Abstract

A transient two-dimensional model describing degenerate four-wave mixing inside saturable gain media is presented. The new model is compared to existing one-dimensional models with their qualitative results confirmed. Large quantitative differences with respect to peak reflectivity and optimum pump fluence are observed. Furthermore, the influence of the beam focus size, the transverse position and the crossing angle on the reflectivity of the grating is investigated using the improved model. It is demonstrated that the phase conjugate reflectivity depends sensitively on the transverse features of the interacting beams with a transverse shift in the position of the pump beams yielding a threefold improvement in reflectivity.

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  1. R. P. M. Green, S. Camacho-Lopez, M. J. Damzen, “Experimental investigation of vector phase conjugation in Nd3+:YAG,” Opt. Lett. 21, 1214–1216 (1996).
    [CrossRef] [PubMed]
  2. R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
    [CrossRef] [PubMed]
  3. P. Sillard, A. Brignon, J. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
    [CrossRef]
  4. A. Brignon, J. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
    [CrossRef]
  5. M. Damzen, R. Green, G. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
    [CrossRef]
  6. G. Smith, M. J. Damzen, “Quasi-CW diode-pumped self-starting adaptive laser with self-Q-switched output,” Opt. Express 15, 6458–6463 (2007).
    [CrossRef] [PubMed]
  7. B. A. Thompson, A. Minassian, M. J. Damzen, “Operation of a 33-W, continuous-wave, self-adaptive, solid-state laser oscillator,” J. Opt. Soc. B 20, 857–862 (2003).
    [CrossRef]
  8. S. Lam, M. Damzen, “Self-adaptive Nd:YLF holographic laser with selectable wavelength operation,” Appl. Phys. B. 76, 237–240 (2003).
    [CrossRef]
  9. M. J. Damzen, Y. Matsumoto, G. J. Crofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996).
    [CrossRef]
  10. A. Minassian, G. Crofts, M. Damzen, “Spectral filtering of gain gratings and spectral evolution of holographic laser oscillators,” IEEE J. Quantum Electron. 36, 802–809 (2000).
    [CrossRef]
  11. P. C. Shardlow, M. J. Damzen, “Phase conjugate self-organized coherent beam combination: a passive technique for laser power scaling,” Opt. Lett. 35, 1082–1084 (2010).
    [CrossRef] [PubMed]
  12. K. S. Syed, G. J. Crofts, M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
    [CrossRef]
  13. R. Green, G. Crofts, M. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
    [CrossRef]
  14. G. J. Crofts, M. J. Damzen, “Numerical modelling of continuous-wave holographic laser oscillators,” Opt. Commun. 175, 397–408 (2000).
    [CrossRef]
  15. M. J. Damzen, R. P. M. Green, G. J. Crofts, “Reflectivity and oscillation conditions of a gain medium in a self-conjugating loop geometry,” Opt. Lett. 19, 34–36 (1994).
    [CrossRef] [PubMed]
  16. K. Syed, R. Green, G. Crofts, M. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
    [CrossRef]
  17. K. S. Syed, G. J. Crofts, R. P. M. Green, M. J. Damzen, “Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media,” J. Opt. Soc. B 14, 2067–2078 (1997).
    [CrossRef]
  18. M. Chi, J. Huignard, P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. B 26, 1578–1584 (2009).
    [CrossRef]

2010

2009

M. Chi, J. Huignard, P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. B 26, 1578–1584 (2009).
[CrossRef]

2007

2003

B. A. Thompson, A. Minassian, M. J. Damzen, “Operation of a 33-W, continuous-wave, self-adaptive, solid-state laser oscillator,” J. Opt. Soc. B 20, 857–862 (2003).
[CrossRef]

S. Lam, M. Damzen, “Self-adaptive Nd:YLF holographic laser with selectable wavelength operation,” Appl. Phys. B. 76, 237–240 (2003).
[CrossRef]

2000

A. Minassian, G. Crofts, M. Damzen, “Spectral filtering of gain gratings and spectral evolution of holographic laser oscillators,” IEEE J. Quantum Electron. 36, 802–809 (2000).
[CrossRef]

G. J. Crofts, M. J. Damzen, “Numerical modelling of continuous-wave holographic laser oscillators,” Opt. Commun. 175, 397–408 (2000).
[CrossRef]

1998

K. S. Syed, G. J. Crofts, M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

P. Sillard, A. Brignon, J. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

1997

K. S. Syed, G. J. Crofts, R. P. M. Green, M. J. Damzen, “Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media,” J. Opt. Soc. B 14, 2067–2078 (1997).
[CrossRef]

1996

R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
[CrossRef] [PubMed]

R. P. M. Green, S. Camacho-Lopez, M. J. Damzen, “Experimental investigation of vector phase conjugation in Nd3+:YAG,” Opt. Lett. 21, 1214–1216 (1996).
[CrossRef] [PubMed]

M. J. Damzen, Y. Matsumoto, G. J. Crofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996).
[CrossRef]

1994

A. Brignon, J. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

M. Damzen, R. Green, G. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

K. Syed, R. Green, G. Crofts, M. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

M. J. Damzen, R. P. M. Green, G. J. Crofts, “Reflectivity and oscillation conditions of a gain medium in a self-conjugating loop geometry,” Opt. Lett. 19, 34–36 (1994).
[CrossRef] [PubMed]

1993

R. Green, G. Crofts, M. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

Brignon, A.

P. Sillard, A. Brignon, J. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

A. Brignon, J. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

Camacho-Lopez, S.

Chi, M.

M. Chi, J. Huignard, P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. B 26, 1578–1584 (2009).
[CrossRef]

Crofts, G.

A. Minassian, G. Crofts, M. Damzen, “Spectral filtering of gain gratings and spectral evolution of holographic laser oscillators,” IEEE J. Quantum Electron. 36, 802–809 (2000).
[CrossRef]

M. Damzen, R. Green, G. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

K. Syed, R. Green, G. Crofts, M. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

R. Green, G. Crofts, M. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

Crofts, G. J.

G. J. Crofts, M. J. Damzen, “Numerical modelling of continuous-wave holographic laser oscillators,” Opt. Commun. 175, 397–408 (2000).
[CrossRef]

K. S. Syed, G. J. Crofts, M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

K. S. Syed, G. J. Crofts, R. P. M. Green, M. J. Damzen, “Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media,” J. Opt. Soc. B 14, 2067–2078 (1997).
[CrossRef]

R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
[CrossRef] [PubMed]

M. J. Damzen, Y. Matsumoto, G. J. Crofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996).
[CrossRef]

M. J. Damzen, R. P. M. Green, G. J. Crofts, “Reflectivity and oscillation conditions of a gain medium in a self-conjugating loop geometry,” Opt. Lett. 19, 34–36 (1994).
[CrossRef] [PubMed]

Damzen, M.

S. Lam, M. Damzen, “Self-adaptive Nd:YLF holographic laser with selectable wavelength operation,” Appl. Phys. B. 76, 237–240 (2003).
[CrossRef]

A. Minassian, G. Crofts, M. Damzen, “Spectral filtering of gain gratings and spectral evolution of holographic laser oscillators,” IEEE J. Quantum Electron. 36, 802–809 (2000).
[CrossRef]

K. Syed, R. Green, G. Crofts, M. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

M. Damzen, R. Green, G. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

R. Green, G. Crofts, M. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

Damzen, M. J.

P. C. Shardlow, M. J. Damzen, “Phase conjugate self-organized coherent beam combination: a passive technique for laser power scaling,” Opt. Lett. 35, 1082–1084 (2010).
[CrossRef] [PubMed]

G. Smith, M. J. Damzen, “Quasi-CW diode-pumped self-starting adaptive laser with self-Q-switched output,” Opt. Express 15, 6458–6463 (2007).
[CrossRef] [PubMed]

B. A. Thompson, A. Minassian, M. J. Damzen, “Operation of a 33-W, continuous-wave, self-adaptive, solid-state laser oscillator,” J. Opt. Soc. B 20, 857–862 (2003).
[CrossRef]

G. J. Crofts, M. J. Damzen, “Numerical modelling of continuous-wave holographic laser oscillators,” Opt. Commun. 175, 397–408 (2000).
[CrossRef]

K. S. Syed, G. J. Crofts, M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

K. S. Syed, G. J. Crofts, R. P. M. Green, M. J. Damzen, “Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media,” J. Opt. Soc. B 14, 2067–2078 (1997).
[CrossRef]

R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
[CrossRef] [PubMed]

M. J. Damzen, Y. Matsumoto, G. J. Crofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996).
[CrossRef]

R. P. M. Green, S. Camacho-Lopez, M. J. Damzen, “Experimental investigation of vector phase conjugation in Nd3+:YAG,” Opt. Lett. 21, 1214–1216 (1996).
[CrossRef] [PubMed]

M. J. Damzen, R. P. M. Green, G. J. Crofts, “Reflectivity and oscillation conditions of a gain medium in a self-conjugating loop geometry,” Opt. Lett. 19, 34–36 (1994).
[CrossRef] [PubMed]

Green, R.

M. Damzen, R. Green, G. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

K. Syed, R. Green, G. Crofts, M. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

R. Green, G. Crofts, M. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

Green, R. P. M.

K. S. Syed, G. J. Crofts, R. P. M. Green, M. J. Damzen, “Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media,” J. Opt. Soc. B 14, 2067–2078 (1997).
[CrossRef]

R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
[CrossRef] [PubMed]

M. J. Damzen, Y. Matsumoto, G. J. Crofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996).
[CrossRef]

R. P. M. Green, S. Camacho-Lopez, M. J. Damzen, “Experimental investigation of vector phase conjugation in Nd3+:YAG,” Opt. Lett. 21, 1214–1216 (1996).
[CrossRef] [PubMed]

M. J. Damzen, R. P. M. Green, G. J. Crofts, “Reflectivity and oscillation conditions of a gain medium in a self-conjugating loop geometry,” Opt. Lett. 19, 34–36 (1994).
[CrossRef] [PubMed]

Huignard, J.

M. Chi, J. Huignard, P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. B 26, 1578–1584 (2009).
[CrossRef]

P. Sillard, A. Brignon, J. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

A. Brignon, J. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

Kim, D. H.

R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
[CrossRef] [PubMed]

Lam, S.

S. Lam, M. Damzen, “Self-adaptive Nd:YLF holographic laser with selectable wavelength operation,” Appl. Phys. B. 76, 237–240 (2003).
[CrossRef]

Matsumoto, Y.

M. J. Damzen, Y. Matsumoto, G. J. Crofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996).
[CrossRef]

Minassian, A.

B. A. Thompson, A. Minassian, M. J. Damzen, “Operation of a 33-W, continuous-wave, self-adaptive, solid-state laser oscillator,” J. Opt. Soc. B 20, 857–862 (2003).
[CrossRef]

A. Minassian, G. Crofts, M. Damzen, “Spectral filtering of gain gratings and spectral evolution of holographic laser oscillators,” IEEE J. Quantum Electron. 36, 802–809 (2000).
[CrossRef]

Petersen, P. M.

M. Chi, J. Huignard, P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. B 26, 1578–1584 (2009).
[CrossRef]

Shardlow, P. C.

Sillard, P.

P. Sillard, A. Brignon, J. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

Smith, G.

Syed, K.

K. Syed, R. Green, G. Crofts, M. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

Syed, K. S.

K. S. Syed, G. J. Crofts, M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

K. S. Syed, G. J. Crofts, R. P. M. Green, M. J. Damzen, “Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media,” J. Opt. Soc. B 14, 2067–2078 (1997).
[CrossRef]

Thompson, B. A.

B. A. Thompson, A. Minassian, M. J. Damzen, “Operation of a 33-W, continuous-wave, self-adaptive, solid-state laser oscillator,” J. Opt. Soc. B 20, 857–862 (2003).
[CrossRef]

Udaiyan, D.

R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
[CrossRef] [PubMed]

Appl. Phys. B.

S. Lam, M. Damzen, “Self-adaptive Nd:YLF holographic laser with selectable wavelength operation,” Appl. Phys. B. 76, 237–240 (2003).
[CrossRef]

IEEE J. Quantum Electron.

P. Sillard, A. Brignon, J. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

A. Brignon, J. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

A. Minassian, G. Crofts, M. Damzen, “Spectral filtering of gain gratings and spectral evolution of holographic laser oscillators,” IEEE J. Quantum Electron. 36, 802–809 (2000).
[CrossRef]

J. Opt. Soc. B

B. A. Thompson, A. Minassian, M. J. Damzen, “Operation of a 33-W, continuous-wave, self-adaptive, solid-state laser oscillator,” J. Opt. Soc. B 20, 857–862 (2003).
[CrossRef]

K. S. Syed, G. J. Crofts, R. P. M. Green, M. J. Damzen, “Vectorial phase conjugation via four-wave mixing in isotropic saturable-gain media,” J. Opt. Soc. B 14, 2067–2078 (1997).
[CrossRef]

M. Chi, J. Huignard, P. M. Petersen, “A general theory of two-wave mixing in nonlinear media,” J. Opt. Soc. B 26, 1578–1584 (2009).
[CrossRef]

Opt. Commun.

M. J. Damzen, Y. Matsumoto, G. J. Crofts, R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123, 182–188 (1996).
[CrossRef]

M. Damzen, R. Green, G. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

K. S. Syed, G. J. Crofts, M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

R. Green, G. Crofts, M. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

G. J. Crofts, M. J. Damzen, “Numerical modelling of continuous-wave holographic laser oscillators,” Opt. Commun. 175, 397–408 (2000).
[CrossRef]

K. Syed, R. Green, G. Crofts, M. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

R. P. M. Green, D. Udaiyan, G. J. Crofts, D. H. Kim, M. J. Damzen, “Holographic laser oscillator which adaptively corrects for polarization and phase distortions,” Phys. Rev. Lett. 77, 3533–3536 (1996).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Left: The four-wave mixing geometry inside the gain medium. In the most general case, four different gratings are written by the beams A1 to A4. From top to bottom: Transmission grating (τ), reflection grating (ρ), pump-pump grating (Δ) and probe-conjugate grating (δ). The blue arrows indicate the polarization. Right: Detailed geometry of the problem. θ is the angle between the z-axis and the wave vector k3.

Fig. 2
Fig. 2

The phase conjugate reflectivities of the transmission and reflection gratings for both the one-dimensional and two-dimensional models. The normalized fluence of the probe beam A3 is Û3 = 10−3 while UP = U1 = U2.

Fig. 3
Fig. 3

Top: The phase conjugate reflectivity RU of the FWM interaction in dependence of the transverse displacement of the pump beam. Bottom: The spatial coupling strength distribution of the gain grating for three different transverse positions of the pump beams. From left to right: Δx = 0.8 mm, Δx = 0.0 mm, Δx = −0.9 mm. The images show the magnitude of κτ, which is directly related to the grating strength. The beams A1, A3 enter at z = 0. A displacement of zero indicates that the pump beams enter the laser rod at the center. All three images share the same color scale. Blue indicates a weak, red a strong grating amplitude.

Fig. 4
Fig. 4

Top: The phase conjugate reflectivity RU of the FWM interaction in dependence of the waist size w0 of all three input beams. The fluences stay constant at their default values. Bottom: Spatial distribution of the grating strength for different beam waist sizes w0. From left to right: w0 = 0.1 mm, w0 = 0.5 mm, w0 = 0.9 mm. The images show the magnitude of κτ and share a common color scale. Blue indicates a weak, red a strong grating amplitude.

Fig. 5
Fig. 5

Top: The phase conjugate reflectivity RU of the FWM interaction in dependence of the angle θ between the k3-vector and the z-axis. Bottom: Spatial distribution of the grating strength for different crossing angles. From left to right (in degree): θ = 1.2, θ = 0.83, θ = 0.5. The images show the magnitude of κτ and share a common color scale. Blue indicates a weak, red a strong grating amplitude.

Equations (12)

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

E j ( r , t ) = A j e i ( k j r ω t )
k 1 = | k | e z , k 3 = | k | [ cos ( θ ) e z + sin ( θ ) e x ]
( Δ n 2 c 0 2 t 2 ) E = 2 i n c 0 2 | k 0 | t 2 ( α E )
α = α 0 exp ( 1 τ l I S 0 t I T ( r , t ) d t )
( i 2 | k | Δ ± sin ( θ j ) x ± cos ( θ j ) z + n c 0 t ) A j ( x , z , t ) = F j ( A , t )
F 1 ( A , t ) = γ A 1 + κ Δ A 2 + κ τ A 3 + κ ρ A 4
F 2 ( A , t ) = κ Δ * A 1 + γ A 2 + κ ρ * A 3 + κ τ * A 4
F 3 ( A , t ) = κ τ * A 1 + κ ρ A 2 + γ A 3 + κ δ A 4
F 4 ( A , t ) = κ ρ * A 1 + κ τ A 2 + κ δ * A 3 + γ A 4
R U = U 4 ( z = 0 ) U 3 ( z = 0 )
U ( z ) = I ( z , t ) d t
U 2 D ( z ) = 1 2 w spot ( z ) I ( x , z , t ) d t d x

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