Method for designing optimized multi-channel grating structures

A method of designing a multi-channel grating structure in a photosensitive material, the grating structure having specified spectral characteristics, the method including:

• storing a plurality of partial grating functions on a machine-readable medium, each partial grating function describing a partial gating structure in the photosensitive material;
• and
• utilizing a computer processor to determine a multi-channel grating design function which describes the multi-channel grating structure, the design function comprising the plurality of partial grating functions;
• wherein, in said multi-channel grating design function:
• each partial grating function represents the application of an exact spectral to spatial domain algorithm to a respective single channel reflection spectrum function, each single channel reflection spectrum function describing a portion of the specified spectral characteristics which relates to a single channel;
• at least one of the partial grating functions is phase shifted by a phase shift relative to the other partial grating functions;
• and
• at least one of the partial grating functions has a center grating position in the photosensitive material which is shifted by a position shift relative to the other partial grating functions.

A method of designing a multi-channel grating structure in a photosensitive material, the grating structure having predetermined spectral characteristics, the method including:

• storing a plurality of partial gating functions on a machine-readable medium, each partial grating function describing a partial grating structure in the photosensitive material;
• and
• utilizing a computer processor to determine a multi-channel grating design function which describes the multi-channel grating structure, the design function comprising plurality of partial grating functions;
• wherein, in said multi-channel grating design function:
• each partial grating function represents the application of an exact spectral to spatial domain algorithm to a respective single channel reflection spectrum function, each single channel reflection spectrum function describing a portion of the predefined spectral characteristics which relates to a single channel;
• at least one of the partial grating functions is phase shifted by a phase shift relative to the other partial grating functions;
• and
• at least one of the partial grating functions is different to the other partial grating functions.

A multi-channel grating structure with a profile of refractive index variation along at least one dimension which is described by a plurality of partial grating functions in which:

• each partial grating function represents the application of an exact spectral to spatial domain algorithm to a respective single channel reflection spectrum function, each said single channel reflection spectrum function describing a portion of predefined spectral characteristics which relate to a single channel,
• at least one of the partial grating functions is phase shifted by a phase shift relative to the other partial grating functions;
• and
• at least one of the partial grating functions has a center grating position which is shifted by a position shift relative to the other partial grating functions,
• such that the multi-channel grating structure comprises non-identical spectral channels and/or non-equidistant channel spacing.