# Elements of Quantum Optics by Professor Dr. Dr. Rer. Nat. Habil. Pierre Meystre, Professor

By Professor Dr. Dr. Rer. Nat. Habil. Pierre Meystre, Professor Murray Sargent III Ph.D. (auth.)

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1-9, but a small time after injection into the wiggler. We see a bunching in position (horizontal axis) and spread in energy (vertical axis). 34 CLASSICAL ELECTROMAGNETIC FIELDS Chap. 1 Electrons with phases between -w and 0 accelerate, while others decelerate, so that after a small time, the phase-space distribution looks like that in Fig. 1-10. Three important things have occurred. First, the electrons now have different energies, more or less accelerated or decelerated, depending on their initial phases.

19) and neglecting combination tones involving x 0 and x 3 in the pump-mode polarizations (Prob. c. (20) Combining the various terms, we find that the third-order polarization components are given by 91~3 ) = ~Neb[lx~1 ll2 + lx~1 li2Jx&1 l + ~Nebx~llx~ll[x~llJ* ei(Kl+Kz-K3-Kolz + ~Neb[x~l)]z [x~l)]* ei(2Kl-Kz-Ko)z (2la) (2Ib) so CLASSICAL NONLINEAR OPTICS Chap. 2 (2Ic) go~s) = ~Neb[lx~l)l2 + lx&l)l2]x~l) + ~Nebx~l)X~l)[xtl)j* ei(Kl+K2-Ko-K3)z + iNeb[x~l)]z [xP>J*ei(2K2-Kl-K3). (2Id) The polarization components 9'&3 > and ga~s) are solely due to the existence of index gratings, which are also resronsible for the factors of 2 in the cross coupling terms for 91~3) and 9'&3 • This asymmetry is sometimes called nonlinear nonreciprocity and was discovered in quantum optics by Chiao, Kelley, and Garrnire (1966).

This is another good reference on classical electromagnetic theory. Problems 1-1. Derive the wave equation from microscopic Maxwell's equations that include a charge density and current. For this, Eqs. (2) and (4) become V·E VxB = p_ f0 ' = l'ol + 1 c2 aE , at respectively. + at is solved by p = -V·P + assume M = Jfree = Pfree Pfree• J V·J = 8P/8t = 0 + VxM + Jfree· For our purposes, = 0, and neglect a term proportional to V p. 1-2. Show using the divergence theorem that fdV(V·P)r = f(P·du)r- fPdV.