Abstract

We discuss an enhancement-of-energy transfer phenomenon that involves the absorption of a photon and takes place in thin surface layers. The enhancement is effected by the resonant excitation of a waveguide mode in the substrate onto which the layer is adsorbed. The system is studied with a pole analysis, allowing the crucial parameters to be identified and physically interpreted. Complete absorption is possible, and a significant enhancement in the photo yield of a photocathode surface layer is calculated. The energy exchange with finite-size incident beams is considered, leading to the conclusion that the device should be highly sensitive to surface layers approaching a monolayer or less in thickness.

© 1982 Optical Society of America

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  1. N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), Chap. V.
  2. N. J. Harrick and A. F. Turner, "A thin film cavity to induce absorption or thermal emission," Appl. Opt. 9, 2111–2114 (1970).
  3. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), Sec. 1.6.
  4. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  5. P. H. Berning, Physics of Thin Films, G. Hass, ed. (Academic, New York, 1963), Vol. 1.
  6. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap. 17.
  7. J. Van Kranendonk and J. E. Sipe, "Foundations of the macroscopic electromagnetic theory of dielectric media," Prog. Opt. 15, 247–350 (1977).
  8. N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 2.
  9. W. H. Weber and G. W. Ford, "Optical electric-field enhancement at a metal surface arising from surface-plasmon excitation," Opt. Lett. 6, 122–124 (1981).
  10. H. J. Simon, D. E. Mitchell, and J. G. Watson, "Optical secondharmonic generation with surface plasmons in silver films," Phys. Rev. Lett. 33, 1531–1534 (1974).
  11. J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second harmonic generation at metal surfaces," Phys. Rev. B 21, 4389–4402 (1980), and references therein.
  12. J. E. Sipe and G. I. Stegeman, "Nonlinear optical response of metal surface," in Surface Polaritons (North-Holland, Amsterdam, in press), and references therein.
  13. I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).
  14. I. Pockrand and J. D. Swalen, "Anomalous dispersion of surface plasma oscillations," J. Opt. Soc. Am. 68, 1147–1151 (1978).
  15. J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7–9 (1980).
  16. See, e.g., H. J. Simon and J. K. Guha, "Directional surface plasmon scattering from silver films," Opt. Commun. 18, 391–394 (1976).
  17. J. G. Endriz, "Calculation of the surface photoelectric effect," Phys. Rev. B 7, 3464–3481 (1973).
  18. T. A. Callcott and E. T. Arakawa, "Volume and surface photoemission processes from plasmon resonance field," Phys. Rev. B 11, 2750–2758 (1975).
  19. J. E. Sipe and J. Becher, "Surface plasmon-assisted photoemission," J. Opt. Soc. Am. 71, 1286–1288 (1981).
  20. Systems somewhat similar to that shown in Fig. 1, but with an absorbing resonator taking the place of our resonator and target, have been studied in the microwave portion of the spectrum and in Refs. 21 and 22. Optical systems of that type include those studied by Cipriani et al. (Ref. 23).
  21. V. Shah and T. Tamir, "Brewster phenomena in lossy structures," Opt. Commun. 23, 113–117 (1977).
  22. A. Amittay, P. D. Einziger, and T. Tamir, "Experimental observation of anomalous electromagnetic absorption in thin-layered media," Appl..Phy. Lett. 38, 754–756 (1981).
  23. J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).
  24. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 19.
  25. L. Levi, Applied Optics (Wiley, New York, 1980), Vol. 2, Chap. 13.
  26. J. E. Sipe, "Bulk-selvedge coupling theory for the optical properties of surfaces," Phys. Rev. B 22, 1589–1599 (1980).
  27. K. Hirschberg and K. Deutscher, Phys. Status Solidi 26, 527–535 (1968).
  28. W. Greschat, H. Heinrich, and P. Romer, "Quantum yield of Cs3Sb photocathodes as a function of thickness and angle of incidence," Electron. Electron Phys. 40A, 397–408 (1976).
  29. P. J. Vernier, "Photoemission," Prog. Opt. 14, 245–325 (1976).
  30. For a review, see P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361–420 (1977).
  31. P. K. Tien and R. Ulrich, "Theory of prism-film coupler and thin-film light guides," J. Opt. Soc. Am. 60, 1325–1337 (1970).
  32. J. E. Midwinter, "Evanescent field coupling into a thin-film waveguide," IEEE J. Quantum Electron. QE-6, 583–590 (1970).
  33. J. E. Sipe, "A new treatment of the growing wave problem in surface optics," Solid State Commun. (to be published, 1981).
  34. R. Ulrich, "Theory of the prism-film coupler by plane-wave analysis," J. Opt. Soc. Am. 60, 1337–1350 (1970).
  35. N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 3, and references therein.

1981 (3)

1980 (3)

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second harmonic generation at metal surfaces," Phys. Rev. B 21, 4389–4402 (1980), and references therein.

J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7–9 (1980).

J. E. Sipe, "Bulk-selvedge coupling theory for the optical properties of surfaces," Phys. Rev. B 22, 1589–1599 (1980).

1978 (2)

I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).

I. Pockrand and J. D. Swalen, "Anomalous dispersion of surface plasma oscillations," J. Opt. Soc. Am. 68, 1147–1151 (1978).

1977 (3)

J. Van Kranendonk and J. E. Sipe, "Foundations of the macroscopic electromagnetic theory of dielectric media," Prog. Opt. 15, 247–350 (1977).

V. Shah and T. Tamir, "Brewster phenomena in lossy structures," Opt. Commun. 23, 113–117 (1977).

For a review, see P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361–420 (1977).

1976 (3)

See, e.g., H. J. Simon and J. K. Guha, "Directional surface plasmon scattering from silver films," Opt. Commun. 18, 391–394 (1976).

W. Greschat, H. Heinrich, and P. Romer, "Quantum yield of Cs3Sb photocathodes as a function of thickness and angle of incidence," Electron. Electron Phys. 40A, 397–408 (1976).

P. J. Vernier, "Photoemission," Prog. Opt. 14, 245–325 (1976).

1975 (1)

T. A. Callcott and E. T. Arakawa, "Volume and surface photoemission processes from plasmon resonance field," Phys. Rev. B 11, 2750–2758 (1975).

1974 (2)

H. J. Simon, D. E. Mitchell, and J. G. Watson, "Optical secondharmonic generation with surface plasmons in silver films," Phys. Rev. Lett. 33, 1531–1534 (1974).

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

1973 (1)

J. G. Endriz, "Calculation of the surface photoelectric effect," Phys. Rev. B 7, 3464–3481 (1973).

1970 (4)

Amittay, A.

A. Amittay, P. D. Einziger, and T. Tamir, "Experimental observation of anomalous electromagnetic absorption in thin-layered media," Appl..Phy. Lett. 38, 754–756 (1981).

Arakawa, E. T.

T. A. Callcott and E. T. Arakawa, "Volume and surface photoemission processes from plasmon resonance field," Phys. Rev. B 11, 2750–2758 (1975).

Becher, J.

Berning, P. H.

P. H. Berning, Physics of Thin Films, G. Hass, ed. (Academic, New York, 1963), Vol. 1.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), Sec. 1.6.

Brillante, A.

I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).

Burke, J. J.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 2.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 3, and references therein.

Callcott, T. A.

T. A. Callcott and E. T. Arakawa, "Volume and surface photoemission processes from plasmon resonance field," Phys. Rev. B 11, 2750–2758 (1975).

Cipriani, J.

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

Deutscher, K.

K. Hirschberg and K. Deutscher, Phys. Status Solidi 26, 527–535 (1968).

Dupeyrat, M.

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

Dupeyrat, R.

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

Einziger, P. D.

A. Amittay, P. D. Einziger, and T. Tamir, "Experimental observation of anomalous electromagnetic absorption in thin-layered media," Appl..Phy. Lett. 38, 754–756 (1981).

Endriz, J. G.

J. G. Endriz, "Calculation of the surface photoelectric effect," Phys. Rev. B 7, 3464–3481 (1973).

Ford, G. W.

Fukui, M.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second harmonic generation at metal surfaces," Phys. Rev. B 21, 4389–4402 (1980), and references therein.

Greschat, W.

W. Greschat, H. Heinrich, and P. Romer, "Quantum yield of Cs3Sb photocathodes as a function of thickness and angle of incidence," Electron. Electron Phys. 40A, 397–408 (1976).

Guha, J. K.

See, e.g., H. J. Simon and J. K. Guha, "Directional surface plasmon scattering from silver films," Opt. Commun. 18, 391–394 (1976).

Harrick, N. J.

N. J. Harrick and A. F. Turner, "A thin film cavity to induce absorption or thermal emission," Appl. Opt. 9, 2111–2114 (1970).

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), Chap. V.

Hasmonay, H.

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Heinrich, H.

W. Greschat, H. Heinrich, and P. Romer, "Quantum yield of Cs3Sb photocathodes as a function of thickness and angle of incidence," Electron. Electron Phys. 40A, 397–408 (1976).

Hirschberg, K.

K. Hirschberg and K. Deutscher, Phys. Status Solidi 26, 527–535 (1968).

Imbert, C.

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap. 17.

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 2.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 3, and references therein.

Levi, L.

L. Levi, Applied Optics (Wiley, New York, 1980), Vol. 2, Chap. 13.

Levy, Y.

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

Midwinter, J. E.

J. E. Midwinter, "Evanescent field coupling into a thin-film waveguide," IEEE J. Quantum Electron. QE-6, 583–590 (1970).

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, and J. G. Watson, "Optical secondharmonic generation with surface plasmons in silver films," Phys. Rev. Lett. 33, 1531–1534 (1974).

Philoptt, M. R.

I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).

Pockrand, I.

I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).

I. Pockrand and J. D. Swalen, "Anomalous dispersion of surface plasma oscillations," J. Opt. Soc. Am. 68, 1147–1151 (1978).

Racine, S.

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

Romer, P.

W. Greschat, H. Heinrich, and P. Romer, "Quantum yield of Cs3Sb photocathodes as a function of thickness and angle of incidence," Electron. Electron Phys. 40A, 397–408 (1976).

Santo, R.

I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).

Shah, V.

V. Shah and T. Tamir, "Brewster phenomena in lossy structures," Opt. Commun. 23, 113–117 (1977).

Simon, H. J.

See, e.g., H. J. Simon and J. K. Guha, "Directional surface plasmon scattering from silver films," Opt. Commun. 18, 391–394 (1976).

H. J. Simon, D. E. Mitchell, and J. G. Watson, "Optical secondharmonic generation with surface plasmons in silver films," Phys. Rev. Lett. 33, 1531–1534 (1974).

Sipe, J. E.

J. E. Sipe and J. Becher, "Surface plasmon-assisted photoemission," J. Opt. Soc. Am. 71, 1286–1288 (1981).

J. E. Sipe, "Bulk-selvedge coupling theory for the optical properties of surfaces," Phys. Rev. B 22, 1589–1599 (1980).

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second harmonic generation at metal surfaces," Phys. Rev. B 21, 4389–4402 (1980), and references therein.

J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7–9 (1980).

J. Van Kranendonk and J. E. Sipe, "Foundations of the macroscopic electromagnetic theory of dielectric media," Prog. Opt. 15, 247–350 (1977).

J. E. Sipe and G. I. Stegeman, "Nonlinear optical response of metal surface," in Surface Polaritons (North-Holland, Amsterdam, in press), and references therein.

J. E. Sipe, "A new treatment of the growing wave problem in surface optics," Solid State Commun. (to be published, 1981).

So, V. C. Y.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second harmonic generation at metal surfaces," Phys. Rev. B 21, 4389–4402 (1980), and references therein.

Stegeman, G. I.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second harmonic generation at metal surfaces," Phys. Rev. B 21, 4389–4402 (1980), and references therein.

J. E. Sipe and G. I. Stegeman, "Nonlinear optical response of metal surface," in Surface Polaritons (North-Holland, Amsterdam, in press), and references therein.

Swalen, J. D.

I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).

I. Pockrand and J. D. Swalen, "Anomalous dispersion of surface plasma oscillations," J. Opt. Soc. Am. 68, 1147–1151 (1978).

Tamir, T.

A. Amittay, P. D. Einziger, and T. Tamir, "Experimental observation of anomalous electromagnetic absorption in thin-layered media," Appl..Phy. Lett. 38, 754–756 (1981).

V. Shah and T. Tamir, "Brewster phenomena in lossy structures," Opt. Commun. 23, 113–117 (1977).

Tien, P. K.

For a review, see P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361–420 (1977).

P. K. Tien and R. Ulrich, "Theory of prism-film coupler and thin-film light guides," J. Opt. Soc. Am. 60, 1325–1337 (1970).

Turner, A. F.

Ulrich, R.

Van Kranendonk, J.

J. Van Kranendonk and J. E. Sipe, "Foundations of the macroscopic electromagnetic theory of dielectric media," Prog. Opt. 15, 247–350 (1977).

Vernier, P. J.

P. J. Vernier, "Photoemission," Prog. Opt. 14, 245–325 (1976).

Watson, J. G.

H. J. Simon, D. E. Mitchell, and J. G. Watson, "Optical secondharmonic generation with surface plasmons in silver films," Phys. Rev. Lett. 33, 1531–1534 (1974).

Weber, W. H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), Sec. 1.6.

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 19.

Appl. Opt. (1)

Appl..Phy. Lett. (1)

A. Amittay, P. D. Einziger, and T. Tamir, "Experimental observation of anomalous electromagnetic absorption in thin-layered media," Appl..Phy. Lett. 38, 754–756 (1981).

Electron. Electron Phys. (1)

W. Greschat, H. Heinrich, and P. Romer, "Quantum yield of Cs3Sb photocathodes as a function of thickness and angle of incidence," Electron. Electron Phys. 40A, 397–408 (1976).

IEEE J. Quantum Electron. (1)

J. E. Midwinter, "Evanescent field coupling into a thin-film waveguide," IEEE J. Quantum Electron. QE-6, 583–590 (1970).

J. Chem. Phys. (1)

I. Pockrand, J. D. Swalen, R. Santo, A. Brillante, and M. R. Philoptt, "Optical properties of organic dye molecules by surface plasmon spectroscopy," J. Chem. Phys. 69, 4001–4011 (1978).

J. Opt. Soc. Am. (4)

Opt. Commun. (3)

J. Cipriani, S. Racine, R. Dupeyrat, H. Hasmonay, M. Dupeyrat, Y. Levy, and C. Imbert, "Raman scattering of Langmuir—Blodgett barium sterate layers using a total reflection method," Opt. Commun. 11, 70–73 (1974).

V. Shah and T. Tamir, "Brewster phenomena in lossy structures," Opt. Commun. 23, 113–117 (1977).

See, e.g., H. J. Simon and J. K. Guha, "Directional surface plasmon scattering from silver films," Opt. Commun. 18, 391–394 (1976).

Opt. Lett. (1)

Phys. Rev. B (4)

J. G. Endriz, "Calculation of the surface photoelectric effect," Phys. Rev. B 7, 3464–3481 (1973).

T. A. Callcott and E. T. Arakawa, "Volume and surface photoemission processes from plasmon resonance field," Phys. Rev. B 11, 2750–2758 (1975).

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, "Analysis of second harmonic generation at metal surfaces," Phys. Rev. B 21, 4389–4402 (1980), and references therein.

J. E. Sipe, "Bulk-selvedge coupling theory for the optical properties of surfaces," Phys. Rev. B 22, 1589–1599 (1980).

Phys. Rev. Lett. (1)

H. J. Simon, D. E. Mitchell, and J. G. Watson, "Optical secondharmonic generation with surface plasmons in silver films," Phys. Rev. Lett. 33, 1531–1534 (1974).

Prog. Opt. (2)

J. Van Kranendonk and J. E. Sipe, "Foundations of the macroscopic electromagnetic theory of dielectric media," Prog. Opt. 15, 247–350 (1977).

P. J. Vernier, "Photoemission," Prog. Opt. 14, 245–325 (1976).

Rev. Mod. Phys. (1)

For a review, see P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361–420 (1977).

Solid State Commun. (1)

J. E. Sipe, "Surface plasmon-enhanced absorption of light by adsorbed molecules," Solid State Commun. 33, 7–9 (1980).

Other (13)

J. E. Sipe and G. I. Stegeman, "Nonlinear optical response of metal surface," in Surface Polaritons (North-Holland, Amsterdam, in press), and references therein.

Systems somewhat similar to that shown in Fig. 1, but with an absorbing resonator taking the place of our resonator and target, have been studied in the microwave portion of the spectrum and in Refs. 21 and 22. Optical systems of that type include those studied by Cipriani et al. (Ref. 23).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 2.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), Sec. 1.6.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

P. H. Berning, Physics of Thin Films, G. Hass, ed. (Academic, New York, 1963), Vol. 1.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap. 17.

J. E. Sipe, "A new treatment of the growing wave problem in surface optics," Solid State Commun. (to be published, 1981).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), Chap. 3, and references therein.

K. Hirschberg and K. Deutscher, Phys. Status Solidi 26, 527–535 (1968).

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967), Chap. V.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 19.

L. Levi, Applied Optics (Wiley, New York, 1980), Vol. 2, Chap. 13.

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