Abstract

Using a self-imaged diffraction coupled model in a Talbot cavity for vertical cavity surface emitting laser arrays, the effect of self-imaged reflections on the lasing threshold of a finite 2-D array was investigated. Array size and the ratio defined by the element diameter/element spacing were found to affect the effective reflectivity as seen from the laser cavities and, ultimately, the device threshold. A general curve showing the dependence of the 2-D coupling coefficient on the array fill factor and array size has been found. Minimum levels of laser facet reflectivities have been obtained as a function of the array fill factor for practical devices with low threshold current densities.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979).
    [CrossRef]
  2. P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977).
    [CrossRef]
  3. See, e.g., D. Botez, “Phased-Locked Arrays of Semiconductor Diode Lasers,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThAl and references therein.
  4. See, e.g., K. Iga, F. Koyama, S. Kinoshita, “Surface Emitting Semiconductor Lasers,” IEEE J. Quantum Electron. QE-24, 1845–1855 (1988) and references therein.
    [CrossRef]
  5. J. L. Jewell et al., “Low Threshold Electrically-Pumped Vertical-Cavity Surface Emitting MicroLasers,” in Postdeadline Papers, Seventh International Conference on Integrated Optics and Optical Fiber Communication, Kobe, Japan (1989), Session 18B2-6.
  6. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: An Application of the Planar Micro-lens,” Appl. Opt. 21, 3456–3460 (1982).
    [CrossRef] [PubMed]
  7. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 403–410 (1936).
  8. J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent Addition of AlGaAs Lasers Using Microlenses and Diffractive Coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
    [CrossRef]
  9. J. R. Leger, “Lateral Mode Control of an AlGaAs Laser Array in a Talbot Cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
    [CrossRef]
  10. F. X. D’Amato, E. T. Siebert, C. Royshoudhuri, “Coherent Operation of an Array of Diode Lasers Using a Spatial Filter in a Talbot Cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
    [CrossRef]
  11. F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers With Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
    [CrossRef]
  12. For simplicity, only the magniude of κ is used throughout this paper by assuming that the phase part of κ, together with the propagation phase, can be arbitrarily adjusted near the vicinity of Talbot planes. In actuality, κ contains rapid oscillations due to the reflection phase term. Some slight phase curvature due to finite self-imaging also introduces a phase shift in κ, but at Talbot planes this phase shift is small.
  13. H. Soda, Y. Motegi, K. Iga, “GaInAsP/InP Surface Emitting Injection Laser with a Ring Electrode,” IEEE J. Quantum Electron. QE-19, 1035–1041 (1983).
    [CrossRef]
  14. Hysteresis in the I–L curve may be expected as self-imaging only occurs for coherent light; i.e., κ will be small before phase-locked operation of individual elements. After the onset of phase locking, self-imaged feedback causes the effective reflectivity to increase and the array will effectively have a lower threshold. For each lasing element without self-imaged feedback, Reff ≈ R2, and the initial lasing threshold will be determined mainly by R1,R2.

1989 (2)

J. R. Leger, “Lateral Mode Control of an AlGaAs Laser Array in a Talbot Cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[CrossRef]

F. X. D’Amato, E. T. Siebert, C. Royshoudhuri, “Coherent Operation of an Array of Diode Lasers Using a Spatial Filter in a Talbot Cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

1988 (3)

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers With Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

See, e.g., K. Iga, F. Koyama, S. Kinoshita, “Surface Emitting Semiconductor Lasers,” IEEE J. Quantum Electron. QE-24, 1845–1855 (1988) and references therein.
[CrossRef]

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent Addition of AlGaAs Lasers Using Microlenses and Diffractive Coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

1983 (1)

H. Soda, Y. Motegi, K. Iga, “GaInAsP/InP Surface Emitting Injection Laser with a Ring Electrode,” IEEE J. Quantum Electron. QE-19, 1035–1041 (1983).
[CrossRef]

1982 (1)

1979 (1)

C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979).
[CrossRef]

1977 (1)

P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977).
[CrossRef]

1936 (1)

F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 403–410 (1936).

Banno, J.

Botez, D.

See, e.g., D. Botez, “Phased-Locked Arrays of Semiconductor Diode Lasers,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThAl and references therein.

D’Amato, F. X.

F. X. D’Amato, E. T. Siebert, C. Royshoudhuri, “Coherent Operation of an Array of Diode Lasers Using a Spatial Filter in a Talbot Cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Goodwin, A. R.

P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977).
[CrossRef]

Henry, C. H.

C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979).
[CrossRef]

Iga, K.

See, e.g., K. Iga, F. Koyama, S. Kinoshita, “Surface Emitting Semiconductor Lasers,” IEEE J. Quantum Electron. QE-24, 1845–1855 (1988) and references therein.
[CrossRef]

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers With Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

H. Soda, Y. Motegi, K. Iga, “GaInAsP/InP Surface Emitting Injection Laser with a Ring Electrode,” IEEE J. Quantum Electron. QE-19, 1035–1041 (1983).
[CrossRef]

K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: An Application of the Planar Micro-lens,” Appl. Opt. 21, 3456–3460 (1982).
[CrossRef] [PubMed]

Jewell, J. L.

J. L. Jewell et al., “Low Threshold Electrically-Pumped Vertical-Cavity Surface Emitting MicroLasers,” in Postdeadline Papers, Seventh International Conference on Integrated Optics and Optical Fiber Communication, Kobe, Japan (1989), Session 18B2-6.

Kinoshita, S.

See, e.g., K. Iga, F. Koyama, S. Kinoshita, “Surface Emitting Semiconductor Lasers,” IEEE J. Quantum Electron. QE-24, 1845–1855 (1988) and references therein.
[CrossRef]

Kirby, P. A.

P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977).
[CrossRef]

Kokubun, Y.

Koyama, F.

See, e.g., K. Iga, F. Koyama, S. Kinoshita, “Surface Emitting Semiconductor Lasers,” IEEE J. Quantum Electron. QE-24, 1845–1855 (1988) and references therein.
[CrossRef]

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers With Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

Leger, J. R.

J. R. Leger, “Lateral Mode Control of an AlGaAs Laser Array in a Talbot Cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[CrossRef]

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent Addition of AlGaAs Lasers Using Microlenses and Diffractive Coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Logan, R. A.

C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979).
[CrossRef]

Meritt, F. R.

C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979).
[CrossRef]

Misawa, S.

Motegi, Y.

H. Soda, Y. Motegi, K. Iga, “GaInAsP/InP Surface Emitting Injection Laser with a Ring Electrode,” IEEE J. Quantum Electron. QE-19, 1035–1041 (1983).
[CrossRef]

Oikawa, M.

Petroff, P. M.

C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979).
[CrossRef]

Royshoudhuri, C.

F. X. D’Amato, E. T. Siebert, C. Royshoudhuri, “Coherent Operation of an Array of Diode Lasers Using a Spatial Filter in a Talbot Cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Scott, M. L.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent Addition of AlGaAs Lasers Using Microlenses and Diffractive Coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Selway, P. R.

P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977).
[CrossRef]

Siebert, E. T.

F. X. D’Amato, E. T. Siebert, C. Royshoudhuri, “Coherent Operation of an Array of Diode Lasers Using a Spatial Filter in a Talbot Cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Soda, H.

H. Soda, Y. Motegi, K. Iga, “GaInAsP/InP Surface Emitting Injection Laser with a Ring Electrode,” IEEE J. Quantum Electron. QE-19, 1035–1041 (1983).
[CrossRef]

Talbot, F.

F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 403–410 (1936).

Thompson, G. H. B.

P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977).
[CrossRef]

Tomomatsu, K.

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers With Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent Addition of AlGaAs Lasers Using Microlenses and Diffractive Coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent Addition of AlGaAs Lasers Using Microlenses and Diffractive Coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

J. R. Leger, “Lateral Mode Control of an AlGaAs Laser Array in a Talbot Cavity,” Appl. Phys. Lett. 55, 334–336 (1989).
[CrossRef]

F. X. D’Amato, E. T. Siebert, C. Royshoudhuri, “Coherent Operation of an Array of Diode Lasers Using a Spatial Filter in a Talbot Cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

F. Koyama, K. Tomomatsu, K. Iga, “GaAs Surface Emitting Lasers With Circular Buried Heterostructure Grown by Metalorganic Chemical Vapor Deposition and Two-Dimensional Laser Array,” Appl. Phys. Lett. 52, 528–529 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

See, e.g., K. Iga, F. Koyama, S. Kinoshita, “Surface Emitting Semiconductor Lasers,” IEEE J. Quantum Electron. QE-24, 1845–1855 (1988) and references therein.
[CrossRef]

H. Soda, Y. Motegi, K. Iga, “GaInAsP/InP Surface Emitting Injection Laser with a Ring Electrode,” IEEE J. Quantum Electron. QE-19, 1035–1041 (1983).
[CrossRef]

J. Appl. Phys. (1)

C. H. Henry, P. M. Petroff, R. A. Logan, F. R. Meritt, “Catastrophic Damage of AlxGa1−xAs Double-Heterostructure Laser Material,” J. Appl. Phys. 50, 3721–3723 (1979).
[CrossRef]

J. Quantum Electron. (1)

P. A. Kirby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, “Observation of Self-Focusing in Stripe Geometry Semiconductor Laser and the Development of a Comprehensive Model of Their Operation,” J. Quantum Electron. QE-13, 705–719 (1977).
[CrossRef]

Philos. Mag. (1)

F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 403–410 (1936).

Other (4)

Hysteresis in the I–L curve may be expected as self-imaging only occurs for coherent light; i.e., κ will be small before phase-locked operation of individual elements. After the onset of phase locking, self-imaged feedback causes the effective reflectivity to increase and the array will effectively have a lower threshold. For each lasing element without self-imaged feedback, Reff ≈ R2, and the initial lasing threshold will be determined mainly by R1,R2.

See, e.g., D. Botez, “Phased-Locked Arrays of Semiconductor Diode Lasers,” in Technical Digest, Topical Meeting on Semiconductor Lasers (Optical Society of America, Washington, DC, 1987), paper ThAl and references therein.

J. L. Jewell et al., “Low Threshold Electrically-Pumped Vertical-Cavity Surface Emitting MicroLasers,” in Postdeadline Papers, Seventh International Conference on Integrated Optics and Optical Fiber Communication, Kobe, Japan (1989), Session 18B2-6.

For simplicity, only the magniude of κ is used throughout this paper by assuming that the phase part of κ, together with the propagation phase, can be arbitrarily adjusted near the vicinity of Talbot planes. In actuality, κ contains rapid oscillations due to the reflection phase term. Some slight phase curvature due to finite self-imaging also introduces a phase shift in κ, but at Talbot planes this phase shift is small.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Device schematic of MOCVD grown GaAs/GaAlAs 5 × 5 SE laser array.

Fig. 2
Fig. 2

The 5 × 5 SE laser array (a) near field and (b) far field patterns. Apparent intensity nonuniformity is partly due to saturation of the video analyzer gain. The array was operated at I = 2.2Ith.

Fig. 3
Fig. 3

Self-imaged SE laser array model: D, element diameter; p, array pitch; and R1, R2, R3, back (bonding side), front (output side), and external mirror power reflectivities, respectively.

Fig. 4
Fig. 4

Two-dimensional coupling coefficient κ as a function of normalized propagation distance for various array sizes. D/p is assumed to be 0.5. Propagation distance is normalized by the first Talbot plane distance 2Z0. Two-dimensional intensity profiles for points marked (a), (b), (c), and (d) corresponding to the 3 × 3 array are shown in Fig. 5.

Fig. 5
Fig. 5

Two-dimensional intensity pattern for 3 × 3 arrays at various positions marked in Fig. 4. Intensity profile for (a) point (a) of Fig. 4; (b) point (b) of Fig. 4; (c) point (c) of Fig. 4; (d) point (d) of Fig. 4. Actual parameters for the original pattern at point (a): D/p = 0.5; p = 10 μm; and λ = 0.885 μm. Note that intensity scales are normalized by the maximum value in each plot.

Fig. 6
Fig. 6

Levels of constant κ as determined by the array fill factor D/p and array size NP at the first Talbot plane.

Fig. 7
Fig. 7

Model for the effective reflectivity.

Fig. 8
Fig. 8

Threshold current density Jth vs array fill factor for various levels of front (output side) reflectivity R2. Shown are results for 6 × 6 arrays with R1 = R3 = 0.95.

Fig. 9
Fig. 9

Dependence of minimum levels of R2 required for set levels of Jth on array fill factor D/p. Shown are results for 6 × 6 arrays with R1 = R3 = 0.95.

Tables (1)

Tables Icon

Table I Parameters Used for Threshold Current Density Calculation of Eq. (4)

Equations (7)

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

2 Z 0 = 2 m p 2 λ ,
κ = G ( x 1 , y 1 , z ) · H * ( x 2 y 2 z ) d x d y ( G ( x 1 , y 1 , z ) · G * ( x 1 , y 1 , z ) d x d y ) 1 / 2 ,
H ( x 2 , y 2 , z ) = j λ z exp ( - j k z ) × { G ( x 1 , y 1 , z ) exp [ - ( j k / 2 z ) ( x 2 - x 1 ) 2 ] × exp [ - ( j k / 2 z ) ( y 2 - y 1 ) 2 ] } d x 1 d y 1 .
J th = e d B eff A 0 2 [ α ac + α in - α ex + α ex L d + 1 d ln ( 1 R 1 R eff ) ] 2 .
R eff = R 2 + ( 1 - R 2 ) R 3 κ 1 exp ( - 2 j k Z 0 ) 1 + ( R 2 R 2 ) κ 1 exp ( - 2 j k Z 0 ) .
R 2 = exp ( U ) - R 1 R 3 κ 1 R 1 - R 3 κ 1 exp ( U ) ,
U = d [ α - ( J th / β ) ] , α = α ac + α in - α ex + α ex L d , β = e d B eff A 0 2 .

Metrics