Claims
- 1. A method of manufacturing an antireflection high spatial-frequency rectangular groove surface-relief grating for a substrate which is exposed to a wave of transverse electric (TE) polarization incident at an angle .phi..sub.1 and of free-space wavelength .lambda..sub.0 in a lossless medium, wherein the grating is characterized by a grating period, groove depth, and filling factor, comprising the steps of:
- determining the plurality of filling factors and corresponding groove depths for said rectangular-groove grating which will make said grating equivalent to a single homogeneous lossy layer of complex effective refractive index, N.sub.2 -jK.sub.2, by solving numerically the simultaneous set of equations: ##EQU21## where N.sub.1 is the effective refractive index in the lossless medium,
- N.sub.2 is the effective refractive index in the equivalent homogeneous layer,
- N.sub.3 is the effective refractive index in the substrate,
- K.sub.2 is the effective extinction coefficient in the equivalent homogeneous layer,
- K.sub.3 is the effective extinction coefficient in the substrate,
- K is the filling factor of the grating,
- d is the groove depth of the grating,
- k.sub.0 is the wave number of the incident wave;
- selecting a filling factor and corresponding groove depth from said plurality of filling factors and corresponding groove depths determined by solving numerically said simultaneous set of equations; and
- forming said rectangular groove surface-relief grating charactermized by said selected filling factor and corresponding groove depth on said substrate.
- 2. The method of claim 1 wherein the step of forming said rectangular groove surface-relief grating on said substrate is accomplished by reactive ion etching.
- 3. The method of claim 1 wherein the step of forming said rectangular groove surface-relief grating on said substrate is accomplished by electron beam lithography.
- 4. The method of claim 1 wherein the step of forming said rectangular groove surface-relief grating on said substrate is accomplished by holography.
- 5. A method of manufacturing an antireflection high spatial-frequency rectangular-groove surface-relief grating for a substrate which is exposed to a wave of transverse magnetic (TM) polarization incident at an angle .phi..sub.1 and of free-space wavelength .lambda..sub.0 in a lossless medium, wherein the grating is characterized by a grating period, groove depth and filling factor, comprising the steps of:
- determining the plurality of filling factors and corresponding groove depths for said rectangular-groove grating which will make said grating equivalent to a single homogeneous lossy layer of complex effective refractive index, N.sub.2 -jK.sub.2, by solving numerically the simultaneous set of equations: ##EQU22## where N.sub.1 is the effective refractive index in the lossless medium,
- N.sub.2 is the effective refractive index in the equivalent homogeneous layer,
- N.sub.2 ' is defined as the real part of the product of
- N.sub.2 -jK.sub.2 and the cosine squared of the complex angle of refraction in the equivalent homogeneous layer,
- N.sub.3 is the effective refractive index in the substrate,
- K.sub.2 is the effective extinction coefficient in the equivalent homogeneous layer,
- K.sub.2 ' is defined as the negative imaginary part of the product of N.sub.2 -jK.sub.2 and the cosine squared of the complex angle of refraction in the equivalent homogeneous layer,
- K.sub.3 is the effective extinction coefficient in the substrate,
- F is the filling factor of the grating,
- d is the groove depth of the grating,
- k.sub.0 is the wave number of the incident wave;
- selecting a filling factor and corresponding groove depth from said plurality of filling factors and corresponding groove depths determined by solving numerically said simultaneous set of equations; and
- forming said rectangular groove surface-relief grating characterized by said selected filling factor and corresponding groove depth on said substrate.
- 6. The method of claim 5 wherein the step of forming said rectangular groove surface-relief grating on said substrate is accomplished by reactive ion etching.
- 7. The method of claim 5 wherein the step of forming said rectangular groove surface-relief grating on said substrate is accomplished by electron beam lithography.
- 8. The method of claim 5 wherein the step of forming said rectangular groove surface-relief grating on said substrate is accomplished by holography.
- 9. A method of manufacturing an antireflection rectangular groove surface-relief grating comprising the steps of:
- selecting a substrate material on which to form the surface-relief grating;
- determining the polarization and range of wavelengths and angles of incidence of the electromagnetic waves incident on said substrate;
- selecting a lossless medium in which said electromagnetic waves propagate;
- determining the plurality of filling factors and corresponding groove depths for said rectangular-groove grating which will make said grating equivalent to a single homogeneous lossy layer;
- selecting a filling factor and corresponding groove depth from said plurality of filling factors and corresponding groove depths; and
- forming said rectangular groove diffraction grating characterized by said selected filling factor and corresponding groove depth on said substrate.
- 10. The method of claim 9 wherein the selected substrate material is a metal.
- 11. The method of claim 10 further comprising the step of forming a dielectric overlay on said rectangular groove surface-relief grating by filling the grooves of said metallic grating with a dielectric material so as to provide a smooth surface.
- 12. The method of claim 9 wherein the selected substrate material is a semiconductor.
- 13. The method of claim 9 wherein the selected substrate material is a dielectric.
- 14. The method of claim 9 wherein the polarization of the electromagnetic waves incident on said substrate is transverse electric.
- 15. The method of claim 9 wherein the polarization of the electromagnetic waves incident on said substrate is transverse magnetic.
- 16. The method of claim 9 wherein the substrate material is gold.
- 17. The method of claim 16 wherein the range of wavelengths of the electromagnetic waves incident on said substrate is from 0.44 microns to 12.0 microns.
- 18. The method of claim 16 wherein said angle of incidence is normal to said substrate, the wavelength .lambda..sub.0 of said electromagnetic wave is 0.5 microns, the polarization of said electromagnetic waves is transverse electric and the filling factor F and normalized groove depth d/.lambda..sub.0 are as follows:
- F=0.11689
- d/.lambda..sub.0 =0.4779.
- 19. The method of claim 16 wherein said angle of incidence is normal to said substrate, the wavelength .lambda..sub.0 of said electromagnetic waves is 0.5 microns, the polarization of said electromagnetic waves is transverse magnetic and the filling factor F and normalized groove depth d/.lambda..sub.0 are as follows:
- F=0.63841
- d/.lambda..sub.0 =0.083629.
- 20. The method of claim 9 wherein the lossless medium is air.
- 21. A method of manufacturing an antireflection overcoated rectangular groove surface-relief grating for a substrate which is exposed to incident waves of random polarization and free-space wavelength .lambda..sub.0 in a lossless medium, wherein the grating is characterized by a grating period, groove depth and filling factor, and the coating layer has a thickness d.sub.c and an index of refraction n.sub.c, comprising the steps of:
- determining the first plurality of filling factors and corresponding groove depths for said overcoated rectangular-groove grating which will make said grating equivalent to a single homogeneous lossy layer of complex effective refractive index, N.sub.2 -jK.sub.2, for incident waves of transverse electric polarization;
- determining the second plurality of filling factors and corresponding groove depths for said overcoated rectangular-groove grating which will make said grating equivalent to a single homogeneous lossy layer of complex effective refractive index, N.sub.2 -jK.sub.2, for incident waves of transverse magnetic polarization;
- selecting a filling factor and corresponding groove depth from said plurality of filling factors and corresponding groove depths for transverse electric polarization which matches with a filling factor and its corresponding groove depth from said second plurality of filling factors and corresponding groove depths for transverse magnetic polarization;
- forming said rectangular-groove surface-relief grating characterized by said selected filling factor and corresponding groove depth on said substrate; and
- forming said coating layer of thickness d.sub.c over the surface of said rectangular-groove surface-relief grating.
- 22. The method of claim 21 wherein the step of determining the first plurality of filling factors and corresponding groove depths for said overcoated rectangular-groove grating for incident waves of transverse electric polarization further comprises solving numerically the simultaneous set of equations: ##EQU23## where N.sub.1c is the effective refractive index in the combined lossless medium and coating layer,
- N.sub.2 is the effective refractive index in the equivalent homogeneous layer,
- N.sub.3 is the effective refractive index in the substrate,
- N.sub.c is the effective refractive index in the coating layer,
- K.sub.1c is the effective extinction coefficient in the combined lossless medium and coating layer,
- K.sub.2 is the effective extinction coefficient in the equivalent homogeneous layer,
- K.sub.3 is the effective extinction coefficient in the substrate,
- F is the filling factor of the grating,
- d is the groove depth of the grating,
- k.sub.0 is the wave number of the incident wave.
- 23. The method of claim 21 wherein the step of determining the second plurality of filling factors and corresponding groove depths for said overcoated rectangular-groove grating for incident waves of transverse magnetic polarization further comprises solving numerically the simultaneous set of equations: ##EQU24## where N.sub.1c is the effective refractive index in the combined lossless medium and coating layer,
- N.sub.2 is the effective refractive index in the equivalent homogeneous layer,
- N.sub.2 ' is defined as the product of N.sub.2 and the cosine squared of the complex angle of refraction in the equivalent homogeneous layer,
- N.sub.3 is the effective refractive index in the substrate,
- K.sub.1c is the effective extinction coefficient in the combined lossless medium and coating layer,
- K.sub.2 is the effective extinction coefficient in the equivalent homogeneous layer,
- K.sub.2 ' is defined as the product of K.sub.2 and the cosine squared of the complex angle of refraction in the equivalent homogeneous layer,
- K.sub.3 is the effective extinction coefficient in the substrate,
- F is the filling factor of the grating,
- d is the groove depth of the grating,
- k.sub.0 is the wave number of the incident wave.
- 24. The method of claim 21 wherein said incident waves of random polarization are normal to said substrate and have a free-space wavelength .lambda..sub.0 of 0.5 microns, the coating layer is a dielectric having index of refraction n.sub.c =1.5, and the filling factor F, normalized groove depth d/.lambda..sub.0 and normalized coating thickness d.sub.c /.lambda..sub.0 are as follows:
- F=0.290
- d/.lambda..sub.0 =0.3207
- d.sub.c /.lambda..sub.0 =0.3207.
- 25. A method of manufacturing an antireflection large-period rectangular-groove surface-relief grating of a substrate which is exposed to incident waves of transverse electric (TE), transverse magnetic (TM), and random polarization, and of free-space wavelength .lambda..sub.0 in a lossless medium, wherein the grating is characterized by a grating period, groove depth, and filling factor, comprising the steps of:
- determining the plurality of filling factors and corresponding groove depths for said rectangular groove grating which will make said grating equivalent to a single homogeneous lossy layer of complex effective refraction index, N.sub.2 -jK.sub.2, for incidence waves of transverse electric polarization in the long wavelength limit;
- selecting a filling factor within a range of 0.4 and 0.6 from said plurality of filling factors to make the grating easier to fabricate;
- selecting a grating period equal to twice the free-space wavelength .lambda..sub.0 ;
- determining the groove depth corresponding to said selected filling factor and said grating period which will make said surface-relief grating antireflecting at said free-space wavelength .lambda..sub.0 for incident waves of normal incidence and transverse electric polarization; and
- forming said rectangular groove surface-relief grating characterized by said selected grating period, filling factor and corresponding groove depth on said substrate.
- 26. The method of claim 15 wherein said substrate is gold, the wavelength of said incident waves is 0.5 microns, the polarization of said incident waves is transverse electric (TE), said incident waves having an angle of incidence normal to said substrate, the grating period is 1.0 microns, the filling factor is 0.5 and the normalized groove depth is 0.295.
- 27. The method of claim 15 wherein the step of determining the groove depth corresponding to said selected filling factor and said grating period which will make said surface-relief grating antireflecting comprises applying the rigorous coupled-wave analysis of dielectric surface-relief gratings for gratings formed from dielectric material.
- 28. The method of claim 15 wherein the step of determining the groove depth corresponding to said selected filling factor and said grating period which will make said surface-relief grating antireflecting comprises applying the rigorous coupled-wave analysis of metallic surface-relief gratings for gratings formed from metallic material.
GOVERNMENT INTEREST
The invention described herein was made with Government support under Contract No. DAAG29-84-K-0024 on a grant from the Joint Services Electronics Program. The Government has certain rights in this invention.
US Referenced Citations (7)