Thermally compensated optical diffraction gratings

A method comprising:

• forming a grating substrate having substantially flat first and second surfaces, which substrate is substantially transparent over an operational wavelength range that includes a design wavelength λ, has a temperature-dependent refractive index nsub, and is immersed in a medium having a temperature-dependent refractive index nmed;
• and
• forming a set of grating lines in or on the substrate that are substantially parallel to the first substrate surface and characterized by a grating spacing Λ,
• wherein:
• the first and second substrate surfaces are non-parallel and form a dihedral angle α;
• the gratings lines are substantially perpendicular to a plane of incidence defined by surface-normal vectors of the first and second substrate surfaces;
• the optical diffraction grating is arranged as a reflection grating arranged to diffract, at a diffraction angle θd′ with respect to the second surface, at least a portion of an optical signal at the design wavelength λ that is incident on the second surface at a design incidence angle θin in the plane of incidence, and
• variation of the diffraction angle θd′ with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at the design incidence angle θin in the plane of incidence, is less than that variation exhibited by a reference diffraction grating that has parallel first and second substrate surfaces but is otherwise identical to the optical diffraction grating.

A method comprising directing an input optical signal onto an optical diffraction grating at a design incidence angle θin so that a portion of the input optical signal is diffracted as an output optical signal at a diffraction angle θd′, wherein:

• the optical diffraction grating comprises (i) a grating substrate having substantially flat first and second surfaces, which substrate is substantially transparent over an operational wavelength range that includes a design wavelength λ, has a temperature-dependent refractive index nsub, and is immersed in a medium having a temperature-dependent refractive index nmed, and (ii) a set of grating lines formed in or on the substrate that are substantially parallel to the first substrate surface and characterized by a grating spacing Λ;
• the first and second substrate surfaces are non-parallel and form a dihedral angle α;
• the gratings lines are substantially perpendicular to a plane of incidence defined by surface-normal vectors of the first and second substrate surfaces;
• the input optical signal is incident on the second surface at the design incidence angle θin,
• the optical diffraction grating is arranged as a reflection grating arranged to diffract, at the diffraction anile θd′ with resect to the second surface, at least a portion of the optical signal at the design wavelength λ that is incident on the second surface at the design incidence angle θin in the plane of incidence, and
• variation of the diffraction angle θd′ with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at the design incidence angle θin in the plane of incidence, is less than that variation exhibited by a reference diffraction grating that has parallel first and second substrate surfaces but is otherwise identical to the optical diffraction grating.