US-12627111-B2 - Method for servocontrolling an optical device comprising a laser and a cavity, making it possible to compensate for an amplitude modulation introduced by a phase modulator

US12627111B2US 12627111 B2US12627111 B2US 12627111B2US-12627111-B2

Abstract

A method for the servo control of an optical device includes a cavity exhibiting resonance around a center frequency ƒ c , a laser and a phase modulator, the method being designed to servo-control the cavity to the laser or vice versa and to compensate for an amplitude modulation introduced by the phase modulator, the method comprising, inter alia, the following steps: A. varying a difference δν between the optical frequency of the laser radiation and the center frequency, such that the optical frequency scans the resonance, the difference being controlled by a parameter of an element of the device, and for each difference δν i i. modulating, at a modulation frequency ƒ mod , a phase of the laser radiation, through a modulation phase φ mod , with the phase modulator, ii. injecting the phase-modulated radiation into the cavity, iii. using a photodiode to detect radiation reflected or transmitted by the cavity and generating an electrical signal (St, Sr) representative of the intensity of the detected radiation, iv. demodulating the electrical signal at the modulation frequency ƒ mod by synchronously generating a first demodulated signal and a second demodulated signal representative of the demodulated electrical signal, respectively at a first demodulation phase φ dem,1 and at a second modulation phase φ dem,2 φ dem,2 ≈φ dem,1 k, where k∈[0; 2π] is different from the first phase, and by filtering the first and the second signal so as to retain only a DC component of the first demodulated signal Vϵ 1 , called error signal 1, and of the second demodulated signal Vϵ 2 , called error signal 2.

Inventors

Gilles Feugnet
Maxime DESCAMPEAUX
Fabien Bretenaker

Assignees

THALES
ECOLE NORMALE SUPERIEURE PARIS-SACLAY
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

Dates

Publication Date: 20260512
Application Date: 20220401
Priority Date: 20210401

Claims (10)

1 . A method for the servo control of an optical device comprising a cavity (C) exhibiting resonance around a center frequency ƒ c , a laser (L) and a phase modulator (PM), said method being designed to servo-control said cavity (C) to said laser (L) or vice versa and to compensate for an amplitude modulation introduced by said phase modulator (PM), said method comprising the following steps: A. using said laser (L) to generate laser radiation (LL) at an optical frequency ƒ within said resonance, B. varying a difference δν between said optical frequency of said laser radiation and said center frequency, such that said optical frequency scans said resonance, said difference being controlled by a parameter of an element of said device, and for each difference δν i i. modulating, at a modulation frequency ƒ mod , a phase of said laser radiation, through a modulation phase φ mod , with the phase modulator (PM), ii. injecting the phase-modulated radiation into said cavity (C), iii. using a photodiode (PD t , PD r ) to detect radiation reflected or transmitted by said cavity and generating an electrical signal (St, Sr) representative of the intensity of said detected radiation, iv. demodulating said electrical signal at said modulation frequency ƒ mod by synchronously generating a first demodulated signal and a second demodulated signal representative of the demodulated electrical signal, respectively at a first demodulation phase φ dem,1 and at a second modulation phase ϕ dem , 2 ⁢ ϕ d ⁢ e ⁢ m , 2 ≈ ϕ d ⁢ e ⁢ m , 1 ± k , where ⁢ k ∈ [ 0 ; 2 ⁢ π ] is different from said first phase, and by filtering the first and the second signal so as to retain only a DC component of the first demodulated signal Vϵ 1 , called error signal 1 , and of the second demodulated signal Vϵ 2 , called error signal 2 , C. computing a function 1 ƒ 2 and a function 2 ƒ 2 respectively representing a change in the error signal 1 and a change in the error signal 2 as a function of said difference for a given value of said first demodulation phase, D. repeating steps B) and C) by varying said first demodulation phase between each repetition until, for a value of the first demodulation phase, called decoupling phase ϕ dem , 1 = ϕ dec , said function 1 or said function 2 has a plateau on a portion of values of said difference comprising 0, said function out of 1 or 2 having the plateau being called PL function, the function not having the plateau being called SP function; E. at said decoupling phase, varying said difference so as to observe an extremum, for what is called a zero difference, said intensity of the light radiation detected by said photodiode, and servo-controlling said element to a value of said parameter that makes it possible to maintain this intensity extremum, F. at said decoupling phase, modulating the phase of said laser radiation, with the phase modulator (PM), using what is called an additional periodic signal at what is called an additional modulation frequency ƒ add in addition to that at said modulation frequency f mod ; G. minimizing, for the SP function, an amplitude of a first harmonic of the additional signal, by varying said first demodulation phase, this minimum being reached for what is called a first additional demolition phrase ϕ dem , 1 = ϕ dec ⁢ 2 , and, at said additional phase, servo-controlling said element to a value of said parameter that makes it possible to maintain this intensity extremum, H. at said decoupling phase ϕ dem , 1 = ϕ dec and at said zero difference, varying said first modulation phase until the PL function is canceled out, and maintaining the canceling out of said PL function by servo-controlling said phase modulator.
2 . The method as claimed in claim 1 , wherein step H) consists in varying a voltage V dc,pm of said phase modulator up to what is called a RAM voltage value that makes it possible to cancel out the PL function and servo-controlling said phase modulator to said RAM voltage.
3 . The method as claimed in claim 1 , wherein, in step iii), said photodiode detects the radiation transmitted by said cavity, said method comprising a step D 1 ), after step D) and before step E), consisting in varying said modulation frequency until a slope of said SP function is at a maximum on said portion of values, by repeating step D for each modulation frequency.
4 . The method as claimed in claim 1 , wherein the additional frequency ƒ add is 10 times lower than the modulation frequency ƒ mod .
5 . An optical device (D) comprising a cavity (C) exhibiting resonance around a center frequency ƒ c and a laser (L) designed to generate laser radiation (LL) at an optical frequency ƒ within said resonance, said device comprising: an element designed to vary a difference &v between said optical frequency of said laser radiation and said center frequency, such that said optical frequency scans said resonance, said difference being controlled by a parameter of said element, a phase modulator (PM) configured to modulate, at a modulation frequency ƒ mod , a phase of said laser radiation, through a modulation phase φ mod , and designed to vary said modulation phase, the phase-modulated radiation being injected into said cavity (C), a photodiode (PDt, PDr) designed to detect radiation transmitted or reflected by said cavity (C) and configured to generate an electrical signal representative of the intensity of said detected radiation, a demodulation system (Dem) designed to demodulate said electrical signal at said modulation frequency ƒ mod , for each difference δν i , by: synchronously generating a first demodulated signal and a second demodulated signal representative of the demodulated electrical signal, respectively at a first demodulation phase φ dem,1 and at a second modulation phase φ dem,2 different from said first demodulation phase, such that ϕ dec , 2 ≈ ϕ dem , 1 ± k , with ⁢ k ∈ [ 0 ; 2 ⁢ π ] , filtering the first and the second signal so as to retain only a DC component of the first demodulated signal, called error signal 1 Vϵ 1 , and of the second demodulated signal, called error signal 2 Vϵ 2 , a processor (UT) connected to the modulation system and designed to: compute a function 1 and a function 2 respectively representing a change in the error signal 1 and a change in the error signal 2 as a function of said difference δν for a given value of said first demodulation phase, determine a value of the first demodulation phase, called decoupling phase ϕ d ⁢ e ⁢ m , 1 = ϕ d ⁢ e ⁢ c , for which said function 1 or said function 2 has a plateau on a portion of values of said difference comprising 0, said function out of X or Y having the plateau being called PL function, the function not having the plateau being called SP function, determine, at said decoupling phase, a difference, called zero difference, for which said intensity of the light radiation detected by said photodiode reaches an extremum, and servo-control said element (E) to a value of said parameter that makes it possible to maintain this intensity extremum, modulate, at said decoupling phase, the phase of said laser radiation, with the phase modulator (PM), using what is called an additional periodic signal at what is called an additional modulation frequency ƒ add in addition to that at said modulation frequency ƒ mod ; minimize, for the SP function, an amplitude of a first harmonic of the additional signal, by varying said second demodulation phase, this minimum being reached for what is called a second additional demodulation phase, and servo-control said element to a value of said parameter that makes it possible to maintain this intensity extremum at said additional phase, determine, at said decoupling phase and at said zero difference, a value of said modulation phase for which said PL function is canceled out, and servo-control said phase modulator (PM) in order to maintain the canceling out of said PL function.
6 . The device as claimed in claim 5 , wherein said element is said laser (L) and said parameter is a DC voltage V dc,L supplied to the laser.
7 . The device as claimed in claim 5 , wherein the element is an acousto-optic modulator (AOM) configured to vary said optical frequency of the laser radiation before it is phase-modulated by said phase modulator, said parameter being an excitation frequency ƒ AOM of said acousto-optic modulator.
8 . The device as claimed in claim 5 , wherein the element is a piezoelectric translation stage to which a component of said cavity is fixed, said stage being designed to vary a length of the cavity, said parameter being said length of the cavity.
9 . The device as claimed in claim 5 , wherein the cavity (C) is a ring cavity comprising an optical fiber (FO) and first and second coupling means (M 1 , M 2 ) configured to couple said radiation injected into said cavity with said optical fiber, the first and second coupling means comprising a mirror or a fiber coupler.
10 . The device as claimed in claim 9 , comprising: an optical splitter (LS) designed to split the laser radiation into a first and a second optical channel (F, F′) so as to inject said laser radiation into the cavity in a first and a second direction, the first optical channel comprises the phase modulator (PM) and an optical circulator (CO) positioned after the phase modulator, the second optical channel comprises an additional phase modulator (PM′), and an additional optical circulator (CO′) positioned after the additional phase modulator, said optical circulator (CO) and said additional optical circulator being designed to direct the laser radiation injected respectively in said second direction and in said first direction and then reflected by the cavity (C) toward an additional reflection photodiode (PDr′) and toward said photodiode (PDr), a first optical path of said first optical channel and a second optical path of said second optical channel between the phase modulator and said cavity, and the additional phase modulator and said cavity, respectively, having a guided-optic configuration.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS This application is a National Stage of International patent application PCT/EP2022/058753, filed on Apr. 1, 2022, which claims priority to foreign French patent application No. FR 2103389, filed on Apr. 1, 2021, the disclosures of which are incorporated by reference in their entireties. FIELD OF THE INVENTION The invention relates to the field of servo-controlling laser optical frequency to a resonant optical cavity or vice versa. BACKGROUND In many applications (gyrometer, gravitational interferometry or even metrology), it is necessary to have a laser source emitting radiation at a highly stable optical frequency. In order to improve the stability of the optical frequency of a laser, it is known to servo-control the laser to the resonance of a resonant optical cavity. The method most commonly used to achieve such servo-control is that known as the Pound Dreyer Hall method, named after its inventors. FIG. 1 schematically shows a device for carrying out this method. The device comprises notably a cavity C exhibiting resonance around a center frequency ƒc and a laser L designed to generate a laser beam LL. The optical frequency of the laser beam is then shifted by an acousto-optic modulator AOM (optional component) to a frequency ƒ=ω/2π within said resonance. The laser beam is then modulated, by a phase modulator PM, by a phase at a modulation frequency fmod=ωmod/2⁢π and a modulation amplitude M. The modulation frequency is applied by a local oscillator OL. Through a harmonic expansion, it may be shown that the phase-modulated beam injected into the cavity has an amplitude Einj such that: Ei⁢n⁢j=J0(M)⁢ei⁢ω⁢t+J1(M)⁢ei⁡(ω+ωm⁢o⁢d)⁢t-J1(M)⁢ei⁡(ω-ωm⁢o⁢d)⁢t, with J being Bessel functions, this equation being valid for low values of M by limiting the expansion to the first sidebands. This equation makes it possible to observe that the phase modulator PM creates lateral frequency components, or sidebands, that are separated from the initial frequency ƒ by multiples of the modulation frequency ƒmod, applied by the oscillator OL via PM. This modulation frequency is chosen, if possible, to be greater than the width of the resonance of the cavity, such that the sidebands are not at resonance with the cavity. Hereinafter, consideration is given only to the two sidebands at ƒ±ƒmod. The laser beam is then injected into the cavity C. Said cavity has a reflection-mode transfer function, denoted Fr, that links the amplitude of the incident electric field and that of the reflected electric field. An optical circulator CO (typically based on a Faraday rotator positioned between two polarization splitter cubes) directs the laser beam reflected by the cavity onto a photodiode, denoted PDr. The signal SI generated by the photodiode is then demodulated by a demodulation system Demo comprising a mixer Mix0 that multiplies the signal SI by the modulation signal applied to PM with a demodulation phase. A low-pass filter LP0 then makes it possible to keep only the DC component of the demodulated signal, the amplitude of which, Vε, called error signal, is then proportional to the difference between the frequency ƒ of the laser and the resonant frequency ƒc of the cavity. Indeed, the amplitude of the error signal is: V⁢ϵ=2⁢G⁢Pc⁢Ps⁢Im[Fr(ω)·Fr(ω+ωmod)_-Fr(ω)_·Fr(ω+ωmod], where Pc and Ps are the power of the fundamental and sideband component, respectively, and G is the conversion gain between the optical power received and the voltage delivered by the photodiode. When the modulation frequency is high enough and when a difference δν between frequency of the laser radiation and the center frequency of the resonance is small enough, it may then be shown that: V⁢ϵ=G⁢8⁢Pc⁢PsΔ⁢fc⁢δ⁢v, where Δƒc is the linewidth of the resonance (for a high-finesse Fabry-Pérot cavity). When the frequency ƒ of the laser and the resonant frequency of the cavity deviate slightly, the two sidebands are unchanged (if they are indeed out of resonance), whereas the phase and the amplitude of the beam at the frequency ƒ change (since it is no longer at resonance). The properties of coherence between the three spectral components of the laser beam then make it possible to measure these fluctuations that result in this linear variation of the demodulated signal, which may thus be used as a frequency error signal, Vε being canceled out when the laser radiation is resonant with a mode of the cavity. A processor UT is then configured to carry out servo control with this error signal Vϵ, via feedback electronics, using conventional servo control methods, for example, without being restrictive, with PI or PID (proportional integral derivative) feedback electronics, alluding to the three modes of action on the error signal of the feedback electronics. This type of feedback for making the error signal converge toward a zero value is well known in automation. With regard to the choice of the modulation frequency to be applied to PM, if th