Planar optical waveguide element, chromatic dispersion compensator, optical filter, optical resonator and methods for designing the element, chromatic dispersion compensator, optical filter and optical resonator

1. A planar optical waveguide element comprising:

a core of an optical waveguide comprising:

an inner side core having protruding portions that form a rib structure; and

an outer side core that is provided on top of the inner side core, and covers upper and lateral surfaces of the protruding portions of the inner side core,

wherein a refractive index of the outer side core is lower than an average refractive index of the inner side core; and

a first Bragg grating pattern and a second Bragg grating pattern which are mutually parallel and extend along a propagation direction of guided light;

wherein the first Bragg grating pattern comprises recessed and protruding portions that are formed on both outer side walls of the core along the propagation direction of guided light;

wherein the second Bragg grating pattern comprises recessed and protruding portions that are formed, along the propagation direction of guided light, on both inner side walls of a groove that is formed on a top portion of the core at a center of the core in a width direction; and

wherein the protruding portions of the first Bragg grating pattern where a core width is wide correspond with the protruding portions of the second Bragg grating pattern where a width of groove is narrow, and the recessed portions of the first Bragg grating pattern where the core width is narrow correspond with the recessed portions of the second Bragg grating pattern where the width of the groove is wide.

2. The planar optical waveguide element according to claim 1 , wherein

each of the first Bragg grating pattern and the second Bragg grating pattern comprise a plurality of isolated single coordinate points where a sign of a gradient of an envelope curve of an amplitude of a Bragg grating is inverted.

3. A planar optical waveguide element comprising:

a core of an optical waveguide comprising:

an inner side core having protruding portions that form a rib structure; and

an outer side core that is provided on top of the inner side core, and covers upper and lateral surfaces of the protruding portions of the inner side core,

wherein a refractive index of the outer side core is lower than an average refractive index of the inner side core;

wherein the optical waveguide comprises a Bragg grating pattern provided on the core;

wherein the Bragg grating pattern only uses discrete values of three or more different pitches;

wherein the discrete values of three or more different pitches are each present in a plurality of locations over an entire length of the optical waveguide; and

wherein, a value which has the highest distribution frequency among all of these discrete values is taken as M, a closest value to the M which is larger than the M is taken as A, and a closest value to the M which is smaller than the M is taken as B, and difference expressed as A−M is equal to a difference expressed as M−B.

4. A planar optical waveguide element comprising:

a core of an optical waveguide comprising:

an inner side core having protruding portions that form a rib structure; and

an outer side core that is provided on top of the inner side core, and covers upper and lateral surfaces of the protruding portions of the inner side core,

wherein a refractive index of the outer side core is lower than an average refractive index of the inner side core;

wherein a gap portion that is disposed at a center of the core in a width direction and extends along the propagation direction of guided light,

wherein the gap portion has a refractive index lower than a refractive index of the core;

wherein the core comprises a first portion and a second portion that are separated by the gap portion; and

wherein a single mode is propagated in the optical waveguide so as to span across the first area and the second area of the core.

5. A chromatic dispersion compensator comprising the planar optical waveguide element according to claim 1 ,

wherein a chromatic dispersion and a dispersion slope in the optical waveguide are compensated by differing a distance over which signal light is propagated in the optical waveguide between entering the optical waveguide and being reflected in accordance with a wavelength, in a plurality of wavelength channels.

6. A design method of the chromatic dispersion compensator according to claim 5 , wherein

the design method comprising:

an optical waveguide cross-sectional structure design process in which, by changing dimensions, in a cross-section perpendicular to the propagation direction of guided light, of the first Bragg grating pattern and the second Bragg grating pattern, and thus equalizing effective refractive indices of the optical waveguide for two mutually independent polarizations that are guided in the optical waveguide, and by then determining a common effective refractive index for the two polarizations, a relationship between the dimensions of the first Bragg grating pattern and the second Bragg grating pattern and the common effective refractive index is obtained;

a Bragg grating pattern design process in which, after a predetermined complex reflectance spectrum is calculated by specifying three of a chromatic dispersion, a dispersion slope, and a reflectance as parameters, a profile of an effective refractive index along the propagation direction of guided light is obtained for the optical waveguide from the complex reflectance spectrum and a desired optical waveguide length; and

a chromatic dispersion compensator design process in which, by converting the profile of the effective refractive index obtained in the Bragg grating pattern design process into a profile of the dimensions of the first Bragg grating pattern and the second Bragg grating pattern based on the relationship between the dimensions of the first Bragg grating pattern and the second Bragg grating pattern and the common effective refractive index obtained in the optical waveguide cross-sectional structure design process, the first Bragg grating pattern and the second Bragg grating pattern are obtained.

7. The design method of the chromatic dispersion compensator according to claim 6 , wherein

the Bragg grating pattern design process further comprises a coarse graining process in which a resolution of discretization of a coordinate axis is taken as more than an amount of change in a pitch which corresponds to a half value of a width of a reflection band; and

the optical waveguide is created by the coarse graining process, the optical waveguide comprising a plurality of isolated single coordinate points where a sign of a gradient of an envelope curve of an amplitude of a Bragg grating is inverted.

8. An optical filter comprising the planar optical waveguide element according to claim 1 .

9. A design method of the optical filter according to claim 8 ,

the design method comprising:

an optical waveguide cross-sectional structure design process in which, by changing dimensions, in a cross-section perpendicular to the propagation direction of guided light, of the first Bragg grating pattern and the second Bragg grating pattern, and thus equalizing effective refractive indices of the optical waveguide for two mutually independent polarizations that are guided in the optical waveguide, and by then determining a common effective refractive index for the two polarizations, a relationship between the dimensions of the first Bragg grating pattern and the second Bragg grating pattern and the common effective refractive index is obtained; a Bragg grating pattern design process in which, after a predetermined complex reflectance spectrum is calculated by specifying both a reflectance and a phase as parameters, a profile of an effective refractive along the waveguide direction of the optical waveguide is obtained from the complex reflectance spectrum and a desired optical waveguide length; and

an optical filter design process in which, by converting the profile of the effective refractive index obtained in the Bragg grating pattern design process into a profile of the dimensions of the first Bragg grating pattern and the second Bragg grating pattern based on the relationship between the dimensions of the first Bragg grating pattern and the second Bragg grating pattern and the common effective refractive index obtained in the optical waveguide cross-sectional structure design process, the first Bragg grating pattern and the second Bragg grating pattern are obtained.

10. The design method of the optical filter according to claim 9 , wherein

the Bragg grating pattern design process further comprises a coarse graining process in which a resolution of discretization of a coordinate axis is taken as more than an amount of change in a pitch which corresponds to a half value of a width of a reflection band; and

the optical waveguide is created by the coarse graining process, the optical waveguide comprising a plurality of isolated single coordinate points where a sign of a gradient of an envelope curve of an amplitude of a Bragg grating is inverted.

11. An optical resonator comprising:

a first optical waveguide which forms a first reflection mirror;

a second optical waveguide which forms a second reflection mirror; and

a third optical waveguide which is disposed between the first optical waveguide and the second optical waveguide,

wherein the first optical waveguide, the third optical waveguide, and the second optical waveguide are connected in series, together forming a single planar optical waveguide; and

each of the first optical waveguide and the second optical waveguide comprise a planar optical waveguide element according claim 1 .

12. A design method of the optical resonator according to claim 11 ,

the design method comprising:

an optical waveguide cross-sectional structure design process in which, by changing dimensions, in a cross-section perpendicular to the propagation direction of guided light, of the first Bragg grating pattern and the second Bragg grating pattern, and thus equalizing effective refractive indices of the optical waveguide for two mutually independent polarizations that are guided in the optical waveguide, and by then determining a common effective refractive index for the two polarizations, a relationship between the dimensions of the first Bragg grating pattern and the second Bragg grating pattern and the common effective refractive index is obtained;

a Bragg grating pattern design process in which, after a predetermined complex reflectance spectrum is calculated by specifying both a reflectance and a phase as parameters, a profile of an effective refractive index along the waveguide direction of the optical waveguide is obtained from the complex reflectance spectrum and a desired optical waveguide length; and

a reflection mirror design process in which, by converting the profile of the effective refractive index obtained in the Bragg grating pattern design process into a profile of the dimensions of the first Bragg grating pattern and the second Bragg grating pattern based on the relationship between the dimensions of the first Bragg grating pattern and the second Bragg grating pattern and the common effective refractive index obtained in the optical waveguide cross-sectional structure design process, the first Bragg grating pattern and the second Bragg grating pattern are obtained.

13. The design method of the optical resonator according to claim 12 , wherein

the Bragg grating pattern design process further comprises a coarse graining process in which a resolution of discretization of a coordinate axis is taken as more than an amount of change in a pitch which corresponds to a half value of a width of a reflection band; and

the first optical waveguide and the second optical waveguide are created by the coarse graining process, the first optical waveguide and the second optical waveguide comprising a plurality of isolated single coordinate points where a sign of a gradient of an envelope curve of an amplitude of a Bragg grating is inverted.