By Myron W. Evans, Ilya Prigogine, Stuart A. Rice
The recent version will give you the sole complete source to be had for non-linear optics, together with specific descriptions of the advances during the last decade from world-renowned specialists.
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Additional info for Advances in Chemical Physics, Vol.119, Part 2. Modern Nonlinear Optics (Wiley 2001)
Lehnert the same equations yields q2 q 2 2 2 Àc r Eþ c rþC ðdiv EÞ ¼ 0 qt2 qt ð45Þ for the electric field. The magnetic field can be determined from the electric field by means of Eq. (2). A divergence operation on Eq. (1) further gives q þ C Á r ðdiv EÞ ¼ 0 qt ð46Þ In some cases this equation will become useful for the analysis, but it does not introduce more information than that already contained in Eq. (45). As will be shown later, Eq. (46) leads to the same dispersion relation for div E 6¼ 0 as Eq.
The possibility of matching a transmitted EM wave to the incident and reflected waves is first investigated. This requires the phases (58) to be matched at every point of the interface x ¼ 0 to the phase (59). This condition becomes r t ¼ nj > 0 st ¼ " dnj > 0 nj ¼ nðsin jÞ ð60Þ where total reflection corresponds to nj > 1. For the transmitted EM wave in vacuo, combination of Eqs. (45) and (59) results in À Á ð61Þ 1 ¼ p2t þ rt2 À q2t þ s2t qt rt ¼À ð62Þ st pt The transmitted wave should further travel in the positive x direction, into region II, and this also applies in the limit where the angle of its wave normal 26 b.
Equations (62) and (60) then yield the condition qt ¼ À d n2j " pt <0 ð63Þ For total reflection, however, there should be no flow of energy into medium II, and the transmitted wave then must represent an energy flow directed parallel to the interface, thereby limited in amplitude to a narrow layer at the vacuum side of the interface . This excludes the negative value of qt given by Eq. (63) and the form (59). It does therefore become impossible to match the inhomogeneous (damped) EM waves in region I by a homogeneous (undamped) EM wave in region II.