SOME CHARACTERISTICS OF REFLECTION FROM A SEMI-INFINITE INVERSE MEDIUM V. V. Filippov and V. G. Kukushkin OF LIGHT UDC 535.3 It is known that under specific conditions it is possible to obtain amplification of a wave reflected from an inverse medium [1]. The very first attempts to explain this phenomenon theoretically [2] led to the problem of choosing one of two possible solutions of the equation of normals for a wave refracted into an inverse me- dium. If we retain the condition of continuity of the solution with a change in the angle of incidence from nor- mal to sliding for the interface of two semi-infinitemedia, it is impossible to obtain amplification of the re- flected wave because in this case the energy coefficient of reflection R always remains less than unity. We can require continuity of the transition of the chosen solution to the interface of two transmissive media when the amplification factor tends to zero [3]. Then, for angles of incidence a which, after the mentioned transi- tion, correspond to angles less than the interfacial angle of total reflection a l, it is necessary to choose a solu- tion with a phase normal which is directed from the interface and with an amplitude increasing with depth. For a > al, the continuity of the mentioned transition can be ensured by choosing an alternative solution, i.e., with a wave normal which is directed toward the interface and with an amplitude increasing in the direction toward the interface. In addition, R > 1, and at the point a = a', the graph of the relation of R to a has a dis- continuity. We should note that the problem of choosing the solutions also remains in the case of laminar- inhomogeneous inverse media, i.e., under conditions closer to experimental ones. As yet, only the behavior of the coefficient of reflection from an inverse medium has been investigated experimentally. It is of definite interest to know other parameters which can be measured experimentally, even more so since they make it possible to obtain additional information, e.g., on the nature of inhomo- geneity of the inverse medium. Such parameters are the phase jump appearing during reflection from an inverse medium and the longitudinal displacement of the reflected beam (the Goos-Hencken effect). Let a homogeneous wave be incident from a transmissive medium with dielectric constant el onto an inverse medium at which the dielectric constant is e 2 = e-it, T < 0. The ratio of the p and s components of the electric-field vector of the reflected wave can be represented in the form [4] E o e~sin~cz--(rl~ 2 q- rl;2)n~q - 2ieirh~l~sin2cx E p o (1) E s let sin z zr -r ~ldl212 E o where r h = ~et eos a and 72 = 7/~-ir are components of the vectors of refraction of the incident and reflected waves along the z axis, which is directed into the inverse medium. The expressions for ~ and ~ are given in [31. The quantities EP and E s are the p and s components of the electric-field vector of the incident wave. As was noted, when a < ~i (sindi = V~e/e'-~, ei>e) ~l~>0, and r < 0, while when a > a i 0~ < 0 and ~?~ > 0. Let us consider the relation of the phase shift 6 = 5p-6 s between the p and s components in the reflected wave to the angle of incidence. From (1), it is easy to obtain tg6 = -4-~ei [((e--eisin2 r162 - z~)l/2-- e-q - eisinZczl}W2sinZtzcos a. (2) el sin~r -- [(e -- el sinz a) 2 + x21112 cos2 a where the sign+ (-) is chosen for a > a i (a < at). For normal incidence, 5 = 0. When a tends to ai 6 tends to the value 6 = arctg ~-2-~-ii ~ (e-~-~- T . (3) When a > a i, the value of 5 changes sign jumpwise, and when a ~ ~/2, 6 --* -Tr (see Fig. 1). Such a change in 6 should lead to a change in the direction of rotation of the field vectors in the reflected wave to the opposite direction during transition of the angle of incidence through the value of a i. Thus, the nature of the choice of Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 31, No. 5, pp. 930-932, November, 1979. Original article submitted September 15, 1978. 0021-9037/79/3105-1451507.50 9 1980 Plenum Publishing Corporation 1451