Segmented complex fiber gratings
AssigneeTemplex Technology, Inc.
InventorsThomas Mossberg, Michael Munroe, Anders Grunnet-Jepsen, John Sweetser
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Abstract
A waveguide that is operative to produce a reflected optical signal having a spectral profile corresponding to a product of a spectral profile of an input optical signal and a predetermined complex-valued spectral filtering function wherein the waveguide includes a plurality of spatially distinct subgratings each possessing a periodic array of diffraction elements. The subgratings are situated and configured based on the predetermined complex-valued spectral filtering function.
Claims2
A waveguide operative to produce a reflected optical signal having a spectral profile corresponding to a product of a spectral profile of an input optical signal and a predetermined complex-valued spectral filtering function, said waveguide comprising:
- a plurality of spatially distinct subgratings, each subgrating possessing a periodic array of diffraction elements, wherein the subgratings are situated and configured based on the predetermined complex-valued spectral filtering function, wherein each of said subgratings has an amplitude, spatial phase shift, beginning and ending position, and spatial period (Ai, xi, xia, xib, and Λi, respectively), wherein the amplitude (Ai) and a phase (−j2πxi/Λi) of each of said subgratings corresponds to a modulus and an argument, respectively, of a complex parameter αi, wherein αi can be expressed as a i = β d i n 0 ∫ m i / ( β Λ i n 0 ) - 1 / ( 2 β d i n 0 ) m i / ( β Λ i n 0 ) + 1 / ( 2 β d i n 0 ) T ( v ) F i ( v ) exp ( - j π n 0 [ v β - 1 / ( n 0 Λ i ) ] ( x i a + x i b ) ) ⅆ v ,
- wherein υ is frequency, n0 is average waveguide refractive index, β=2/c, c is the vacuum speed of light, di=xib−xia, mi is a diffraction order of an ith subgrating, Fi(υ)=(jC/N)sinc(πn0di[υβ−1/(n0Λi]), C is a constant, N is a number of subgratings, T(υ) is a complex-valued spectral filtering function, and j is a square root of −1.
A waveguide, comprising a plurality of spatially distinct subgratings, each subgrating including a periodic array of diffraction elements, the subgratings being situated and configured to produce an output signal corresponding to a product of a predetermined complex-valued spectral transfer function and a spectral profile of an input optical signal received by the waveguide, wherein an ith subgrating has an amplitude, spatial phase shift, beginning and ending position, and spatial period (Ai, xi, xia, xib, and Λi, respectively), wherein a complex amplitude (αi) of the subgrating corresponds to a i = β d i n 0 ∫ m i / ( β Λ i n 0 ) - 1 / ( 2 β d i n 0 ) m i / ( β Λ i n 0 ) + 1 / ( 2 β d i n 0 ) T ( v ) F i ( v ) exp ( - j π n 0 [ v β - 1 / ( n 0 Λ i ) ] ( x i a + x i b ) ) ⅆ v ,
- wherein υ is frequency, Ai and xi are determined by the amplitude and phase of αi, respectively, αi=Aiexp(−j2πxi/Λi), β=2/c, c is the vacuum speed of light, di=xib−xia, mi is a diffraction order of an ith subgrating, Fi(υ)=(jC/N)sinc(πn0di[υβ−1/(n0Λi]), C is a constant, N is a number of subgratings, and T(υ) is the predetermined complex-valued spectral transfer function, j is a square root of −1, and n0 is a background effective refractive index of the waveguide.
Dependencies are inferred from the claim text.