Methods and apparatus of tracking/locking resonator free spectral range and its application in resonator fiber optic gyroscope

A method of locking a free spectral range (FSR) of a gyroscope resonator in a resonator fiber optic gyroscope system and a laser modulation frequency of an optical beam coupled to an input port of the gyroscope resonator to each other, the method comprising:

• modulating a clockwise optical beam emitted from a laser with a laser modulation frequency of (n+0.5) times the FSR, where n is zero or a positive integer;
• coupling the modulated clockwise optical beam into a clockwise input port of the gyroscope resonator;
• receiving a signal from a clockwise reflection detector;
• demodulating a first harmonic of the signal received from the clockwise reflection detector at a first-lock-in-amplifier;
• receiving a demodulated first-harmonic signal from the first-lock-in-amplifier at a clockwise-resonance-tracking servo;
• providing feedback to the laser from the clockwise-resonance-tracking servo in order to lock the laser to the gyroscope resonator;
• receiving a signal from a clockwise transmission detector;
• demodulating a second harmonic of the signal received from the clockwise transmission detector at a second-lock-in-amplifier;
• providing feedback from the second-lock-in-amplifier to a second servo;
• demodulating a first harmonic of the signal received from the clockwise transmission detector at a third-lock-in-amplifier;
• and
• providing feedback from the third-lock-in-amplifier to the clockwise-resonance-tracking servo to correct errors in a clockwise resonance tracking loop.

A resonator fiber optic gyroscope system, comprising:

• a gyroscope resonator having a clockwise input port and a counter-clockwise input port and a free spectral range (FSR) corresponding to the resonator round trip length;
• a first laser configured to couple a clockwise optical beam into to the clockwise input port;
• a clockwise modulator to impose a modulation frequency equivalent to (n+0.5) times the FSR on the clockwise optical beam before the clockwise optical beam is coupled into the clockwise input port, where n is a positive integer;
• a clockwise circulator;
• a clockwise reflection detector to detect the clockwise optical beam output from a clockwise reflection port;
• a first-lock-in-amplifier to receive a signal from the clockwise reflection detector, wherein the first-lock-in-amplifier demodulates at the first harmonic of the modulation frequency of the clockwise optical beam;
• a clockwise-resonance-tracking servo to receive output from the first-lock-in-amplifier and to provide feedback to the first laser to lock the first laser to the gyroscope resonator;
• a clockwise transmission detector to detect an optical beam output from the counter-clockwise input port;
• a second servo;
• a second-lock-in-amplifier to receive a signal from the clockwise transmission detector, wherein the second-lock-in-amplifier demodulates at the second harmonic of the modulation frequency of the clockwise optical beam and provides feedback to the second servo;
• a third-lock-in-amplifier to receive a signal from the clockwise transmission detector, wherein the third-lock-in-amplifier demodulates at the first harmonic of the modulation frequency of the clockwise optical beam and provides feedback to the clockwise-resonance-tracking servo to correct errors in a clockwise resonance tracking loop,
• a second laser configured to couple a counter-clockwise optical beam into to the counter-clockwise input port;
• a counter-clockwise modulator to impose a modulation frequency equivalent to (p+0.5) times the FSR on the counter-clockwise optical beam before the counter-clockwise optical beam is coupled into the counter-clockwise input port, where p is zero or a positive integer and where p does not equal n;
• a counter-clockwise circulator;
• a counter-clockwise reflection detector to detect the counter-clockwise optical beam output from a counter-clockwise reflection port;
• a fourth-lock-in-amplifier to receive a signal from the counter-clockwise reflection detector, wherein the fourth-lock-in-amplifier demodulates at the first harmonic of the modulation frequency of the counter-clockwise optical beam;
• a counter-clockwise-resonance-tracking servo to receive output from the fourth-lock-in-amplifier and to provide feedback to the second laser to lock the second laser to the gyroscope resonator;
• a counter-clockwise transmission detector to detect an optical beam output from the clockwise input port;
• and
• the fifth-lock-in-amplifier to receive a signal from the counter-clockwise transmission detector, wherein the fifth-lock-in-amplifier demodulates at the first harmonic of the modulation frequency of the counter-clockwise optical beam and provides feedback to the counter-clockwise-resonance-tracking servo to correct errors in a counter-clockwise resonance tracking loop,
• wherein one of:
• the modulation frequency of the clockwise optical beam is locked to the (n+0.5)FSR through the second servo;
• or the FSR is locked to 1/(n+0.5) times the modulation frequency of the clockwise optical beam through the second servo.