Etalons with dispersive coatings

An etalon for selectively passing spectral lines of interest, comprising:

• a substrate having a first major surface and a second, opposite major surface, and
• a coating formed upon at least one of said major surfaces of said substrate, said coating having a spatially varying index of refraction profile through a depth thereof for providing phase shafts at the wavelength or wavelengths of interest, the profile being selected so as to provide said etalon with a prescribed variation of phase with wavelength that matches a dispersion characteristic of a source of the radiation signal, wherein said coating includes a rugate coating having a spatially varying index of refraction profile n(x) that is a summation of a plurality of sinusoidal index of refraction profiles, wherein n(x) is given by the expression:
• n(x)=n.sub.o+.SIGMA. n.sub.i sin(K.sub.i x+.phi..sub.i) H((n.sub.i K(x-x.sub.o))/(n.sub.o u.sub.i))
• n(x)=n.sub.o+.SIGMA. n.sub.i sin(K.sub.i x+.phi..sub.i) H((n.sub.i K(x-x.sub.o))/(n.sub.o u.sub.i))
• Where n.sub.o is an average index of refraction through the rugate coating, where n.sub.i is a peak index of refraction variation at the ith wavelength .lambda..sub.i, where K=4.pi.n.sub.o /.lambda..sub.i, where .phi..sub.i is a starting phase of the index of refraction variation, where x is the distance into the rugate coating, where H is an envelope function or apodizing function or finite extend, and where tanh.sup.2 u.sub.i/ 4 is the reflectivity of the coating at the ith wavelength.

Apparatus for detecting radiation having wavelengths of interest comprising:

• an etalon;
• and
• detector means,
• said etalon disposed for receiving and transmitting therethrough radiation at a wavelength or wavelengths of interest, said etalon including a substrate and a dispersive coating, said substrate having a first major surface and second, opposite major surface, the radiation being incident upon said first major surface, and said dispersive coating formed upon at least one of said major surfaces of said substrate, said dispersive coating having a spatially varying index of refraction profile through a depth thereof for providing phase shifts at the wavelength or wavelengths of interest, the profile being selected to match a desired dispersive characteristic of a source of a radiation signal having the wavelength or wavelengths of interest;
• and
• said detector means disposed relative to said etalon for detecting a presence of radiation at the wavelength or wavelengths of interest that passes through said etalon;
• said detector means disposed relative to said etalon for detecting a presence of radiation at the wavelength or wavelengths of interest that passes through said etalon;
• wherein said dispersive coating includes a rugate coating having a spatially varying index of refraction profile n(x) that is a summation of a plurality of sinusoidal index of refraction profiles, wherein n(x) is given by the expression:
• n(x)=n.sub.o+.SIGMA. n.sub.i sin(K.sub.i x+.phi..sub.i) H((n.sub.i K(x-x.sub.o))/(n.sub.o u.sub.i))
• Where n.sub.o is an average index of refraction through the rugate coating, where n.sub.i is a peak index of refraction variation at the ith wavelength .lambda..sub.i, where K=4.pi.n.sub.o /.lambda..sub.i, where .phi..sub.i is a starting phase of the index of refraction variation, where x is the distance into the rugate coating, where H is an envelope function or apodizing function or finite extend, and where tanh.sup.2 u.sub.i/ 4 is the reflectivity of the coating at the ith wavelength.