Total internal reflection and evanescent gain

doi:10.1364/OE.19.021404

Total internal reflection and evanescent gain

Jon Olav Grepstad and Johannes Skaar »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 21404-21418 (2011)
http://dx.doi.org/10.1364/OE.19.021404

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Abstract

Total internal reflection occurs for large angles of incidence, when light is incident from a high-refractive-index medium onto a low-index medium. We consider the situation where the low-index medium is active. By invoking causality in its most fundamental form, we argue that evanescent gain may or may not appear, depending on the analytic and global properties of the permittivity function. For conventional, weak gain media, we show that there is an absolute instability associated with infinite transverse dimensions. This instability can be ignored or eliminated in certain cases, for which evanescent gain prevails.

OCIS Codes
(140.3380) Lasers and laser optics : Laser materials
(250.4480) Optoelectronics : Optical amplifiers
(260.2110) Physical optics : Electromagnetic optics
(160.3918) Materials : Metamaterials

ToC Category:
Physical Optics

History
Original Manuscript: July 1, 2011
Revised Manuscript: August 22, 2011
Manuscript Accepted: September 25, 2011
Published: October 14, 2011

Citation
Jon Olav Grepstad and Johannes Skaar, "Total internal reflection and evanescent gain," Opt. Express 19, 21404-21418 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21404

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References

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).
P. R. Callary and C. K. Carniglia, “Internal-reflection from an amplifying layer,” J. Opt. Soc. Am.66, 775–779 (1976). [CrossRef]
W. Lukosz and P. P. Herrmann, “Amplification by reflection from an active medium,” Opt. Commun.17, 192–195 (1976). [CrossRef]
R. F. Cybulski and C. K. Carniglia, “Internal-reflection from an exponential amplifying region,” J. Opt. Soc. Am.67, 1620–1627 (1977). [CrossRef]
R. F. Cybulski and M. P. Silverman, “Investigation of light amplification by enhanced internal-reflection .1. theoretical reflectance and transmittance of an exponentially nonuniform gain region,” J. Opt. Soc. Am.73, 1732–1738 (1983). [CrossRef]
A. A. Kolokolov, “Determination of the reflection coefficient of a plane monochromatic wave,” J. Commun. Technol. Electron.43, 837–845 (1998).
A. A. Kolokolov, “Fresnel formulas and the principle of causality,” Phys. Usp.42, 931–940 (1999). [CrossRef]
J. Fan, A. Dogariu, and L. J. Wang, “Amplified total internal reflection,” Opt. Express11, 299–308 (2003). [CrossRef] [PubMed]
K. J. Willis, J. B. Schneider, and S. C. Hagness, “Amplified total internal reflection: theory, analysis, and demonstration of existence via FDTD,” Opt. Express16, 1903–1913 (2008). [CrossRef] [PubMed]
A. Siegman, “Fresnel reflection, Lenserf reflection, and evanescent gain,” Opt. Photon. News21, 38–45 (2010). [CrossRef]
C. J. Koester, “Laser action by enhanced total internal reflection,” IEEE J. Quantum Electron.2, 580–584 (1966). [CrossRef]
B. Y. Kogan, V. M. Volkov, and S. A. Lebedev, “Superluminescence and generation of stimulated radiation under internal-reflection conditions,” JETP Lett.16, 100–101 (1972).
S. A. Lebedev, V. M. Volkov, and B. Y. Kogan, “Value of the gain for light internally reflected from a medium with inverted population,” Opt. Spectrosc.35, 565–566 (1973).
M. P. Silverman and J. R. F. Cybulski, “Investigation of light amplification by enhanced internal reflection. Part II. Experimental determination of the single-pass reflectance of an optically pumped gain region,” J. Opt. Soc. Am.73, 1739–1743 (1983). [CrossRef]
B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E78, 036603 (2008). [CrossRef]
J. Skaar, “Fresnel equations and the refractive index of active media,” Phys. Rev. E73, 026605 (2006). [CrossRef]
A. Lakhtakia, J. B. Geddes, and T. G. Mackay, “When does the choice of the refractive index of a linear, homogeneous, isotropic, active, dielectric medium matter?” Opt. Express15, 17709–17714 (2007). [CrossRef] [PubMed]
L. V. Ahlfors, Complex Analysis (McGraw-Hill International Editions, 1979).
P. A. Sturrock, “Kinematics of growing waves,” Phys. Rev.112, 1488–1503 (1958). [CrossRef]
R. J. Briggs, Electron-Stream Interactions with Plasmas (MIT Press, 1964).

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[1] 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).

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

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

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

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

[6] R. F. Cybulski and M. P. Silverman, “Investigation of light amplification by enhanced internal-reflection .1. theoretical reflectance and transmittance of an exponentially nonuniform gain region,” J. Opt. Soc. Am.73, 1732–1738 (1983). [CrossRef]

[7] A. A. Kolokolov, “Determination of the reflection coefficient of a plane monochromatic wave,” J. Commun. Technol. Electron.43, 837–845 (1998).

[8] A. A. Kolokolov, “Fresnel formulas and the principle of causality,” Phys. Usp.42, 931–940 (1999). [CrossRef]

[9] J. Fan, A. Dogariu, and L. J. Wang, “Amplified total internal reflection,” Opt. Express11, 299–308 (2003). [CrossRef] [PubMed]

[10] K. J. Willis, J. B. Schneider, and S. C. Hagness, “Amplified total internal reflection: theory, analysis, and demonstration of existence via FDTD,” Opt. Express16, 1903–1913 (2008). [CrossRef] [PubMed]

[11] A. Siegman, “Fresnel reflection, Lenserf reflection, and evanescent gain,” Opt. Photon. News21, 38–45 (2010). [CrossRef]

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

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

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

[15] M. P. Silverman and J. R. F. Cybulski, “Investigation of light amplification by enhanced internal reflection. Part II. Experimental determination of the single-pass reflectance of an optically pumped gain region,” J. Opt. Soc. Am.73, 1739–1743 (1983). [CrossRef]

[16] B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E78, 036603 (2008). [CrossRef]

[17] J. Skaar, “Fresnel equations and the refractive index of active media,” Phys. Rev. E73, 026605 (2006). [CrossRef]

[18] A. Lakhtakia, J. B. Geddes, and T. G. Mackay, “When does the choice of the refractive index of a linear, homogeneous, isotropic, active, dielectric medium matter?” Opt. Express15, 17709–17714 (2007). [CrossRef] [PubMed]

[19] L. V. Ahlfors, Complex Analysis (McGraw-Hill International Editions, 1979).

[20] P. A. Sturrock, “Kinematics of growing waves,” Phys. Rev.112, 1488–1503 (1958). [CrossRef]

[21] R. J. Briggs, Electron-Stream Interactions with Plasmas (MIT Press, 1964).

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Total internal reflection and evanescent gain