Multilayer thin film attenuators
An optical element has layers formed on a substrate, including alternating first and second layers having first and second refractive indices, n L and n H that exhibit a spectral characteristic, providing, for incident light at a predetermined wavelength and directed toward the optical element within a range of angles bounded by first and second incident angles θ 1 and θ 2 , between 0 and 80 degrees and differing by at least 1 degree, substantially linear polarization-averaged attenuation of the incident light energy wherein, for any incident angle θ n between θ 1 and θ 2 , Aθ n is the corresponding polarization-averaged attenuation, and wherein the polarization-averaged attenuation at Aθ n at angle θ 1 is less than or equal to an optical density value of 0.2 and the polarization-averaged attenuation Aθ n at angle θ 2 exceeds an optical density value of 4.
1. An optical element comprising:
at least one substrate having at least one surface;
and
a plurality of layers formed on the at least one surface of the at least one substrate, the plurality of layers including alternating first and second layers, the first layers having a first refractive index, n L , and the second layers having a second refractive index, n H , greater than the first refractive index, wherein the plurality of layers exhibit a spectral characteristic,
the spectral characteristic providing, for incident light at a predetermined wavelength and directed to the optical element within a range of incident angles bounded by a first incident angle θ 1 and a second incident angle θ 2 , wherein the first and second incident angles θ 1 and θ 2 are between 0 and 80 degrees and wherein the difference between the first and second incident angles θ 1 and θ 2 is at least 1 degree,
a monotonic relation of the polarization-averaged attenuation of the incident light energy given by:
Aθ n =−log 10 (( Tp n +Ts n )/2)
wherein, for any incident angle θ n that lies within the range between and including angles θ 1 and θ 2 ,
Aθ n is the corresponding polarization-averaged attenuation in terms of optical density,
Tp n is the transmission, at angle θ n , of light energy of a first polarization axis, and
Ts n is the transmission, at angle θ n , of light energy of a second polarization axis that is orthogonal to the first polarization axis, and
−0.1 OD≦ Ap n −As n ≦+0.1 OD;
wherein OD is optical density,
Ap n =−log 10 (Tp n ) is the attenuation, at angle θ n , to light energy of the first polarization axis, and
As n =−log 10 (Ts n ) is the attenuation, at angle θ n , to light energy of the second polarization axis that is orthogonal to the first polarization axis, and
wherein the polarization-averaged attenuation Aθ n at angle θ 1 is less than or equal to an optical density value of 0.2 and the polarization-averaged attenuation Aθ n at angle θ 2 exceeds an optical density value of 2.
2. The optical element of claim 1 wherein the difference between the first and second incident angles θ 1 and θ 2 exceeds 2 degrees.
3. The optical element of claim 1 wherein the polarization-averaged attenuation at angle θ 2 exceeds an optical density value of 3.
4. The optical element of claim 1 wherein the polarization-averaged attenuation at angle θ 2 exceeds an optical density value of 4.
5. The optical element of claim 1 wherein
−0.02 OD≦ Ap n −As n ≦+0.02 OD.
6. The optical element of claim 1 wherein
−0.01 OD≦ Ap n −As n ≦+0.01 OD.
7. The optical element of claim 1 wherein the plurality of layers includes one or more of: SiO 2 , Ta 2 O 5 , Nb 2 O 5 , HfO 2 , TiO 2 , and Al 2 O 5 .
8. An optical element comprising:
at least one substrate having at least one surface;
and
a plurality of layers formed on the at least one surface of the at least one substrate, the plurality of layers including alternating first and second layers, the first layers having a first refractive index, n L , and the second layers having a second refractive index, n H , greater than the first refractive index, wherein the plurality of layers exhibit a spectral characteristic,
the spectral characteristic providing, for incident light at a predetermined wavelength and directed toward the optical element within a range of incident angles bounded by a first incident angle θ 1 and a second incident angle θ 2 ,
wherein the first and second incident angles θ 1 and θ 2 are between 0 and 80 degrees and wherein the difference between the first and second incident angles θ 1 and θ 2 is at least 1 degree, substantially linear polarization-averaged attenuation of the incident light energy given by:
Aθ n =−log 10 (( Tp n +Ts n )/2)
wherein, for any incident angle θ n that lies within the range between and including angles θ 1 and θ 2 ,
Aθ n is the corresponding polarization-averaged attenuation in terms of optical density,
Tp n is the transmission, at angle θ n , of light energy of a first polarization axis, and
Ts n is the transmission, at angle θ n , of light energy of a second polarization axis that is orthogonal to the first polarization axis, and
wherein the polarization-averaged attenuation Aθ n at angle θ 1 is less than or equal to an optical density value of 0.2 and the polarization-averaged attenuation Aθ n at angle θ 2 exceeds an optical density value of 4;
wherein
−0.1 OD≦ Ap n −As n ≦+0.1 OD;
wherein
OD is the optical density,
Ap n =−log 10 (Tp n ) is attenuation, at angle θ n , to light energy of the first polarization axis,
and
As n =−log 10 (Ts n ) is attenuation, at angle θ n , to light energy of the second polarization axis.