System and Method for Phase Stabilization of Optical Sources
There is described a system and method for controlling the phase relationship between two optical signals and an optical frequency comb. Two optical mixers are configured to generate beat signals based on the optical signals and the optical frequency comb. A first detector is configured to measure the relative phase between the two beat signals, and a second detector is configured to measure the relative phase between one of the beat signals and a reference signal. One or more control signals based on the measurements are then used to control the phases of the optical signals to maintain a desired phase relationship between the optical signals and the optical frequency comb. The system and method can be configured such that the optical frequency comb is symmetric about a central frequency, and the phase relationship is resilient to noise induced by the generation of the optical frequency comb.
1 . A system comprising:
a first optical source configured to generate a first optical signal;
a second optical source configured to generate a second optical signal;
a first optical mixer configured to generate a first beat signal based on an optical frequency comb and the first optical signal;
a second optical mixer configured to generate a second beat signal based on the optical frequency comb and the second optical signal;
a first detector configured to output a first measurement signal based on the first and second beat signals;
a second detector configured to output a second measurement signal based on the second beat signal and a reference signal; and
a signal processor configured to generate one or more control signals based on the first and second measurement signals for adjusting one or more of the first optical source and the second optical source to maintain a phase relationship between the first optical signal, the second optical signal, and the optical frequency comb.
2 . The system of claim 1 , wherein
the first optical signal has a first frequency;
the second optical signal has a second frequency;
the first optical mixer is configured to generate the first beat signal based on the first optical signal and a first comb tooth of the optical frequency comb nearest to the first frequency; and
the second optical mixer is configured to generate the second beat signal based on the second optical signal and a second comb tooth of the optical frequency comb nearest to the second frequency.
3 . The system of claim 1 , further comprising a modulator configured to generate the frequency comb, the frequency comb being symmetric about a comb source frequency.
4 . The system of claim 3 , wherein
the first optical signal has a first phase ϕ 1 given by ϕ 1 =2πf 1 t+φ 1 , where f 1 is a first frequency, t represents time, and φ 1 is a first phase offset;
the second optical signal has a second phase ϕ 2 given by ϕ 2 =2πf 2 t+φ 2 , where f 2 is a second frequency, t represents time, and φ 2 is a second phase offset; and
the phase relationship is such that the average of the first frequency f 1 and the second frequency f 2 is substantially equal to the comb source frequency.
5 . The system of claim 3 , wherein the phase relationship is at least partially resilient to noise induced by the modulator.
6 . The system of claim 3 , wherein the frequency comb is generated based on a local oscillator signal, and the comb source frequency is a local oscillator frequency.
7 . The system of claim 1 , wherein the first optical mixer comprises a 50:50 beamsplitter and the second optical mixer comprises a 50:50 beamsplitter.
8 . The system of claim 1 , wherein the first beat signal and second beat signal each comprise a primary beat and a plurality of secondary beats at frequencies greater than the primary beat.
9 . The system of claim 1 , wherein the reference signal is one of a radio-frequency reference signal and a microwave reference signal.
10 . A method comprising:
generating a first beat signal based on an optical frequency comb and a first optical signal;
generating a second beat signal based on the optical frequency comb and a second optical signal;
measuring the phase of the first beat signal with respect to the second beat signal to produce a first phase measurement signal;
measuring the phase of the second beat signal with respect to a reference signal to produce a second phase measurement signal; and
controlling one or more of the first optical signal and the second optical signal based on the first and second phase measurement signals to maintain a phase relationship between the first optical signal, the second optical signal, and the optical frequency comb.
11 . The method of claim 10 , wherein
the first optical signal has a first frequency;
the second optical signal has a second frequency;
the generating of the first beat signal is based on the first optical signal and a first comb tooth of the optical frequency comb nearest to the first frequency; and
the generating of the second beat signal is based on the second optical signal and a second comb tooth of the optical frequency comb nearest to the second frequency.
12 . The method of claim 10 , further comprising generating the optical frequency comb such that it is symmetric about a central frequency.
13 . The method of claim 12 , wherein
the first optical signal has a first phase ϕ 1 given by ϕ 1 =2πf 1 t+φ 1 , where f 1 is a first frequency, t represents time, and φ 1 is a first phase offset;
the second optical signal has a second phase ϕ 2 given by ϕ 2 =2πf 2 t+φ 2 , where f 2 is a second frequency, t represents time, and φ 2 is a second phase offset; and
the phase relationship is such that the average of the first frequency f 1 and the second frequency f 2 is substantially equal to the central frequency.
14 . The method of claim 12 , wherein the phase relationship is at least partially resilient to noise induced in the generating of the optical frequency comb.
15 . The method of claim 10 , further comprising filtering one or more of the first beat signal and the second beat signal to remove high-frequency beats.