Chapter 21 nonlinear optics

... ∇2 E − ∂ 2E = −S, c2 ∂t2 (21. 4-1) 906 CHAPTER 21 NONLINEAR OPTICS where S = −µo ∂ PNL ∂t2 (21. 4-2) is regarded as a radiation source, and PNL = 2dE2 (21. 4-3) is the nonlinear component of the ... exp(j∆kz), dz (21. 4-27a) (21. 4-27b) where ∆k = k3 − 2k1 and g2 = 4ℏω η d2 (21. 4-28) 910 CHAPTER 21 NONLINEAR OPTICS Assuming two collinear waves with perfect phase matching (∆...

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... References 10 5 10 8 13 5 13 7 15 0 15 8 16 1 17 0 18 0 18 5 19 4 2 01 204 207 4 .1 4.2 4.3 4.4 4.5 4.6 4.7 The Intensity-Dependent Refractive Index 207 211 2 21 228 235 240 247 2 51 Descriptions of the Intensity-Dependent ... Stimulated Rayleigh-Wing Scattering Problems References 11 The Electrooptic and Photorefractive Effects 11 .1 11. 2 11 .3 11 .4 11 .5 11 .6 11 .7...

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... u2 dζ 1− u4 u2 1 /2 = ± − u2 2 1− (1 − u2 )2 u2 2 1 /2 (2. 7 .28 ) This result is simplified algebraically to give u2 du2 = ± − u2 u2 − 2 dζ 1 /2 , or du2 2 = 2 − u2 u2 − 2 dζ 1 /2 (2. 7 .29 ) This equation ... represented as |A2 | A2 |A2 | A2 |A2 | A2 i 2 ∗ = A A∗ = |A |2 = |A | = e , A2 2 2 where 2 denotes the phase of A2 We hence find that A3 (z) = i n1 ω n3 ω1 1 /2 A1...

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... represented as ˜ P (r, t) = P3 (r)e−i3ωt + c.c., (3. 2 .35 ) where P3 (r) = 0χ (3) (3 )E1 (3. 2 .36 ) Here χ (3) (3 ) is an abbreviated form of the quantity χ (3) (3 = ω + ω + ω) The nonlinear susceptibility ... ˆ p (3) = ψ (0) μ ψ (3) + ψ (1) μ ψ (2) + ψ (2) μ ψ (1) + ψ (3) μ ψ (0) (3. 2.29) Formulas for ψ (0) , ψ (1) , ψ (2) , ψ (3) , are given by Eqs (3. 2.9), (3. 2.10), (3. 2.16), (3. 2...

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... = (4. 4. 14) and that according to Eq (4. 4.10), the mean polarizability is given by α = α3 + α1 3 (4. 4.15) Using Eq (4. 4.9), we find that the refractive index is given by n2 = + N α3 + α1 (4. 4.16) ... References b 1.8 2. 34 2 .42 3 .47 4. 0 1 .4 3 .4 2 .48 2.7 3.1×10−22 9.8×10−20 2.5×10−21 1 .4 10−18 5.6×10−19 6.2×10−23 2.8×10−18 2.1×10−20 6.2×10−20 2.9×10−16 5.1×10− 14 1.3×10−15 3.3×...

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... S.-W., 2000 Opt Lett 25, 254 Wang, C.C., 1970 Phys Rev B2, 20 45 Wynne, J.J., 1969 Phys Rev 178, 12 95 Nonlinear Optics of Conjugated Polymers Hermann, J.P., Ducuing, J., 1974 J Appl Phys 45, 51 00 ... A312 (5. 5.4) Consequently the nonlinear polarization can be expressed as P= A123 E × F (5. 5 .5) The experimental setup used by Rentzipis et al to study these effects is shown in Fig...

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... six coupled equations [ (6. 6.10), (6. 6.11), (6. 6.12), (6. 6.15), (6. 6.17), (6. 6.18)] for the six quantities p0 , p1 , p−1 , w0 , w1 , w−1 We note that w0 is given by Eq (6. 6.15) in terms of known ... c.c.; (6. 6 .6) hence, E0 and E1 represent the complex amplitudes of the pump and probe waves, respectively 3 16 ♦ Nonlinear Optics in the Two-Level Approximation Equations (6. 6.3) a...

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... the nonlinear polarization is given by pNL = χ (3) |A|2 A (7. 1. 17) Steady-state self-trapping can be described by these equations We consider first the solution of Eqs (7. 1.16) and (7. 1. 17) for ... half-band-gap energy This strategy, however, precludes the use of one-photon-resonant nonlinearities (c) replaced by α = α0 + βI, (7. 3.33) where β is the two-photon absorption coefficient Two...

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... ω and k1x equations (8. 4.17) and (8. 4. 18) can be written as dA1 = iκA2 e−i dx dA2 = iκ ∗ A1 ei dx kx kx (8. 4. 18) k2x ≡ kx , the coupled , (8. 4.19a) , (8. 4.19b) 8. 4 Acoustooptics 419 where we have ... the right-hand side of Eq (8. 4.6) is small, the change in the dielectric tensor ij is given by ( )il = − ij jk −1 j k kl (8. 4 .8) 8. 4 Acoustooptics 417 F IGURE 8. 4.4 Geometry of a...

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... t) + c.c., p2 = −1 ∗ γe ρ0 ρ A1 (9. 3.18) (9. 3. 19) We introduce Eqs (9. 3 .9) into the wave equation (9. 3.16) along with Eqs (9. 3.18) and (9. 3. 19) , make the slowly-varying amplitude approximation, ... Technology, 196 5 Chiao, R.Y., Townes, C.H., Stoicheff, B.P., 196 4 Phys Rev Lett 12, 592 Damzen, M.J., Hutchinson, H., 198 3 IEEE J Quantum Electron QE- 19, Gaeta, A.L., Boyd, R.W., 199...

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... = ωL − ωS (10. 3 .10) We next find the solution to Eq (10. 3.1) with a force term of the form of Eq (10. 3.9) We adopt a trial solution of the form q = q( )ei(Kz− ˜ t) + c.c (10. 3.11) 10. 3 Stimulated ... encountered in nonlinear optics and also describe, for example, any forward four-wave mixing process in the 10. 4 Stokes–Anti-Stokes Coupling in Stimulated Raman Scattering 489 constan...

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... (11. 5.1) through (11. 5.4)) by + + (sI0 + β) ND − ND0 = γ ne0 ND0 , (11. 6.5a) j0 = constant, (11. 6.5b) j0 = ne0 eμE0 + jph,0 , (11. 6.5c) + ND0 = ne0 + NA (11. 6.5d) Equations (11. 6.5a) and (11. 6.5d) ... the quantity πc Vλ/2 = , ωn3 r63 = (11. 3.9) (11. 3.10) which is known as the half-wave voltage Eq (11. 3.9) then becomes =π V Vλ/2 (11. 3 .11) Note that a half-wave (π radians) of retar...

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... Eqs (12. 5.3) and (12. 5.4), we represent Vmg as Vmg = −μmg Ee−iωt + E ∗ eiωt (12. 5.16) 12. 5 Multiphoton Absorption and Multiphoton Ionization 553 F IGURE 12. 5.3 (a) The first term in Eq (12. 5.17) ... Starting with the expressions for the rates of one-, two-, and three-photon absorption quoted above, deduce expressions for the one-, two-, and three-photon absorption coefficients α, β, and...

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... beam through a gas-filled capillary waveguide 13. 7 Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics 579 13. 7 Nonlinear Optics of Plasmas and Relativistic Nonlinear Optics A plasma ... effect of Chapter 11 being an obvious exception (13. 4.2) 13 ♦ Ultrafast and Intense-Field Nonlinear Optics 572 which corresponds to an intensity of∗ Iat = 2 cEat = × 1016...

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... Rothenberg, Opt Lett 17, 134 0 (1992) G Yang and Y R Shen, Opt Lett 9,510 (1984) 558 13 Ultrafast and Intense- Field Nonlinear Optics Sections 3.4 and 73.5: Intense- Field Nonlinear Optics and Motion of a ... Problem of Chapter 13 Ultrafast and Intense- Field Nonlinear Optics FIGURE 13. 5.1 Motion of a free electron in (a) a linearly polarized laser...

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