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These three state equations are compared with exact numerical results in Fig. 5-3. 4 are indistinguishable from the plot of Eq. 5-42). Hermann (1980) reaches the same conclusions. Carmichael and Agrawal (1980, 1981) have extended the full hierarchy treat­ ment to inhomogeneous broadening and to a Doppler-broadened medium in partic­ ular. In Fig. 5-4 are shown the effects of Doppler broadening on absorptive bistability in the mean-field limit. In this figure C is held constant while γ2#/Ύτ is varied.

3-6) where Β0 contains all intensity-independent phase shifts such as background index or plate detuning contributions. Phase shifts of the form of Eq. 3-6 ) arise when there is a nonlinear refractive index, n 0 + n£ , or for Bloch equations far enough off resonance. , free spectral range divided by instrument width. For Ι γ = 0, 8 = B0 s 2T//R so the R 82/ T 2 term in Eq. 3-5) is of order unity and is as important as the unity term. 9; thus 82 is much smaller than 12 as needed in Eq. 3 -5 ). This simple model, Eqs.

5-32) 1 +2X ' where Ep = Eß = Ey//T and X = κ 2 |Ep|2/Ύ l · Then σ 0 = σ Γ = σ and by Eq. , C > 4 as found by Szöke et al. 1) for purely absorptive bistability neglecting standing waves. Now assume Eq. 5-27) holds and standing-wave effects are fully present (A = 0 still); then by Eq. 5-34) and by Eq. 937, about 24% larger than 8. One concludes that standing waves increase the a 0L/T needed for bistability. Now return to Eq. 5-27) and retain the dispersive Δ terms. 1, yielding 2C > 4[1 + (1 + i 2)l/2].

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