By Myron W. Evans, Ilya Prigogine, Stuart A. Rice
The recent version will give you the sole complete source on hand for non-linear optics, together with exact 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)
77) and (78), which yield o ¼ kcðsin aÞ v ¼ cðsin aÞ ð88Þ where the phase and group velocities o=k and qo=qk are both equal to v. Equation (81) then takes the form ! q2 1 q 1 q2 1 q 2 2 2 2 E Ez þ À k ðcos aÞ ¼ ÀðtgaÞ þ ðcos aÞ À À k j qr 2 r qr r 2 qr 2 r qr ð89Þ We introduce the function G0 Á G ¼ Ez þ ðcot aÞEj G ¼ RðrÞ exp ½iðÀot þ kzÞ ð90Þ 32 b. lehnert where G0 is an amplitude factor and RðrÞ is a dimensionless function of r. A and Appendix B. Using Eqs. (89), (90) and (78), the electric and magnetic field components become Er ¼ ÀiG0 ½yðcos aÞ2 À1 q 1 qf ½ð1 À r2 DÞG ¼ À þ ioAr qr r0 qr ð92Þ Ej ¼ G0 ðtgaÞr2 DG ¼ ioAj À Á Ez ¼ G0 1 À r2 D G ¼ Àikf þ ioAz ð93Þ Br ¼ ÀG0 ½cðcos aÞÀ1 r2 DG ¼ ÀikAj ð95Þ ð94Þ and Bj ¼ ÀiG0 ðsin aÞ½ycðcos aÞ2 À1 ¼ ikAr À 1 qAz r0 qr q ½ð1 À r2 DÞG qr ð96Þ À1 Bz ¼ ÀiG0 ½ycðcos aÞ q 1 1 1 q þ ðr2 DGÞ ¼ ðrAj Þ qr r r0 r qr ð97Þ Consequently, the function G can be considered as a generating function from which the entire electromagnetic field of an elementary axisymmetric EMS mode can be determined, in analogy with the generating function (37) of a steady equilibrium state.
2. Here we also notice that, for a photon with nonzero rest mass, the intrinsic properties of the wavepacket are expected to be clearly visible in the rest frame K 0 . Among other things, this applies to the components (134)–(137), which then represent steady electric and magnetic fields being entirely localized to the r 0 z0 plane, thereby also having strong components in the axial direction of propagation. This property clearly supports the photon model with a static magnetic field part Bð3Þ as deduced by Evans and Vigier [5–7,45], and where the axial electric and magnetic field components of Eqs.
For large r, both I1 and I0 tend to infinity, whereas K1 and K0 tend to zero. Consequently, a nonzero form of the solutions (83) and (84) becomes infinite either at r ¼ 0 or at large values of r. As a next step we assume the value " y2 ¼ 0 corresponding to a phase velocity where jo=kj ¼ c. Then Eqs. (74)–(76) reduce to ! 1 ðEr ; Ej Þ ¼ 0 Dr À r2 Dr E z ¼ 0 ð85Þ where Dr ¼ q2 1 q þ qr2 r qr ð86Þ 31 optical effects of an extended electromagnetic theory The solutions then have the form ðEr ; Ej Þ / k1 r þ k2 r Ez / k3 ln r þ k4 ð87Þ where k1 , k2 , k3 , k4 are constants.