By Allen H. Cherin
This ebook is particularly invaluable for an advent to makes use of and purposes of fiber optics
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Additional resources for Introduction to Optical Fibers
34 2. Interaction of "Matter and Electromagnetic Fields response functions under various circumstances is one of the principal objectivcs of this book and will be dealt with in various chapters. In the following we first will recall some basic results of time-dependent perturbation theory. 145) where U obeys the equation . ata U(t, to) = [H + Hext(t)]U(t, to) . e. H- ext -- eiH(t-to)/nHext (t)e-iH(t-to)/n . 149) = 1, dt' fIext(t')S(t', t o) . 150) can be obtained by iteration. The general treatment will be discussed in Chap.
156). 6. 133) to relate the longitudinal contribution to the current-current correlation function to the density-density correlation function. 155) is canceled exactly. 7. 85) of the vector potential, to derive a representation of the photon Green's function in terms of the photon annilation and creation operators a q ).. and a~)... 8. 225) 3. One-Particle Properties Naively, one might expect that at least approximate solutions of the manyparticle problem in the form of the eigenvalues and eigenfunctions of the Hamiltonian, as introduced in the last chapter, would be an unambigous condition for proceeding further.
Q aeeount for the two orthogonal transverse modes (>.. = 1,2). q)j = Oij ).. 74) -2 ' q where the right-hand side is just the Fourier transform of the transverse 0 funetion. (q) beeomes more transparent if we eonsider their equation of motion. (q, t) is a solution of q2 u).. ( q,t ) 1 a2 u).. qJt r,t e . 3 . 76) together with the dispersion relation Wq = Iqlco . (q, t) - ul( -q, t)) e iqr . ,Oqq'. 82) whieh obviously obey the usual boson eommutation relations of ereation and annihilation operators, weH known from the treatment of harmonie oseillators: 22 2.