Optical coupled-resonator filters with asymmetric coupling

• US 20060159392A1
• Filed: 01/11/2006
• Published: 07/20/2006
• Est. Priority Date: 07/15/2003
• Status: Active Grant

• Current Assignee: Massachusetts Institute of Technology
• Original Assignee: Massachusetts Institute of Technology
• Inventors: Popovic, Milos
• Granted Patent: US 7,292,751 B2
• Time in Patent Office: Days
• US Class Current: 385/27
• CPC Class Codes: G02B 6/12007 forming wavelength selective elements, e.g. multiplexer, demultiplexer
• CPC Class Codes: G02B 6/29343 Cascade of loop resonators
• CPC Class Codes: G02B 6/29383 Adding and dropping

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.

Claims

1-38. -38. (canceled)

39. An optical filter having associated drop-port and through-port spectral responses and comprising:

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

²<sub>N−

1</sub>, 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

;

$j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_1\right)+\frac{1}{{\mathrm{\tau <br><br>}}_{01}}+\frac{1}{{\mathrm{\tau <br><br>}}_e}+\frac{{\mathrm{\mu <br><br>}}_1^2}{j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_2\right)+\frac{1}{{\mathrm{\tau <br><br>}}_{02}}+\frac{{\mathrm{\mu <br><br>}}_2^2}{j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_3\right)+\frac{1}{{\mathrm{\tau <br><br>}}_{03}}+\mathrm{\dots <br><br>}+\frac{{\mathrm{\mu <br><br>}}_{N-1}^2}{j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_N\right)+\frac{1}{{\mathrm{\tau <br><br>}}_{0<br><br>N}}+\frac{1}{{\mathrm{\tau <br><br>}}_d}}}},$

has the same zeros in ω

as the following expression;

$j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_1^{\mathrm{\prime <br><br>}}\right)+\frac{1}{{\mathrm{\tau <br><br>}}_e^{\mathrm{\prime <br><br>}}}+\frac{{\mathrm{\mu <br><br>}}_1^{\mathrm{\prime <br><br>2}}}{j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_2^{\mathrm{\prime <br><br>}}\right)+\frac{{\mathrm{\mu <br><br>}}_2^{\mathrm{\prime <br><br>2}}}{j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_3^{\mathrm{\prime <br><br>}}\right)+\mathrm{\dots <br><br>}+\frac{{\mathrm{\mu <br><br>}}_{N-1}^{\mathrm{\prime <br><br>2}}}{j<br><br>\left(\mathrm{\omega <br><br>}-{\mathrm{\omega <br><br>}}_N^{\mathrm{\prime <br><br>}}\right)+\frac{1}{{\mathrm{\tau <br><br>}}_d^{\mathrm{\prime <br><br>}}}}}},$

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<sup>′

2</sup>, μ

₂<sup>′

2</sup>, . . . , μ

<sub>N−

1</sub>²and a plurality of ideal resonance frequencies ω

₁^′

, . . . , ω

_N^′

, the terms 1/τ

_e′

, μ

₁<sup>′

2</sup>, μ

₂<sup>′

2</sup>, . . . , μ

<sub>N−

1</sub><sup>′

2</sup>, 1/τ

_d^′

and ω

₁^′

, . . . , ω

_N^′

being selected so that the terms 1/τ

_e^′

, μ

₂<sup>′

2</sup>, . . . , μ

<sub>N−

1</sub><sup>′

2</sup>, 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, and

wherein at least one of the ideal energy coupling coefficients 1/τ

_e, μ

₁², μ

₂², . . . , μ

<sub>N−

1</sub>², 1/τ

_d is different from the at least one corresponding energy coupling coefficient in the set 1/τ

_e′

, μ

₁<sup>′

2</sup>, μ

₂<sup>′

2</sup>, . . . , μ

<sub>N−

1</sub>²

40. The optical filter of claim 39 wherein the sequence of N−

1 energy coupling coefficients μ

₁², μ

₂², . . . , μ

<sub>N−

1</sub>² is an asymmetric sequence of values.

41. The optical filter of claim 39 wherein the sequence of N+1 energy coupling coefficients 1/τ

_e, μ

₁², μ

₂², . . . , μ

<sub>N−

a</sub>², 1/τ

_d is an asymmetric sequence of values.

42. The optical filter of claim 39 wherein said drop-port spectral response of said ideal lossless optical filter has a flat-top shape.

43. The optical filter of claim 42 wherein said drop-port spectral response of said ideal lossless optical filter is maximally flat.

44. The optical filter of claim 42 wherein said drop-port spectral response of said ideal lossless optical filter is equiripple.

45. The optical filter of claim 42 wherein the energy coupling coefficients 1/τ

₂, μ

₁², μ

₂², . . . , μ

<sub>N−

1</sub>², 1/τ

_d are further selected so that an insertion loss of said optical filter is at minimum

46. The optical filter of claim 39 wherein the energy coupling coefficients 1/τ

_e, μ

₁², μ

₂², . . . , μ

<sub>N−

1</sub>², 1/τ

_d are further selected so that the first coupling coefficient is stronger than the last coupling coefficient.

47. The optical filter of claim 39 wherein the energy coupling coefficients 1/τ

_e, μ

₁², μ

₂², . . . , μ

<sub>N−

1</sub>², 1/τ

_d are further selected so that the first coupling coefficient is weaker than the last coupling coefficient.

48. The optical filter of claim 39 wherein said plurality of series-coupled optical resonators comprises microring resonators.

49. The optical filter of claim 39 wherein said ideal resonance frequencies ω

′

₁, . . . , ω

′

_N of the ideal lossless optical filter are equal to said resonance frequencies ω

₁, . . . , ω

_N of said optical filter.

50. The optical filter of claim 39 wherein said resonance frequencies ω

₁, . . . , ω

_N of said optical filter are equal.

51. A multistage optical filter comprising a plurality of incoherently-cascaded filter stages, wherein at least one filter stage comprises an optical filter according to claim 39.

52. A multistage optical filter according to claim 51, wherein:

each filter stage has an associated set of input ports and output ports; and

wherein the stages are incoherently cascaded such that for each stage except a first stage, the input port is connected to the output port of another stage;

for each stage except the last the output port is connected to the input port of another stage; and

there is no optical feedback between stages.

55. The multistage optical filter of claim 51 further comprising a third filter stage incoherently cascaded to the second filter stage, wherein the third filter stage has a distribution of coupling coefficients equal to the respective distribution of coupling coefficients of the first filter stage.

56. An optical filter comprising:

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

<sub>N−

1</sub>²,

the plurality of resonators including at least three resonators,

wherein the sequence of N−

1 energy coupling coefficients μ

₁², μ

₂², . . . , μ

<sub>N−

1</sub>² of the optical resonating structure is an asymmetric sequence of values.

57. A method for designing an optical filter having associated drop-port and through-port spectral responses and comprising:

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

<sub>N−

1</sub>², 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<sup>′

2</sup>, μ

₂<sup>′

2</sup>, . . . , μ

<sub>N−

1</sub>² and a plurality of ideal resonance frequencies ω

₁^′

, . . . , ω

_N^′

, the terms 1/τ

_e ^′

, μ

₁<sup>′

2</sup>, μ

₂<sup>′

2</sup>,μ

<sub>N−

1</sub><sup>′

2</sup>, 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<sup>′

2</sup>, μ

₂<sup>′

2</sup>, . . . , μ

<sub>N−

1</sub><sup>′

2</sup>, 1/τ

_d^′

, thus resulting in said set of energy coupling coefficients 1/τ

_e, μ

₁², μ

₂², . . . , μ

<sub>N−

1</sub>², 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.

58. A method based on the method of claim 57, where in addition one of the N+1 terms 1/τ

_e^′

, μ

₁<sup>′

2</sup>, μ

₂<sup>′

2</sup>, . . . , μ

<sub>N−

1</sub><sup>′

2</sup>, 1/τ

_d ′

is varied continuously;

the remaining N terms are uniquely varied, keeping them positive-real valued, so that the complex-plane pole locations remain unchanged during the variation.

59. The method of claim 58, wherein the value of said one varied term is chosen so that the insertion loss of the drop port is unchanged upon a small change of the varied term.

60. The method of claim 59, wherein a value among several possible values of said one varied term is chosen such that the insertion loss is at a minimum.

61. The method of claim 58, wherein a value among several possible values of said one varied term is chosen such that 1/τ

_e>

1/τ

_d.

62. The method of claim 58, wherein a value among several possible values of said one varied term is chosen such that 1/τ

_e<

1/τ

_d.