Abstract

We measure the complex-valued spatial coherence function of a multimode broad-area laser diode using Young’s classical double slit experiment realized with a digital micromirror device. We use this data to construct the coherent modes of the beam and to simulate its propagation before and after the measurement plane. When comparing the results to directly measured intensity profiles, we find excellent correspondence to the extent that even small details of the beam can be predicted. We also consider the number of measurement points required to model the beam with sufficient accuracy.

© 2014 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
    [CrossRef]
  3. B. Anderson and P. Fuhr, Opt. Eng. 32, 926 (1993).
    [CrossRef]
  4. M. Santarsiero and R. Borghi, Opt. Lett. 31, 861 (2006).
    [CrossRef]
  5. Y. Mejia and A. Gonzalez, Opt. Commun. 273, 428 (2007).
    [CrossRef]
  6. D. Dudley, W. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
    [CrossRef]
  7. M. Sheikh and N. Riza, IEEE Photon. Technol. Lett. 21, 666 (2009).
    [CrossRef]
  8. H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.
  9. A. C. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
    [CrossRef]
  10. N. Stelmakh, IEEE Photon. Technol. Lett. 18, 1618 (2006).
    [CrossRef]
  11. H. Partanen, J. Tervo, and J. Turunen, Appl. Opt. 52, 3221 (2013).
    [CrossRef]

2013

2009

M. Sheikh and N. Riza, IEEE Photon. Technol. Lett. 21, 666 (2009).
[CrossRef]

2007

Y. Mejia and A. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

2006

N. Stelmakh, IEEE Photon. Technol. Lett. 18, 1618 (2006).
[CrossRef]

M. Santarsiero and R. Borghi, Opt. Lett. 31, 861 (2006).
[CrossRef]

2003

D. Dudley, W. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

1993

B. Anderson and P. Fuhr, Opt. Eng. 32, 926 (1993).
[CrossRef]

1989

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

1967

A. C. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
[CrossRef]

Anderson, B.

B. Anderson and P. Fuhr, Opt. Eng. 32, 926 (1993).
[CrossRef]

Borghi, R.

Dudley, D.

D. Dudley, W. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

Duncan, W.

D. Dudley, W. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

Friberg, A. T.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Fuhr, P.

B. Anderson and P. Fuhr, Opt. Eng. 32, 926 (1993).
[CrossRef]

Gonzalez, A.

Y. Mejia and A. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Mejia, Y.

Y. Mejia and A. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

Osten, W.

H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.

Partanen, H.

H. Partanen, J. Tervo, and J. Turunen, Appl. Opt. 52, 3221 (2013).
[CrossRef]

H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.

Peterhaensel, S.

H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.

Pruss, C.

H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.

Riza, N.

M. Sheikh and N. Riza, IEEE Photon. Technol. Lett. 21, 666 (2009).
[CrossRef]

Santarsiero, M.

Schell, A. C.

A. C. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
[CrossRef]

Sheikh, M.

M. Sheikh and N. Riza, IEEE Photon. Technol. Lett. 21, 666 (2009).
[CrossRef]

Slaughter, J.

D. Dudley, W. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

Stelmakh, N.

N. Stelmakh, IEEE Photon. Technol. Lett. 18, 1618 (2006).
[CrossRef]

Tervo, J.

H. Partanen, J. Tervo, and J. Turunen, Appl. Opt. 52, 3221 (2013).
[CrossRef]

H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.

Tervonen, E.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Turunen, J.

H. Partanen, J. Tervo, and J. Turunen, Appl. Opt. 52, 3221 (2013).
[CrossRef]

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Appl. Opt.

Appl. Phys. B

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Sheikh and N. Riza, IEEE Photon. Technol. Lett. 21, 666 (2009).
[CrossRef]

N. Stelmakh, IEEE Photon. Technol. Lett. 18, 1618 (2006).
[CrossRef]

IEEE Trans. Antennas Propag.

A. C. Schell, IEEE Trans. Antennas Propag. 15, 187 (1967).
[CrossRef]

Opt. Commun.

Y. Mejia and A. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

Opt. Eng.

B. Anderson and P. Fuhr, Opt. Eng. 32, 926 (1993).
[CrossRef]

Opt. Lett.

Proc. SPIE

D. Dudley, W. Duncan, and J. Slaughter, Proc. SPIE 4985, 14 (2003).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

H. Partanen, S. Peterhaensel, C. Pruss, W. Osten, J. Tervo, and J. Turunen, in Fringe 2013, W. Osten, ed. (Springer, 2014), p. 879.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Measurement system. (b) Arrangement of the micromirrors, Young’s slits, and the laser spot.

Fig. 2.
Fig. 2.

Example of interference fringes with slits at positions x1=129.6μm and x2=21.6μm. (a) Fringes recorded directly by the camera and (b) the normalized interference patterns defined in Eq. (5).

Fig. 3.
Fig. 3.

Measured coherence function with driving current 700 mA. (a) Absolute value |J(x1,x2)|, (b) normalized absolute value |μ(x1,x2)|, (c) directly measured phase ϕ(x1,x2), and (d) phase retrieved by canceling the spherical phase introduced by the imaging system.

Fig. 4.
Fig. 4.

Beam propagation from 64 to 60 mm. (a) Simulated from measured coherence data. (b) Directly measured intensity profiles. (c)–(e) Simulated (solid black) and measured (dashed red) intensities at three particular distances.

Fig. 5.
Fig. 5.

Normalized absolute values of mutual intensity functions with four driving currents.

Fig. 6.
Fig. 6.

Normalized first 47 and last 12 eigenvalues with four driving currents.

Fig. 7.
Fig. 7.

Beam intensity profiles in the 700 mA case propagated to z=30mm with different numbers of sampling points.

Equations (8)

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

J(x1,x2)=mImvm*(x1)vm(x2).
J(x1,x2)vm(x1)dx1=Imvm(x2),
μ(x1,x2)=J(x1,x2)[I(x1)I(x2)]1/2=|μ(x1,x2)|exp[iϕ(x1,x2)],
I(x)=I1(x)+I2(x)+2[I1(x)I2(x)]1/2×|μ(x1,x2)|cos[ϕ(x1,x2)+4πadλ0x],
C(x)=I(x)I1(x)I2(x)2[I1(x)I2(x)]1/2=|μ(x1,x2)|cos[ϕ(x1,x2)+4πadλ0x].
J(x1,x2,z)=Fkx2{Fkx11[A(kx1,kx2)×exp(ikz1z)]exp(ikz2z)},
A(kx1,kx2)=Fx21{Fx1[J(x1,x2)]}
ϕ(x1,x2)=k02Mf(x12x22)=B(x12x22),

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