Dispersive rugate coatings

An optical device for selectively transmitting or reflecting radiation having spectral lines of interest, comprising:

• a substrate having a surface;
• and
• a coating formed upon said surface of said substrate, said coating having a spatially varying index of refraction profile through a depth thereof, the profile being selected so as to provide said optical device with a prescribed phase shift at the spectral lines of interest wherein said coating includes a rugate coating having a spatially varying index of refraction profile n(x) that varies in accordance with a sinusoidal function, wherein n(x) is given by the expression:
• n(x)=n.sub.o [1+.intg.H(n.sub.i K(x-x.sub.o)/n.sub.o u(K))sin(Kx+.phi.(K))dK/K]
• where n.sub.o is equal to the average index of refraction, K=4.pi.n.sub.o /.lambda.,.theta.'is the internal angle in the coating and .lambda. is the wavelength, where u(K)=4tanh.sup.-1 [R(K)].sup.1/2 is a number of cycles in the coating to achieve a desired reflectivity R(K), n.sub.1 is the peak deviation of the index from n.sub.o for a single wavelength, where .phi.(K) is the phase of the reflected light as a function of K, where x is a distance into the coating, and where H is an envelope or apodizing function located at x.sub.o whose extent defines the region of index variation at the wavelength .lambda..

An optical device for selectively passing a wavelength or wavelengths 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 or refraction profile through a depth thereof for providing a phase shift at the wavelength or wavelengths of interest, the profile being selected so as to provide said optical device with a dispersion characteristic that matches a dispersion characteristic of a source of a radiation signal having the wavelength or wavelengths of interest wherein said coating includes a rugate coating having a spatially varying index of refraction profile n(x) that varies in accordance with a sinusoidal function, wherein n(x) is given by the expression:
• n(x)=n.sub.o [1+.intg.H(n.sub.i K(x-x.sub.o)/n.sub.o u(K))sin(Kx+.phi.(K))dK/K]
• wherein n.sub.o is equal to the average index of refraction, K=4.pi.n.sub.o /.lambda., .theta.'is the internal angle in the coating and .lambda.is the wavelength, where u(K)=4tanh.sup.-1 [R(K)].sup.1/2 is a number of cycles in the coating to achieve a desired reflectivity R(K), n.sub.1 is the peak deviation of the index from n.sub.o for a single wavelength, where .phi.(K) is the phase of the reflected light as a function of K, where x is a distance into the coating, and where H is an envelope or apodizing function located at x.sub.o whose extend defines the region of index variation at the wavelength .lambda..

Apparatus for detecting a presence of a source of radiation, comprising:

• an optical element disposed for receiving a radiation signal having a wavelength or wavelengths of interest, said optical element including a dispersive coating on at least one surface thereof, said dispersive coating having a spatially varying index of refraction profile through a depth thereof for providing a phase shift at the wavelength or wavelengths of interest, the profile being selected to produce a desired dispersion characteristic and wherein said coating includes a rugate coating having a spatially varying index of refraction profile n(x) that varies in accordance with a sinusoidal function, wherein n(x) is given by the expression:
• n(x) =n.sub.o [1+.intg.H(n.sub.i K(x-x.sub.o)/n.sub.o u(K))sin(Kx+.phi.(K))dK/K]
• where n.sub.o is equal to the average index of refraction, K=4.pi.n.sub.o /.lambda., .theta.'is the internal angle in the coating and .lambda. is the wavelength, where u(K)=4tanh.sup.-1 [R(K)].sup.1/2 is a number of cycles in the coating to achieve a desired reflectivity R(K), n.sub.1 is the peak deviation of the index from n.sub.o for a single wavelength, where .phi.(K) is the phase of the reflected light as a function of K, where x is a distance into the coating, and where H is an envelope or apodizing function located at x.sub.o whose extent defines the region of index variation at the wavelength .lambda..