Abstract

We investigate the reflection of plane waves of s and p polarization from the interface between a homogeneous transparent medium and an amplifying medium with a gain profile decreasing exponentially with depth of penetration. For angles of incidence less than critical angle, the reflectance curves are essentially the same as those deduced from the usual Fresnel formulas for two transparent media. In the vicinity of critical angle, the reflection coefficients are virtually the same for both polarizations and are greater than unity. Beyond critical angle, the reflectances fall toward unity as grazing incidence is approached. Both the reflectance and the far-field transmittance peak in the immediate vicinity of critical angle. For angles less than critical angle, the transmittance can be 2 orders of magnitude greater than the reflectance. Certain values of gain parameters and incident angle lead to singularities in the theoretical reflectance. At these points the usual neglect of the effect of the transmitted wave on the population inversion is no longer valid.

© 1983 Optical Society of America

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  1. C. J. Koester, “Laser action by enhanced internal reflection,” J. Quantum Electron. QE-2, 580–584 (1966).
    [CrossRef]
  2. E. P. Ippen and C. V. Shank, “Evanescent-field-pumped dye laser,” Appl. Phys. Lett. 21, 301–302 (1972).
    [CrossRef]
  3. B. Ya. Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100–101 (1972).
  4. S. A. Lebedev, V. M. Volkov, and B. Ya. Kogan, “Value of the gain for light internally reflected from a medium with inverted population,” Opt. Spectrosc. 35, 565–566 (1973).
  5. S. A. Lebedev and B. Y. Kogan, “Light Amplification by internal reflection from an inverted medium,” Opt. Spectrosc. 48, 564–565 (1980).
  6. G. N. Romanov and S. S. Shakhidzhanov, “Amplification of electromagnetic field in total internal reflection from a region of inverted population,” JETP Lett. 16, 209–211 (1972).
  7. B. B. Boiko, V. G. Leshchenko, and N. S. Petrov, “Behavior of heterogeneous electromagnetic waves on the boundary between absorbing (amplifying) and transparent isotropic media,” Zh. Prikl. Spektrosk. 19, 669–674 (1972).
  8. B. B. Boiko, N. S. Petrov, and I. Z. Dzhilavdari, “Reflection of electromagnetic waves from interface with amplifying medium,” Zh. Prikl. Spektrosk. 18, 727–729 (1973).
  9. A. A. Kolokolov, “Reflection of plane waves from an amplifying medium,” JETP Lett. 21, 312–313 (1975).
  10. W. Lukosz and P. P. Herrmann, “Amplification by reflection from an active medium,” Opt. Commun. 17, 192–195 (1976).
    [CrossRef]
  11. P. R. Callary and C. K. Carniglia, “Internal reflection from an amplifying layer,” J. Opt. Soc. Am. 66, 775–779 (1976).
    [CrossRef]
  12. B. B. Boiko, I. Z. Dzhilavdari, G. I. Olefit, and N. S. Petrov, “Reflection of light by a plane-parallel transparent layer in contact with an inverse medium,” Zh. Prikl. Spektrosk. 26, 747–750 (1977).
  13. A. A. Kolokolov, “Structure of the lateral wave in the reflection of a beam from an active medium,” Opt. Spectrosc. 44, 568–571 (1978).
  14. B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Reflection of light on the boundary of an exponentially inhomogeneous amplifying medium (parallel polarization),” Zh. Prikl. Spektrosk. 22, 545–547 (1975).
  15. N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from a semi-infinite exponentially inhomogeneous amplifying medium,” Zh. Prikl. Spectrosk. 23, 705–709 (1975).
  16. N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from an exponentially nonuniform amplifying medium in the case of parallel polarization,” Zh. Prikl. Spektrosk. 24, 1038–1043 (1976).
  17. B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Amplification by reflection from a medium with population inversion,” Zh. Prikl. Spektrosk. 25, 148–150 (1976).
  18. R. F. Cybulski and C. K. Carniglia, “Internal reflection from an exponentially amplifying region,” J. Opt. Soc. Am. 67, 1620–1627 (1977).
    [CrossRef]
  19. Yu. N. Luk’yanov and V. G. Pan’kin, “Light reflection from an amplifying medium,” Rad. Eng. Electron. Phys. 24, 21–25 (1979).
  20. R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an inverted medium,” J. Opt. Soc. Am. 71, 1641 (1981).
  21. S. A. Lebedev and B. Ya. Kogan, “Mechanism of anomalous light reflection from an inverted medium,” Opt. Spectrosc. 48, 647–649 (1980).
  22. K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Thin-film waveguide evanescent dye laser and its gain measurement,” J. Appl. Phys. 51, 3090–3092 (1980).
    [CrossRef]
  23. K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Amplified oscillation in a slab-type optical directional coupler with an activated rhodamine 6G top layer,” Appl. Phys. Lett. 37, 129–130 (1980).
    [CrossRef]
  24. K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
    [CrossRef]
  25. R. F. Cybulski and M. P. Silverman, “Reflectance from an exponentially nonuniform gain region,” J. Opt. Soc. Am. 72, 1735 (1982).
  26. M. P. Silverman and R. F. Cybulski, “Light amplification by reflection from an inverted medium,” Bull. Am. Phys. Soc. 28, 852 (1983).
  27. R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an exponential amplifying region,” Opt. Lett. 8, 142–144 (1983).
    [CrossRef] [PubMed]
  28. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 17–22.
  29. S. A. Tuccio and F. C. Strome, “Design and operation of a tunable continuous dye laser,” Appl. Opt. 11, 64–73 (1972).
    [CrossRef] [PubMed]

1983 (2)

M. P. Silverman and R. F. Cybulski, “Light amplification by reflection from an inverted medium,” Bull. Am. Phys. Soc. 28, 852 (1983).

R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an exponential amplifying region,” Opt. Lett. 8, 142–144 (1983).
[CrossRef] [PubMed]

1982 (1)

R. F. Cybulski and M. P. Silverman, “Reflectance from an exponentially nonuniform gain region,” J. Opt. Soc. Am. 72, 1735 (1982).

1981 (2)

K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
[CrossRef]

R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an inverted medium,” J. Opt. Soc. Am. 71, 1641 (1981).

1980 (4)

S. A. Lebedev and B. Ya. Kogan, “Mechanism of anomalous light reflection from an inverted medium,” Opt. Spectrosc. 48, 647–649 (1980).

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Thin-film waveguide evanescent dye laser and its gain measurement,” J. Appl. Phys. 51, 3090–3092 (1980).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Amplified oscillation in a slab-type optical directional coupler with an activated rhodamine 6G top layer,” Appl. Phys. Lett. 37, 129–130 (1980).
[CrossRef]

S. A. Lebedev and B. Y. Kogan, “Light Amplification by internal reflection from an inverted medium,” Opt. Spectrosc. 48, 564–565 (1980).

1979 (1)

Yu. N. Luk’yanov and V. G. Pan’kin, “Light reflection from an amplifying medium,” Rad. Eng. Electron. Phys. 24, 21–25 (1979).

1978 (1)

A. A. Kolokolov, “Structure of the lateral wave in the reflection of a beam from an active medium,” Opt. Spectrosc. 44, 568–571 (1978).

1977 (2)

B. B. Boiko, I. Z. Dzhilavdari, G. I. Olefit, and N. S. Petrov, “Reflection of light by a plane-parallel transparent layer in contact with an inverse medium,” Zh. Prikl. Spektrosk. 26, 747–750 (1977).

R. F. Cybulski and C. K. Carniglia, “Internal reflection from an exponentially amplifying region,” J. Opt. Soc. Am. 67, 1620–1627 (1977).
[CrossRef]

1976 (4)

P. R. Callary and C. K. Carniglia, “Internal reflection from an amplifying layer,” J. Opt. Soc. Am. 66, 775–779 (1976).
[CrossRef]

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from an exponentially nonuniform amplifying medium in the case of parallel polarization,” Zh. Prikl. Spektrosk. 24, 1038–1043 (1976).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Amplification by reflection from a medium with population inversion,” Zh. Prikl. Spektrosk. 25, 148–150 (1976).

W. Lukosz and P. P. Herrmann, “Amplification by reflection from an active medium,” Opt. Commun. 17, 192–195 (1976).
[CrossRef]

1975 (3)

A. A. Kolokolov, “Reflection of plane waves from an amplifying medium,” JETP Lett. 21, 312–313 (1975).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Reflection of light on the boundary of an exponentially inhomogeneous amplifying medium (parallel polarization),” Zh. Prikl. Spektrosk. 22, 545–547 (1975).

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from a semi-infinite exponentially inhomogeneous amplifying medium,” Zh. Prikl. Spectrosk. 23, 705–709 (1975).

1973 (2)

B. B. Boiko, N. S. Petrov, and I. Z. Dzhilavdari, “Reflection of electromagnetic waves from interface with amplifying medium,” Zh. Prikl. Spektrosk. 18, 727–729 (1973).

S. A. Lebedev, V. M. Volkov, and B. Ya. Kogan, “Value of the gain for light internally reflected from a medium with inverted population,” Opt. Spectrosc. 35, 565–566 (1973).

1972 (5)

E. P. Ippen and C. V. Shank, “Evanescent-field-pumped dye laser,” Appl. Phys. Lett. 21, 301–302 (1972).
[CrossRef]

B. Ya. Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100–101 (1972).

G. N. Romanov and S. S. Shakhidzhanov, “Amplification of electromagnetic field in total internal reflection from a region of inverted population,” JETP Lett. 16, 209–211 (1972).

B. B. Boiko, V. G. Leshchenko, and N. S. Petrov, “Behavior of heterogeneous electromagnetic waves on the boundary between absorbing (amplifying) and transparent isotropic media,” Zh. Prikl. Spektrosk. 19, 669–674 (1972).

S. A. Tuccio and F. C. Strome, “Design and operation of a tunable continuous dye laser,” Appl. Opt. 11, 64–73 (1972).
[CrossRef] [PubMed]

1966 (1)

C. J. Koester, “Laser action by enhanced internal reflection,” J. Quantum Electron. QE-2, 580–584 (1966).
[CrossRef]

Boiko, B. B.

B. B. Boiko, I. Z. Dzhilavdari, G. I. Olefit, and N. S. Petrov, “Reflection of light by a plane-parallel transparent layer in contact with an inverse medium,” Zh. Prikl. Spektrosk. 26, 747–750 (1977).

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from an exponentially nonuniform amplifying medium in the case of parallel polarization,” Zh. Prikl. Spektrosk. 24, 1038–1043 (1976).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Amplification by reflection from a medium with population inversion,” Zh. Prikl. Spektrosk. 25, 148–150 (1976).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Reflection of light on the boundary of an exponentially inhomogeneous amplifying medium (parallel polarization),” Zh. Prikl. Spektrosk. 22, 545–547 (1975).

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from a semi-infinite exponentially inhomogeneous amplifying medium,” Zh. Prikl. Spectrosk. 23, 705–709 (1975).

B. B. Boiko, N. S. Petrov, and I. Z. Dzhilavdari, “Reflection of electromagnetic waves from interface with amplifying medium,” Zh. Prikl. Spektrosk. 18, 727–729 (1973).

B. B. Boiko, V. G. Leshchenko, and N. S. Petrov, “Behavior of heterogeneous electromagnetic waves on the boundary between absorbing (amplifying) and transparent isotropic media,” Zh. Prikl. Spektrosk. 19, 669–674 (1972).

Callary, P. R.

Carniglia, C. K.

Cybulski, R. F.

M. P. Silverman and R. F. Cybulski, “Light amplification by reflection from an inverted medium,” Bull. Am. Phys. Soc. 28, 852 (1983).

R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an exponential amplifying region,” Opt. Lett. 8, 142–144 (1983).
[CrossRef] [PubMed]

R. F. Cybulski and M. P. Silverman, “Reflectance from an exponentially nonuniform gain region,” J. Opt. Soc. Am. 72, 1735 (1982).

R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an inverted medium,” J. Opt. Soc. Am. 71, 1641 (1981).

R. F. Cybulski and C. K. Carniglia, “Internal reflection from an exponentially amplifying region,” J. Opt. Soc. Am. 67, 1620–1627 (1977).
[CrossRef]

Dzhilavdari, I. Z.

B. B. Boiko, I. Z. Dzhilavdari, G. I. Olefit, and N. S. Petrov, “Reflection of light by a plane-parallel transparent layer in contact with an inverse medium,” Zh. Prikl. Spektrosk. 26, 747–750 (1977).

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from an exponentially nonuniform amplifying medium in the case of parallel polarization,” Zh. Prikl. Spektrosk. 24, 1038–1043 (1976).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Amplification by reflection from a medium with population inversion,” Zh. Prikl. Spektrosk. 25, 148–150 (1976).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Reflection of light on the boundary of an exponentially inhomogeneous amplifying medium (parallel polarization),” Zh. Prikl. Spektrosk. 22, 545–547 (1975).

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from a semi-infinite exponentially inhomogeneous amplifying medium,” Zh. Prikl. Spectrosk. 23, 705–709 (1975).

B. B. Boiko, N. S. Petrov, and I. Z. Dzhilavdari, “Reflection of electromagnetic waves from interface with amplifying medium,” Zh. Prikl. Spektrosk. 18, 727–729 (1973).

Fukao, T.

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Thin-film waveguide evanescent dye laser and its gain measurement,” J. Appl. Phys. 51, 3090–3092 (1980).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Amplified oscillation in a slab-type optical directional coupler with an activated rhodamine 6G top layer,” Appl. Phys. Lett. 37, 129–130 (1980).
[CrossRef]

Furukawa, S.

K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
[CrossRef]

Hamano, O.

K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Thin-film waveguide evanescent dye laser and its gain measurement,” J. Appl. Phys. 51, 3090–3092 (1980).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Amplified oscillation in a slab-type optical directional coupler with an activated rhodamine 6G top layer,” Appl. Phys. Lett. 37, 129–130 (1980).
[CrossRef]

Herrmann, P. P.

W. Lukosz and P. P. Herrmann, “Amplification by reflection from an active medium,” Opt. Commun. 17, 192–195 (1976).
[CrossRef]

Ippen, E. P.

E. P. Ippen and C. V. Shank, “Evanescent-field-pumped dye laser,” Appl. Phys. Lett. 21, 301–302 (1972).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 17–22.

Koester, C. J.

C. J. Koester, “Laser action by enhanced internal reflection,” J. Quantum Electron. QE-2, 580–584 (1966).
[CrossRef]

Kogan, B. Y.

S. A. Lebedev and B. Y. Kogan, “Light Amplification by internal reflection from an inverted medium,” Opt. Spectrosc. 48, 564–565 (1980).

Kogan, B. Ya.

S. A. Lebedev and B. Ya. Kogan, “Mechanism of anomalous light reflection from an inverted medium,” Opt. Spectrosc. 48, 647–649 (1980).

S. A. Lebedev, V. M. Volkov, and B. Ya. Kogan, “Value of the gain for light internally reflected from a medium with inverted population,” Opt. Spectrosc. 35, 565–566 (1973).

B. Ya. Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100–101 (1972).

Kolokolov, A. A.

A. A. Kolokolov, “Structure of the lateral wave in the reflection of a beam from an active medium,” Opt. Spectrosc. 44, 568–571 (1978).

A. A. Kolokolov, “Reflection of plane waves from an amplifying medium,” JETP Lett. 21, 312–313 (1975).

Lebedev, S. A.

S. A. Lebedev and B. Y. Kogan, “Light Amplification by internal reflection from an inverted medium,” Opt. Spectrosc. 48, 564–565 (1980).

S. A. Lebedev and B. Ya. Kogan, “Mechanism of anomalous light reflection from an inverted medium,” Opt. Spectrosc. 48, 647–649 (1980).

S. A. Lebedev, V. M. Volkov, and B. Ya. Kogan, “Value of the gain for light internally reflected from a medium with inverted population,” Opt. Spectrosc. 35, 565–566 (1973).

B. Ya. Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100–101 (1972).

Leshchenko, V. G.

B. B. Boiko, V. G. Leshchenko, and N. S. Petrov, “Behavior of heterogeneous electromagnetic waves on the boundary between absorbing (amplifying) and transparent isotropic media,” Zh. Prikl. Spektrosk. 19, 669–674 (1972).

Luk’yanov, Yu. N.

Yu. N. Luk’yanov and V. G. Pan’kin, “Light reflection from an amplifying medium,” Rad. Eng. Electron. Phys. 24, 21–25 (1979).

Lukosz, W.

W. Lukosz and P. P. Herrmann, “Amplification by reflection from an active medium,” Opt. Commun. 17, 192–195 (1976).
[CrossRef]

Olefit, G. I.

B. B. Boiko, I. Z. Dzhilavdari, G. I. Olefit, and N. S. Petrov, “Reflection of light by a plane-parallel transparent layer in contact with an inverse medium,” Zh. Prikl. Spektrosk. 26, 747–750 (1977).

Pan’kin, V. G.

Yu. N. Luk’yanov and V. G. Pan’kin, “Light reflection from an amplifying medium,” Rad. Eng. Electron. Phys. 24, 21–25 (1979).

Petrov, N. S.

B. B. Boiko, I. Z. Dzhilavdari, G. I. Olefit, and N. S. Petrov, “Reflection of light by a plane-parallel transparent layer in contact with an inverse medium,” Zh. Prikl. Spektrosk. 26, 747–750 (1977).

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from an exponentially nonuniform amplifying medium in the case of parallel polarization,” Zh. Prikl. Spektrosk. 24, 1038–1043 (1976).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Amplification by reflection from a medium with population inversion,” Zh. Prikl. Spektrosk. 25, 148–150 (1976).

B. B. Boiko, I. Z. Dzhilavdari, and N. S. Petrov, “Reflection of light on the boundary of an exponentially inhomogeneous amplifying medium (parallel polarization),” Zh. Prikl. Spektrosk. 22, 545–547 (1975).

N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from a semi-infinite exponentially inhomogeneous amplifying medium,” Zh. Prikl. Spectrosk. 23, 705–709 (1975).

B. B. Boiko, N. S. Petrov, and I. Z. Dzhilavdari, “Reflection of electromagnetic waves from interface with amplifying medium,” Zh. Prikl. Spektrosk. 18, 727–729 (1973).

B. B. Boiko, V. G. Leshchenko, and N. S. Petrov, “Behavior of heterogeneous electromagnetic waves on the boundary between absorbing (amplifying) and transparent isotropic media,” Zh. Prikl. Spektrosk. 19, 669–674 (1972).

Romanov, G. N.

G. N. Romanov and S. S. Shakhidzhanov, “Amplification of electromagnetic field in total internal reflection from a region of inverted population,” JETP Lett. 16, 209–211 (1972).

Saito, T.

K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Thin-film waveguide evanescent dye laser and its gain measurement,” J. Appl. Phys. 51, 3090–3092 (1980).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Amplified oscillation in a slab-type optical directional coupler with an activated rhodamine 6G top layer,” Appl. Phys. Lett. 37, 129–130 (1980).
[CrossRef]

Sasaki, K.

K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Thin-film waveguide evanescent dye laser and its gain measurement,” J. Appl. Phys. 51, 3090–3092 (1980).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Amplified oscillation in a slab-type optical directional coupler with an activated rhodamine 6G top layer,” Appl. Phys. Lett. 37, 129–130 (1980).
[CrossRef]

Serizawa, M.

K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
[CrossRef]

Shakhidzhanov, S. S.

G. N. Romanov and S. S. Shakhidzhanov, “Amplification of electromagnetic field in total internal reflection from a region of inverted population,” JETP Lett. 16, 209–211 (1972).

Shank, C. V.

E. P. Ippen and C. V. Shank, “Evanescent-field-pumped dye laser,” Appl. Phys. Lett. 21, 301–302 (1972).
[CrossRef]

Silverman, M. P.

R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an exponential amplifying region,” Opt. Lett. 8, 142–144 (1983).
[CrossRef] [PubMed]

M. P. Silverman and R. F. Cybulski, “Light amplification by reflection from an inverted medium,” Bull. Am. Phys. Soc. 28, 852 (1983).

R. F. Cybulski and M. P. Silverman, “Reflectance from an exponentially nonuniform gain region,” J. Opt. Soc. Am. 72, 1735 (1982).

R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an inverted medium,” J. Opt. Soc. Am. 71, 1641 (1981).

Strome, F. C.

Tuccio, S. A.

Volkov, V. M.

S. A. Lebedev, V. M. Volkov, and B. Ya. Kogan, “Value of the gain for light internally reflected from a medium with inverted population,” Opt. Spectrosc. 35, 565–566 (1973).

B. Ya. Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett. 16, 100–101 (1972).

Appl. Opt. (1)

Appl. Phys. Lett. (3)

E. P. Ippen and C. V. Shank, “Evanescent-field-pumped dye laser,” Appl. Phys. Lett. 21, 301–302 (1972).
[CrossRef]

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Amplified oscillation in a slab-type optical directional coupler with an activated rhodamine 6G top layer,” Appl. Phys. Lett. 37, 129–130 (1980).
[CrossRef]

K. Sasaki, T. Saito, M. Serizawa, S. Furukawa, and O. Hamano, “Thin-film waveguiding evanescent dye laser with a corner reflecting resonator,” Appl. Phys. Lett. 39, 300–301 (1981).
[CrossRef]

Bull. Am. Phys. Soc. (1)

M. P. Silverman and R. F. Cybulski, “Light amplification by reflection from an inverted medium,” Bull. Am. Phys. Soc. 28, 852 (1983).

J. Appl. Phys. (1)

K. Sasaki, T. Fukao, T. Saito, and O. Hamano, “Thin-film waveguide evanescent dye laser and its gain measurement,” J. Appl. Phys. 51, 3090–3092 (1980).
[CrossRef]

J. Opt. Soc. Am. (4)

R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an inverted medium,” J. Opt. Soc. Am. 71, 1641 (1981).

R. F. Cybulski and M. P. Silverman, “Reflectance from an exponentially nonuniform gain region,” J. Opt. Soc. Am. 72, 1735 (1982).

P. R. Callary and C. K. Carniglia, “Internal reflection from an amplifying layer,” J. Opt. Soc. Am. 66, 775–779 (1976).
[CrossRef]

R. F. Cybulski and C. K. Carniglia, “Internal reflection from an exponentially amplifying region,” J. Opt. Soc. Am. 67, 1620–1627 (1977).
[CrossRef]

J. Quantum Electron. (1)

C. J. Koester, “Laser action by enhanced internal reflection,” J. Quantum Electron. QE-2, 580–584 (1966).
[CrossRef]

JETP Lett. (3)

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G. N. Romanov and S. S. Shakhidzhanov, “Amplification of electromagnetic field in total internal reflection from a region of inverted population,” JETP Lett. 16, 209–211 (1972).

A. A. Kolokolov, “Reflection of plane waves from an amplifying medium,” JETP Lett. 21, 312–313 (1975).

Opt. Commun. (1)

W. Lukosz and P. P. Herrmann, “Amplification by reflection from an active medium,” Opt. Commun. 17, 192–195 (1976).
[CrossRef]

Opt. Lett. (1)

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S. A. Lebedev and B. Y. Kogan, “Light Amplification by internal reflection from an inverted medium,” Opt. Spectrosc. 48, 564–565 (1980).

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Yu. N. Luk’yanov and V. G. Pan’kin, “Light reflection from an amplifying medium,” Rad. Eng. Electron. Phys. 24, 21–25 (1979).

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N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from a semi-infinite exponentially inhomogeneous amplifying medium,” Zh. Prikl. Spectrosk. 23, 705–709 (1975).

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N. S. Petrov, B. B. Boiko, and I. Z. Dzhilavdari, “Reflection of light from an exponentially nonuniform amplifying medium in the case of parallel polarization,” Zh. Prikl. Spektrosk. 24, 1038–1043 (1976).

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Figures (6)

Fig. 1
Fig. 1

Geometric configuration of the system.

Fig. 2
Fig. 2

Theoretical reflectance of s- and p-polarized waves as a function of incident angle for the parameters θc, = 89°, γ = 2.6 × 10−5, and d = 96λ.

Fig. 3
Fig. 3

Theoretical reflectance curve of s- and p-polarized waves in the vicinity of critical angle for the same parameters as in Fig. 2. Heavy line represents exponential-gain model; broken line with discontinuity at θc represents uniform-gain model.

Fig. 4
Fig. 4

Development of amplification profile in the theoretical reflectance curve as a function of gain coefficient: 1, γ = 0.0; 2, γ = 1.0 × 10−6; 3, γ = 2.0 × 10−6; and 4, γ= 3.0 × 10−6. In all cases θc = 89° and d = 96λ.

Fig. 5
Fig. 5

Development of amplification profile in the theoretical reflectance curve as a function of characteristic thickness d: 1, d = 0; 2, d = 5λ; 3, d = 10λ; and 4, d = 15λ. In all cases θc = 89° and γ = 2.6 × 10−5.

Fig. 6
Fig. 6

Far-field transmittance T as a function of incident angle for parameters θc = 89°, γ = 2.6 × 10−5, and d = 96λ. Theoretical reflectance R is shown for comparison. In the vicinity of critical angle, R and T are both greater than one. Beyond θc, R falls toward unity at grazing incidence, but T is strictly zero.

Equations (41)

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n = 1 - i γ exp ( - z / d )
I ( z ) = I 0 exp ( - σ a p N z )
d = ( σ a p N ) - 1
sin θ c = 1 / n .
sin ϕ ( z ) = n sin θ / [ 1 - i γ exp ( - z / d ) ] .
sin ψ = n sin θ ,
( z ) = 1 - 2 i γ exp ( - z / d ) .
E s = j ^ F ( z ) exp [ i ( k x x - ω t ) ] ,
k x = k n sin θ
k = 2 π / λ
ξ = α exp ( - z / 2 d ) ,
α = 2 d k ( - 2 i γ ) 1 / 2 ,
d 2 F d ξ 2 + 1 ξ d F d ξ + [ ( 2 d k cos ψ ) 2 ξ 2 + 1 ] F = 0
F ( ξ ) = A J ν ( ξ ) ,
ν = - i 2 d k cos ψ
H p = j ^ G ( z ) exp [ i ( k x x - ω t ) ] ,
d 2 G d ξ 2 + 1 ξ d G d ξ - 2 [ 1 - 1 ( ξ ) ] d G d ξ + [ 2 k d ( cos ψ ) 2 ξ 2 + 1 ] G = 0.
d 2 G d ξ 2 + [ 1 ξ - 1 2 d 2 k 2 ξ ] d G d ξ + [ ( 2 d k cos ψ ) 2 ξ 2 + 1 ] G = 0.
G ( ξ ) = j = 0 a j ξ ν + 2 j ,
a j + 1 = a j ( ν + 2 j ) / ( 2 d 2 k 2 ) - 1 ( ν + 2 j + 2 ) 2 - ν 2 .
ξ ν [ exp ( - z / 2 d ) ] ν = exp ( i k cos ψ z ) .
r s = E s E s | z = 0 = n cos θ - i ( α / 2 d k ) J ν ( α ) / J ν ( α ) n cos θ + i ( α / 2 d k ) J ν ( α ) / J ν ( α ) ,
r p = H p H p | z = 0 = cos θ / n - ( i α / [ 2 d k ( 1 - 2 i γ ) ] ) G ( α ) / G ( α ) cos θ / n + ( i α / [ 2 d k ( 1 - 2 i γ ) ] ) G ( α ) / G ( α ) ,
r s = n cos θ - cos ψ n cos θ + cos ψ ,
r p = cos θ / n - cos ψ cos θ / n + cos ψ
d S e / d z = G S e .
G = 2 k γ ,
G = σ e n * - σ a n ,
n + n * = N = constant ,
d n * / d t = σ a p n S p / h ν p - n * / τ s - σ e n * S t / h ν t + σ a n S t / h ν t = 0 ,
γ = ( σ e σ a p S p / h ν p - σ a / τ s ) N 2 k [ σ a p S p / h ν p + ( σ e + σ a ) S t / h ν t + 1 / τ s ] .
γ = σ e σ a p ( S p / h ν p ) N 2 k [ σ a p S p / h ν p + 1 / τ s ] .
h ν p ^ / ( σ a p S p ) τ s
γ = σ e σ a p ( S p / h ν p ) N τ s ( 2 k ) - 1
γ = σ e N ( 2 k ) - 1
S t = c 8 π Re [ E t × H t * ] ,
S t ( ξ ) = c 8 π A J ν ( ξ ) 2 Re [ î n sin θ - k ^ ( i ξ * / 2 d k ) ( J ν ( ξ ) / J ν ( ξ ) ) * ] ,
S t f = c 8 π A | ( α / 2 ) ν Γ ( ν + 1 ) | 2 ( î sin ψ + k ^ cos ψ ) ,
A = 2 n cos θ E i ( n cos θ + cos ψ ) J ν ( α ) - i ( α / 2 d k ) J ν + 1 ( α ) ,
T f = S t f · k ^ S i · k ^ .
T f = | 2 n cos θ ( α / 2 ) ν / Γ ( ν + 1 ) ( n cos θ + cos ψ ) J ν ( α ) - i ( α / 2 d k ) J ν + 1 ( α ) | 2 cos ψ cos θ .