Abstract

We propose that self-pumped degenerate four-wave mixing may be used to produce novel diode laser systems where lasing is based on non-linear guiding of the laser beams inside the active semiconductor. The fundamental process responsible for the interaction is spatial hole burning in semiconductor amplifiers. The gain and index gratings created by the modulation of the carrier density in the active gain medium lead to selective amplification of one spatial mode and suppression of all other modes. This mechanism allows the laser system to be operated far above its threshold with an almost diffraction limited output beam. The third order nonlinear susceptibility of the non-linear material, which determines the strength of the induced gratings, depends on the angle between the interacting beams in the four-wave mixing configuration. It is shown theoretically that a narrow range of angles exist where the induced gratings are strong and where mode suppression of higher order spatial modes are obtained simultaneously. Experimental evidence sustaining these findings is given.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. P. Kürz, R. Nagar, and T. Mukai, �??Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode�??, Appl. Phys. Lett. 68, 1180-1182 (1996).
    [CrossRef]
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    [CrossRef]
  5. K. Paschke, R. Günter, J. Fricke, F. Bugge, G. Erbert and G. Tränkle, �??High power and high spectral brightness in 1060 nm α-DFB lasers with long resonators,�?? Electron. Lett. 39, 369-370 (2003).
    [CrossRef]
  6. J. Buus and M. Danielsen, �??Carrier diffusion and higher-order transversal modes in spectral dynamics of semiconductor-laser,�?? IEEE J. Quantum Electron. QE-13, 669-674 (1977).
    [CrossRef]
  7. J.-M. Verdiell and R. Frey, �??A broad-area mode-coupling model for multiple-stripe semiconductor lasers,�?? IEEE J. Quantum Electron. QE-26, 270-279 (1990).
    [CrossRef]
  8. R. K. Jain and R. C. Lind, �??Degenerate four wave mixing in semiconductor doped glasses,�?? J. Opt. Soc. Am. 73, 647-653 (1983).
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  9. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 2nd ed., New York, 1993).
  10. H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Syst. Techn. J. 48, 2909-2947 (1969).

Appl. Phys. Lett.

M. Lucente, J. G. Fujimoto, and G. M. Carter, �??Spatial and frequency dependence of four-wave mixing in broad-area diode lasers,�?? Appl. Phys. Lett. 53, 1897-1899 (1988).
[CrossRef]

P. Kürz, R. Nagar, and T. Mukai, �??Highly efficient phase conjugation using spatially nondegenerate four-wave mixing in a broad-area laser diode�??, Appl. Phys. Lett. 68, 1180-1182 (1996).
[CrossRef]

Bell Syst. Techn. J.

H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Syst. Techn. J. 48, 2909-2947 (1969).

Electron. Lett.

K. Paschke, R. Günter, J. Fricke, F. Bugge, G. Erbert and G. Tränkle, �??High power and high spectral brightness in 1060 nm α-DFB lasers with long resonators,�?? Electron. Lett. 39, 369-370 (2003).
[CrossRef]

IEEE J. Quantum Electron.

J. Buus and M. Danielsen, �??Carrier diffusion and higher-order transversal modes in spectral dynamics of semiconductor-laser,�?? IEEE J. Quantum Electron. QE-13, 669-674 (1977).
[CrossRef]

J.-M. Verdiell and R. Frey, �??A broad-area mode-coupling model for multiple-stripe semiconductor lasers,�?? IEEE J. Quantum Electron. QE-26, 270-279 (1990).
[CrossRef]

R. J. Lang, K. Dzurko, A. A. Hardy, S. Demard, A. Schoenfelder, and D. Welch, �??Theory of grating-confined broad-area lasers,�?? IEEE J. Quantum Electron. QE-34, 2196-2210 (1998).
[CrossRef]

H. Nakajima and R. Frey, �??Collinear nearly degenerate four-wave mixing in intracavity amplifying media,�?? IEEE J. Quantum Electron. QE-22, 1349-1354 (1986).
[CrossRef]

J. Opt. Soc. Am.

Other

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 2nd ed., New York, 1993).

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Figures (4)

Fig. 1.
Fig. 1.

Configuration of the four-wave mixing in the active semiconductor amplifier. The four waves A i, i=1…4, interact inside the diode laser gain medium. The wave A 3 is generated by reflection from the external mirror M. Gain and refractive index gratings are induced by interference between A 1 and A 4 and between A 2 and A 3. The four-wave mixing process in the semiconductor amplifier provides a reflectivity |A 4(L)| 2/|A 3(L)| 2 that together with the mirror reflection at M leads to stable laser oscillations.

Fig. 2.
Fig. 2.

Normalized χ 4MW versus θ [in units of 1/(k(D τs )] between the interfering laser beams.

Fig. 3.
Fig. 3.

Plot of the upper and lower boundary of the output angle θ from Eq. (11). The upper boundary (green curve) is plotted as a function of the saturation. The lower boundary is plotted with the cavity length as parameter; blue solid curve corresponds to L=0.5mm and red solid curve to L=1mm.

Fig. 4.
Fig. 4.

Intensity output profiles: Output intensity (arbitrary units) as a function of angle θ (unit degrees) for different pumping levels (a) I=0.95 A, (b) I=1.23 A, (c) I=1.40 A, and (d) I=1.40 A (without external mirror). The output profiles (a)-(c) clearly show the diffraction pattern from the induced four-wave mixing gratings in the semiconductor amplifier.

Equations (12)

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d N d t = I q V N τ s + D 2 N g ( N ) E 0 2
N = N + Δ n exp ( i Δ k y )
Δ n = a ( N N 0 ) 1 τ s + D 4 π 2 Λ 2 + E 0 2 E s 2 τ s ( E 1 E 4 * + E 3 E 2 * ) ω 0
N = I τ s q V + N 0 E 0 2 E S 2 1 + E 0 2 E S 2
χ ( N ) = n c ω ( β + i ) g ( N )
= n c ω ( β + i ) a [ ( N N 0 ) + Δ n exp ( i Δ k y ) ]
χ 4 W M ( N ) = n c ω β + i ω 0 a 2 ( N N 0 ) 1 τ s + D 4 π 2 Λ 2 + E 0 2 E S 2 τ s ( E 1 E 4 * + E 3 E 2 * )
χ 4 W M = χ 4 W M , opt 1 + k 2 θ 2 D τ s + E 0 2 E S 2 = χ 4 W M , opt 1 + E 0 2 E S 2 ( 1 1 + E S 2 k 2 D τ s E S 2 + E 0 2 θ 2 )
θ 1 2 = 1 k 1 + E 0 2 E S 2 D τ s
δ = 4 π L λ n sin 2 ( θ 2 )
θ crit = 2 arc sin ( n λ 2 L )
2 arc sin = ( n λ 2 L ) < θ < 1 k 1 + E 0 2 E S 2 D τ s

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