Download Advances in Chemical Physics, Vol.119, Part 2. Modern by Myron W. Evans, Ilya Prigogine, Stuart A. Rice PDF

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)

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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 kzފ 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 ŠÀ1 q 1 qf ½ð1 À r2 DÞGŠ 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 aފÀ1 r2 DG ¼ ÀikAj ð95Þ ð94Þ and Bj ¼ ÀiG0 ðsin aÞ½ycðcos aÞ2 ŠÀ1 ¼ ikAr À 1 qAz r0 qr q ½ð1 À r2 DÞGŠ qr ð96Þ À1 Bz ¼ ÀiG0 ½ycðcos aފ   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.

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