Optical coupled-resonator filters with asymmetric coupling
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Abstract
An optical filter includes at least one waveguide structure. The optical filter also includes a plurality of optical resonators that are aligned in an coupled arrangement with the at least one waveguide structure so as to produce an asymmetric distribution of coupling coefficients.
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Citations
62 Claims
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1-38. -38. (canceled)
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39. An optical filter having associated drop-port and through-port spectral responses and comprising:
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a first and a second optical waveguide structure; and
an optical resonating structure optically coupled to said first optical waveguide structure so as to define a first energy coupling coefficient 1/τ
e and to said second optical waveguide structure so as to define a last energy coupling coefficient 1/τ
d,the optical resonating structure including a plurality of N series-coupled resonators defining a plurality of N−
1 energy coupling coefficients μ
12, μ
22, . . . , μ
2N−
1, a plurality of N resonator losses 1/τ
01, 1/τ
02, . . . , 1/τ
0N and a plurality of N resonance frequencies (ω
1, . . . , ω
N of the resonators, wherein the set of N+1 energy coupling coefficients defined by the first energy coupling coefficient, the plurality of N−
1 energy coupling coefficients of the resonators and the last coupling coefficient are selected so that the following expression in a complex frequency ω
;
has the same zeros in ω
as the following expression;
the zeros of the latter expression representing the poles of a drop-port spectral response of an ideal lossless optical filter having;
a first and a second ideal optical waveguide structure, an ideal optical resonating structure coupled to said first ideal optical waveguide structure so as to define a first ideal energy coupling coefficient 1/τ
e'"'"' and to said second ideal optical waveguide structure so as to define a last ideal energy coupling coefficient 1/τ
d'"'"',the ideal optical resonating structure including a plurality of N series-coupled ideal resonators defining a plurality of N−
1 ideal energy coupling coefficients μ
1′
2, μ
2′
2, . . . , μ
N−
12and a plurality of ideal resonance frequencies ω
1′
, . . . , ω
N′
, the terms 1/τ
e′
, μ
1′
2, μ
2′
2, . . . , μ
N−
1′
2, 1/τ
d′
and ω
1′
, . . . , ω
N′
being selected so that the terms 1/τ
e′
, μ
2′
2, . . . , μ
N−
1′
2, 1/τ
d′
are a symmetric sequence of values and so that the spectral response of the drop-port of the ideal lossless filter has the same shape of the spectral response of the drop-port of said optical filter, andwherein at least one of the ideal energy coupling coefficients 1/τ
e, μ
12, μ
22, . . . , μ
N−
12, 1/τ
d is different from the at least one corresponding energy coupling coefficient in the set 1/τ
e′
, μ
1′
2, μ
2′
2, . . . , μ
N−
12 - View Dependent Claims (40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55)
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56. An optical filter comprising:
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a first and second optical waveguide, an optical resonating structure optically coupled to said first waveguide to define a first energy coupling coefficient, and to said second waveguide to define a last energy coupling coefficient, the optical resonating structure including a plurality of N series-coupled resonators defining a plurality of N−
1 energy coupling coefficients μ
12, μ
22, . . . , μ
N−
12,the plurality of resonators including at least three resonators, wherein the sequence of N−
1 energy coupling coefficients μ
12, μ
22, . . . , μ
N−
12 of the optical resonating structure is an asymmetric sequence of values.
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57. A method for designing an optical filter having associated drop-port and through-port spectral responses and comprising:
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a first and a second optical waveguide structure; and
an optical resonating structure optically coupled to said first optical waveguide structure so as to define a first energy coupling coefficient 1/τ
e and to said second optical waveguide structure so as to define a last energy coupling coefficient 1/τ
d, the optical resonating structure including a plurality of N series-coupled resonators defining a plurality of N−
1 energy coupling coefficients μ
12, μ
22, . . . , μ
N−
12, a plurality of N resonator losses 1/τ
01, 1/τ
02, . . . , 1/τ
0N and a plurality of N resonance frequencies ω
1, . . . , ω
N of the resonators,the method comprising the steps of;
designing an ideal lossless optical filter comprising a first and a second ideal optical waveguide structure, and an ideal optical resonating structure coupled to said first ideal optical waveguide structure so as to define a first ideal energy coupling coefficient 1/τ
′
eand to said second ideal optical waveguide structure so as to define a last ideal energy coupling coefficient 1/τ
′
d,the ideal optical resonating structure including a plurality of N ideal lossless series-coupled resonators defining a plurality of N−
1 ideal energy coupling coefficients μ
1′
2, μ
2′
2, . . . , μ
N−
12 and a plurality of ideal resonance frequencies ω
1′
, . . . , ω
N′
, the terms 1/τ
e ′
, μ
1′
2, μ
2′
2,μ
N−
1′
2, 1/τ
d′
being selected so that the spectral response of the drop-port of the ideal lossless filter has a shape equal to said drop-port spectral response associated to said optical filter;
said ideal resonance frequencies and ideal energy coupling coefficients defining the values of a set of N complex-valued poles of the lossless filter response functions;
evaluating the alteration of said N complex-valued poles when said plurality of N resonator losses 1/τ
01, 1/τ
02, . . . , 1/τ
0N is introduced in the drop-port response function of said ideal lossless optical filter;
assigning corrections to the terms 1/τ
e, μ
1′
2, μ
2′
2, . . . , μ
N−
1′
2, 1/τ
d′
, thus resulting in said set of energy coupling coefficients 1/τ
e, μ
12, μ
22, . . . , μ
N−
12, 1/τ
d of said optical filter, so as to restore said values of the N complex-valued poles of the ideal lossless filter response functions, and therefore restore the drop-port response shape. - View Dependent Claims (58, 59, 60, 61, 62)
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Specification