FAST MODULATION OF THE RESONANT FREQUENCY OF AN OPTICAL RESONATOR

Abstract

The invention relates to a method for modulating the resonant frequency of an optical resonator (1) in accordance with a periodic, not necessarily harmonic, modulation signal (U.sub.mod(t)). Fast modulation of an optical resonator is intended to be made possible in which the current resonant frequency follows the modulation signal (U.sub.mod(t)) as precisely as possible, and specifically at a fundamental frequency of the modulation signal in the kHz range. To do this, the invention proposes the following method steps: deriving an error signal (E(t)) from a light field circulating in the resonator (1), wherein the error signal (E(t)) indicates the deviation of the optical frequency of the light field from a target value, deriving a first actuating signal (S.sub.1(t)) from the error signal (E(t)) by means of a controller (6), generating a second actuating signal (S.sub.2(t)), which has actuating-signal components at one or more harmonics (f.sub.mod, 2f.sub.mod, . . . ) of the fundamental frequency (f.sub.mod) of the modulation signal (U.sub.mod(t)), and applying a superposition signal made up of the first and the second actuating signal (S.sub.1(t), S.sub.2(t)) to an actuator (3) that changes the optical path length of the resonator (1). In other words, the invention makes use of a combination of control and narrow-band feed-forward control tuned to the spectrum of the modulation signal (U.sub.mod(t)) and of the error signal (E(t)) to modulate the resonant frequency. Preferably, the feed-forward control used for generating the second actuating signal (S.sub.2(t)) is automatically adapted in accordance with the error signal (E(t)). In addition, the invention relates to an accordingly configured optical system.

Claims

1. A method for modulating the resonant frequency of an optical resonator in accordance with a periodic modulation signal, comprising the following method steps: deriving an error signal from a light field circulating in the resonator, wherein the error signal indicates the deviation of the optical frequency of the light field from a target value, deriving a first actuating signal from the error signal by means of a controller, generating a second actuating signal, which has actuating-signal components at one or more harmonics of the fundamental frequency of the modulation signal, and applying a superposition signal made up of the first and the second actuating signal to an actuator that changes the optical path length of the resonator.

2. Method according to claim 1, wherein the phase and the amplitude of each actuating-signal component of the second actuating signal are individually set such that the amplitude of the error signal is minimal at the associated harmonics.

3. Method according to claim 1, wherein the second actuating signal is derived from the error signal.

4. Method according to claim 3, wherein each actuating-signal component is generated by phase-sensitive demodulation of the error signal at the associated harmonics, transfer of the resulting complex detection signal into a complex control signal in accordance with a transfer function and modulation of the associated harmonics in accordance with the complex control signal.

5. Method according to claim 4, wherein an individual transfer function is associated with each actuating-signal component.

6. Method according to claim 4, wherein the transfer function is adapted such that the amplitude of the error signal is minimized at the associated harmonics.

7. Method according to claim 1, wherein the optical resonator is a laser resonator and the target value is a fixed frequency of a reference laser applied with an offset that varies in accordance with the modulation signal.

8. Method according to claim 1, wherein the optical resonator is a laser resonator of a laser to be frequency-modulated and wherein the error signal is generated by coupling the laser to be frequency-modulated to an additional, passive optical resonator, the resonant frequency of which is modulated in accordance with the modulation signal.

9. Method according to claim 1, wherein the optical resonator is a passive optical resonator and wherein the error signal is generated by coupling to a laser which is frequency-modulated in accordance with the modulation signal.

10. Method according to claim 9, wherein the laser radiation of the frequency-modulated laser is amplified and is converted by resonant frequency multiplication and/or sum-frequency generation by means of a non-linear optical crystal in the optical resonator.

11. Method according to claim 10, wherein the spectrum of the converted laser radiation has a fluorescence frequency, which corresponds to an optical transition in an atom, i.e. a line in the electronic excitation spectrum of the atom, and a back-pumping frequency, the distance of which from the fluorescence frequency corresponds to the hyperfine splitting of the optical transition.

12. Method according to claim 11, wherein the fluorescence frequency is modulated in a sawtooth shape in accordance with the modulation signal, wherein the fundamental frequency of the modulation signal is 1-50 kHz, preferably 5-10 kHz, and the modulation amplitude of the fluorescence frequency is 5-500 MHz, preferably 100-300 MHz.

13. Method according to claim 10, wherein the fluorescence frequency corresponds to the wavelength of the sodium line at 589 nm and the frequency distance of the back-pumping frequency from the fluorescence frequency is +/−1.7 GHz.

14. A system comprising an optical resonator, at least one actuator, which is configured to change optical path length of the resonator, a modulation-signal generator, which is configured to generate a periodic modulation signal, an error-signal detector, which is configured to derive an error signal from a light field circulating in the resonator, wherein the error signal indicates the deviation of the optical frequency of the light field from a target value, a controller, which is configured to derive a first actuating signal from the error signal, a feed-forward control apparatus, which is configured to generate a second actuating signal, which has actuating-signal components at one or more harmonics of the fundamental frequency of the modulation signal, wherein the controller and the feed-forward control apparatus are connected to the actuator, such that a superposition signal made up of the first and the second actuating signal is applied to said actuator.

15. System according to claim 14, wherein the feed-forward control apparatus has a multi-channel structure, wherein each channel is assigned to an actuating-signal component of the second actuating signal and wherein each channel comprises: an IQ demodulator, which is configured to generate a complex detection signal by phase-sensitive demodulation of the error signal at the associated harmonics, an IQ controller, which is connected downstream of the IQ demodulator and is configured to convert the complex detection signal into a complex control signal in accordance with a transfer function, an IQ modulator, which is connected downstream of the IQ controller and is configured to generate the actuating-signal component by modulation of the associated harmonics in accordance with the complex control signal, wherein the feed-forward control apparatus comprises an adder, which is connected to the IQ modulators of all the channels and is configured to generate the second actuating signal by addition of the actuating-signal components.

16. System according to claim 15, wherein the IQ controller of each channel is configured to adapt the transfer function such that the amplitude of the detection signal is minimized.

17. System according to claim 14, wherein the optical resonator is a laser resonator and wherein the error-signal detector is configured to generate the error signal by coupling the laser resonator to a reference laser that emits at a fixed frequency, wherein the target value is a fixed frequency of a reference laser applied with an offset that varies in accordance with the modulation signal.

18. System according to claim 14, wherein the optical resonator is a laser resonator of a laser to be frequency-modulated and wherein the error-signal detector is configured to generate the error signal by coupling the laser resonator of the laser to be frequency-modulated to an additional, passive optical resonator, the resonant frequency of which is modulated in accordance with the modulation signal.

19. System according to claim 17, wherein the optical resonator is the external resonator of a VECSEL or ECDL.

20. System according to claim 14, wherein the optical resonator is a passive optical resonator and wherein the error-signal detector is configured to generate the error signal by coupling the passive optical resonator to a laser which is frequency-modulated in accordance with the modulation signal.

21. System according to claim 20, wherein a non-linear optical crystal is located in the passive optical resonator, which is configured to convert the laser radiation of the frequency-modulated laser by resonant frequency multiplication and/or sum-frequency generation.

22. System according to claim 21, wherein the spectrum of the converted laser radiation has a fluorescence frequency, which corresponds to an optical transition in an atom, i.e. a line in the electronic excitation spectrum of the atom, and a back-pumping frequency, the distance of which from the fluorescence frequency corresponds to the hyperfine splitting of the optical transition.

23. System according to claim 22, wherein the modulation signal is sawtooth-shaped, wherein the fundamental frequency of the modulation signal is 1-50 kHz, preferably 5-10 kHz, and the resulting modulation amplitude of the fluorescence frequency is 5-500 MHz, preferably 100-300 MHz.

24. System according to claim 23, wherein the fluorescence frequency corresponds to the wavelength of the sodium line at 589 nm and the frequency distance of the back-pumping frequency from the fluorescence frequency is +/−1.7 GHz.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE INVENTION

[0045] Exemplary embodiments will be explained in greater detail in the following with reference to the drawings, in which:

[0046] FIG. 1 is a block diagram of a laser system in a first embodiment;

[0047] FIG. 2 is a schematic view of the actuation of the actuators of an optical resonator;

[0048] FIG. 3 is a block diagram of a laser system in a second embodiment;

[0049] FIG. 4 is a block diagram of a laser system in a third embodiment;

[0050] FIG. 5 is a schematic view of a multi-channel feedback controller;

[0051] FIG. 6 is a block diagram of a laser system for generating a laser guide star;

[0052] FIG. 7 is a schematic view of a phase-locked loop for the frequency modulation of the laser source in the laser system from FIG. 6.

DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

[0053] Identical or corresponding elements are provided with identical reference signs in the drawings.

[0054] In all the exemplary embodiments, the resonant frequency, i.e. the optical path length of an optical resonator 1, is intended to be modulated, and specifically in accordance with a modulation signal U.sub.mod(t) which is periodic, but not harmonic. In the exemplary embodiments shown, the modulation signal U.sub.mod(t) is sawtooth-shaped. The modulation signal U.sub.mod(t) is generated by means of a modulation-signal generator 2. As shown in FIGS. 1 and 4, the optical resonator may e.g. be a laser resonator comprising a gain medium, wherein the frequency of the emitted laser radiation is intended to be modulated in accordance with the modulation signal U.sub.mod(t). The optical path-length modulation is generated by a signal U.sub.act(t) applied to an actuator 3, which is e.g. a piezo actuating element, which is (optionally) amplified by means of a suitable power amplifier 4.

[0055] An error-signal detector 5 is provided to derive an error signal E(t) from a light field circulating in the resonator 1, wherein the error signal E(t) indicates the deviation of the optical frequency of the light field from a target value. The target value may be the resonant frequency of the optical resonator itself (FIG. 3), of a second resonator (FIG. 4), or the optical frequency of another light field, which is used as a reference (FIG. 1). A controller 6, i.e. a PID controller, generates a first actuating signal S.sub.1(t), which is fed back to the actuator 3 of the optical resonator 1. The control loop formed by the error-signal detector 5 and the controller 6 corresponds to standard control for stabilizing an optical resonator to the frequency of a light field, e.g. in accordance with a Pound-Drever-Hall method or a Hänsch-Couillaud method.

[0056] The modulation signal U.sub.mod(t) and the signal U.sub.act(t) applied to the actuator 3 contain frequency components at harmonics f.sub.mod, 2f.sub.mod, 3f.sub.mod, . . . of the fundamental frequency f.sub.mod of the modulation signal U.sub.mod(t). In the sawtooth-shaped signal curve shown having a vertical signal drop, the modulation signal U.sub.mod(t) contains distinct frequency components at higher harmonics. The frequencies of these harmonics are outside the zo control bandwidth of the closed control loop formed by the controller 6. The reasons for this are e.g. mechanical resonances and/or a low-pass characteristic of the actuator 3.

[0057] In order to generate the signal U.sub.act(t) applied to the actuator 3 such that the desired optical path length of the resonator 1 results in accordance with the modulation signal U.sub.mod(t), the closed control loop formed by the controller 6 is supplemented by a feed-forward control apparatus 7. This generates a second actuating signal S.sub.2(t), which has actuating-signal components at (some) harmonics f.sub.n=n×f.sub.mod, i.e. f.sub.mod, 2f.sub.mod, 3f.sub.mod, . . . of the fundamental frequency f.sub.mod of the modulation signal U.sub.mod(t). In other words, the feed-forward control apparatus 7 has narrow-band amplification at the harmonics f.sub.n of the modulation signal U.sub.mod(t). The power of the closed control loop comprising the controller 6 is limited if it is a question of a narrow-band interference, in particular at frequencies close to or above the mechanical resonant frequencies of the actuator 3. Therefore, the additional feed-forward control apparatus 7 is designed such that it has high amplification at the harmonic components of the fundamental frequency of the modulation signal U.sub.mod(t). The combined amplification behavior of the closed control loop and the feed-forward control corresponds to that of a single loop filter of which the spectrally modulated amplification makes it possible to effectively counteract the interference spectrum, depending on the modulation signal U.sub.mod(t) and the response behavior of the actuator 3.

[0058] The controller 6 and the feed-forward control apparatus 7 are connected to the actuator 3 (optionally to an interposed amplifier 4) by means of an adder 8, such that the signal U.sub.act(t), as a superposition signal made up of the first actuating signal S.sub.1(t) and the second actuating signal S.sub.2(t), is applied to the actuator 3. Alternatively, it may be advantageous to use separate actuators 3a and 3b for the controller 6 and the feed-forward control apparatus 7, as shown in FIG. 2, e.g. a slow “woofer” 3a for the controller 6 and a faster “tweeter” 3b for the feed-forward control apparatus 7.

[0059] In the exemplary embodiments shown, the modulation-signal generator 2 and the feed-forward control apparatus 7 are combined to form a modulation unit 9. The modulation-signal generator 2 generates the modulation signal U.sub.mod(t) and also phase-synchronous signals at the frequencies f.sub.mod, 2f.sub.mod, 3f.sub.mod, . . . , which are fed to the feed-forward control apparatus 7.

[0060] In the exemplary embodiments shown, depending on the application, the error signal E(t) can be generated in various ways:

[0061] In the exemplary embodiment in FIG. 1, the optical resonator 1 is a laser resonator (i.e. comprising a gain medium in the resonator) of a laser frequency-modulated in accordance with the modulation signal U.sub.mod(t), wherein the error signal E(t) is generated by coupling said laser to a reference laser 10 that emits at a fixed frequency. The coupling is carried out by superposing the laser radiation of the reference laser 10, comprising the laser radiation coupled out of the laser resonator 1 of the frequency-modulated laser, on a photodetector (not shown) of the error-signal detector 5, wherein the beat signal is mixed with a high-frequency signal of a local oscillator (not shown), which is frequency-modulated in accordance with the modulation signal U.sub.mod(t), e.g. by using a voltage-controlled oscillator (VCO). To do this, in FIG. 1 the modulation signal U.sub.mod(t) is fed to the error-signal detector 5. The thus modulated beat signal underlies the described combination of control by the controller 6 and feed-forward control by the feed-forward control apparatus 7 as an error signal E(t), such that the modulation is transferred to the laser resonator, the resonant frequency of which then follows the modulation signal U.sub.mod(t) as a result.

[0062] In the exemplary embodiment in FIG. 3, the optical resonator 1 is a passive optical resonator, wherein the error signal E(t) is generated by coupling to a laser 11 which is frequency-modulated in accordance with the modulation signal U.sub.mod(t). In this configuration, the frequency-modulated laser radiation is already present and the zo resonant frequency of the optical resonator 1 is intended to follow the frequency of the laser radiation. The coupling is expediently carried out by coupling the laser radiation emitted by the laser 11 into the optical resonator 1. The error signal E(t) can then be derived from the laser radiation that is reflected by the resonator 1 or transmitted by the resonator by means of the error-signal detector 5, e.g. by means of a Pound-Drever-Hall technique or a Hänsch-Couillaud technique.

[0063] In the exemplary embodiment in FIG. 4, the optical resonator 1 is in turn a laser resonator, wherein the error signal E(t) is generated by coupling to another, passive optical resonator 12, the resonant frequency of which is modulated in accordance with the modulation signal U.sub.mod(t). In this configuration, a passive optical resonator 12 is therefore already present, the resonant frequency of which is modulated in accordance with the modulation signal U.sub.mod(t). The optical path length of this optical resonator is intended to be transferred to the laser resonator 1. The coupling is expediently carried out by coupling the laser radiation coupled out of the laser resonator 1 into the passive resonator 12. The error signal E(t) is then derived from the laser radiation that is reflected by the passive resonator 12 or transmitted by the resonator 12 by means of the error-signal detector 5, e.g. in turn by means of a Pound-Drever-Hall technique or a Hänsch-Couillaud technique.

[0064] FIG. 5 illustrates the multi-channel structure of the feed-forward control apparatus 7. The error signal E(t) is supplied into the feed-forward control apparatus 7 and is analyzed in a narrow band in the individual channels, which each operate at harmonics f.sub.n, in order to generate an actuating-signal component in each channel, i.e. a frequency component of the second actuating signal at the respectively associated harmonics f.sub.n. If the error signal E(t) contains frequency components for which the controller 6 is not capable of compensating, actuating-signal components are generated in narrow bands, i.e. at precisely these frequencies, in the relevant channels of the feed-forward control apparatus 7, which components are adapted in terms of phase and amplitude such that the interfering frequency components in the error signal E(t) are counteracted. As shown in FIG. 5, to do this, each channel comprises an IQ demodulator 13, which is configured to generate a complex detection signal by phase-sensitive demodulation of the error signal at the associated harmonics f.sub.n. A corresponding signal 14.sub.1, 14.sub.2, . . . 14.sub.n is fed to each channel of the feed-forward control apparatus 7 by the modulation-signal generator 2. The IQ demodulator 13 of each channel operates in accordance with the known IQ method. Furthermore, an IQ controller 15 is provided in each channel, which is configured to convert the complex-valued detection signal of the IQ demodulator 13, having a real part (I signal) and an imaginary part (Q signal), into a likewise complex control signal in accordance with a transfer function. In each channel there is additionally a pre-compensation element 16, which is configured to apply an individual phase correction of the control signal on the basis of previously stored parameters in each channel. In order to ensure the convergence of the combined control and feed-forward control, basic knowledge of the phase response of the entire system may be helpful or even required. This includes each component from the input of the modulation-signal generator 2 up to and including the actuator 3, in particular components having non-trivial phase behavior, such as the amplifier 4. This information is used to subject the real and imaginary part of the control signal in each channel (upstream or downstream of the IQ controller 15) to pre-compensation. This pre-compensation is expediently carried out by means of the pre-compensation element 15 by rotating each IQ coordinate system. In this process, the system-dependent and frequency-dependent rotational angles can be determined in advance as a result of a vector network analysis of the entire system. Lastly, each channel comprises an IQ modulator 17 arranged downstream of the IQ controller 15. The IQ modulator 17 mixes the complex (and pre-compensated) control signal with the corresponding signal 14.sub.1, 14.sub.2, . . . 14.sub.n, again in accordance with the quadrature method. The actuating-signal components thus generated can be individually controlled by means of the IQ controller 15 in accordance with phase and amplitude in each channel. An additional adder 18 superposes all the actuating-signal components on the second actuating signal S.sub.2(t), which is then fed to the actuator 3 of zo the optical resonator 1 together with the first actuating signal S.sub.1(t).

[0065] The function and effect of the multi-channel feed-forward control apparatus 7 shown in FIG. 5 are determined by converting the detection signal into the control signal in each channel. This conversion determines the response of the feed-forward control to the error signal E(t). The conversion is expediently carried out in accordance with a predetermined transfer function.

[0066] Optionally, the transfer function can be automatically (slowly, i.e. at a frequency that is lower than the fundamental frequency of the modulation signal) adapted in order to compensate for changes to the or in the closed control loop due to external influences (pressure, temperature, ageing). For this adaptation, a microcontroller or FPGA may be used, which is used for the implementation of the entire modulation unit 9. This results in a combination of control by the controller 6 and adaptive feed-forward control by the multi-channel feed-forward control apparatus 7, which together achieve effective compensation of undesired frequency components in the modulation of the optical path length of the resonator 7 in accordance with the modulation signal U.sub.mod(t).

[0067] The laser system in FIG. 6 for generating an artificial guide star is constructed similarly to the system in FIG. 3. It uses a frequency-modulated laser 11. The frequency-modulated laser radiation at 1178 nm is generated by means of an optical phase-locked loop 19, the details of which are shown in FIG. 7. Said loop operates by coupling the laser 11 to a fixed-frequency reference laser 20 having a modulated offset frequency, i.e. the optical frequency of the laser 11 is locked to the optical frequency of the fixed-frequency reference laser with a frequency offset, which corresponds to the desired frequency modulation in accordance with the sawtooth-shaped modulation signal U.sub.mod(t). In this way, the optical frequency of the laser 11 can be based on a frequency normal (by the fixed-frequency reference laser 20 being based on a frequency normal, e.g. a calibrated wavelength-measuring device or an atom or molecule resonance). For the coupling, the laser radiation of the laser 11 and the laser radiation of the fixed-frequency reference laser 20 are superposed on a photodetector 21. The frequency and phase of the resulting beat signal are detected by means of a suitable phase/frequency detector (PFD) 23 (optional after passing a frequency-divider stage 22). The frequency-divider stage 22 may be advantageous for increasing the uniqueness range of the PFD 23 and therefore for obtaining stable coupling even at laser-line widths in the MHz range. A high-frequency signal that has been frequency-modulated by a defined offset frequency in accordance with the modulation signal U.sub.mod(t) is generated by means of a HF signal generator 24, which is actuated by the modulation-signal generator 2. When determining the modulation amplitude of the high-frequency signal, potential frequency division in the frequency-divider stage 22 needs to be taken into account. A PID controller 25 stabilizes the detection signal of the PFD 23, such that, as a result, the laser radiation of the laser 11 is frequency-modulated relative to the fixed-frequency reference laser 20 in accordance with the modulation signal U.sub.mod(t). In this process, the HF signal generator 24 predetermines the modulation amplitude and the offset frequency compared with the frequency of the fixed-frequency reference laser 20.

[0068] The laser 11 is e.g. a diode laser, wherein the PID controller 25 controls the injection current of the laser diode (not shown) in order to modulate the frequency.

[0069] An additional frequency modulation superposed on the above-described frequency modulation is also carried out, wherein the associated details are not shown in FIGS. 6 and 7 for the sake of clarity. This additional modulation is carried out at two frequencies simultaneously. One modulation frequency is 1.7 GHz. By means of this modulation frequency, the spectrum of the radiation emitted by the laser light source 11 obtains a sideband at 1.7 GHz relative to the carrier frequency modulated in a sawtooth shape in accordance with the modulation signal U.sub.mod(t). This sideband is ultimately a basis for the generation of radiation at the back-pumping frequency according to the hyperfine splitting of the sodium D-line. The additional modulation frequency is in the range between 5 and 100 MHz. By means of this modulation, yet another sideband is generated, which serves to provide coupling to the optical resonator 1 in accordance with the Pound-Drever-Hall method by means of the error-signal detector 5.

[0070] The thus frequency-modulated laser radiation of the laser 11 is amplified in an optical amplifier 26. A Raman fiber amplifier, as described in EP 2 081 264 A1, is suitable, for example. The Raman fiber amplifier 26 amplifies the frequency-modulated radiation of the laser 11. The amplification bandwidth of the Raman fiber amplifier 26 is accordingly large. At the output of the Raman fiber amplifier 26, the power of the laser radiation is approx. 30 to 40 W.

[0071] The proposed control and adaptive feed-forward control method is then used to make the resonant frequency of the optical resonator 1 precisely follow the frequency of the laser 11 which has been chirped in a sawtooth-shaped manner. The amplified laser radiation is resonantly frequency-multiplied. To do this, a non-linear crystal (not shown) is used, which is located inside the optical resonator 1. In this process, the amplified laser radiation is converted by frequency multiplication and sum-frequency generation. The spectrum of the laser radiation at the output of the optical resonator includes intensities at the (chirped) sodium fluorescence frequency and the back-pumping frequency at a fixed relative frequency distance therefrom.

[0072] Another application of the proposed combined control and adaptive feed-forward control comes about in the modulation of the resonant frequency of an ECDL or VECSEL resonator. In a VECSEL, effects such as spectral hole burning can make it difficult to achieve high power output in single-frequency operation. Such effects can be reduced by modulation of the optical path length of the resonator. In this respect, the proposed method can be used for a defined periodic modulation (at fundamental frequencies of 1-100 kHz) of the optical path length of the VECSEL resonator, e.g. by periodic tilting, rotating or otherwise moving a frequency-selective resonator element, such as an etalon.