Abstract

Two-beam coupling is demonstrated in CS2 and other transparent Kerr liquids by use of frequency chirped, picosecond 532-nm-wavelength pulses with several polarization combinations. As the temporal delay between pulses is varied within the coherence time, the first pulse always loses energy while the second pulse gains this energy. The transferred energy at a fixed delay varies linearly with irradiance. The results are consistent with energy transfer from transient refractive gratings that are due to stimulated Rayleigh-wing scattering.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Staebler and J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
    [CrossRef]
  2. E. P. Ippen and C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
    [CrossRef]
  3. A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131 (1979).
    [CrossRef]
  4. Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
    [CrossRef]
  5. B. S. Wherrett, A. L. Smirl, and T. G. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. 19, 680 (1983), and references therein.
    [CrossRef]
  6. S. L. Palfrey and T. F. Heinz, “Coherent interactions in pump-probe absorption measurements: the effect of phase gratings,” J. Opt. Soc. Am. B 2, 674 (1985).
    [CrossRef]
  7. D. Rogovin, T. P. Shen, J. Scholl, T. Dutton, and P. Rentzepis, “Polarization-resolved coherent transient beam combination in optical Kerr media,” Opt. Lett. 15, 1132 (1990).
    [CrossRef] [PubMed]
  8. T. E. Dutton, R. M. Rentzepis, T. P. Shen, J. Scholl, and D. Rogovin, “Picosecond degenerate two-wave mixing,” J. Opt. Soc. Am. B 9, 1843 (1992).
    [CrossRef]
  9. P. S. Spencer and K. A. Shore, “Pump–probe propagation in a passive Kerr nonlinear optical medium,” J. Opt. Soc. Am. B 12, 67 (1995).
    [CrossRef]
  10. K. D. Dorkenoo, D. Wang, N. P. Xuan, J. P. Lecoq, R. Chevalier, and G. Rivoire, “Stimulated Rayleigh-wing scattering with two-beam coupling in CS2,” J. Opt. Soc. Am. B 12, 37 (1995).
    [CrossRef]
  11. G. Rivoire and D. Wang, “Dynamics of CS2 in the large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460 (1993).
    [CrossRef]
  12. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992), p. 389.
  13. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960), p. 377.
  14. N. Bloembergen and P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett. 16, 81 (1966).
    [CrossRef]
  15. M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
    [CrossRef]
  16. S. Miller, “Ultrasensitive technique for measuring two-photon absorption,” Ph.D. dissertation (University of North Texas, Denton, Texas, 1991).
  17. T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
    [CrossRef]
  18. E. P. Ippen and C. V. Shank, “Picosecond response of a high-repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 24, 92 (1975).
    [CrossRef]
  19. G. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 58.
  20. R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430 (1969).
    [CrossRef]
  21. R. W. Minck, E. E. Hagenlocker, and W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett. 17, 229 (1966).
    [CrossRef]
  22. W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256 (1984).
    [CrossRef]

1995 (2)

1993 (1)

G. Rivoire and D. Wang, “Dynamics of CS2 in the large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460 (1993).
[CrossRef]

1992 (2)

T. E. Dutton, R. M. Rentzepis, T. P. Shen, J. Scholl, and D. Rogovin, “Picosecond degenerate two-wave mixing,” J. Opt. Soc. Am. B 9, 1843 (1992).
[CrossRef]

T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
[CrossRef]

1991 (1)

M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
[CrossRef]

1990 (1)

1985 (1)

1984 (1)

W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256 (1984).
[CrossRef]

1983 (1)

B. S. Wherrett, A. L. Smirl, and T. G. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. 19, 680 (1983), and references therein.
[CrossRef]

1981 (1)

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

1979 (1)

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131 (1979).
[CrossRef]

1975 (1)

E. P. Ippen and C. V. Shank, “Picosecond response of a high-repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 24, 92 (1975).
[CrossRef]

1972 (1)

D. Staebler and J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

1969 (1)

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430 (1969).
[CrossRef]

1966 (2)

R. W. Minck, E. E. Hagenlocker, and W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett. 17, 229 (1966).
[CrossRef]

N. Bloembergen and P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 58.

Amodei, J.

D. Staebler and J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Bloembergen, N.

N. Bloembergen and P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

Boggess, T. G.

B. S. Wherrett, A. L. Smirl, and T. G. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. 19, 680 (1983), and references therein.
[CrossRef]

Boyd, R. W.

M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992), p. 389.

Chevalier, R.

Chiao, R. Y.

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430 (1969).
[CrossRef]

Coulter, D. R.

T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
[CrossRef]

Dorkenoo, K. D.

Dutton, T.

Dutton, T. E.

Gaeta, A. L.

M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
[CrossRef]

Godine, J.

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430 (1969).
[CrossRef]

Gruneisen, M. T.

M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
[CrossRef]

Hagan, D. J.

T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
[CrossRef]

Hagenlocker, E. E.

R. W. Minck, E. E. Hagenlocker, and W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett. 17, 229 (1966).
[CrossRef]

Harter, D. J.

M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
[CrossRef]

Heinz, T. F.

Ippen, E. P.

E. P. Ippen and C. V. Shank, “Picosecond response of a high-repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 24, 92 (1975).
[CrossRef]

E. P. Ippen and C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
[CrossRef]

Lallemand, P.

N. Bloembergen and P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960), p. 377.

Lecoq, J. P.

Lessing, H. E.

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131 (1979).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960), p. 377.

MacDonald, K. R.

M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
[CrossRef]

Miller, S.

S. Miller, “Ultrasensitive technique for measuring two-photon absorption,” Ph.D. dissertation (University of North Texas, Denton, Texas, 1991).

Minck, R. W.

R. W. Minck, E. E. Hagenlocker, and W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett. 17, 229 (1966).
[CrossRef]

Palfrey, S. L.

Perry, J. W.

T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
[CrossRef]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960), p. 377.

Rado, W. G.

R. W. Minck, E. E. Hagenlocker, and W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett. 17, 229 (1966).
[CrossRef]

Rentzepis, P.

Rentzepis, R. M.

Rivoire, G.

K. D. Dorkenoo, D. Wang, N. P. Xuan, J. P. Lecoq, R. Chevalier, and G. Rivoire, “Stimulated Rayleigh-wing scattering with two-beam coupling in CS2,” J. Opt. Soc. Am. B 12, 37 (1995).
[CrossRef]

G. Rivoire and D. Wang, “Dynamics of CS2 in the large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460 (1993).
[CrossRef]

Rogovin, D.

Scholl, J.

Shank, C. V.

E. P. Ippen and C. V. Shank, “Picosecond response of a high-repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 24, 92 (1975).
[CrossRef]

E. P. Ippen and C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
[CrossRef]

Shen, T. P.

Shore, K. A.

Smirl, A. L.

B. S. Wherrett, A. L. Smirl, and T. G. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. 19, 680 (1983), and references therein.
[CrossRef]

Soileau, M. J.

W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256 (1984).
[CrossRef]

Spencer, P. S.

Staebler, D.

D. Staebler and J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Tauc, J.

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

Van Stryland, E. W.

T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
[CrossRef]

W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256 (1984).
[CrossRef]

Vardeny, Z.

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

von Jena, A.

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131 (1979).
[CrossRef]

Wang, D.

K. D. Dorkenoo, D. Wang, N. P. Xuan, J. P. Lecoq, R. Chevalier, and G. Rivoire, “Stimulated Rayleigh-wing scattering with two-beam coupling in CS2,” J. Opt. Soc. Am. B 12, 37 (1995).
[CrossRef]

G. Rivoire and D. Wang, “Dynamics of CS2 in the large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460 (1993).
[CrossRef]

Wei, T. H.

T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
[CrossRef]

Wherrett, B. S.

B. S. Wherrett, A. L. Smirl, and T. G. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. 19, 680 (1983), and references therein.
[CrossRef]

Williams, W. E.

W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256 (1984).
[CrossRef]

Xuan, N. P.

Appl. Phys. (1)

A. von Jena and H. E. Lessing, “Coherent coupling effects in picosecond absorption experiments,” Appl. Phys. 19, 131 (1979).
[CrossRef]

Appl. Phys. B (1)

T. H. Wei, D. J. Hagan, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

E. P. Ippen and C. V. Shank, “Picosecond response of a high-repetition rate CS2 optical Kerr gate,” Appl. Phys. Lett. 24, 92 (1975).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. T. Gruneisen, K. R. MacDonald, A. L. Gaeta, R. W. Boyd, and D. J. Harter, “Laser beam combining in potassium vapor,” IEEE J. Quantum Electron. 27, 128 (1991).
[CrossRef]

B. S. Wherrett, A. L. Smirl, and T. G. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. 19, 680 (1983), and references therein.
[CrossRef]

J. Appl. Phys. (1)

D. Staebler and J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

J. Chem. Phys. (1)

G. Rivoire and D. Wang, “Dynamics of CS2 in the large spectral bandwidth stimulated Rayleigh-wing scattering,” J. Chem. Phys. 99, 9460 (1993).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (2)

Z. Vardeny and J. Tauc, “Picosecond coherence coupling in the pump and probe technique,” Opt. Commun. 39, 396 (1981).
[CrossRef]

W. E. Williams, M. J. Soileau, and E. W. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256 (1984).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

R. Y. Chiao and J. Godine, “Polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect,” Phys. Rev. 185, 430 (1969).
[CrossRef]

Phys. Rev. Lett. (2)

R. W. Minck, E. E. Hagenlocker, and W. G. Rado, “Stimulated pure rotational Raman scattering in deuterium,” Phys. Rev. Lett. 17, 229 (1966).
[CrossRef]

N. Bloembergen and P. Lallemand, “Complex intensity-dependent index of refraction, frequency broadening of stimulated Raman lines, and stimulated Rayleigh scattering,” Phys. Rev. Lett. 16, 81 (1966).
[CrossRef]

Other (5)

G. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 58.

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992), p. 389.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1960), p. 377.

S. Miller, “Ultrasensitive technique for measuring two-photon absorption,” Ph.D. dissertation (University of North Texas, Denton, Texas, 1991).

E. P. Ippen and C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. Vol. 18 of Topics in Applied Physics (Springer-Verlag, Berlin, 1977), p. 83.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Normalized probe transmittance as a function of time delay of the probe in toluene (open circles) and in a dilute solution of silicon naphthalocyanine (SiNc) (closed circles) having a linear transmittance of 98.6%. The solid and the dashed curves are theoretical fits (described in the text).

Fig. 2
Fig. 2

Excite–probe experimental setup. Detector D measures the probe beam transmittance. Both beams are linearly chirped; b and r represent the blue and red shifts. The earlier pulse interacts with the higher frequency part of its spectrum, whereas the later pulse interacts with the lower-frequency part.

Fig. 3
Fig. 3

SRWS signal dependence on polarization: (a) parallel-linear, (b) perpendicular-linear, (c) opposite-circular, and (d) same-circular polarization. Experimental conditions: I10=1.9 GW/cm2 and τp=17 ps. The circles are experimental data; solid curves represent theoretical fits assuming a linear chirp, C=0.75.

Fig. 4
Fig. 4

Magnitude of the SRWS signal (difference between peak and valley) as a function of excitation irradiance (circles). The theoretical curve is generated by Eq. (23) with the same value for linear chirp used in fitting the data from Fig. 3.

Fig. 5
Fig. 5

Interference pattern given by first-order autocorrelation for (from top to bottom) -120-, -46.6-, 0-, 46.6-, and 120-ps time delay at 1.06 µm.

Fig. 6
Fig. 6

Maxima (filled circles) and minima (open circles) of the interference pattern from Fig. 5 as a function of time delay. The solid curve is a Gaussian fit giving the coherence time of the pulses, τcoh=13.7 ps (HW1/eM) at 532 nm.

Fig. 7
Fig. 7

SRWS signal for different laser pulse widths: 17 ps (open circles) and 25 ps (filled circles). The values for the linear-chirp coefficient used in fitting the data are C=0.85 for the 17-ps pulse and C=0.6 for the 25-ps pulse.

Fig. 8
Fig. 8

(a) Linear chirp weighted by the Gaussian pulse (solid curve) and the linear chirp by itself (dashed curve) (b) are used for fitting the data (filled circles).

Tables (1)

Tables Icon

Table 1 Relative Signal for Different Polarization Combinations

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

E(r, t)=Re[A(t)exp(i{k·r-[ω+Δω(t)]t})],
A(t)=E0 exp-12tτp2.
E(r, t, τ)=Ae exp(i{ke·r-[ω+Δω(t)]t})+Ap exp(i{kp·r-[ω+Δω(t-τ)]×(t-τ)}),
I=n0c02|E|2.
I=n0c02[AeAe*+ApAp*+(AeAp* exp(iq·r)×exp{-i[ω+Δω(t-τ)]τ}exp(-iΩt)+c.c.)].
In0c02{AeAe*+ApAp*+[AeAp* exp(iq·r)×exp(-iωτ)exp(-iΩt)+c.c.]}.
τrot dnNLdt+nNL=n2I,
nNL(t)=n2τrot-tI(t)exp[(t-t)/τrot]dt.
nNL=n0n2c02(|Ae|2+|Ap|2)+AeAp* exp[i(q·r-Ωt)]exp(-iωτ)1-iΩτrot+c.c..
2E-1c22(n2/E)t2=0,
n2=(n0+nNL)2n02+2n0nNL.
d2dz2(Ap exp{i[kpz-ω(t-τ)]})
=n02c22t2(Ap exp{i[kpz-ω(t-τ)]})+n02n20c2t2|Ae|2+|Ap|2+|Ae|21+iΩτrotAp exp{i[kpz-ω(t-τ)]}.
dApdz=in0n20ω2|Ae|2+|Ap|2+|Ae|21+iΩτrotAp.
dIpdz=n0c02Ap* dApdz+Ap dAp*dz.
dIpdz=n2ωcIeIp 2Ωτrot1+(Ωτrot)2.
E(r, t)=E0 exp[i(k·r-ωt)]exp-12tτp2(1+iC),
dIpdz=αgIeIp,
g=n2ωc2Ωτrot1+(Ωτrot)2.
signal(τ)=Ep,outEp,in=2π-dt0rdrIp2π-dt0rdrIp0,
signal(τ)=2π-0y exp(-x2-y2)×expαΔΦ0 2τ/tm1+(τ/tm)2×exp[-(x-τ/τp)2]exp[-(yrpe)2]dydx,
Ip=Ip01+αΔΦ0 2Ωτrot1+(Ωτrot)2,
signal(τ)=1+αΔΦ0(1+rpe2)22Ωτrot1+(Ωτrot)2×exp-12ττp2=1+αΔΦ0(1+rpe2)22τ/tm1+(τ/tm)2×exp-12ττp2.
τmax,min±τptmτp2+tm2,
ΔTpv=22 exp(-1/2) αΔΦ0Cτrotτp.
τp=τc1+C2.

Metrics