Grating design
View Patent ↗A method of designing a multi-channel grating structure in a waveguide material, the method comprising the step of utilizing a multi-channel grating design function describing an envelope of a refractive index variation defining the multi-channel grating structure in the waveguide material, wherein the multi-channel grating design function deviates from a periodic sampling function multiplied by a single channel grating design function.
1. A method of designing a multi-channel grating structure with multi-channel spectral response characteristics in a waveguide material, the method comprising:
utilising an aperiodic multi-channel grating design function describing an envelope of a refractive index variation defining the multi-channel grating structure in the waveguide material, the design function being a solution to an inverse scattering problem for the multi-channel spectral response characteristics as described by more than one partial single channel response function, each partial single channel response function describing one channel of the multi-channel spectral response characteristics and at least one of the partial single channel response functions being phase shifted relative to the other partial single channel response functions.
2. A method as claimed in claim 1 , wherein the method further comprises providing the multi-channel grating design function by solving an inverse scattering problem for multi-channel spectral response characteristics as described by more than one partial single channel response function, each partial single channel response function describing one channel of the multi-channel spectral response characteristics and at least one partial single channel response function being phase shifted relative to the other partial single channel response functions.
3. A method as claimed in claim 2 , wherein each of the partial single channel response functions are phased shifted relative to the other partial single channel response functions.
4. A method as claimed in claim 1 , wherein the method further comprises the step of determining phase shifts of the partial single channel response functions for which an optimisation criterion is met.
5. A method as claimed in claim 4 , wherein the method further comprises determining phase shifts for which a maximum amplitude of the multi-channel grating design function is minimised.
6. A method as claimed in claim 4 , wherein the method further comprises determining phase shifts for which a maximum difference between a minimum amplitude and a maximum amplitude of the multi-channel grating design function is minimised.
7. A method as claimed in claim 4 , wherein the method further comprises determining phase shifts for which a mean-square-deviation of the amplitude of the multi-channel grating design function is minimised.
8. A method as claimed in claim 4 , wherein the determining the phase shifts comprises at least one of:
direct scanning through all combinations;
conducting a variational analysis;
using extremum search numerical techniques; and
a simulated annealing—Monte Carlo approach.
9. A method as claimed in claim 1 , wherein the method further comprises determining approximate values for the phase shifts.
10. A method as claimed in claim 9 , wherein the determining of the approximate values comprises:
forming a periodic sampling function by summation of periodic functions each describing a refractive index variation along the waveguide, wherein at least one periodic function includes an associated periodic function phase shift relative to the other periodic functions;
determining associated periodic function phase shifts for which an optimisation criteria is met; and
using the associated periodic function phase shifts as the approximate phase shifts.
11. A method as claimed in claim 10 , wherein the summation of the periodic functions comprises a Fourier analysis.
12. A method as claimed in claim 11 , wherein the result of the Fourier analysis represents a form of the expression:
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13. A method as claimed in claim 10 , wherein the determining of the associated periodic function phase shifts further comprises determining associated periodic function phase shift values for which a maximum amplitude of the periodic sampling function is minimised.
14. A method as claimed in claim 10 , wherein the determining of the associated periodic function phase shifts further comprises determining associated periodic function phase shifts for which a difference between a maximum amplitude and a minimum amplitude of the periodic sampling function is minimised.
15. A method as claimed in claim 10 , wherein the determining of the set of associated phase shifts further comprises determining a set of associated phase shifts for which a mean-square-deviation of the amplitude of the periodic sampling function is minimised.
16. A method as claimed in claim 13 , wherein the determining of the associated periodic function phase shifts comprises at least one of:
direct scanning through all combinations;
conducting a variational analysis;
using extremum search numerical techniques; and
a simulated annealing—Monte Carlo approach.
17. A method as claimed in claim 10 , wherein the periodic function phase shifts are used as the phase shifts to calculate the multi-channel grating design function.
18. A method as claimed in claim 10 , wherein the method comprises conducting a further optimisation process using the periodic function phase shifts as seeding values for the phase shifts and using the results of the optimisation process for calculating the multi-channel grating design function.
19. A method as claimed in claim 1 , wherein the grating is multi-dimensional, and wherein the multi-channel grating design function is multi-dimensional.
20. A multi-channel grating structure created utilising the design method as claimed in claim 1 .