Method and apparatus for operating optical wavemeter and wavemeter comprising same
There is provided a method, apparatus and system for calibrating and operating an optical wavemeter. In calibration, training optical signals with known wavelengths are input to a wavemeter, and corresponding photodetector measurements are obtained. Optical parameters of the wavemeter are then estimated based on the measurements. The optical parameters are indicative of a length difference ΔL between two unequal-length waveguides in an optical delay line of the wavemeter; and scattering parameters of a multi-mode interferometer (MMI) coupler of the wavemeter. The estimation process involves a (e.g. golden-section) search to determine one or more output values for at least one of the optical parameters, based on an objective function which indicates a difference expected and actual measurements. The expected measurements are generated based on a numerical model incorporating candidate values for the optical parameters.
1. A method comprising:
for each input optical signal of a set of training optical signals input to a wavemeter, the training optical signals having known and differing wavelengths:
by a first multi-mode interferometer (MMI) coupler or optical signal splitter of the wavemeter, separating the input optical signal into at least two portions;
by each of two unequal-length waveguides of an optical delay line structure of the wavemeter, receiving a respective one of said two portions;
by a second MMI coupler of the wavemeter, receiving outputs of the two unequal-length waveguides:
by a plurality of photodetectors of the wavemeter, monitoring outputs of at least the second MMI coupler:
obtaining a corresponding set of measurements from the plurality of photodetectors; and
estimating optical parameters of the wavemeter based on the sets of measurements and an indication of the known and differing wavelengths,
wherein the optical parameters are indicative of at least:
a length difference ΔL between the two unequal-length waveguides; and
scattering parameters of the second MMI coupler operatively coupled to outputs of the two unequal-length waveguides,
wherein said estimating the optical parameters comprises:
performing a search operation to determine one or more output values for at least one of the optical parameters, such that said one or more output values causes a predetermined condition in an objective function, the objective function indicative of a difference between the sets of measurements and an expected value for the sets of measurements, the expected value generated based on a numerical model which incorporates candidate values for said optical parameters.
2. The method of claim 1 , wherein the objective function is an error function, and the predetermined condition is achieving a minimal value.
3. The method of claim 1 , wherein the numerical model generates said expected value by multiplying a matrix A by a vector x, the matrix A indicative of estimated values for the scattering parameters, the vector x indicative of an estimated value for a phase shift between the two portions of the input optical signal propagating in the two unequal-length waveguides, the phase shift being due to said length difference ΔL.
4. The method of claim 3 , wherein the matrix A is a 3×3 matrix such that, for m ranging from 1 to 3 inclusive, row m of the matrix A is given by:
p 0 |2| s m2 ∥s m1 | cos(φ m )2| s m2 ∥s m1 | sin(φ m )1/√{square root over (2)}(| s m1 | 2 +|s m2 | 2 ); and
the vector x is given by:
[
cos
(
θ
)
sin
(
θ
)
2
]
,
or alternatively wherein row m of the matrix A is given by:
2| s m2 ∥s m1 | cos(φ m )2| s m2 ∥s m1 | sin(φ m )1/√{square root over (2)}(| s m1 | 2 +|s m2 | 2 ); and
the vector x is given by:
p
0
[
cos
(
θ
)
sin
(
θ
)
2
]
,
where p 0 is power of the input optical signal, s m1 and s m2 are respective ones of the estimated values for the scattering parameters, om represents a complex phase angle between s m1 and s m2 , and θ is the estimated value for the phase shift between the two portions of the input optical signal.
5. The method of claim 1 , further comprising, following said estimating the optical parameters, using the optical parameters to determine a wavelength or frequency of a subsequent optical signal input to the wavemeter, based on a further corresponding set of measurements from the plurality of photodetectors.
6. The method of claim 5 , wherein:
the numerical model generates said expected value by multiplying a matrix A by a vector x, the matrix A indicative of estimated values for the scattering parameters, the vector x indicative of an estimated value for a phase shift between the two portions of the input optical signal propagating in the two unequal-length waveguides, the phase shift being due to said length difference ΔL; and
wherein determining the wavelength or frequency comprises:
computing an inverse of the matrix A;
multiplying said inverse by a vector representing the further set of measurements to obtain a result vector; and
further processing of the result vector.
7. The method of claim 6 , wherein the inverse is a Moore-Penrose inverse.
8. The method of claim 5 , further comprising:
obtaining a first one or more temperature readings indicative of temperature of the optical delay line structure during said estimating of the optical parameters; and
obtaining a second one or more temperature readings indicative of temperature of the optical delay line structure during inputting of said subsequent optical signal to the wavemeter,
wherein said determining the wavelength or frequency of the subsequent optical signal is further based on the first one or more temperature readings and the second one or more temperature readings.
9. The method of claim 1 , wherein each set of measurements includes a measurement indicative of total optical signal power of a corresponding one of the set of training optical signals, and wherein said estimating the optical parameters is further based on the measurements indicative of total optical signal power.
10. The method of claim 1 , wherein each set of measurements includes measurements from at least three photodetectors, of the plurality of photodetectors, coupled to at least three respective outputs of the second MMI coupler.
11. The method of claim 1 , wherein:
(a) the optical parameters indicative of the length difference ΔL comprise one or more optical parameters indicative of a phase shift between the two portions of the input optical signal propagating in the two unequal-length waveguides; or
(b) the optical parameters are further indicative of one or more of:
scattering parameters of the first MMI coupler or optical signal splitter;
optical parameters of at least one of the plurality of photodetectors; and
electrical parameters of said at least one of the plurality of photodetectors; or
both (a) and (b).
12. A wavemeter comprising:
a first multi-mode interferometer (MMI) coupler or optical signal splitter configured to separate an input optical signal into at least two portions;
an optical delay line structure operatively coupled to outputs of the first MMI coupler and comprising two unequal-length waveguides each configured to receive a respective one of said two portions;
a second MMI coupler operatively coupled to outputs of the two unequal-length waveguides;
a plurality of photodetectors operatively coupled to at least outputs of the second MMI coupler; and
an electronic device operatively coupled to the plurality of photodetectors and comprising one or more processing components configured, in a calibration mode, to:
obtain, for each training signal of a set of training optical signals input to the wavemeter, a corresponding set of measurements from the plurality of photodetectors, the training optical signals having known and differing wavelengths; and
estimate optical parameters of the wavemeter based on the sets of measurements and an indication of the known and differing wavelengths,
wherein the optical parameters are indicative of at least:
a length difference ΔL between said two unequal-length waveguides; and
scattering parameters of the second MMI coupler,
wherein said estimating the optical parameters comprises, by the electronic device:
performing a search operation to determine one or more output values for at least one of the optical parameters, such that said one or more output values causes a predetermined condition in an objective function, the objective function indicative of a difference between the sets of measurements and an expected value for the sets of measurements, the expected value generated based on a numerical model which incorporates candidate values for said optical parameters.
13. The wavemeter of claim 12 , wherein the second MMI coupler has two or more input ports and three or more output ports.
14. The wavemeter of claim 12 , wherein an input port of the first MMI coupler or optical signal splitter, configured to receive the input optical signal, is coupled to an optical switch, the optical switch controllable to select one of a plurality of reference optical signals for frequency measurement thereof.
15. The wavemeter of claim 12 , wherein the objective function is an error function, and the predetermined condition is achieving a minimal value.
16. The wavemeter of claim 12 , wherein the numerical model is a linear algebraic model.
17. The wavemeter of claim 12 , wherein the electronic device is further configured, following said estimating the optical parameters, to use the optical parameters to determine a wavelength or frequency of a subsequent optical signal input to the wavemeter, based on a further corresponding set of measurements from the plurality of photodetectors.
18. The wavemeter of claim 17 , wherein:
the numerical model generates said expected value by multiplying a matrix A by a vector x, the matrix A indicative of estimated values for the scattering parameters, the vector x indicative of an estimated value for a phase shift between the two portions of the input optical signal propagating in the two unequal-length waveguides, where the input optical signal is one of the training signals, the phase shift being due to said length difference ΔL; and
wherein determining the wavelength or frequency comprises:
computing an inverse of the matrix A;
multiplying said inverse by a vector representing the further set of measurements to obtain a result vector; and
further processing of the result vector.
19. The wavemeter of claim 17 , wherein the electronic device is further configured to:
obtain a first one or more temperature readings indicative of temperature of the optical delay line structure during said estimating of the optical parameters; and
obtain a second one or more temperature readings indicative of temperature of the optical delay line structure during inputting of said subsequent optical signal to the wavemeter,
wherein said determining the wavelength or frequency of the subsequent optical signal is further based on the first one or more temperature readings and the second one or more temperature readings.
20. The wavemeter of claim 12 , wherein each set of measurements includes a measurement indicative of total optical signal power of a corresponding one of the set of training optical signals, and wherein said estimating the optical parameters is further based on the measurements indicative of total optical signal power.
21. The wavemeter of claim 12 , wherein the plurality of photodetectors comprises at least three photodetectors coupled to at least three respective outputs of the second MMI coupler.
22. The wavemeter of claim 12 , wherein:
(a) the optical parameters indicative of the length difference ΔL comprise one or more optical parameters indicative of a phase shift between two respective portions of an optical signal propagating in the two unequal-length waveguides; or
(b) the optical parameters are further indicative of one or more of:
scattering parameters of the first MMI coupler or optical signal splitter;
optical parameters of at least one of the plurality of photodetectors; and
electrical parameters of said at least one of the plurality of photodetectors; or
both (a) and (b).