By Myron W Evans

The recent version will give you the sole entire source on hand for non-linear optics, together with designated descriptions of the advances over the past decade from world-renowned experts.

summary: the hot variation will give you the sole complete source to be had for non-linear optics, together with special descriptions of the advances during the last decade from world-renowned specialists

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In addition, Eqs. (118)–(124) show that ð" r; Er ; Bj Þ are of zero order in the smallness parameter e of the definition (98), ðEj ; Br ; Bz Þ are of first order in e, and Ez of second order. Because of the symmetry conditions integration of the local forces (160) results in vanishing electric and magnetic volume forces Fe and Fm as given by Eqs. (13). Of the Poynting vector S and the electromagnetic momentum vector g 42 b. lehnert of the propagating wavepacket, only the component due to Er Br À Er Bz is of interest in forming the integral of expression (12), that is, in the z direction of propagation.

As expected, the intrinsic current system and magnetic field are purely poloidal in the rest frame, whereas the magnetic field in the laboratory system is helical. The helicity of the photon field has also been considered in an analysis by Evans [28] and Dvoeglazov [62]. In this connection it should finally be mentioned that Comay [63] and Hunter [64] have discussed the Bð3Þ field concept by Evans and Vigier on the basis of conventional electromagnetic theory where the 4-current of Eq. (22) vanishes in the vacuum.

To investigate the contributions to the volume integrals of Eqs. (12) and (13), we can thus restrict ourselves in studying the symmetry properties with respect to the axial direction, that is, to the center "z ¼ 0 of the propagating wavepacket. With the chosen symmetric form (140) for G, it is then seen from Eqs. (118)– (124) that ð" r; Er ; Bj ; Bz Þ become antisymmetric with respect to "z, whereas ðEj ; Ez ; Br Þ become symmetric. In addition, Eqs. (118)–(124) show that ð" r; Er ; Bj Þ are of zero order in the smallness parameter e of the definition (98), ðEj ; Br ; Bz Þ are of first order in e, and Ez of second order.