Abstract

A reliable technique for measuring near field phase fronts of phased-array semiconductor lasers is proposed and demonstrated. Laterally sheared interferograms are generated in a ring-type interferometer with zero optical path difference between two beams, eliminating problems due to equal optical path requirements in other systems. Fourier transform methods are used to extract phase difference information from the nonuniformly illuminated interferograms, and phase discontinuities between adjacent stripes of carrier-guided laser arrays are observed. Test data agree with theoretical predictions and far field interpretations.

© 1990 Optical Society of America

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References

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  1. D. F. Welch, W. Streifer, R. L. Thornton, T. Paoli, “2.4 W CW, 770 nm Laser Arrays with Nonabsorbing Mirrors,” Electron. Lett. 23, 525–527 (1987).
    [CrossRef]
  2. Y. Twu, S. Wang, J. R. Whinnery, A. Dienes, “Mode Characteristics of Phase-Locked Semiconductor Laser Arrays At and Above Threshold,” IEEE J. Quantum Electron. QE-23, 788–795 (1987).
  3. J. R. Heidel, R. R. Rice, H. R. Appelman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
    [CrossRef]
  4. S. Thaniyavarn, W. Dougherty, “Generation of a Single-Lobe Radiation Pattern from a Phased-Array Laser Using a Near Contact Variable-Phase-Shift Zone Plate,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThA3.
  5. G. C. Dente, K. A. Wilson, T. C. Salvi, D. Depatie, “Phase and Spatial Coherence Measurements on Diode Arrays: Comparison to Supermode Theory,” Appl. Phys. Lett. 51, 9–11 (1987).
    [CrossRef]
  6. N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
    [CrossRef]
  7. J. Yaeli, “Phase Measurement of Laser Diode Array Radiation,” Appl. Phys. Lett. 49, 427–429 (1986).
    [CrossRef]
  8. C. P. Cherng, M. Osiński, J. G. McInerney, “Near-Field Phase Measurements of Phased-Array Diode Laser by Shearing Interferometry,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM9.
  9. W. T. Welford, Aberrations of the Symmetrical Optical System (Adam Hilger, London, 1974).
  10. D. Malacara, Optical Shop Testing (Wiley, New York, 1977), Chap. 4.
  11. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  12. W. W. Macy, “Two-Dimensional Fringe-Pattern Analysis,” Appl. Opt. 22, 3898–3901 (1983).
    [CrossRef] [PubMed]
  13. R. J. Green, J. G. Walker, D. W. Robinson, “Investigation of the Fourier-Transform Method of Fringe Pattern Analysis,” Opt. Lasers Eng. 8, 29–44 (1988).
    [CrossRef]
  14. W. H. Steel, Interferometry (Cambridge U. P., London, 1967), Chaps. 3 & 5.
  15. K. H. Baird, G. R. Hanes, “Interferometers,” in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, New York, 1967), Chap. 9.

1988 (1)

R. J. Green, J. G. Walker, D. W. Robinson, “Investigation of the Fourier-Transform Method of Fringe Pattern Analysis,” Opt. Lasers Eng. 8, 29–44 (1988).
[CrossRef]

1987 (4)

D. F. Welch, W. Streifer, R. L. Thornton, T. Paoli, “2.4 W CW, 770 nm Laser Arrays with Nonabsorbing Mirrors,” Electron. Lett. 23, 525–527 (1987).
[CrossRef]

Y. Twu, S. Wang, J. R. Whinnery, A. Dienes, “Mode Characteristics of Phase-Locked Semiconductor Laser Arrays At and Above Threshold,” IEEE J. Quantum Electron. QE-23, 788–795 (1987).

G. C. Dente, K. A. Wilson, T. C. Salvi, D. Depatie, “Phase and Spatial Coherence Measurements on Diode Arrays: Comparison to Supermode Theory,” Appl. Phys. Lett. 51, 9–11 (1987).
[CrossRef]

N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
[CrossRef]

1986 (2)

J. Yaeli, “Phase Measurement of Laser Diode Array Radiation,” Appl. Phys. Lett. 49, 427–429 (1986).
[CrossRef]

J. R. Heidel, R. R. Rice, H. R. Appelman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

1983 (1)

1982 (1)

Appelman, H. R.

J. R. Heidel, R. R. Rice, H. R. Appelman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

Baird, K. H.

K. H. Baird, G. R. Hanes, “Interferometers,” in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, New York, 1967), Chap. 9.

Carson, N. W.

N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
[CrossRef]

Cherng, C. P.

C. P. Cherng, M. Osiński, J. G. McInerney, “Near-Field Phase Measurements of Phased-Array Diode Laser by Shearing Interferometry,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM9.

Dente, G. C.

G. C. Dente, K. A. Wilson, T. C. Salvi, D. Depatie, “Phase and Spatial Coherence Measurements on Diode Arrays: Comparison to Supermode Theory,” Appl. Phys. Lett. 51, 9–11 (1987).
[CrossRef]

Depatie, D.

G. C. Dente, K. A. Wilson, T. C. Salvi, D. Depatie, “Phase and Spatial Coherence Measurements on Diode Arrays: Comparison to Supermode Theory,” Appl. Phys. Lett. 51, 9–11 (1987).
[CrossRef]

Dienes, A.

Y. Twu, S. Wang, J. R. Whinnery, A. Dienes, “Mode Characteristics of Phase-Locked Semiconductor Laser Arrays At and Above Threshold,” IEEE J. Quantum Electron. QE-23, 788–795 (1987).

Dougherty, W.

S. Thaniyavarn, W. Dougherty, “Generation of a Single-Lobe Radiation Pattern from a Phased-Array Laser Using a Near Contact Variable-Phase-Shift Zone Plate,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThA3.

Evans, G. A.

N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
[CrossRef]

Goldstein, B.

N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
[CrossRef]

Green, R. J.

R. J. Green, J. G. Walker, D. W. Robinson, “Investigation of the Fourier-Transform Method of Fringe Pattern Analysis,” Opt. Lasers Eng. 8, 29–44 (1988).
[CrossRef]

Hanes, G. R.

K. H. Baird, G. R. Hanes, “Interferometers,” in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, New York, 1967), Chap. 9.

Heidel, J. R.

J. R. Heidel, R. R. Rice, H. R. Appelman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

Ina, H.

Kobayashi, S.

Lurie, M.

N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
[CrossRef]

Macy, W. W.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1977), Chap. 4.

Masin, V. J.

N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
[CrossRef]

McInerney, J. G.

C. P. Cherng, M. Osiński, J. G. McInerney, “Near-Field Phase Measurements of Phased-Array Diode Laser by Shearing Interferometry,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM9.

Osinski, M.

C. P. Cherng, M. Osiński, J. G. McInerney, “Near-Field Phase Measurements of Phased-Array Diode Laser by Shearing Interferometry,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM9.

Paoli, T.

D. F. Welch, W. Streifer, R. L. Thornton, T. Paoli, “2.4 W CW, 770 nm Laser Arrays with Nonabsorbing Mirrors,” Electron. Lett. 23, 525–527 (1987).
[CrossRef]

Rice, R. R.

J. R. Heidel, R. R. Rice, H. R. Appelman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

Robinson, D. W.

R. J. Green, J. G. Walker, D. W. Robinson, “Investigation of the Fourier-Transform Method of Fringe Pattern Analysis,” Opt. Lasers Eng. 8, 29–44 (1988).
[CrossRef]

Salvi, T. C.

G. C. Dente, K. A. Wilson, T. C. Salvi, D. Depatie, “Phase and Spatial Coherence Measurements on Diode Arrays: Comparison to Supermode Theory,” Appl. Phys. Lett. 51, 9–11 (1987).
[CrossRef]

Steel, W. H.

W. H. Steel, Interferometry (Cambridge U. P., London, 1967), Chaps. 3 & 5.

Streifer, W.

D. F. Welch, W. Streifer, R. L. Thornton, T. Paoli, “2.4 W CW, 770 nm Laser Arrays with Nonabsorbing Mirrors,” Electron. Lett. 23, 525–527 (1987).
[CrossRef]

Takeda, M.

Thaniyavarn, S.

S. Thaniyavarn, W. Dougherty, “Generation of a Single-Lobe Radiation Pattern from a Phased-Array Laser Using a Near Contact Variable-Phase-Shift Zone Plate,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThA3.

Thornton, R. L.

D. F. Welch, W. Streifer, R. L. Thornton, T. Paoli, “2.4 W CW, 770 nm Laser Arrays with Nonabsorbing Mirrors,” Electron. Lett. 23, 525–527 (1987).
[CrossRef]

Twu, Y.

Y. Twu, S. Wang, J. R. Whinnery, A. Dienes, “Mode Characteristics of Phase-Locked Semiconductor Laser Arrays At and Above Threshold,” IEEE J. Quantum Electron. QE-23, 788–795 (1987).

Walker, J. G.

R. J. Green, J. G. Walker, D. W. Robinson, “Investigation of the Fourier-Transform Method of Fringe Pattern Analysis,” Opt. Lasers Eng. 8, 29–44 (1988).
[CrossRef]

Wang, S.

Y. Twu, S. Wang, J. R. Whinnery, A. Dienes, “Mode Characteristics of Phase-Locked Semiconductor Laser Arrays At and Above Threshold,” IEEE J. Quantum Electron. QE-23, 788–795 (1987).

Welch, D. F.

D. F. Welch, W. Streifer, R. L. Thornton, T. Paoli, “2.4 W CW, 770 nm Laser Arrays with Nonabsorbing Mirrors,” Electron. Lett. 23, 525–527 (1987).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Adam Hilger, London, 1974).

Whinnery, J. R.

Y. Twu, S. Wang, J. R. Whinnery, A. Dienes, “Mode Characteristics of Phase-Locked Semiconductor Laser Arrays At and Above Threshold,” IEEE J. Quantum Electron. QE-23, 788–795 (1987).

Wilson, K. A.

G. C. Dente, K. A. Wilson, T. C. Salvi, D. Depatie, “Phase and Spatial Coherence Measurements on Diode Arrays: Comparison to Supermode Theory,” Appl. Phys. Lett. 51, 9–11 (1987).
[CrossRef]

Yaeli, J.

J. Yaeli, “Phase Measurement of Laser Diode Array Radiation,” Appl. Phys. Lett. 49, 427–429 (1986).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

G. C. Dente, K. A. Wilson, T. C. Salvi, D. Depatie, “Phase and Spatial Coherence Measurements on Diode Arrays: Comparison to Supermode Theory,” Appl. Phys. Lett. 51, 9–11 (1987).
[CrossRef]

N. W. Carson, V. J. Masin, M. Lurie, B. Goldstein, G. A. Evans, “Measurement of the Coherence of a Single-Mode Phase-Locked Diode Laser Array,” Appl. Phys. Lett. 51, 643–645 (1987).
[CrossRef]

J. Yaeli, “Phase Measurement of Laser Diode Array Radiation,” Appl. Phys. Lett. 49, 427–429 (1986).
[CrossRef]

Electron. Lett. (1)

D. F. Welch, W. Streifer, R. L. Thornton, T. Paoli, “2.4 W CW, 770 nm Laser Arrays with Nonabsorbing Mirrors,” Electron. Lett. 23, 525–527 (1987).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Twu, S. Wang, J. R. Whinnery, A. Dienes, “Mode Characteristics of Phase-Locked Semiconductor Laser Arrays At and Above Threshold,” IEEE J. Quantum Electron. QE-23, 788–795 (1987).

J. R. Heidel, R. R. Rice, H. R. Appelman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lasers Eng. (1)

R. J. Green, J. G. Walker, D. W. Robinson, “Investigation of the Fourier-Transform Method of Fringe Pattern Analysis,” Opt. Lasers Eng. 8, 29–44 (1988).
[CrossRef]

Other (6)

W. H. Steel, Interferometry (Cambridge U. P., London, 1967), Chaps. 3 & 5.

K. H. Baird, G. R. Hanes, “Interferometers,” in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, New York, 1967), Chap. 9.

S. Thaniyavarn, W. Dougherty, “Generation of a Single-Lobe Radiation Pattern from a Phased-Array Laser Using a Near Contact Variable-Phase-Shift Zone Plate,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThA3.

C. P. Cherng, M. Osiński, J. G. McInerney, “Near-Field Phase Measurements of Phased-Array Diode Laser by Shearing Interferometry,” in Technical Digest, Conference on Laser and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WM9.

W. T. Welford, Aberrations of the Symmetrical Optical System (Adam Hilger, London, 1974).

D. Malacara, Optical Shop Testing (Wiley, New York, 1977), Chap. 4.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of a ring (or Sagnac) interferometer.

Fig. 2
Fig. 2

Experimental setup for phase difference measurements: BS, beam splitter; M, mirror; PP, parallel plate; and PC, personal computer.

Fig. 3
Fig. 3

Interference pattern of carrier-guided laser array formed by the two counter-propagating beams at the output of the ring interferometer. The relative shear is 5 μm.

Fig. 4
Fig. 4

Near field intensity distribution of one interfering beam.

Fig. 5
Fig. 5

Far field pattern of the laser array corresponding to the near field of Fig. 4.

Fig. 6
Fig. 6

Phase difference plot across the facet, retrieved from data of Fig. 3, showing that the laser array is operating in its highest-order supermode. The solid and broken lines at the bottom of the figure indicate the position of the individual stripe emitters.

Fig. 7
Fig. 7

Interference pattern at the output of the ring interferometer with 10-μm (one-stripe spacing) relative shear.

Fig. 8
Fig. 8

Interference pattern at the output of the ring interferometer with 20-μm (two-stripe spacing) relative shear.

Fig. 9
Fig. 9

Retrieved phase difference plot with 10-μm (one-stripe spacing) relative shear.

Fig. 10
Fig. 10

Retrieved phase difference plot with 20-μm (two-stripe spacing) relative shear.

Equations (11)

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i f ( x , y ) = a ( x , y ) + b ( x , y ) cos [ Φ ( x , y ) + 2 π f o y ] ,
i f ( x , y ) = a ( x , y ) + c ( x , y ) exp [ 2 π i f o y ] + c * ( x , y ) exp [ - 2 π i f o y ] ,
c ( x , y ) = ½ b ( x , y ) exp [ i Φ ( x , y ) ]
I ( x , f ) = A ( x , f ) + C ( x , f - f o ) + C * ( x , f + f o ) ,
Φ ( x , y ) = Im [ ln ½ b ( x , y ) + i Φ ( x , y ) ] ,
Φ ( x , y ) = Φ ( x , y ) - 2 π ( δ f x x + δ f y y ) .
E ( y ) = A ( y ) exp [ i ϕ ( y ) + i π y 2 R λ ] ,
E 1 ( y ) = A 1 ( y ) exp [ i ϕ 1 ( y ) ] = A 1 ( y ) exp [ i ϕ ( y ) + i π y 2 R λ ] ,
E 2 ( y ) = A 2 ( y ) exp [ i ϕ 2 ( y ) + i κ y sin ξ ] = A 1 ( y + Δ y ) exp [ i ϕ ( y + Δ y ) + i π ( y + Δ y ) 2 R λ + i κ y sin ξ ] ,
i f ( y ) = A 1 2 ( y ) + A 2 2 ( y ) + 2 A 1 ( y ) A 2 ( y ) × cos ( ϕ 1 - ϕ 2 - κ y sin ξ + 2 π y Δ y R λ + π Δ y 2 R λ ) .
a = A 1 2 + A 2 2 ,             b = 2 A 1 A 2 ,             i f = I ,             - κ y sin ξ + 2 π y Δ y R λ = 2 π f o y , Φ = ϕ 1 - ϕ 2 + π Δ y 2 R λ .

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