chip-based frequency combs.
In the preceding descriptions, the starting point was always unstable light sources. If a light source with small frequency fluctuations is present around a frequency fl, the principle of the invention can also be used to transmit this stability to the difference frequency f2-fl. The variations of the light source frequency are additionally suppressed by the lower (e.g., quadratic or cubic) dependence of the difference frequency.
Finally, the following is generally noted for the choice of materials: The materials used for waveguide systems at wavelength λ * 1.5 pm are usually silicon oxide, titanium oxide, silicon or silicon nitride. As the mirror substrate, any material can be used which is transparent in the targeted wavelength range and can be milled and polished (or otherwise formed in the correct shape) into the correct shape. For the mentioned 1.5 pm wavelength quartz glass and silicon are useful. As the support (cf bracket 3 in Fig. 1), metals, crystals (e.g., silicon or quartz glass) or ceramics may be used.
REFERENCE LIST 1 First mirror 2 Second mirror 3 Support 3a Fabry-Perot resonator 4 Laser 4a Electro-optical modulator 4b Polarizing beam splitter 4c Quarter wave retardation optics 4d Demodulator 5 Beam splitter 6 Acousto-optical frequency shifter 6a Second electro-optical modulator 6b Second polarizing beam splitter 6c Second quarter wave retardation optics 6d Second demodulator 6e Structured phase plate 7 Oscillator 8 Temperature controller 9 Frequency multiplier 10 Further acousto-optic modulator 10a Further electro-optical modulator 10 Third demodulator 11 Optical circulator 12 Heating current source 13 Further polarization optics 14 Frequency divider 15 Frequency comb 16 Photodiode 17 Further frequency multiplier 17a Frequency comparator 18 First laser light source 19 Second laser light source 20 Third laser light source 21 First waveguide 22 Second waveguide 23 Third waveguide 24 First ring resonator 25 Second ring resonator 26 Third ring resonator 27 First he detector 28 second detector 29 third detector 30 first beam splitter 31 second beam splitter 32 fourth detector 33 third beam splitter 34 fifth detector 35 paired ring resonator pair 36 optical output 37 electronic modules 38 electronics

权利要求:
Claims (25)
[1]
A method of generating a reference frequency λ f using a first optical resonator (3a; 24) and a second optical resonator (25), the first resonator (3a; 24) having a first resonator mode having a first frequency f i and the second resonator (25) a second resonator mode having a second frequency f2, wherein the frequencies of the two resonator modes are functions of an operating parameter BP, in particular a temperature, and assume the values fl and f2 at a predetermined value BP0 of the operating parameter, so that fl (BP0) = fl and f2 (BP0) = f2, wherein the resonators (3a; 24,25) are designed such that the first derivative of the frequencies fl (BP), f2 (BP) after BP or at least one difference quotient around BP0 except one Deviation of a maximum of ± 0.1% match, wherein light of the first frequency fl is stabilized by means of the first resonator to the first frequency fl and light of the second frequency f2 by means of the second resonator on the second frequency f2, and the difference between the stabilized frequencies fl and f2, λf = | fl - f2 |, being determined to obtain the stabilized reference frequency λ f.
[2]
2. The method according to claim 1, characterized in that the first optical resonator (3a; 24) has a resonator length Li and a linear temperature coefficient β2 and the second optical resonator (25) has a resonator length L2 and a linear temperature coefficient β2, wherein the resonators (3a 24, 25) are designed so that m1 * ß1 * L2 * n2 = m2 * ß2 * L1 * n1 except for a maximum deviation of ± 0.1% with m2, m2 integers corresponding to the number of wavelengths of the and n2, n2 correspond to the refractive indices for the first resonator mode in the first resonator (3a, 24) and the second resonator mode in the second resonator (25) or in the first and the second resonator (35 ) coupled modes and a mode spectrum split due to the coupling includes the first resonator mode and the second resonator mode.
[3]
3. The method according to any one of claims 1 to 2, characterized in that the first resonator (3a) simultaneously forms the second resonator and is identical to this.
[4]
4. The method according to claim 3, characterized in that the mode coupling is generated by means of an at least partially reflective element.
[5]
5. The method according to any one of claims 1 to 2, characterized in that the mode coupling is generated by evanescent coupling of the first resonator with the second resonator.
[6]
6. The method according to any one of claims 1 to 3, characterized in that the two resonator modes are each characterized by a longitudinal index and two transverse indices, wherein the first resonator and the second resonator have the same longitudinal index and at least one different transverse index.
[7]
7. Method according to one of claims 1 to 6, characterized in that light of a third frequency f3 is generated and stabilized by means of a resonator (3a; 26), where f3 has a greater dependence on the operating parameter, in particular on the temperature, than λf. that a comparison frequency f4 by f4 = | f3 - fl | or f4 = | f3 - f2 | and that the ratio f4 / λf or the difference f4-λf is determined and for controlling operating parameter control means, in particular temperature control means (12), which regulate the operating parameter, in particular the temperature, of the first resonator (3a; 24) and / or second Resonator (3a, 25) are provided is used.
[8]
8. The method according to claim 7, characterized in that for stabilizing the light of the third frequency f3, the first resonator (3a; 24) and / or the second resonator (3a; 25) or a third resonator (26) are used.
[9]
9. The method according to any one of claims 7 to 8, characterized in that the light of the third frequency f3 is formed by a comb mode of a frequency comb (15).
[10]
10. The method according to any one of claims 1 to 9, characterized in that a Fabry-Perot resonator (3a) is used as the first resonator and / or as the second resonator.
[11]
11. The method according to any one of claims 1 to 10, characterized in that as the first resonator and / or as a second resonator, an optical ring resonator (24, 25) is used.
[12]
12. The method according to any one of claims 1 to 11, characterized in that as a first resonator (3a; 24) and / or as a second resonator (3a; 25) is used as a waveguide on an optical chip formed optical resonator.
[13]
13. A device for generating a reference frequency λf, wherein a first optical resonator (3a, 24) is provided, which has a first resonator mode having a first frequency f1, and a second optical resonator (25), which has a second resonator mode having a second frequency f2, wherein the frequencies of the two resonator modes are functions of an operating parameter BP, in particular a temperature, and assume the values fl and f2 at a predetermined value BP0 of the operating parameter, so that fl (BP0) = fl and f2 (BP0) = f2, wherein the resonators (3a, 24, 25) are designed so that the first derivative of the frequencies fl (BP), f2 (BP) after BP or at least a difference quotient around BP0 match up to a deviation of ± 0.1% , the apparatus further comprising first light generating means (4; 18) for generating light of the first frequency fl and second light generating means (4,6; 19) for generating light of the second frequency f2 most light generating means (4; 18) and the second light generating means (4, 6; 19) preferably comprise at least one laser in total, the apparatus further comprising first stabilizing means for stabilizing the first frequency fl and second stabilizing means for stabilizing the second frequency f2, and determining means are provided to determine the difference between the stabilized frequencies fl and f2, λf = | fl - f2 |, and to obtain the stabilized reference frequency λf.
[14]
14. The device according to claim 13, characterized in that the first optical resonator (3a, 24) has a resonator length Li and a linear temperature coefficient β2 and the second optical resonator (25) has a resonator length L2 and a linear temperature coefficient β2, wherein the resonators ( 3a, 24, 25) are designed such that mi * ßi * L2 * n2 = m2 * ß2 * Li * ni with the exception of a maximum deviation of ± 0.1% with m2, m2 integers corresponding to the number of wavelengths and n2, n2 correspond to the refractive indices for the first resonator mode in the first resonator (3a; 24) and the second resonator mode in the second resonator (25) or that in the first and second resonators ( 35) coupled modes are present and a mode spectrum split due to the coupling contains the first resonator mode and the second resonator mode.
[15]
A device according to any one of claims 13 to 14, characterized in that the first stabilizing means comprise first modulating means (4a; 37) for modulating sidebands to the first frequency light fl and first demodulating means (4d; 27,37) having a first detector for generating a first error signal by means of the modulated light of the first frequency fl reflected back or transmitted to the first detector, and first control means (37) for controlling the first light generating means (4; 18) based on the first error signal such that the first frequency and second demodulation means (6d, 28, 37) with a second detector to reflect back to the second detector or transmitted modulated light second frequency f2 to generate a second error signal, and second e control means (37) for determining, based on the second error signal, the second light generating means (4, 6; 19) so that the second frequency f2 is stabilized.
[16]
16. Device according to one of claims 13 to 15, characterized in that the first resonator (3a) simultaneously forms the second resonator and is identical to this.
[17]
17. The device according to claim 16, characterized in that an at least partially reflective element is provided to generate the mode coupling.
[18]
18. Device according to one of claims 13 to 15, characterized in that the first resonator is evanescently coupled to the second resonator to produce the mode-locking.
[19]
19. Device according to one of claims 13 to 16, characterized in that the two resonator modes are each characterized by a longitudinal index and two transverse indices, wherein the first resonator and the second resonator have the same longitudinal index and at least one different transverse index.
[20]
20. Device according to one of claims 13 to 19, characterized in that third light generating means (4, 10; 20) are provided for generating light of a third frequency f3 and a resonator (3a; 26) for stabilization, wherein f3 a greater dependence of the operating parameter, in particular of the temperature, as λf, that a comparison frequency f4 is given by f4 = | f3 - fl | or f4 = | f3 - f2 | is provided, wherein further determining means (lOd) are provided to determine the ratio f4 / Äf or the difference f4-Äf, and that operating parameter control means, in particular temperature control means (12) are provided to the operating parameter, in particular the temperature of the first Resonator (3a; 24) and / or the second resonator (3a; 25) depending on the ratio f4 / Äf or the difference f4-Äf to control.
[21]
21. Device according to claim 20, characterized in that the resonator for stabilizing the light of the third frequency f3 is the first resonator (3a; 24) and / or the second resonator (3a; 25) or a third resonator (26).
[22]
22. Device according to one of claims 20 to 21, characterized in that the third light generating means comprise a frequency comb (15) to form the light of the third frequency f3 as a comb mode of the frequency comb (15).
[23]
23. Device according to one of claims 13 to 22, characterized in that the first resonator and / or the second resonator is a Fabry-Perot resonator (3a).
[24]
24. Device according to one of claims 13 to 23, characterized in that it is in the first resonator and / or the second resonator to an optical ring resonator (24, 25).
[25]
25. Device according to one of claims 13 to 24, characterized in that the first resonator (3a; 24) and / or the second resonator (3a; 25) is formed as a waveguide on an optical chip.

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同族专利:

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公开号 | 公开日

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AT518549B1|2017-11-15|

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US10558173B2|2020-02-11|

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EP3440514A1|2019-02-13|

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WO2017173472A1|2017-10-12|

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JP2019519754A|2019-07-11|

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AT518549B1|2016-04-06|2017-11-15|Technische Universität Wien|Method and device for generating a reference frequency|AT518549B1|2016-04-06|2017-11-15|Technische Universität Wien|Method and device for generating a reference frequency|

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US10979167B2|2018-10-01|2021-04-13|Huawei Technologies Co., Ltd.|Systems and method of multi-laser wavelength control|

法律状态:

优先权:

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申请号 | 申请日 | 专利标题

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ATA50282/2016A|AT518549B1|2016-04-06|2016-04-06|Method and device for generating a reference frequency|ATA50282/2016A| AT518549B1|2016-04-06|2016-04-06|Method and device for generating a reference frequency|

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US16/091,333| US10558173B2|2016-04-06|2017-04-05|Method and device for producing a reference frequency|

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PCT/AT2017/060084| WO2017173472A1|2016-04-06|2017-04-05|Method and device for producing a reference frequency|

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EP17717613.8A| EP3440514B1|2016-04-06|2017-04-05|Method and device for generating a reference frequency|

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JP2018552667A| JP2019519754A|2016-04-06|2017-04-05|Method and apparatus for generating reference frequency|