Abstract

We investigate theoretically the effect of two-dimensional photonic crystal (PC) defect waveguide parameters embedded into vertical-cavity surface-emitting lasers (VCSELs) on static operation of PC-VCSEL, including spatial hole burning (SHB) and temperature in the active regions. In structures with larger pitch of PC holes, SHB occurs dramatically and temperature increases in the active region. In large-hole diameter to pitch ratio, SHB has little effect and temperature is decreased in the active regions. We also show that with higher input current, temperature rises and SHB occurs.

© 2012 Optical Society of America

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References

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  1. S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley, 2003).
  2. C. Wilmsen, H. Temkin, and L. A. Coldren, Vertical-Cavity Surface-Emitting Lasers Design, Fabrication, Characterization and Applications (Cambridge University, 1999).
  3. K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Quantum Electron. 6, 1201–1215 (2000).
    [CrossRef]
  4. J. Gao, “An analytical method to determine small-signal model parameters for vertical-cavity surface emitting lasers,” J. Lightwave Technol. 28, 1332–1337 (2010).
    [CrossRef]
  5. L.-G. Zei, S. Ebers, J.-R. Kropp, and K. Peterman, “Noise performance of multimode VCSELs,” J. Lightwave Technol. 19, 884–892 (2001).
    [CrossRef]
  6. J. Perchoux, A. Rissons, and J.-C. Mollier, “Multimode VCSEL model for wide frequency-range RIN simulation,” Opt. Commun. 281, 162–169 (2008).
    [CrossRef]
  7. M. S. Alias, S. Shaari, P. O. Leisher, and K. D. Choquette, “Single transverse mode control of VCSEL by photonic crystal and trench patterning,” Photon. Nanostruct. 8, 38–46 (2010).
    [CrossRef]
  8. N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1439–1445 (2003).
    [CrossRef]
  9. N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
    [CrossRef]
  10. P. S. Ivanov, M. Dragas, M. Cryan, and J. M. Rorison, “Theoretical investigation of transverse optical modes in photonic-crystal waveguides imbedded into proton-implanted and oxide-confined vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 22, 2270–2276 (2005).
    [CrossRef]
  11. P. Ivanov and J. Rorison, “Theoretical optimization of transverse waveguiding in oxide-confined VCSELs with internal photonic crystals,” J. Opt. Soc. Am. B 26, 2461–2468 (2009).
    [CrossRef]
  12. M. Dems, I.-S. Chung, P. Nyakas, S. Bischoff, and K. Panajotov, “Numerical methods for modeling photonic-crystal VCSELs,” Opt. Express 18, 16042–16054 (2010).
    [CrossRef]
  13. P. S. Ivanov and J. M. Rorison, “Theoretical investigation of static and dynamic characteristics of vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals,” Opt. Quantum Electron. 42, 193–213 (2010).
    [CrossRef]
  14. G. Haghighat, V. Ahmadi, and S. Pahlavan, “Analysis of SHB and thermal characteristics in PC-VCSEL considering photonic crystal parameters,” Proc. SPIE 8308, 83082G (2011).
    [CrossRef]
  15. Y. G. Zhao and J. G. McInerney, “Transverse-mode control of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1950–1958 (1996).
    [CrossRef]
  16. H. C. Casey and M. B. Panish, Heterostructure Lasers(Academic, 1978).
  17. Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
    [CrossRef]
  18. W. Nakwaski, “Simplified modeling of photonic-crystal-confined vertical-cavity surface-emitting diode lasers,” Opt. Appl. 35, 579–589 (2005).
  19. G. Haghighat and V. Ahmadi, “Threshold analysis of vertical-cavity surface-emitting laser with internal photonic crystal waveguide,” in IEEE Conference Symposium on Photonics and Optoelectronics (SOPO, 2012), pp. 1–2.

2011

G. Haghighat, V. Ahmadi, and S. Pahlavan, “Analysis of SHB and thermal characteristics in PC-VCSEL considering photonic crystal parameters,” Proc. SPIE 8308, 83082G (2011).
[CrossRef]

2010

M. S. Alias, S. Shaari, P. O. Leisher, and K. D. Choquette, “Single transverse mode control of VCSEL by photonic crystal and trench patterning,” Photon. Nanostruct. 8, 38–46 (2010).
[CrossRef]

P. S. Ivanov and J. M. Rorison, “Theoretical investigation of static and dynamic characteristics of vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals,” Opt. Quantum Electron. 42, 193–213 (2010).
[CrossRef]

J. Gao, “An analytical method to determine small-signal model parameters for vertical-cavity surface emitting lasers,” J. Lightwave Technol. 28, 1332–1337 (2010).
[CrossRef]

M. Dems, I.-S. Chung, P. Nyakas, S. Bischoff, and K. Panajotov, “Numerical methods for modeling photonic-crystal VCSELs,” Opt. Express 18, 16042–16054 (2010).
[CrossRef]

2009

2008

J. Perchoux, A. Rissons, and J.-C. Mollier, “Multimode VCSEL model for wide frequency-range RIN simulation,” Opt. Commun. 281, 162–169 (2008).
[CrossRef]

2005

2003

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1439–1445 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

2001

2000

K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

1996

Y. G. Zhao and J. G. McInerney, “Transverse-mode control of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1950–1958 (1996).
[CrossRef]

1995

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

Ahmadi, V.

G. Haghighat, V. Ahmadi, and S. Pahlavan, “Analysis of SHB and thermal characteristics in PC-VCSEL considering photonic crystal parameters,” Proc. SPIE 8308, 83082G (2011).
[CrossRef]

G. Haghighat and V. Ahmadi, “Threshold analysis of vertical-cavity surface-emitting laser with internal photonic crystal waveguide,” in IEEE Conference Symposium on Photonics and Optoelectronics (SOPO, 2012), pp. 1–2.

Alias, M. S.

M. S. Alias, S. Shaari, P. O. Leisher, and K. D. Choquette, “Single transverse mode control of VCSEL by photonic crystal and trench patterning,” Photon. Nanostruct. 8, 38–46 (2010).
[CrossRef]

Bischoff, S.

Casey, H. C.

H. C. Casey and M. B. Panish, Heterostructure Lasers(Academic, 1978).

Choquette, K. D.

M. S. Alias, S. Shaari, P. O. Leisher, and K. D. Choquette, “Single transverse mode control of VCSEL by photonic crystal and trench patterning,” Photon. Nanostruct. 8, 38–46 (2010).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1439–1445 (2003).
[CrossRef]

Chung, I.-S.

Coldren, L. A.

C. Wilmsen, H. Temkin, and L. A. Coldren, Vertical-Cavity Surface-Emitting Lasers Design, Fabrication, Characterization and Applications (Cambridge University, 1999).

Cryan, M.

Danner, A. J.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1439–1445 (2003).
[CrossRef]

Dems, M.

Dragas, M.

Ebers, S.

Gao, J.

Haghighat, G.

G. Haghighat, V. Ahmadi, and S. Pahlavan, “Analysis of SHB and thermal characteristics in PC-VCSEL considering photonic crystal parameters,” Proc. SPIE 8308, 83082G (2011).
[CrossRef]

G. Haghighat and V. Ahmadi, “Threshold analysis of vertical-cavity surface-emitting laser with internal photonic crystal waveguide,” in IEEE Conference Symposium on Photonics and Optoelectronics (SOPO, 2012), pp. 1–2.

Iga, K.

K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

Ivanov, P.

Ivanov, P. S.

P. S. Ivanov and J. M. Rorison, “Theoretical investigation of static and dynamic characteristics of vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals,” Opt. Quantum Electron. 42, 193–213 (2010).
[CrossRef]

P. S. Ivanov, M. Dragas, M. Cryan, and J. M. Rorison, “Theoretical investigation of transverse optical modes in photonic-crystal waveguides imbedded into proton-implanted and oxide-confined vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 22, 2270–2276 (2005).
[CrossRef]

Kropp, J.-R.

Leisher, P. O.

M. S. Alias, S. Shaari, P. O. Leisher, and K. D. Choquette, “Single transverse mode control of VCSEL by photonic crystal and trench patterning,” Photon. Nanostruct. 8, 38–46 (2010).
[CrossRef]

McInerney, J. G.

Y. G. Zhao and J. G. McInerney, “Transverse-mode control of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1950–1958 (1996).
[CrossRef]

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

Mollier, J.-C.

J. Perchoux, A. Rissons, and J.-C. Mollier, “Multimode VCSEL model for wide frequency-range RIN simulation,” Opt. Commun. 281, 162–169 (2008).
[CrossRef]

Nakwaski, W.

W. Nakwaski, “Simplified modeling of photonic-crystal-confined vertical-cavity surface-emitting diode lasers,” Opt. Appl. 35, 579–589 (2005).

Nyakas, P.

Pahlavan, S.

G. Haghighat, V. Ahmadi, and S. Pahlavan, “Analysis of SHB and thermal characteristics in PC-VCSEL considering photonic crystal parameters,” Proc. SPIE 8308, 83082G (2011).
[CrossRef]

Panajotov, K.

Panish, M. B.

H. C. Casey and M. B. Panish, Heterostructure Lasers(Academic, 1978).

Perchoux, J.

J. Perchoux, A. Rissons, and J.-C. Mollier, “Multimode VCSEL model for wide frequency-range RIN simulation,” Opt. Commun. 281, 162–169 (2008).
[CrossRef]

Peterman, K.

Rissons, A.

J. Perchoux, A. Rissons, and J.-C. Mollier, “Multimode VCSEL model for wide frequency-range RIN simulation,” Opt. Commun. 281, 162–169 (2008).
[CrossRef]

Rorison, J.

Rorison, J. M.

P. S. Ivanov and J. M. Rorison, “Theoretical investigation of static and dynamic characteristics of vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals,” Opt. Quantum Electron. 42, 193–213 (2010).
[CrossRef]

P. S. Ivanov, M. Dragas, M. Cryan, and J. M. Rorison, “Theoretical investigation of transverse optical modes in photonic-crystal waveguides imbedded into proton-implanted and oxide-confined vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 22, 2270–2276 (2005).
[CrossRef]

Shaari, S.

M. S. Alias, S. Shaari, P. O. Leisher, and K. D. Choquette, “Single transverse mode control of VCSEL by photonic crystal and trench patterning,” Photon. Nanostruct. 8, 38–46 (2010).
[CrossRef]

Temkin, H.

C. Wilmsen, H. Temkin, and L. A. Coldren, Vertical-Cavity Surface-Emitting Lasers Design, Fabrication, Characterization and Applications (Cambridge University, 1999).

Wilmsen, C.

C. Wilmsen, H. Temkin, and L. A. Coldren, Vertical-Cavity Surface-Emitting Lasers Design, Fabrication, Characterization and Applications (Cambridge University, 1999).

Yokouchi, N.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1439–1445 (2003).
[CrossRef]

Yu, S. F.

S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley, 2003).

Zei, L.-G.

Zhao, Y. G.

Y. G. Zhao and J. G. McInerney, “Transverse-mode control of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1950–1958 (1996).
[CrossRef]

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

Appl. Phys. Lett.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Etching depth dependence of the effective refractive index in two-dimensional photonic-crystal-patterned vertical-cavity surface-emitting laser structures,” Appl. Phys. Lett. 82, 1344–1346 (2003).
[CrossRef]

IEEE J. Quantum Electron.

Y. G. Zhao and J. G. McInerney, “Transverse-mode control of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1950–1958 (1996).
[CrossRef]

K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Quantum Electron. 6, 1201–1215 (2000).
[CrossRef]

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 9, 1439–1445 (2003).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Appl.

W. Nakwaski, “Simplified modeling of photonic-crystal-confined vertical-cavity surface-emitting diode lasers,” Opt. Appl. 35, 579–589 (2005).

Opt. Commun.

J. Perchoux, A. Rissons, and J.-C. Mollier, “Multimode VCSEL model for wide frequency-range RIN simulation,” Opt. Commun. 281, 162–169 (2008).
[CrossRef]

Opt. Express

Opt. Quantum Electron.

P. S. Ivanov and J. M. Rorison, “Theoretical investigation of static and dynamic characteristics of vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals,” Opt. Quantum Electron. 42, 193–213 (2010).
[CrossRef]

Photon. Nanostruct.

M. S. Alias, S. Shaari, P. O. Leisher, and K. D. Choquette, “Single transverse mode control of VCSEL by photonic crystal and trench patterning,” Photon. Nanostruct. 8, 38–46 (2010).
[CrossRef]

Proc. SPIE

G. Haghighat, V. Ahmadi, and S. Pahlavan, “Analysis of SHB and thermal characteristics in PC-VCSEL considering photonic crystal parameters,” Proc. SPIE 8308, 83082G (2011).
[CrossRef]

Other

H. C. Casey and M. B. Panish, Heterostructure Lasers(Academic, 1978).

S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley, 2003).

C. Wilmsen, H. Temkin, and L. A. Coldren, Vertical-Cavity Surface-Emitting Lasers Design, Fabrication, Characterization and Applications (Cambridge University, 1999).

G. Haghighat and V. Ahmadi, “Threshold analysis of vertical-cavity surface-emitting laser with internal photonic crystal waveguide,” in IEEE Conference Symposium on Photonics and Optoelectronics (SOPO, 2012), pp. 1–2.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of the oxide-confined GaAs-based 850 nm PC-VCSEL.

Fig. 2.
Fig. 2.

Radial carrier concentration for different values of injected current with dh/Λ=0.4.

Fig. 3.
Fig. 3.

Carrier concentration versus radius of active region for different hole radius of the PC at the same currents (I=2.5mA).

Fig. 4.
Fig. 4.

Radial distribution of temperature in active region of VCSEL and PC-VCSEL at the same currents.

Fig. 5.
Fig. 5.

Radial distribution of temperature rise for different injection currents with dh/Λ=0.4.

Fig. 6.
Fig. 6.

(a) Radial distribution of thermal lensing coefficient for different values of injected current with dh/Λ=0.4. (b) Radial distribution of self-focusing coefficient for different values of injected current with dh/Λ=0.4. (c) Sum of self-focusing and thermal lensing effects, which is the total variation on the refractive index.

Fig. 7.
Fig. 7.

Comparison of output power of PC-VCSEL (dh/Λ=0.4) with VCSEL as a function of injection current.

Tables (2)

Tables Icon

Table 1. Physical Parameters of VCSEL [12,13]

Tables Icon

Table 2. Parameters Used in the Simulation [12,13]

Equations (19)

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

Dn1rr(rNr)Γzj=1mcneff,jg(N(r))Sj|ψj(r)|2Nτn+J(r)qd=0,
Γzj=1mcneff,jGjSjSjτp+βsΓzBbN2=0,
g(N(r))Pa|Et(r)|2hν,
Pa=12πs2actcnrε0|ψt(r)|2dσ,
|Et(r)¯|2=|ψt(r)|212s|ψt(r)|2dr,
1s2|ψt(r)|2rdr=1,
|ψt(r)|2=|ϕ(r,θ)|2dθ,
Nr|r=0=Nr|r=rs=0,
2ϕ(r,θ)+(k02nr2βj2)ϕ(r,θ)=0,
nr=nr0+ig0λ4π,
n¯(r)={nr0+ig0λ4π,rsnr0Δn,r>s1,in holes,
(inrk0)ψ|n=N=0.
Rk,new=Rk(neff1nr01),
1rr(rT(r)r)+1kTQ(r)=0,
T(z=0)=T0
Tz|z=h=Tr|r=0=Tr|r=rs=0,
Q(r)=ρspcJ2(r)+V(r)(1ηspfsp)d[jth+(J(r)jth)(1ηi)],
J(r)={j0r<sj0exp((rs)/r0rs,
V(r)={2KBTqlnj0jsr<s2KBTq(lnj0jsrsr0)rs,

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