Abstract

We propose and analyze a beam-shaping mechanism that in broad-area semiconductor amplifiers occurs due to spatial pump modulation on a micrometer scale. The study, performed under realistic parameters and conditions, predicts a spatial (angular) filtering of the radiation, which leads to a substantial improvement of the spatial quality of the beam during amplification. Quantitative analysis of spatial filtering performance is presented based on numerical integration of the paraxial propagation model and on analytical estimations.

© 2012 Optical Society of America

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  1. T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsäßer, Chaos Solitons Fractals 10, 845 (1999).
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    [CrossRef]
  4. V. Raab and R. Menzel, Opt. Lett. 27, 167 (2002).
    [CrossRef]
  5. S. K. Mandre, I. Fischer, and W. Elsäßer, Opt. Lett. 28, 1135 (2003).
    [CrossRef]
  6. V. I. Bespalov and V. I. Talanov, J. Exp. Theor. Phys. Lett. 3, 307 (1966).
  7. K. Staliunas, R. Herrero, and R. Vilaseca, Phys. Rev. A 80, 013821 (2009).
    [CrossRef]
  8. M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
    [CrossRef]
  9. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef]
  10. S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
    [CrossRef]
  11. ISO Standard 11146, “Lasers and laser-related equipment. Test methods for laser beam widths, divergence angles and beam propagation ratios” (2005).
  12. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer-Verlag, 1999).
  13. G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
    [CrossRef]
  14. H. Adachihara, O. Hess, E. Abraham, P. Ru, and J. V. Moloney, J. Opt. Soc. Am. B 10, 658 (1993).
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    [CrossRef]
  16. K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
    [CrossRef]

2011 (1)

M. Radziunas and K. Staliunas, Euro. Phys. Lett. 95, 14002 (2011).
[CrossRef]

2010 (1)

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

2009 (2)

K. Staliunas, R. Herrero, and R. Vilaseca, Phys. Rev. A 80, 013821 (2009).
[CrossRef]

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef]

2008 (1)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

2006 (1)

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

2003 (2)

2002 (1)

1999 (1)

T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsäßer, Chaos Solitons Fractals 10, 845 (1999).
[CrossRef]

1993 (1)

1989 (1)

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

1988 (1)

L. Goldberg and M. K. Chun, Appl. Phys. Lett. 53, 1900 (1988).
[CrossRef]

1966 (1)

V. I. Bespalov and V. I. Talanov, J. Exp. Theor. Phys. Lett. 3, 307 (1966).

Abraham, E.

Adachihara, H.

Agrawal, G. P.

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, J. Exp. Theor. Phys. Lett. 3, 307 (1966).

Botey, M.

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

Burkhard, T.

T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsäßer, Chaos Solitons Fractals 10, 845 (1999).
[CrossRef]

Chow, W. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer-Verlag, 1999).

Christodoulides, D. N.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Chun, M. K.

L. Goldberg and M. K. Chun, Appl. Phys. Lett. 53, 1900 (1988).
[CrossRef]

El-Ganainy, R.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Elsäßer, W.

S. K. Mandre, I. Fischer, and W. Elsäßer, Opt. Lett. 28, 1135 (2003).
[CrossRef]

T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsäßer, Chaos Solitons Fractals 10, 845 (1999).
[CrossRef]

Fischer, I.

S. K. Mandre, I. Fischer, and W. Elsäßer, Opt. Lett. 28, 1135 (2003).
[CrossRef]

T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsäßer, Chaos Solitons Fractals 10, 845 (1999).
[CrossRef]

Goldberg, L.

L. Goldberg and M. K. Chun, Appl. Phys. Lett. 53, 1900 (1988).
[CrossRef]

Herrero, R.

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, Phys. Rev. A 80, 013821 (2009).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Hess, O.

Koch, S. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer-Verlag, 1999).

Ledeerer, F.

Longhi, S.

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef]

Makris, K. G.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Mandre, S. K.

Menzel, R.

Michaelis, D.

Moloney, J. V.

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Raab, V.

Radziunas, M.

M. Radziunas and K. Staliunas, Euro. Phys. Lett. 95, 14002 (2011).
[CrossRef]

Ru, P.

Staliunas, K.

M. Radziunas and K. Staliunas, Euro. Phys. Lett. 95, 14002 (2011).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, Phys. Rev. A 80, 013821 (2009).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Stegeman, G. I.

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, J. Exp. Theor. Phys. Lett. 3, 307 (1966).

Ultanir, E. A.

Vilaseca, R.

K. Staliunas, R. Herrero, and R. Vilaseca, Phys. Rev. A 80, 013821 (2009).
[CrossRef]

Ziegler, M. O.

T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsäßer, Chaos Solitons Fractals 10, 845 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

L. Goldberg and M. K. Chun, Appl. Phys. Lett. 53, 1900 (1988).
[CrossRef]

Chaos Solitons Fractals (1)

T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsäßer, Chaos Solitons Fractals 10, 845 (1999).
[CrossRef]

Euro. Phys. Lett. (1)

M. Radziunas and K. Staliunas, Euro. Phys. Lett. 95, 14002 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

J. Exp. Theor. Phys. Lett. (1)

V. I. Bespalov and V. I. Talanov, J. Exp. Theor. Phys. Lett. 3, 307 (1966).

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Phys. Rev. A (2)

K. Staliunas, R. Herrero, and R. Vilaseca, Phys. Rev. A 80, 013821 (2009).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, Phys. Rev. A 82, 013828 (2010).
[CrossRef]

Phys. Rev. E (1)

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef]

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef]

Other (2)

ISO Standard 11146, “Lasers and laser-related equipment. Test methods for laser beam widths, divergence angles and beam propagation ratios” (2005).

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer-Verlag, 1999).

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Figures (3)

Fig. 1.
Fig. 1.

Planar semiconductor amplifier structure with fishnet electrodes. The pump profile is periodically modulated in space with transverse and longitudinal periods d and d. The incident beam of low spatial quality is amplified while its spatial structure is progressively improved. A part of the radiation is, however, lost in sideband components.

Fig. 2.
Fig. 2.

Spatial dispersion curves showing real and imaginary parts of k, for (a), (d) Q=0.8, (b), (e) Q=1, and (c), (f) Q=1.6 as obtained from Eq. (3). (g) Transverse profile of the noisy injected beam determined by a Gaussian (width 13 μm, peak intensity I0). (h)–(j) Intensities of the propagating beam according to Eq. (1) for the three above considered values of Q. Thick vertical lines indicate interfaces between the 1.5 mm long amplifier (left) and transparent homogeneous media (right). Curves at the right side of panels show transverse field intensity distributions at the right limit of the integration domain.

Fig. 3.
Fig. 3.

(a) Dependence of the beam quality factor on geometry factor Q for short (L=0.380mm4d) (orange) and long (L=1.52mm16d) amplifier (green) for random beams with initial M02=3.25 (solid) and M02=5.07 (dashed). (b) Dependence of the beam quality factor on the amplifier length for M02=5.07 and Q=0.8 (black), 0.9 (blue), 1.0 (red), 1.1 (purple), 1.2 (orange), and 1.3 (green).

Equations (6)

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

Az=i22Ax2+[p(x,z)11+|A|2(1iαH)iαHγ]A,
A(x,z)=eikxa0(z)+a1(z)eiqxiqz+a1(z)e+iqxiqz+
da0/dz=(i2k2+g)a0+(1iαH)m(a1+a1),
da±1/dz=(i2(k±q)2+iq+g)a±1+(1iαH)ma0.
k,0=k22,k,±1=k22±2m2(i+αH)2+k2q2,
Δk=m1.5+6αH2/q.

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