CN115986547A - Large-dynamic-range and high-sensitivity PDH frequency stabilization method with double modulation depths - Google Patents
Large-dynamic-range and high-sensitivity PDH frequency stabilization method with double modulation depths Download PDFInfo
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Abstract
The invention discloses a double-modulation-depth PDH frequency stabilization method with a large dynamic range and high sensitivity. Firstly, the laser frequency is far away from the resonant frequency of the optical resonant cavity, the interference signal is subjected to orthogonal down-mixing and arc tangent operation to obtain an initial phase difference, and the automatic phase matching of a PDH demodulation reference signal is realized; then dividing the PDH error signal by the square of the transmission power to obtain a new error signal with a larger linear dynamic range; and finally, a new error signal with a large dynamic range under a large modulation depth and an error signal with high sensitivity under a small modulation depth are respectively adopted as feedback signals of primary lock and frequency stabilization fine lock of PDH capture, and accurate locking of the laser frequency/the cavity length of the resonant cavity is achieved. The method not only expands the linear dynamic range of PDH frequency stabilization, reduces the scanning and capturing time of the laser frequency/the cavity length of the resonant cavity, but also improves the anti-interference capability of the system after the laser frequency stabilization/the locking of the cavity length of the optical resonant cavity, and can be widely applied to the fields of laser frequency stabilization, locking of the cavity length of the resonant cavity and the like.
Description
Technical Field
The invention belongs to the technical field of laser frequency stabilization and optical resonant cavity length locking, and particularly relates to a double-modulation-depth PDH frequency stabilization method with a large dynamic range and high sensitivity.
Background
PDH (Pound-Drever-Hall) technology is one of the most commonly used methods for active frequency stabilization of lasers or for locking the cavity length of optical resonators at present. A frequency discrimination error signal of which the laser frequency deviates from the resonant frequency of the optical resonant cavity is obtained by adopting a radio frequency electro-optic phase modulation technology and an optical heterodyne spectroscopy technology of the optical resonant cavity. When the optical resonant cavity is taken as a reference, the cavity length/current of the laser is controlled and adjusted by utilizing the feedback of the error signal, so that the frequency of the laser can be stabilized on the resonant frequency of the optical resonant cavity; conversely, the error signal is used to feedback control the cavity length of the locked-in optical resonator when the laser frequency is used as a reference. The linear dynamic range and sensitivity of the error signal are the main indicators affecting the stability and accuracy of the laser frequency stabilization/cavity length locking. The error signal is usually obtained by using 0 order and +/-1 order sideband beat frequency generated by electro-optic phase modulation of laser at the modulation depth of about 1.08rad, the linear dynamic range of the error signal is small, the wide-range fast locking of the laser frequency/cavity length is difficult to realize, and even under the locking condition, when the environmental temperature fluctuation is large or the environment vibrates, the laser frequency/cavity length is easy to lose the lock. In view of the above problems, currently, the control range of the system is mostly expanded by a nonlinear control method or by acquiring a signal with a wider linear interval, where the nonlinear control method includes methods such as a linear quadratic gaussian control (LQG) method and a time-varying kalman filter, so as to implement expansion of the dynamic range of the PDH technology, but the algorithm is cumbersome; further, a signal with a larger linear dynamic range can be obtained by near-Q phase demodulation, combination of multiple odd-order frequency-modulated in-phase demodulated signals, normalization with a transmission power signal, or the like, but the sensitivity of the PDH technique is reduced.
Disclosure of Invention
In order to solve the problems in the background art, the invention discloses a PDH frequency stabilization method with double modulation depths, a large dynamic range and high sensitivity. The invention not only enlarges the linear dynamic range of PDH frequency stabilization, reduces the scanning and capturing time of laser frequency/resonant cavity length, but also improves the anti-interference capability of the system after the laser frequency stabilization/optical resonant cavity length locking, and can be widely applied to the fields of laser frequency stabilization, resonant cavity length locking and the like.
The technical scheme adopted by the invention for realizing the aim comprises the following steps:
1. a double-modulation depth large-dynamic-range and high-sensitivity PDH frequency stabilizing device comprises:
the device comprises a laser, an optical isolator, an electro-optic phase modulator, a first photoelectric detector, a polarization spectroscope, a quarter-wave plate, an optical resonant cavity and a second photoelectric detector;
laser emitted by the laser enters the optical isolator, the laser emitted from the optical isolator enters the electro-optic phase modulator, is modulated and then enters the polarization beam splitter for transmission, the laser transmitted from the polarization beam splitter is light in a p-polarization state and enters the optical resonant cavity through the quarter-wave plate for reflection and transmission, the laser reflected from the optical resonant cavity returns to the quarter-wave plate so that the p-polarization state is converted into an s-polarization state, the laser returns to the polarization beam splitter for reflection, the laser reflected from the polarization beam splitter enters the first photoelectric detector to be received, and the laser transmitted from the optical resonant cavity enters the second photoelectric detector to be received.
The photoelectric phase modulator also comprises a signal acquisition and processing module, wherein the output ends of the first photoelectric detector and the second photoelectric detector are connected to the input end of the signal acquisition and processing module, the output end of the signal acquisition and processing module is connected to the electro-optical phase modulator, and the output end of the signal acquisition and processing module is connected to the laser or the optical resonant cavity.
The signal acquisition and processing module specifically comprises a digital frequency synthesizer, a phase shifter, a first multiplier, a first low-pass filter, an arc tangent operation module, a gain module, a triangular wave scanning module, a second multiplier, a square operation module, a second low-pass filter, a first threshold judgment module, a division operation module, a first data selector, a PID control module, a second threshold judgment module and a second data selector;
one output end of the digital frequency synthesizer is connected to the input end of the gain module, the output end of the gain module is connected to the driving input end of the electro-optical phase modulator, the other two orthogonal output ends of the digital frequency synthesizer are connected to the two input ends of the phase shifter, the two output ends of the phase shifter are respectively connected to the input ends of the first multiplier and the second multiplier, the first photoelectric detector is connected to the input ends of the first multiplier and the second multiplier, the output ends of the first multiplier and the second multiplier are respectively connected to the input ends of the first low-pass filter and the second low-pass filter, the output end of the first low-pass filter is connected to one input end of the arc tangent operation module, and the output end of the second low-pass filter is divided into three paths and is respectively connected to the input ends of the arc tangent operation module, the division operation module and the first data selector;
the output end of the second photoelectric detector is divided into three paths and is respectively connected to the input ends of the squaring operation module, the first threshold judgment module and the second threshold judgment module, the output end of the squaring operation module is connected to the other input end of the division operation module, the output end of the division operation module is respectively connected to the other input ends of the first data selector and the second threshold judgment module, the output end of the first threshold judgment module is connected to the selection control end of the first data selector, the output end of the first data selector is connected to the input end of the PID control module, the output ends of the PID control module and the triangular wave scanning module are respectively connected to the two data input ends of the second data selector, the output end of the second threshold judgment module is connected to the selection control end of the second data selector, and the output end of the second data selector is connected to the optical resonant cavity after digital-to-analog conversion.
When the device is used for stabilizing the laser frequency emitted by the laser, the laser adopts a laser with adjustable laser frequency, and the optical resonant cavity adopts an optical resonant cavity with fixed cavity length;
when the device is used for locking the cavity length of the optical resonant cavity, the laser adopts a laser with laser frequency, and the optical resonant cavity adopts an optical resonant cavity with adjustable cavity length.
2. A large dynamic range and high sensitivity PDH frequency stabilization method with double modulation depths comprises the following steps:
step 1) laser emitted by a laser enters an electro-optic phase modulator after passing through an optical isolator, the electro-optic phase modulator generates a phase modulation signal to perform phase modulation on the laser, the phase-modulated laser sequentially passes through a polarization beam splitter and a quarter wave plate and then enters an optical resonant cavity and is reflected and transmitted back and forth in the cavity for multiple times, the laser reflected from the optical resonant cavity is reflected reversely through the quarter wave plate, the polarization state is changed from a p state to an s state, then the laser is reflected to a first photoelectric detector through the polarization beam splitter to generate multi-beam interference, an interference signal is obtained by detection, the interference signal is sampled and subjected to analog-to-digital conversion to obtain a reflected multi-beam interference signal I r1 (t); wherein the sampling frequency for sampling the interference signal is higher than the laser phase modulation frequency omega of the electro-optic phase modulator m 2 times of the total weight of the powder.
The reflected multi-beam interference signal I r1 (t) is represented as follows:
wherein, I r1 (t) represents an interference signal detected by a photoelectric detector at the reflection end of the optical resonant cavity at the time t, and j represents the highest order of a laser frequency sideband generated after laser phase modulation, namely the highest order of the laser frequency sideband (edge frequency for short) generated by the laser phase modulation of the electro-optic phase modulator is j order; DC terms and p.omega m term represents the DC component and ω of the interference signal, respectively m With the remainder being ω m A frequency multiplication component of (a); e 0 Representing the laser amplitude, ω c Representing the fundamental frequency of the laser, l the cavity length of the optical resonator, ω m Denotes the phase modulation frequency, k denotes the order of the modulation sideband, k =0 to j-1; j is a unit of k (β) is a first Bessel function of the kth order at a modulation depth of β; re { } and Im { } are respectively expressed byRepresenting the real and imaginary parts of the complex number; f [ omega, l]Representing the reflection coefficient of the optical resonator as a function of the incident laser frequency ω and the cavity length l; f omega, l]The conjugate of the reflection coefficient of the optical resonant cavity is shown, n is the refractive index of air in the cavity, and i is an imaginary number unit. r represents the cavity mirror reflectivity of the two optical cavities and FSR represents the free spectral range of the optical cavity.
Step 2) generating two paths of orthogonal reference signals with the same frequency as the phase modulation signals by a digital frequency synthesizer, wherein the two paths of orthogonal reference signals comprise cosine reference signals
And a sinusoidal reference signal->
Two paths of orthogonal reference signals respectively interfere with a reflected multi-beam interference signal I after moving the same phase through a phase shifter r1 (t) after being multiplied by two respective multipliers (903, 908) and filtered by low-pass filters (904, 910) in sequence, the quadrature down-mixing operation is completed, the direct current component is retained, a pair of quadrature harmonic amplitude signals are obtained, and the quadrature harmonic amplitude signals comprise a sinusoidal component S I And a cosine component S Q ；
The quadrature harmonic amplitude signal is simplified into a simple trigonometric function form and then is respectively expressed as:
R(k)＝F[ω c +kω m ,l]F*[ω c +(k+1)ω m ,l]-F*[ω c -kω m ,l]F[ω c -(k+1)ω m ,l]
wherein S is I 、S Q Respectively representing sine and cosine components in the quadrature harmonic amplitude signal, LPF]Representing a low-pass filtering operation, and R (k) represents omega generated by the beat frequency of the kth order and the kth +1 order sidebands and the-kth order and the- (k + 1) th order sidebands respectively m Is called the amplitude coefficient of the kth order, | R (k) | is the modulus of the amplitude coefficient R (k) of the kth order,
is the phase angle of the amplitude factor R (k) of the kth order>
Is the initial phase difference, omega, between a frequency-doubled component of the interference signal and the sinusoidal reference signal m Representing the phase modulation frequency, J k (β) is a first-class Bessel function of a k-th order when the modulation depth is β, k represents an order of a modulation sideband, k =0 to j-1,j represents a highest-order of a sideband frequency after laser modulation, and t represents time. />
Step 3) performing arc tangent operation on a pair of orthogonal harmonic amplitude signals in an arc tangent operation module to obtain a phase
The calculation is as follows:
adjusting the laser frequency of the laser or the cavity length of the optical resonant cavity to make the frequency intervals between the laser fundamental frequency and the side frequency thereof and the resonant frequency of the optical resonant cavity more than twice the full width at half maximum of the optical resonant cavity, and determining the phase position
As an initial phase difference->
When the frequency interval between the laser fundamental frequency and its side frequency and the resonant frequency of the optical resonant cavity is greater than twice the full width at half maximum, the fundamental laser and its modulation side band laser are totally reflected, i.e. the reflection coefficients of the corresponding frequencies are pure real numbers, and the phase of the amplitude coefficient of the first order is the same as the phase of the second order
k =0 to j-1,j represents the highest order of the side frequency after laser modulation, and a frequency multiplication component of the interference signal is used in this case as followsThe formula calculates the initial phase difference of the sinusoidal reference signal->
Then, the obtained initial phase difference is utilized
The phase-shifted quadrature reference signals are fed back to the phase shifter to shift the phase of the two quadrature reference signals, so as to realize interference signals I r1 (t) automatically matching a frequency multiplication component with the phase of the sinusoidal reference signal, thereby ensuring the linearity and high sensitivity of the error signal in a frequency discrimination interval;
step 4) sinusoidal component S in orthogonal harmonic amplitude signal I After the phase matching is finished, the error signal S is used as an error signal S after the phase matching PDH The expression is:
wherein k represents the order of the modulation sideband, k = 0-j-1,j represents the highest order of the laser frequency sideband generated after laser phase modulation, namely the highest order of the laser frequency sideband (sideband frequency for short) generated by the laser phase modulation of the electro-optic phase modulator is j order; e 0 Denotes the laser amplitude, J k (β) is a first Bessel function of the kth order at a modulation depth of β; r (k) represents omega generated by respectively beating frequency of kth order and kth +1 order sidebands and kth order and- (k + 1) th order sidebands m Is called the amplitude coefficient of the kth order, | R (k) | is the modulus of the amplitude coefficient R (k) of the kth order,
is the phase angle of the amplitude coefficient R (k) of the kth order, and t represents the time; />
Represents one of the interference signalsWhen the laser phase modulation frequency is lower than the full width at half maximum of the optical resonant cavity, the phase difference after matching is 0 degree; when the laser phase modulation frequency is higher than the full width at half maximum of the optical resonant cavity, the phase difference after matching is 90 degrees;
and step 5) receiving and detecting the light transmitted from the optical resonant cavity by a second photoelectric detector to obtain a direct current power signal, sampling the direct current power signal, and performing analog-to-digital conversion to obtain a transmission power signal P tran The expression is:
wherein, P tran Representing the transmitted power signal, l representing the cavity length of the optical resonator, ω m Representing the phase modulation frequency, | k | representing the absolute value of k, J |k| (beta) is a first Bessel function of the k order or the-k order when the modulation depth is beta, and j represents the highest order of the side frequency after laser modulation; t (ω, l) represents the transmission coefficient of the optical resonator as a function of the incident laser frequency ω and the cavity length l; t (omega, l) represents the conjugation of the transmission coefficient of the optical resonant cavity, n is the refractive index of air in the cavity, i is an imaginary number unit, r represents the reflectivity of the cavity mirror of the two optical resonant cavities, and FSR represents the free spectral range of the optical resonant cavity;
then the error signal S after phase matching PDH With the square P of the transmitted power signal tran 2 Division operation is carried out in the division operation module to obtain a new error signal S new The calculation formula is as follows:
step 6) to this point, the error signal S after phase matching is obtained in real time PDH New error signal S new And a transmission power signal P tran Then, the three signals in real time are used for realizing the automatic locking of the cavity length of the optical resonant cavity/the laser frequency of the laser, and the automatic locking mainly comprises a scanning stage, a capturing stage, a preliminary locking stage and an accurate locking stage so as to realize the frequency stabilization control.
The step 6) is specifically as follows:
step 6.1) scanning, capturing and preliminary locking:
firstly, a signal acquisition and processing module controls and adjusts the amplitude of a driving signal of an electro-optic phase modulator to realize laser phase modulation of large modulation depth of laser;
then the output end of the triangular wave scanning module is connected to the laser or the optical resonant cavity under the control of the second data selector, and the triangular wave scanning signal sent by the triangular wave scanning module is utilized to carry out triangular wave pre-scanning on the laser frequency of the laser sent by the laser/the cavity length of the optical resonant cavity to obtain a new error signal S new Maximum value of S newmax And a transmission power signal P tran Transmission peak value P of tranmax And with the new error signal S new Maximum value of S newmax Is taken as the lock capture threshold S th ；
Then, the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity is captured in a locking interval, the output end of the division operation module is connected to the PID control module under the control of the triangular wave scanning signal and the control of the first data selector, and the PID control module inputs a new error signal S new The following judgment and processing are performed:
when the new error signal S new Has not reached a maximum value S newmax Or not from the maximum value S newmax Falls below the lock acquisition threshold S th During the operation, the triangular wave prescan of the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity is kept, and no processing is carried out;
when the new error signal S new From the maximum value S newmax Falls below the lock acquisition threshold S th The output of the PID control module is controlled by the second data selectorThe end of the triangular wave is connected with a laser or an optical resonant cavity, and the triangular wave scanning signal is switched to S new The output signal processed by the PID control module is used as an input signal to carry out feedback control on the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity, and the PID control module is further used for carrying out feedback control on the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity so as to enable a new error signal S to be generated new Fluctuating near zero to realize preliminary locking;
step 6.2) accurate locking:
the output end of the second low-pass filter is connected to a PID control module by the control of the first data selector, and the PID control module inputs an error signal S after phase matching PDH I.e. the input of the PID control module is derived from the new error signal S new Switching to the phase-matched error signal S PDH Meanwhile, the phase modulation depth is reduced to a small modulation depth by adjusting the amplitude of a driving signal of the electro-optical phase modulator, and only 0 order and +/-1 order side frequency components are reserved under the small modulation depth. And the output end of the PID control module is kept connected with the laser or the optical resonant cavity under the control of the second data selector, and the PID control module is utilized to perform feedback control on the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity, so that the error signal S after phase matching PDH Fluctuating around zero, achieving accurate locking.
In the step 6.1), when the PID control module is used for feedback control, the final transmission power signal P tran Will be at the transmission peak P tranmax The vicinity fluctuation is specifically determined as follows:
when transmitting the power signal P tran The fluctuation amount in a fixed period of time is less than the transmission peak value P tranmax When the frequency is one third, the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity realize initial locking, and the next step of accurate locking is carried out;
when transmitting the power signal P tran The fluctuation amount in a fixed period of time is not less than the transmission peak value P tranmax And when one third of the total quantity of the PID control module is less than the total quantity of the PID control module, the PID parameter in the PID control module is adjusted.
The step 6.1) is to adjust the amplitude of the driving signal of the electro-optic phase modulator to carry out laser phase modulation with large modulation depth according to the first Bessel function J of the kth (k is a positive integer) order k The properties of (. Beta.) were judged as follows:
for a certain fixed modulation depth β, when k is>Beta +1, then J k (β)<0.1 when k<If β +1, then J k (β)>0.1, i.e. J k The high-order side frequency components with the order greater than beta +1 corresponding to the (beta) can be ignored, the side frequency components with the order greater than or equal to the beta +1 can not be ignored, and the order j of the highest order of the laser frequency sideband under the large modulation depth is greater than or equal to 2.
In the process of carrying out the steps 6.1) to 6.2), carrying out the following judgment in real time for judgment and processing:
when transmitting the power signal P tran Is greater than or equal to the transmission peak value P tranmax When the modulation depth is one-half of the modulation depth, the modulation depth of the electro-optic phase modulator is small, the output end of the second low-pass filter is connected to the PID control module under the control of the first data selector, the input of the PID control module is an error signal, and the PID control module is utilized to perform feedback control on the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity, so that the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity are accurately locked;
when transmitting the power signal P tran Less than the transmission peak value P tranmax Is one half and is greater than or equal to the transmission peak value P tranmax The modulation depth of the electro-optic phase modulator is switched to a large modulation depth again, the output end of the division operation module is connected to the PID control module through the control of the first data selector, and the input of the PID control module is switched to a new error signal S new The PID control module is used for carrying out feedback control on the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity, so that the laser frequency of the laser emitted by the laser/the cavity length of the optical resonant cavity is locked again;
if the external interference is very large, the transmitted power signal P is caused tran Is less than P tranmax OfIn one case, the output end of the triangular wave scanning module is connected to the laser or the optical resonant cavity by the control of the second data selector, and the triangular wave scanning signal sent by the triangular wave scanning module is used for controlling the laser frequency/cavity length of the optical resonant cavity sent by the laser, namely, the control signal of the laser frequency/cavity length of the optical resonant cavity sent by the laser is switched to the triangular wave scanning signal again, and the step 6.1) is returned to perform scanning, capturing and locking again.
In the present invention, the error signal S PDH For processing at small modulation depths, the error signal S at small modulation depths PDH Has the characteristics of high sensitivity and narrow linear dynamic range, and the new error signal S new For processing at large modulation depth, a new error signal S at large modulation depth new Has the characteristics of large linear dynamic range and low sensitivity. The modulation depth of the laser phase modulation of the electro-optic phase modulator is increased, the linear dynamic range of the laser phase modulation and the modulation depth of the laser phase modulation of the electro-optic phase modulator are increased, and the sensitivity is reduced; the modulation depth is reduced, the linear dynamic range of the modulation depth and the modulation depth is reduced, and the sensitivity is improved.
The reflected multi-beam interference signal is derived from an interference signal detected by a photoelectric detector at the reflection end of an optical resonant cavity in a PDH technology, and the transmission power signal is a direct-current power signal detected by the photoelectric detector at the transmission end of the optical resonant cavity.
In the specific implementation, the cavity length of the optical resonant cavity, i.e. the resonant frequency thereof, is taken as an example.
The modulation frequency of the laser phase modulation of the electro-optic phase modulator is smaller than the full width at half maximum of the optical resonant cavity, the modulation depth beta which is larger than or equal to 1.2rad is large modulation depth, and the modulation depth beta which is smaller than 1.2rad is small modulation depth. In a specific implementation, the large modulation depth is set to be beta 1 =1.80rad, small modulation depth β 2 ＝1.08rad。
Firstly, carrying out quadrature down-mixing and arc tangent operation on an obtained interference signal and a pair of quadrature reference signals to obtain an initial phase difference, and using a phase shifter to shift the phase, so that automatic matching of the phase is realized, and manual adjustment of the phase shifter is avoided; then, a new error signal is generated by utilizing the error signal after phase matching and the transmission power signal of the resonant cavity after square matching, the linear dynamic range is expanded, and the scanning and capturing time of the laser frequency/the cavity length of the resonant cavity is reduced; and finally, a new error signal with a large dynamic range under a large modulation depth and an error signal with high sensitivity under a small modulation depth are switched to be used as the input of the PID feedback control module, so that the locking precision is ensured, the anti-interference capability of the system after the laser frequency stabilization/optical resonant cavity length locking is improved, and the laser frequency/cavity length is less prone to losing the lock.
Compared with the background art, the invention has the beneficial effects that:
(1) The invention obtains the initial phase difference by carrying out orthogonal down-mixing and arc tangent operation on the reflected multi-beam interference signals and the same-frequency local oscillation signals obtained under different modulation depths, and realizes the automatic phase matching of the two signals by using the phase shifter, thereby ensuring the linearity and high slope of the error signals in a frequency discrimination interval and avoiding the process of manually adjusting the phase shifter.
(2) The invention obtains a new error signal with larger linear dynamic range by simultaneously utilizing the reflection error signal and the transmission power signal, enlarges the linear dynamic range by increasing the phase modulation depth, and reduces the scanning and capturing time of the laser frequency of the laser/the cavity length of the optical resonant cavity in the automatic locking process.
(3) According to the invention, the new error signal under the large modulation depth and the error signal under the small modulation depth are switched to be used as the input of the PID control module, so that the locking of the large dynamic range and the high sensitivity of the laser frequency/cavity length is realized, the anti-interference capability of the system after the laser frequency stabilization/optical resonant cavity length locking is improved while the locking precision is ensured, and the laser frequency/cavity length is less prone to losing the lock.
Drawings
FIG. 1 is a schematic block diagram of an apparatus for the method of the present invention.
Fig. 2 is a schematic block diagram of a signal acquisition and processing module of the method of the present invention.
Fig. 3 is a schematic diagram of the error signal and the new error signal in the method of the present invention.
Fig. 4 is a simulation diagram of the relationship between the linear dynamic range and the modulation depth of the error signal and the new error signal in the method of the present invention.
In the figure: 1. the device comprises a laser, 2, an optical isolator, 3, an electro-optical phase modulator, 4, a first photoelectric detector, 5, a polarization beam splitter, 6, a quarter wave plate, 7, an optical resonant cavity, 8, a second photoelectric detector, 9, a signal acquisition and processing module, 901, a digital frequency synthesizer, 902, a phase shifter, 903, a first multiplier, 904, a first low-pass filter, 905, an arc tangent operation module, 906, a gain module, 907, a triangular wave scanning module, 908, a second multiplier, 909, a square operation module, 910, a second low-pass filter, 911, a first threshold judgment module, 912, a division operation module, 913, a first data selector, 914, a PID control module, 915, a second threshold judgment module, 916 and a second data selector.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
As shown in fig. 1, the specific implementation method uses the following optical paths: the device comprises a laser 1, an optical isolator 2, an electro-optic phase modulator 3, a first photoelectric detector 4, a polarization spectroscope 5, a quarter-wave plate 6, an optical resonant cavity 7, a second photoelectric detector 8 and a signal acquisition and processing module 9; the laser 1, the optical isolator 2, the electro-optic phase modulator 3, the polarization beam splitter 5, the quarter-wave plate 6, the optical resonant cavity 7 and the second photoelectric detector 8 can be arranged through an optical axis.
Laser emitted by a laser 1 enters an optical isolator 2, the laser emitted from the optical isolator 2 enters an electro-optic phase modulator 3, is modulated and then enters a polarization spectroscope 5 to be transmitted, the laser transmitted from the polarization spectroscope 5 is light in a p-polarization state and enters an optical resonant cavity 7 through a quarter-wave plate 6 to be reflected and transmitted, the laser reflected from the optical resonant cavity 7 returns to the quarter-wave plate 6 to be converted from the p-polarization state to an s-polarization state, and returns to the polarization spectroscope 5 to be reflected, and the laser reflected from the polarization spectroscope 5 enters a first photoelectric beam splitterThe detector 4 is received to obtain a reflected multi-beam interference signal I r1 (t), the laser transmitted from the optical resonant cavity 7 is incident on the second photodetector 8 and received to obtain a transmission power signal P tran (ii) a The output ends of the first photodetector 4 and the second photodetector 8 are connected to the input end of the signal acquisition and processing module 9, the output end of the signal acquisition and processing module 9 is connected to the electro-optical phase modulator 3, and the output end of the signal acquisition and processing module 9 is connected to the laser 1 or the optical resonant cavity 7.
The signal acquisition and processing module 9 receives the detection signals output by the first photodetector 4 and the second photodetector 8, outputs a sine drive signal to the electro-optic phase modulator 3, and outputs a PID control signal U PID To the controlled object, the controlled object can be the laser 1 or the optical resonator 7.
As shown in fig. 2, the signal collecting and processing module 9 specifically includes a digital frequency synthesizer 901, a phase shifter 902, a first multiplier 903, a first low-pass filter 904, an arc tangent operation module 905, a gain module 906, a triangular wave scanning module 907, a second multiplier 908, a square operation module 909, a second low-pass filter 910, a first threshold judgment module 911, a division operation module 912, a first data selector 913, a PID control module 914, a second threshold judgment module 915, and a second data selector 916;
one of the output terminals of the digital frequency synthesizer 901 is connected to the input terminal of the gain module 906, the output terminal of the gain module 906 is connected to the driving input terminal of the electro-optical phase modulator 3 in the optical path of fig. 1, the other two quadrature output terminals of the digital frequency synthesizer 901 are connected to the two input terminals of the phase shifter 902, the two output terminals of the phase shifter 902 are respectively connected to the input terminals of the first multiplier 903 and the second multiplier 908, the reflected multi-beam interference signal I of the first photodetector 4 is r1 (t) the inputs are connected to the input terminals of a first multiplier 903 and a second multiplier 908, the output terminals of the first multiplier 903 and the second multiplier 908 are connected to the input terminals of a first low-pass filter 904 and a second low-pass filter 910, respectively, the output terminal of the first low-pass filter 904 is connected to one input terminal of an arctangent operation module 905, and the output terminal of the second low-pass filter 910 is connected to the input terminal of a second low-pass filter 910The output end is divided into three paths and respectively connected to the input ends of the arctangent operation module 905, the division operation module 912 and the first data selector 913;
transmission power signal P at the output of the second photodetector 8 tran The output end of the squaring operation module 909 is connected to the other input end of the division operation module 912, the output end of the division operation module 912 is connected to the other input end of the first data selector 913 and the second threshold judgment module 915, the output end of the first threshold judgment module 911 is connected to the selection control end of the first data selector 913, the output end of the first data selector 913 is connected to the input end of the PID control module 914, the output ends of the PID control module 914 and the triangular wave scanning module 907 are connected to the two data input ends of the second data selector 916, the output end of the second threshold judgment module 915 is connected to the selection control end of the second data selector 916, and the output end of the second data selector 916 is connected to the optical resonant cavity 7 after digital-to-analog conversion, specifically to the input end of the piezoelectric ceramic installed on one cavity mirror of the optical resonant cavity 7.
The specific implementation process of the invention is as follows:
as shown in fig. 1, laser light emitted by a laser 1 enters an electro-optic phase modulator 3 through an isolator 2 for phase modulation, and then is transmitted by a polarization beam splitter 5 and enters an optical resonant cavity 7 through a quarter-wave plate 6. The cavity length of the optical resonant cavity 7 can be controlled by piezoelectric ceramic PZT mounted on a facet mirror. The light reflected by the optical resonant cavity 7 passes through the quarter-wave plate 6 again, the polarization state is changed from the p state to the s state, the light is reflected by the polarization spectroscope 5, multi-beam interference is generated at the first photoelectric detector 4, the light is detected and converted, and the interference signal is called as a reflected multi-beam interference signal I r1 (t); the transmitted light is detected and converted by a second photoelectric detector 8 after passing through an optical resonant cavity 7, and the detected direct current signal is called a transmission power signal P tran . Reflecting multi-beam interference signal I r1 (t) and the transmitted power signal P tran Respectively composed of signal acquisition and processing modules9 sampling, analog-to-digital conversion and subsequent signal processing.
Reflecting multiple-beam interference signal I r1 (t) is represented as follows:
wherein, I r1 (t) represents the interference signal detected by the first photodetector 4 at the reflecting end of the optical resonator 7 at time t, j represents the highest order of the side frequency, DC terms and p.omega m term is the DC component and ω, respectively, of the interference signal m With the remainder being ω m A frequency multiplication component of; e 0 Representing the laser amplitude, ω c Representing the fundamental frequency, ω, of the laser m The modulation frequency is represented, l represents the cavity length of the optical resonant cavity, k represents the order of a modulation sideband, and k =0 to j-1; j is a unit of k (β) is a first Bessel function of the kth order at a modulation depth of β; re { } and Im { } respectively represent taking the real part and the imaginary part of the complex number; f [ omega, l]Represents the reflection coefficient of the optical resonator 7 as a function of the incident laser frequency ω and the cavity length l; f omega, l]Representing the conjugate of the reflection coefficient of the optical cavity 7, n being the index of refraction of the air in the cavity, and i being the imaginary unit. r represents the cavity mirror reflectivity of both optical cavities 7 and FSR represents the free spectral range of the optical cavity 7.
Transmitted power signal P tran The expression of (b) is as follows:
wherein, P tran Represents the transmitted power signal, l represents the cavity length of the optical resonant cavity (7), omega m To representPhase modulation frequency, | k | denotes the absolute value of k, J |k| (β) is a first type of bessel function of the k-th or-k-th order at a modulation depth β, T (ω, l) representing the transmission coefficient of the optical resonator (7) as a function of the incident laser frequency ω and the cavity length l; t (omega, l) represents the conjugation of the transmission coefficient of the optical resonant cavity (7), n is the refractive index of air in the cavity, i is an imaginary number unit, r represents the reflectivity of two cavity mirrors of the optical resonant cavity (7), and FSR represents the free spectral range of the optical resonant cavity (7).
As shown in FIG. 2, in obtaining reflected multi-beam interference signal I r1 After (t), firstly, performing orthogonal down-mixing operation, specifically including the following steps: the digital frequency synthesizer 901 generates a pair of quadrature signals and shifts the same phase by the phase shifter 902 to obtain a pair of quadrature reference signals
The reflected multi-beam interference signal I is respectively processed by a first multiplier 903 and a second multiplier 908 r1 (t) is multiplied by the pair of orthogonal reference signals, and then filtered by the first low-pass filter 904 and the second low-pass filter 910 to obtain an orthogonal harmonic amplitude signal (including a cosine component S) Q Sinusoidal component S I ). In which the sinusoidal component S I After the phase matching is finished, the error signal S is obtained PDH . So far, the orthogonal down-mixing operation is completed, and the operation is respectively expressed as follows after the operation is simplified into a simple trigonometric function form:
R(k)＝F[ω c +kω m ,l]F*[ω c +(k+1)ω m ,l]-F*[ω c -kω m ,l]F[ω c -(k+1)ω m ,l] (6)
wherein S is I 、S Q Respectively representing sine and cosine components in the quadrature harmonic amplitude signal, LPF]Representing a low-pass filtering operation, and R (k) represents omega generated by the beat frequency of the kth order and the kth +1 order sidebands and the-kth order and the- (k + 1) th order sidebands respectively m Is called the amplitude coefficient of the k-th orderWhere | R (k) | is the modulus of the k-th order amplitude coefficient R (k),
is the phase angle of the amplitude factor R (k) of the kth order>
Is the initial phase difference between the frequency multiplication component of the interference signal and the sinusoidal reference signal.
Then, performing arc tangent operation on the orthogonal harmonic amplitude signal to obtain an interference signal I r1 And (t) a frequency multiplication component and the phase of the sinusoidal reference signal, which comprises the following specific processes: the quadrature harmonic amplitude signals obtained by the first low pass filter 904 and the second low pass filter 910 are subjected to an arc tangent operation by an arc tangent operation module 905 to obtain a phase
The formula is as follows:
adjusting the laser frequency of the laser 1 or the cavity length of the optical resonant cavity 7 to make the frequency intervals between the laser fundamental frequency and the side frequency thereof and the resonant frequency of the optical resonant cavity 7 larger than twice of the full width at half maximum of the optical resonant cavity 7, and determining the phase position
As an initial phase difference->
At the moment, both the fundamental frequency laser and the laser of the modulation sideband thereof are totally reflected, namely the reflection coefficients of the corresponding frequencies are pure real numbers, and the phase angle of the amplitude coefficient of the arbitrary order is->
Equal to zero. The phase obtained by inverse tangent operation at this time>
I.e. reflecting multiple beam interference signalsI r1 (t) a frequency doubled component out of phase with the sinusoidal reference signal>
The specific calculation process is as follows: />
Then, the obtained initial phase difference is utilized
The phase shifter 902 is fed back to shift the phase of the two orthogonal reference signals to realize the reflection of the multi-beam interference signal I r1 (t) automatically matching a frequency multiplication component with the phase of the sinusoidal reference signal to ensure the error signal S PDH Linearity and high sensitivity in the frequency discrimination interval. The expression of the error signal after phase matching is as follows:
wherein the content of the first and second substances,
representing the phase difference after matching a frequency doubling component of the interference signal and the sinusoidal reference signal, wherein when the laser phase modulation frequency is lower than the full width at half maximum of the optical resonant cavity, the phase difference after matching is 0 degree; when the laser phase modulation frequency is higher than the full width at half maximum of the optical resonator, the phase difference after matching is 90 degrees.
Then using the phase-matched error signal S PDH And a transmission power signal P tran The square of (a) obtains a new error signal with a larger linear dynamic range, as follows: transmitted power signal P tran The square P of the transmitted power signal is obtained through the square operation module 909 tran 2 。
Then the error signal S after phase matching is processed by the division module 912 PDH With the square P of the transmitted power signal tran 2 By divisionObtaining a new error signal S new The calculation formula is as follows:
thus, an error signal S is obtained PDH New error signal S new And a transmitted power signal P tran The schematic diagram of the two error signals is shown in fig. 3, and the two error signals and the phase are shown.
The three signals are then used to realize the automatic locking of the cavity length of the optical resonant cavity 7, which mainly comprises the scanning, capturing and preliminary locking stages and the precise locking stage.
First, the laser phase modulation of a large modulation depth of the laser is realized by adjusting the gain of the gain module 906 so that the phase modulation depth β is 1.80 rad.
Then, the output end of the triangular wave scanning module 907 is connected to the laser 1 or the optical resonant cavity 7 by the control of the second data selector 916, and the triangular wave scanning signal sent by the triangular wave scanning module 907 is used for triangular wave pre-scanning the cavity length of the optical resonant cavity 7 to obtain a new error signal S new Maximum value S of newmax And a transmission power signal P tran Transmission peak value P of tranmax And defines S newmax Is the lock capture threshold S th 。
In this phase, the output of the first data selector 913 is selected as the new error signal S new The output of the second data selector 916 is selected to be the output of the triangle wave scan module 907.
Then, the laser frequency emitted by the laser 1/the cavity length of the optical resonant cavity 7 are captured in the locking interval, the output end of the division module 912 is connected to the PID control module 914 under the control of the triangular scanning signal and the first data selector 913, and the PID control module 914 inputs a new error signal S new The following determination and processing are performed:
when the new error signal S new Has not reached a maximum value S newmax Or notFrom a maximum value S newmax Falls below the lock acquisition threshold S th During the operation, the triangular wave prescan of the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7) is kept, and no processing is carried out;
when the new error signal S new From the maximum value S newmax Falls below the lock acquisition threshold S th Then, the output terminal of the PID control module 914 is connected to the laser 1 or the optical resonator 7 by the control of the second data selector 916, and the triangular wave scanning signal is switched to S new The output signal processed by the PID control module 914 as the input signal is used to control the laser frequency emitted by the laser 1/the cavity length of the optical resonant cavity 7, and then the PID control module 914 is used to perform feedback control on the laser frequency emitted by the laser 1/the cavity length of the optical resonant cavity 7, so that the new error signal S is generated new Fluctuating near zero to realize preliminary locking;
the transmission power signal P is used for feedback control by the PID control module 914 tran Will be at the transmission peak P tranmax The vicinity fluctuation is specifically determined as follows:
when transmitting the power signal P tran The fluctuation amount in a fixed period of time is less than the transmission peak value P tranmax One third of the first, the laser frequency of the laser emitted by the laser 1/the cavity length of the optical resonant cavity 7 realize the initial locking, and the next step of accurate locking is carried out;
to this end, a new error signal S with a large linear dynamic range at large modulation depths is used new The capture of the resonance region and the primary locking of the laser frequency of the laser/the cavity length of the optical resonant cavity are realized.
When transmitting the power signal P tran The fluctuation amount in a fixed period of time is not less than the transmission peak value P tranmax One third of the time, the PID parameters in the PID control module (914) are adjusted.
In the process of adjusting the amplitude of the driving signal of the electro-optical phase modulator 3 to carry out laser phase modulation with large modulation depth, according to the first Bessel function J of the k-th order k The properties of (. Beta.) were judged as follows:
for a certain fixed modulation depth β, when k is>Beta +1, then J k (β)<0.1 when k<If β +1, then J k (β)>0.1, i.e. J k (beta) the corresponding high-order side frequency components with the order greater than beta +1 can be ignored, the side frequency components with the order greater than or equal to beta +1 can not be ignored, and the highest order j of the high-order side frequency under the large modulation depth is greater than or equal to 2;
the output terminal of the second low pass filter 910 is connected to the PID control module 914 through the control of the first data selector 913, and the PID control module 914 inputs the phase-matched error signal S PDH I.e. the input of the PID control module 914 is changed from the new error signal S new Switching to the phase-matched error signal S PDH While the phase modulation depth β is 1.00rad, the order j of the highest order of the laser frequency sidebands generated by laser phase modulation, by adjusting the gain of the gain module 906 2 ＝1。
The output end of the PID control module 914 is kept connected to the laser 1 or the optical resonant cavity 7 by the control of the second data selector 916, and the PID control module 914 is utilized to perform feedback control on the laser frequency of the laser emitted by the laser 1/the cavity length of the optical resonant cavity 7, so that the error signal S after phase matching PDH Fluctuating around zero, achieving accurate locking.
To this end, an error signal S with high sensitivity at small modulation depths is used PDH Precise locking of the laser frequency of the laser/the cavity length of the optical resonant cavity is achieved.
The interference of external environment vibration and the like can affect the locking, so that the locking of the laser frequency/optical resonant cavity length of the laser deviates from the resonant center instantly, and even the locking is lost.
In the process of carrying out the steps 6.1) to 6.2), carrying out the following judgment in real time for judgment and processing:
when transmitting the power signal P tran Is greater than or equal to the transmission peak value P tranmax Is a small modulation depth, and the output of the second low-pass filter (910) is made by the control of the first data selector (913)The end of the PID control module (914) is connected with the PID control module (914), the input of the PID control module (914) is an error signal, and the PID control module (914) is utilized to perform feedback control on the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7) so that the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7) are accurately locked;
when transmitting the power signal P tran Less than the transmission peak value P tranmax Is one half and is greater than or equal to the transmission peak value P tranmax The modulation depth of the electro-optic phase modulator 3 is switched to a large modulation depth again, the output end of the division module 912 is connected to the PID control module 914 through the control of the first data selector 913, the input of the PID control module 914 is switched to 1.80rad again, and a new error signal S is generated new The PID control module 914 is used for carrying out feedback control on the laser frequency of the laser emitted by the laser 1/the cavity length of the optical resonant cavity 7, so that the laser frequency of the laser emitted by the laser 1/the cavity length of the optical resonant cavity 7 is locked again;
if the external interference is very large, the transmitted power signal P is caused tran Is less than P tranmax When the voltage is one tenth of the voltage, the output end of the triangular wave scanning module 907 is connected to the laser 1 or the optical resonant cavity 7 by the control of the second data selector 916, the triangular wave scanning signal emitted by the triangular wave scanning module 907 is used to control the laser frequency emitted by the laser 1/the cavity length of the optical resonant cavity 7, that is, the control signal of the laser frequency emitted by the laser 1/the cavity length of the optical resonant cavity 7 is switched to the triangular wave scanning signal again, and the step 6.1) is returned to perform scanning, capturing and locking again.
In conclusion, the method firstly carries out orthogonal down-mixing and arc tangent operation on the obtained interference signal and a pair of orthogonal reference signals to obtain an initial phase difference, and uses the phase shifter to carry out phase shifting, thereby realizing automatic phase matching, ensuring the linearity and high sensitivity of an error signal in a frequency discrimination interval and avoiding the process of manually adjusting the phase shifter; then, a new error signal is generated through the error signal after phase matching and the square of the transmission power signal of the resonant cavity, the linear dynamic range is expanded, and the scanning and capturing time of the laser frequency/the length of the resonant cavity is reduced; and finally, a new error signal with a large dynamic range under a large modulation depth and an error signal with high sensitivity under a small modulation depth are switched to be used as the input of the PID feedback control module, so that the anti-interference capability of a locked system is improved while the locking precision of the laser frequency stability/optical resonant cavity length is ensured, and the laser frequency/cavity length is less prone to losing lock.
The above detailed description is intended to illustrate the present invention, not to limit the present invention, and any modifications and changes made within the spirit of the present invention and the scope of the claims fall within the scope of the present invention.
Claims (8)
1. A double-modulation depth large dynamic range and high sensitivity PDH frequency stabilizer is characterized in that:
the photoelectric phase-locked loop comprises a laser (1), an optical isolator (2), an electro-optic phase modulator (3), a first photoelectric detector (4), a polarization spectroscope (5), a quarter-wave plate (6), an optical resonant cavity (7) and a second photoelectric detector (8);
laser emitted by a laser (1) enters an optical isolator (2), the laser emitted from the optical isolator (2) enters an electro-optic phase modulator (3), after modulation, the laser enters a polarization beam splitter (5) to be transmitted, the laser transmitted from the polarization beam splitter (5) is light in a p-polarization state and enters an optical resonant cavity (7) through a quarter-wave plate (6) to be reflected and transmitted, the laser reflected from the optical resonant cavity (7) returns to pass through the quarter-wave plate (6) to be converted from the p-polarization state into an s-polarization state, the laser returns to the polarization beam splitter (5) to be reflected, the laser reflected from the polarization beam splitter (5) enters a first photoelectric detector (4) to be received, and the laser transmitted from the optical resonant cavity (7) enters a second photoelectric detector (8) to be received.
2. The large dynamic range and high sensitivity PDH frequency stabilizer with double modulation depths as claimed in claim 1, wherein:
the photoelectric phase modulator is characterized by further comprising a signal acquisition and processing module (9), wherein the output ends of the first photoelectric detector (4) and the second photoelectric detector (8) are connected to the input end of the signal acquisition and processing module (9), the output end of the signal acquisition and processing module (9) is connected to the electro-optic phase modulator (3), and the output end of the signal acquisition and processing module (9) is connected to the laser (1) or the optical resonant cavity (7).
3. The large dynamic range and high sensitivity PDH frequency stabilizer with double modulation depths as claimed in claim 2, wherein:
the signal acquisition and processing module (9) specifically comprises a digital frequency synthesizer (901), a phase shifter (902), a first multiplier (903), a first low-pass filter (904), an arc tangent operation module (905), a gain module (906), a triangular wave scanning module (907), a second multiplier (908), a square operation module (909), a second low-pass filter (910), a first threshold judgment module (911), a division operation module (912), a first data selector (913), a PID control module (914), a second threshold judgment module (915) and a second data selector (916);
one output end of the digital frequency synthesizer (901) is connected to an input end of a gain module (906), output ends of the gain module (906) are connected to a driving input end of the electro-optical phase modulator (3), the other two orthogonal output ends of the digital frequency synthesizer (901) are connected to two input ends of a phase shifter (902), two output ends of the phase shifter (902) are respectively connected to input ends of a first multiplier (903) and a second multiplier (908), a first photoelectric detector (4) is connected to input ends of the first multiplier (903) and the second multiplier (908), output ends of the first multiplier (903) and the second multiplier (908) are respectively connected to input ends of a first low-pass filter (904) and a second low-pass filter (910), an output end of the first low-pass filter (904) is connected to one input end of an arc tangent operation module (905), and an output end of the second low-pass filter (910) is divided into three paths and is respectively connected to input ends of an arc tangent operation module (905), a division operation module (912) and a first data selector (913);
the output end of the second photoelectric detector (8) is divided into three paths and is respectively connected to the input ends of a square operation module (909), a first threshold judgment module (911) and a second threshold judgment module (915), the output end of the square operation module (909) is connected to the other input end of a division operation module (912), the output end of the division operation module (912) is respectively connected to the other input ends of a first data selector (913) and a second threshold judgment module (915), the output end of the first threshold judgment module (911) is connected to the selection control end of the first data selector (913), the output end of the first data selector (913) is connected to the input end of a PID control module (914), the output ends of the PID control module (914) and a triangular wave scanning module (907) are respectively connected to the two data input ends of a second data selector (916), the output end of the second threshold judgment module (915) is connected to the selection control end of a second data selector (916), and the output end of the second data selector (916) is connected to the optical resonant cavity (7) after digital-to-analog-digital-to-digital conversion.
4. The large dynamic range, high sensitivity PDH frequency stabilization device with dual modulation depths as claimed in claim 1, wherein:
when the device is used for stabilizing the laser frequency emitted by the laser, the laser (1) adopts a laser with adjustable laser frequency, and the optical resonant cavity (7) adopts an optical resonant cavity with fixed cavity length;
when the device is used for locking the cavity length of the optical resonant cavity, the laser (1) adopts a laser with laser frequency, and the optical resonant cavity (7) adopts an optical resonant cavity with adjustable cavity length.
5. A double-modulation depth large-dynamic-range and high-sensitivity PDH frequency stabilization method is characterized in that: the method comprises the following steps:
step 1) laser emitted by a laser (1) enters an electro-optic phase modulator (3) after passing through an optical isolator (2), the electro-optic phase modulator (3) generates a phase modulation signal to perform phase modulation on the laser, the phase-modulated laser sequentially passes through a polarization beam splitter (5) and a quarter wave plate (6) and then enters an optical resonant cavity (7) to be reflected and transmitted for multiple times back and forth in the cavity, the polarization state of the laser reflected from the optical resonant cavity (7) is changed from a p state to an s state after reversely passing through the quarter wave plate (6), and then the laser is changed from the p state to the s stateReflected by the polarization spectroscope (5) to the first photoelectric detector (4) to generate multi-beam interference, interference signals are obtained by detection, and the interference signals are sampled and subjected to analog-to-digital conversion to obtain reflected multi-beam interference signals I r1 (t)；
Step 2) generating two paths of orthogonal reference signals with the same frequency as the phase modulation signals by a digital frequency synthesizer (901), wherein the two paths of orthogonal reference signals comprise cosine reference signals
And a sinusoidal reference signal->
Two paths of orthogonal reference signals are respectively subjected to phase shifting with the same phase by a phase shifter (902) and then are respectively subjected to reflection multi-beam interference signals I r1 (t) sequentially multiplying by two respective multipliers (903, 908) and filtering by low-pass filters (904, 910) to finish quadrature down-mixing operation, retaining direct-current components, and obtaining a pair of quadrature harmonic amplitude signals, wherein the quadrature harmonic amplitude signals comprise sinusoidal components S I And a cosine component S Q ；
Step 3) performing arc tangent operation on a pair of orthogonal harmonic amplitude signals in an arc tangent operation module (905) to obtain a phase
The calculation is as follows:
adjusting the laser frequency of the laser (1) or the cavity length of the optical resonant cavity (7) to ensure that the frequency intervals between the laser fundamental frequency and the side frequency thereof and the resonant frequency of the optical resonant cavity (7) are both more than twice of the full width at half maximum of the optical resonant cavity (7), and determining the phase position at the moment
As an initial phase difference->
Then, the obtained initial phase difference is utilized
Feeding back to a phase shifter (902) to shift the phase of the two orthogonal reference signals;
step 4) sinusoidal component S in orthogonal harmonic amplitude signal I After the phase matching is finished, the error signal S is used as an error signal S after the phase matching PDH The expression is:
wherein k represents the order of modulation sideband, k = 0-j-1,j represents the order of the highest order of laser frequency sideband generated after laser phase modulation, and E 0 Denotes the laser amplitude, J k (β) is a first Bessel function of the kth order at a modulation depth of β; r (k) represents omega generated by beat frequency of kth order and kth +1 order sidebands and-kth order and- (k + 1) order sidebands respectively m Is called the amplitude coefficient of the kth order, | R (k) | is the modulus of the amplitude coefficient R (k) of the kth order,
is the phase angle of the amplitude coefficient R (k) of the kth order, and t represents the time; />
Representing the phase difference after matching a frequency doubling component of the interference signal and the sinusoidal reference signal, wherein when the laser phase modulation frequency is lower than the full width at half maximum of the optical resonant cavity, the phase difference after matching is 0 degree; when the laser phase modulation frequency is higher than the full width at half maximum of the optical resonant cavity, the phase difference after matching is 90 degrees;
step 5) the light transmitted from the optical resonant cavity (7) is received and detected by a second photoelectric detector (8) to obtain a direct current power signalSampling the DC power signal, analog-to-digital converting to obtain transmission power signal P tran The expression is:
wherein, P tran Represents the transmitted power signal, l represents the cavity length of the optical resonant cavity (7), omega m Representing the phase modulation frequency, | k | representing the absolute value of k, J |k| (beta) is a first Bessel function of the k order or the-k order when the modulation depth is beta, and j represents the highest order of the side frequency after laser modulation; t (ω, l) represents the transmission coefficient of the optical resonator (7) as a function of the incident laser frequency ω and the cavity length l; t (omega, l) represents the conjugation of the transmission coefficient of the optical resonant cavity (7), n is the refractive index of air in the cavity, i is an imaginary number unit, r represents the reflectivity of two cavity mirrors of the optical resonant cavity (7), and FSR represents the free spectral range of the optical resonant cavity (7);
then the error signal S after phase matching PDH With the square P of the transmitted power signal tran 2 Dividing to obtain new error signal S new The calculation formula is as follows:
step 6) to this point, the error signal S after phase matching is obtained in real time PDH New error signal S new And a transmission power signal P tran Then, the three signals in real time are used for realizing the automatic locking of the cavity length of the optical resonant cavity (7)/the laser frequency of the laser (1) so as to realize frequency stabilization control.
6. The large dynamic range and high sensitivity PDH frequency stabilization method with double modulation depths as claimed in claim 5, wherein:
the step 6) is specifically as follows:
step 6.1) scanning, capturing and preliminary locking:
firstly, adjusting the amplitude of a driving signal of an electro-optic phase modulator (3) to realize laser phase modulation of large modulation depth of laser;
then sending out a triangular wave scanning signal to carry out triangular wave pre-scanning on the laser frequency of the laser sent out by the laser (1)/the cavity length of the optical resonant cavity (7) to obtain a new error signal S new Maximum value of S newmax And a transmission power signal P tran Transmission peak value P of tranmax And with the new error signal S new Maximum value of S newmax Is taken as the lock capture threshold S th ；
Then, the locking interval of the laser frequency emitted by the laser (1)/the cavity length of the optical resonant cavity (7) is captured, and a PID control module (914) inputs a new error signal S under the control of a triangular wave scanning signal new The following judgment and processing are performed:
when the new error signal S new Has not reached a maximum value S newmax Or not from the maximum value S newmax Falls below the lock acquisition threshold S th During the operation, the triangular wave prescan of the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7) is kept, and no processing is carried out;
when the new error signal S new From the maximum value S newmax Falls below the lock acquisition threshold S th At the time, the triangular wave scanning signal is switched to S new The output signal which is used as the input signal and processed by the PID control module (914) carries out feedback control on the laser frequency emitted by the laser (1)/the cavity length of the optical resonant cavity (7), and then the PID control module (914) is used for carrying out feedback control on the laser frequency emitted by the laser (1)/the cavity length of the optical resonant cavity (7), so that a new error signal S is generated new Fluctuating near zero to realize preliminary locking;
step 6.2) accurate locking:
PID control module(914) Inputting the phase-matched error signal S PDH Meanwhile, the phase modulation depth is reduced to a small modulation depth by adjusting the amplitude of a driving signal of the electro-optic phase modulator (3), and the PID control module (914) is utilized to perform feedback control on the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7), so that the error signal S after phase matching PDH Fluctuating around zero, achieving accurate locking.
7. The large dynamic range and high sensitivity PDH frequency stabilization method with double modulation depths as claimed in claim 5, wherein:
in the step 6.1), when the feedback control is performed by the PID control module (914), the following determination is specifically made:
when transmitting the power signal P tran The fluctuation amount in a fixed period of time is less than the transmission peak value P tranmax One third of the total laser frequency is the laser frequency emitted by the laser (1)/the cavity length of the optical resonant cavity (7) to realize primary locking, and the next step of accurate locking is carried out;
when transmitting the power signal P tran The fluctuation amount in a fixed period of time is not less than the transmission peak value P tranmax One third of the time, the PID control module (914) adjusts the PID parameters.
8. The large dynamic range and high sensitivity PDH frequency stabilization method with double modulation depths as claimed in claim 5, wherein:
in the process of carrying out the steps 6.1) to 6.2), carrying out the following judgment in real time for judgment and processing:
when transmitting the power signal P tran Is greater than or equal to the transmission peak value P tranmax When the modulation depth is one-half of the modulation depth, the modulation depth of the electro-optic phase modulator (3) is small, the input of the PID control module (914) is an error signal, and the PID control module (914) is utilized to perform feedback control on the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7), so that the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7) are accurately locked;
when transmitting the power signal P tran Less than the transmission peak value P tranmax Is one half and is equal to or more than the transmission peak value P tranmax Is switched to the large modulation depth again, and the input of the PID control module (914) is switched to the new error signal S new The PID control module (914) is used for carrying out feedback control on the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7) so as to relock the laser frequency of the laser emitted by the laser (1)/the cavity length of the optical resonant cavity (7);
if the transmitted power signal P tran Is less than P tranmax And when the laser frequency is one tenth of the laser frequency, the laser frequency and the cavity length of the optical resonant cavity (7) are controlled, and the step 6.1) is returned to perform scanning, capturing and locking again.
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