The total internal reflectance of a homogeneous amplifying medium in contact with a thin silver film which is evaporated on a high-index prism is determined theoretically with the help of the Fresnel formulas. At the angle of incidence for surface-plasmon excitation the reflectance is reasonantly enhanced when the gain of the amplifying medium exceeds a value determined by the absorption of the metal film. For any value of gain above threshold there exists a thickness of the silver film for which the reflectance has a singular point. A device utilizing this resonance would be possible near 1 μ where the absorption of the silver is at a minimun and high-gain dyes are available.

Enhanced total reflection with surface plasmons

The explanation of wave behavior upon total internal reflection from a gainy medium has defied consensus for 40 years. We examine this question using both the finite-difference time-domain (FDTD) method and theoretical analyses. FDTD simulations of a localized wave impinging on a gainy half space are based directly on Maxwell's equations and make no underlying assumptions. They reveal that amplification occurs upon total internal reflection from a gainy medium; conversely, amplification does not occur for incidence below the critical angle. Excellent agreement is obtained between the FDTD results and an analytical formulation that employs a new branch cut in the complex "propagation-constant" plane.

https://www.eecs.wsu.edu/~schneidj/journal-papers/gainy.pdf

Amplified total internal reflection: theory, analysis, and demonstration of existence via FDTD

The reflectance from an amplifying region in which the gain decreases exponentially with distance from the surface is calculated as a function of incident angle. The results are similar in some respects to the reflectance from a uniform amplifying layer reported previously. In particular, a singular point occurs in the reflectance for certain values of the thickness of the amplifying region. However, the results for the exponential case do not explain the previously reported observation of large reflectance from a pumped laser dye. An asymptotic form of the reflectance for a thick amplifying region is presented. The results for asymptotic case are compared with various other theories of reflection from an amplifying region.

Internal reflection from an exponential amplifying region

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.

Investigation of light amplification by enhanced internal reflection. Part I. Theoretical reflectance and transmittance of an exponentially nonuniform gain region

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.

Total internal reflection and evanescent gain

The reflectance of a homogeneous amplifying layer between two transparent regions is determined theoretically with the help of the Fresnel formulas. The transparent region containing the incident beam has a higher refractive index, corresponding to an internal reflection configuration. In the limit of infinite layer thickness, the reflectance is a continuous monotonic function of incident angle, greater than unity for all angles. For certain finite values of layer thickness, the reflectance has a singular point. The results explain the reported observation of a reflectance of 1000 from an excited laser dye in contact with a quartz prism.

P. R. Callary

Papers

Internal reflection from an amplifying layer