Abstract

A mathematical model to describe the far-field of a high-power laser diode (LD) beam is presented. The laser beam propagation is studied by the vector Rayleigh–Sommerfeld far-field diffraction integral formula The far-field distribution of the LD beam is studied in detail; the light polarized parallel and perpendicular to the junction plane are all considered. This model is employed to predict the light intensity of high-power LDs. The computed intensity distributions are in a good agreement with the corresponding measurements. This model can be easily used to analyze the propagation properties of the high-power LD beam.

© 2013 Optical Society of America

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References

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2012 (4)

2011 (2)

2009 (3)

2008 (1)

2007 (1)

2006 (1)

2004 (1)

2003 (1)

A. Kozlowska and A. Malag, “Far-field emission characteristics of high-power laser diodes,” Proc. SPIE 5120, 178–183 (2003).
[CrossRef]

1994 (1)

1993 (1)

X. Zeng, “Far-field solution of the Helmholtz equation for double heterostructure diode lasers,” Appl. Phys. A 57, 243–247 (1993).
[CrossRef]

An, Y.

Boiko, D. L.

Burns, D.

Byrne, D.

R. Phelan, J. O’Carroll, and D. Byrne, “In0.75Ga0.25As/InP multiple quantum-well discrete-mode laser diode emitting at 2 μm,” IEEE Photon. Technol. Lett. 24, 652–654 (2012).
[CrossRef]

Chen, S.

Cheng, W.

Chu, S.

Creedon, K. J.

Dong, H.

Feng, Z.

George, J.

Huska, K.

Kansky, J. E.

Kemp, A.

Klinkhammer, S.

Kozlowska, A.

A. Kozlowska and A. Malag, “Far-field emission characteristics of high-power laser diodes,” Proc. SPIE 5120, 178–183 (2003).
[CrossRef]

Lang, L.

J. J. Lim, S. Sujecki, and L. Lang, “Design and simulation of next-generation high-power, high-brightness laser diodes,” IEEE J. Sel. Top. Quantum Electron. 15, 993–1008 (2009).
[CrossRef]

Lim, J. J.

J. J. Lim, S. Sujecki, and L. Lang, “Design and simulation of next-generation high-power, high-brightness laser diodes,” IEEE J. Sel. Top. Quantum Electron. 15, 993–1008 (2009).
[CrossRef]

Lin, S.

Liu, X.

Liu, Y.

Lu, Y.

Maclean, A. J.

Malag, A.

A. Kozlowska and A. Malag, “Far-field emission characteristics of high-power laser diodes,” Proc. SPIE 5120, 178–183 (2003).
[CrossRef]

Nemoto, S.

O’Carroll, J.

R. Phelan, J. O’Carroll, and D. Byrne, “In0.75Ga0.25As/InP multiple quantum-well discrete-mode laser diode emitting at 2 μm,” IEEE Photon. Technol. Lett. 24, 652–654 (2012).
[CrossRef]

Oak, S. M.

Otsuka, K.

Phelan, R.

R. Phelan, J. O’Carroll, and D. Byrne, “In0.75Ga0.25As/InP multiple quantum-well discrete-mode laser diode emitting at 2 μm,” IEEE Photon. Technol. Lett. 24, 652–654 (2012).
[CrossRef]

Redmond, S. M.

Roth, P. W.

Seihgal, R.

Shi, S.

Sujecki, S.

J. J. Lim, S. Sujecki, and L. Lang, “Design and simulation of next-generation high-power, high-brightness laser diodes,” IEEE J. Sel. Top. Quantum Electron. 15, 993–1008 (2009).
[CrossRef]

S. Sujecki, “Stability of steady-state high-power semiconductor laser models,” J. Opt. Soc. Am. B 24, 1053–1060(2007).
[CrossRef]

Vasil’ev, P. P.

Wang, B.

Xie, S.

Yeh, P.

Yeh, S.

Zeng, X.

X. Zeng, Z. Feng, and Y. An, “Far-field expression of a high-power laser diode,” Appl. Opt. 43, 5168–5172 (2004).
[CrossRef]

X. Zeng, “Far-field solution of the Helmholtz equation for double heterostructure diode lasers,” Appl. Phys. A 57, 243–247 (1993).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. A (1)

X. Zeng, “Far-field solution of the Helmholtz equation for double heterostructure diode lasers,” Appl. Phys. A 57, 243–247 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. J. Lim, S. Sujecki, and L. Lang, “Design and simulation of next-generation high-power, high-brightness laser diodes,” IEEE J. Sel. Top. Quantum Electron. 15, 993–1008 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Phelan, J. O’Carroll, and D. Byrne, “In0.75Ga0.25As/InP multiple quantum-well discrete-mode laser diode emitting at 2 μm,” IEEE Photon. Technol. Lett. 24, 652–654 (2012).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (4)

Proc. SPIE (1)

A. Kozlowska and A. Malag, “Far-field emission characteristics of high-power laser diodes,” Proc. SPIE 5120, 178–183 (2003).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Facet of a high-power LD chip and the related coordinate system.

Fig. 2.
Fig. 2.

Calculated intensity profile Ix and Iz in the perpendicular plane (xz plane) for SCT060-830-Z1-01.

Fig. 3.
Fig. 3.

Calculated intensity profile and the measured data of I in the perpendicular plane (xz plane) for SCT060-830-Z1-01.

Fig. 4.
Fig. 4.

Calculated intensity profile Iy and Iz in the parallel plane (yz plane) for SCT060-830-Z1-01.

Fig. 5.
Fig. 5.

Calculated intensity profile and the measured data of I in the parallel plane (yz plane) for SCT060-830-Z1-01.

Fig. 6.
Fig. 6.

Calculated intensity profile Ix and Iz in the perpendicular plane (xz plane) for Hamamatsu L8933.

Fig. 7.
Fig. 7.

Calculated intensity profile and the measured data of I in the perpendicular plane (xz plane) for Hamamatsu L8933.

Fig. 8.
Fig. 8.

Calculated intensity profile Iy and Iz in the parallel plane (yz plane) for Hamamatsu L8933.

Fig. 9.
Fig. 9.

Calculated intensity profile and the measured data of I in the parallel plane (yz plane) for Hamamatsu L8933.

Equations (21)

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2E(r)+k2E(r)=0,
E(r)=12πsE(r0)G(r,r0)nds,
G(r,r0)=exp(ik|rr0|)/|rr0|.
Ex(r)=12πEx(r0)(exp(ik|rr0|)/|rr0|)zds,
Ey(r)=12πEy(r0)(exp(ik|rr0|)/|rr0|)zds,
Ez(r)=12π[Ex(r0)(exp(ik|rr0|)/|rr0|)x+Ey(r0)(exp(ik|rr0|)/|rr0|)y]ds.
Ex(x,y,z)=izλexp(ikr)r2++Ex(x0,y0)exp(ikxx0+yy0r)dx0dy0,
Ey(x,y,z)=izλexp(ikr)r2++Ey(x0,y0)exp(ikxx0+yy0r)dx0dy0,
Ez(x,y,z)=iλexp(ikr)r2++[Ex(x0,y0)(xx0)+Ex(x0,y0)×(yy0)],exp(ikxx0+yy0r)dx0dy0.
Ey(x0,y0)=Ey0exp(p|x0|qy02),
Ex(x0,y0)=Ex0exp(p|x0|qy02),
Ey(x0,y0)=Ey0exp(p|x0|qy02),
Ex(x,y,z)=izEx0λr2πqexp(k2y24qr2)2pr2p2r2+k2x2exp(ikr),
Ey(x,y,z)=izEy0λr2πqexp(k2y24qr2)2pr2p2r2+k2x2exp(ikr),
Ez(x,y,z)=iλπqexp(k2y24qr2)2pp2r2+k2x2,×[Ex0(x+2kxrip2r2+k2x2)+Ey0(yziky2rq)]exp(ikr).
Ix(x,y,z)=z2πEx02λ2q(2pp2r2+k2x2)2exp(k2y22qr2),
Iy(x,y,z)=z2πEy02λ2q(2pp2r2+k2x2)2exp(k2y22qr2),
Iz(x,y,z)=π2λ2q2exp(k2y22qr2)(2pp2r2+k2x2)2,×[Ex0(x+2kxrip2r2+k2x2)+Ey0(yziky2rq)]2,
I(x,y,z)=Ix(x,y,z)+Iy(x,y,z)+Iz(x,y,z),=π2λ2q2exp(k2y22qr2)(2pp2r2+k2x2)2,×{z2Ex02+z2Ey02+[Ex0(x+2kxrip2r2+k2x2)+Ey0(yziky2rq)]2}.
I(x,0,z)=Ix(x,0,z)+Iy(x,0,z)+Iz(x,0,z).
I(0,y,z)=Ix(0,y,z)+Iy(0,y,z)+Iz(0,y,z).

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