Abstract

Two physically separated laser diode arrays were simultaneously injection-locked to the same master laser. The modulus of their mutual coherence function was measured, and the resulting value 0.96 ± 0.06 was close to the maximum allowed value of 1. The spatial phase of the two injection-locked outputs did not vary from each other by more than 0.05 wave (λ/20), apart from a phase difference that grew linearly with position, due to the tilt between the two interfering beams. Requirements for the coherent combination of injection-locked laser diode arrays are discussed.

© 1991 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986) Chap. 29.
  2. L. Goldberg, J. F. Weller, “Injection Locking and Single-Mode Fiber Coupling of a 40-Element Laser Diode Array,” Appl. Phys. Lett. 50, 1713–1715 (June1987).
    [Crossref]
  3. S.-Q. Shang, H. J. Metcalf, “Narrowband, High Power Light from Diode Lasers,” Appl. Opt. 28, 1618–1623 (1989).
    [Crossref] [PubMed]
  4. M. Jansen et al., “Coherent Operation of Injection Locked Monolithic Surface-Emitting Diode Laser Arrays,” Appl. Phys. Lett. 54, 2634–2636 (1989).
    [Crossref]
  5. After submission of this paper the author was made aware of the recent work of Verdiell who has also injection-locked two laser diode arrays simultaneously [J. M. Verdiell et al., “Efficient Diffraction-Limited Beam Combining of Semiconductor Laser Diode Arrays Using Photorefractive BaTiO3,” Conference on Lasers and Electro-Optics, 1990 Technical Digest Series, Vol. 7 (Optical Society of America, Washington, DC, 1990), postdead-line paper CPDP27].
  6. A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987), p. 543.
  8. J. P. Hohimer, A. Owyoung, G. R. Hadley, “Single-Channel Injection Locking of a Diode-Laser Array with a CW Dye Laser,” Appl. Phys. Lett. 47, 1244–1246 (1985).
    [Crossref]

1989 (2)

S.-Q. Shang, H. J. Metcalf, “Narrowband, High Power Light from Diode Lasers,” Appl. Opt. 28, 1618–1623 (1989).
[Crossref] [PubMed]

M. Jansen et al., “Coherent Operation of Injection Locked Monolithic Surface-Emitting Diode Laser Arrays,” Appl. Phys. Lett. 54, 2634–2636 (1989).
[Crossref]

1987 (1)

L. Goldberg, J. F. Weller, “Injection Locking and Single-Mode Fiber Coupling of a 40-Element Laser Diode Array,” Appl. Phys. Lett. 50, 1713–1715 (June1987).
[Crossref]

1985 (1)

J. P. Hohimer, A. Owyoung, G. R. Hadley, “Single-Channel Injection Locking of a Diode-Laser Array with a CW Dye Laser,” Appl. Phys. Lett. 47, 1244–1246 (1985).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987), p. 543.

Goldberg, L.

L. Goldberg, J. F. Weller, “Injection Locking and Single-Mode Fiber Coupling of a 40-Element Laser Diode Array,” Appl. Phys. Lett. 50, 1713–1715 (June1987).
[Crossref]

Hadley, G. R.

J. P. Hohimer, A. Owyoung, G. R. Hadley, “Single-Channel Injection Locking of a Diode-Laser Array with a CW Dye Laser,” Appl. Phys. Lett. 47, 1244–1246 (1985).
[Crossref]

Hohimer, J. P.

J. P. Hohimer, A. Owyoung, G. R. Hadley, “Single-Channel Injection Locking of a Diode-Laser Array with a CW Dye Laser,” Appl. Phys. Lett. 47, 1244–1246 (1985).
[Crossref]

Jansen, M.

M. Jansen et al., “Coherent Operation of Injection Locked Monolithic Surface-Emitting Diode Laser Arrays,” Appl. Phys. Lett. 54, 2634–2636 (1989).
[Crossref]

Marathay, A. S.

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).

Metcalf, H. J.

Owyoung, A.

J. P. Hohimer, A. Owyoung, G. R. Hadley, “Single-Channel Injection Locking of a Diode-Laser Array with a CW Dye Laser,” Appl. Phys. Lett. 47, 1244–1246 (1985).
[Crossref]

Shang, S.-Q.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986) Chap. 29.

Verdiell, J. M.

After submission of this paper the author was made aware of the recent work of Verdiell who has also injection-locked two laser diode arrays simultaneously [J. M. Verdiell et al., “Efficient Diffraction-Limited Beam Combining of Semiconductor Laser Diode Arrays Using Photorefractive BaTiO3,” Conference on Lasers and Electro-Optics, 1990 Technical Digest Series, Vol. 7 (Optical Society of America, Washington, DC, 1990), postdead-line paper CPDP27].

Weller, J. F.

L. Goldberg, J. F. Weller, “Injection Locking and Single-Mode Fiber Coupling of a 40-Element Laser Diode Array,” Appl. Phys. Lett. 50, 1713–1715 (June1987).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987), p. 543.

Appl. Opt. (1)

Appl. Phys. Lett. (3)

M. Jansen et al., “Coherent Operation of Injection Locked Monolithic Surface-Emitting Diode Laser Arrays,” Appl. Phys. Lett. 54, 2634–2636 (1989).
[Crossref]

L. Goldberg, J. F. Weller, “Injection Locking and Single-Mode Fiber Coupling of a 40-Element Laser Diode Array,” Appl. Phys. Lett. 50, 1713–1715 (June1987).
[Crossref]

J. P. Hohimer, A. Owyoung, G. R. Hadley, “Single-Channel Injection Locking of a Diode-Laser Array with a CW Dye Laser,” Appl. Phys. Lett. 47, 1244–1246 (1985).
[Crossref]

Other (4)

A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986) Chap. 29.

After submission of this paper the author was made aware of the recent work of Verdiell who has also injection-locked two laser diode arrays simultaneously [J. M. Verdiell et al., “Efficient Diffraction-Limited Beam Combining of Semiconductor Laser Diode Arrays Using Photorefractive BaTiO3,” Conference on Lasers and Electro-Optics, 1990 Technical Digest Series, Vol. 7 (Optical Society of America, Washington, DC, 1990), postdead-line paper CPDP27].

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1987), p. 543.

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Figures (4)

Fig. 1
Fig. 1

Simplified schematic of the experiment. The polarization of the master laser is parallel to the plane of the pn junction of the laser diode arrays (the plane in which the figure is drawn).

Fig. 2
Fig. 2

Modulus of the mutual coherence function |g(τ)| for the master laser is plotted vs delay time τ. The open circles are data points, and the solid line is a least-squares fit of a Gaussian function to the data. The rms coherence time derived from the fit and Eq. (3) is Δτ = 5.6 ± 0.25 ns.

Fig. 3
Fig. 3

Spectrum of the master laser g(ν) is plotted as a function of the detuning from line center. The dots are the data points, and the solid line represents a least-squares fit of a Gaussian function to the data. The rms bandwidth derived from the fit to several spectra and Eq. (3) is Δν = 14.6 ± 0.7 MHz.

Fig. 4
Fig. 4

Spatial intensity profiles parallel to the laser diode array pn junction are shown for the injection-locked outputs from laser diode array 1(a), array 2(b), and the interference between them (c). The least-squares fit of Eq. 1 to the data is indicated by the dots. The modulus of the mutual coherence function derived from the fit is |g12(τ = 1 ns)| = 0.96 ± 0.06. Curves a, b, and c are offset for the purpose of display.

Equations (5)

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I ( x ) = I 1 ( x ) + I 2 ( x ) + 2 | g 12 ( τ ) | I 1 ( x ) I 2 ( x ) · cos ( b · x + Δ ϕ ) .
g 12 ( τ ) = E 1 ( t + τ ) E 2 * ( t ) | E 1 | 2 | E 2 | 2 .
( Δ τ ) 2 = τ 2 | g ( τ ) | 2 d τ | g ( τ ) | 2 d τ , ( Δ ν ) 2 = 0 ( ν ν ¯ ) 2 | g ( ν ) | 2 d ν 0 | g ( ν ) | 2 d ν .
Δ τ Δ ν 1 4 π .
Δ Φ = sin 1 ( ω o ω ω m ) ,

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