Abstract

We demonstrate a Finite-Difference Time-Domain (FDTD) phase methodology to estimate resonant wavelengths in Fabry-Perot (FP) cavity structures. We validate the phase method in a conventional Vertical-Cavity Surface-Emitting Laser (VCSEL) structure using a transfer-matrix method, and compare results with a FDTD reflectance method. We extend this approach to a Sub-Wavelength Grating (SWG) and a Photonic Crystal (Phc) slab, either of which may replace one of the Distributed Bragg Reflectors (DBRs) in the VCSEL, and predict resonant conditions with varying lithographic parameters. Finally, we compare the resonant tunabilities of three different VCSEL structures, taking quality factors into account.

© 2007 Optical Society of America

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References

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  1. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, (Wiley Interscience, 1995).
  2. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (Wiley Interscience, 1991).
    [CrossRef]
  3. A. Yariv, Optical Electronics in Modern Communications, (Oxford University Press, 1997).
  4. E. Bisaillon, D. Tan, B. Faraji, A. G. Kirk, L. Chrowstowski, and D. V. Plant, "High reflectivity air-bridge subwavelength grating reflector and Fabry-Perot cavity in AlGaAs/GaAs," Opt. Express. 14, 2573-2582 (2006).
    [CrossRef] [PubMed]
  5. S. Boutami, B. B. Bakir, J.-L. Leclercq, X. Letartre, P. Rojo-Romeo, M. Garrigues, P. Viktorovitch, I. Sagnes, L. Legratiet, and M. Strassner, "Highly selective and compact tunable MOEMS photonic crystal Fabry-Perot filter," Opt. Express. 14, 3129-3137 (2006).
    [CrossRef] [PubMed]
  6. M. C. Y. Huang, Y. Zhou and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
    [CrossRef]
  7. C. J. Chang-Hasnain, "Tunable VCSEL," IEEE J. Sel. Top. Quantum Electron. 6, 978-987 (2000).
    [CrossRef]
  8. S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  9. W. Suh, M. F. Yanik, O. Solgaard, and S. Fana, "Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs," Appl. Phys. Lett. 82, 1999-2001 (2003).
    [CrossRef]
  10. O. Kilic, S. Kim, W. Suh, Y.-A. Peter, A. S. Sudbø, M. F. Yanik, S. Fan, and O. Solgaard, "Photonic Crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders," Opt. Lett. 29, 2782-2784 (2004).
    [CrossRef] [PubMed]

2007 (1)

M. C. Y. Huang, Y. Zhou and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
[CrossRef]

2006 (2)

E. Bisaillon, D. Tan, B. Faraji, A. G. Kirk, L. Chrowstowski, and D. V. Plant, "High reflectivity air-bridge subwavelength grating reflector and Fabry-Perot cavity in AlGaAs/GaAs," Opt. Express. 14, 2573-2582 (2006).
[CrossRef] [PubMed]

S. Boutami, B. B. Bakir, J.-L. Leclercq, X. Letartre, P. Rojo-Romeo, M. Garrigues, P. Viktorovitch, I. Sagnes, L. Legratiet, and M. Strassner, "Highly selective and compact tunable MOEMS photonic crystal Fabry-Perot filter," Opt. Express. 14, 3129-3137 (2006).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

W. Suh, M. F. Yanik, O. Solgaard, and S. Fana, "Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs," Appl. Phys. Lett. 82, 1999-2001 (2003).
[CrossRef]

2002 (1)

S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2000 (1)

C. J. Chang-Hasnain, "Tunable VCSEL," IEEE J. Sel. Top. Quantum Electron. 6, 978-987 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

W. Suh, M. F. Yanik, O. Solgaard, and S. Fana, "Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs," Appl. Phys. Lett. 82, 1999-2001 (2003).
[CrossRef]

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

C. J. Chang-Hasnain, "Tunable VCSEL," IEEE J. Sel. Top. Quantum Electron. 6, 978-987 (2000).
[CrossRef]

Nature Photon. (1)

M. C. Y. Huang, Y. Zhou and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
[CrossRef]

Opt. Express. (2)

E. Bisaillon, D. Tan, B. Faraji, A. G. Kirk, L. Chrowstowski, and D. V. Plant, "High reflectivity air-bridge subwavelength grating reflector and Fabry-Perot cavity in AlGaAs/GaAs," Opt. Express. 14, 2573-2582 (2006).
[CrossRef] [PubMed]

S. Boutami, B. B. Bakir, J.-L. Leclercq, X. Letartre, P. Rojo-Romeo, M. Garrigues, P. Viktorovitch, I. Sagnes, L. Legratiet, and M. Strassner, "Highly selective and compact tunable MOEMS photonic crystal Fabry-Perot filter," Opt. Express. 14, 3129-3137 (2006).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. B (1)

S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Other (3)

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, (Wiley Interscience, 1995).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (Wiley Interscience, 1991).
[CrossRef]

A. Yariv, Optical Electronics in Modern Communications, (Oxford University Press, 1997).

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Figures (10)

Fig. 1.
Fig. 1.

(a). A simple diagram of a FP cavity assuming for normal incidence. Resonances occur when the roundtrip inside a cavity is a multiple of 2πm (m=0,±1,±2…) and (b) a schematic diagram of a simple VCSEL structure forming a FP cavity.

Fig. 2.
Fig. 2.

Resonant wavelengths of the VCSEL structure for various cavity lengths (L) estimated by (a) the phase analysis and (b) the notch reflectivity in the DBR stopband.

Fig. 3.
Fig. 3.

The schematic diagram of two VCSEL structures, consisting of the air gap, 27.5 DBR pairs, and (a) the SWG and (b) the Phc slab forming the FP cavity.

Fig. 4.
Fig. 4.

(a). Reflectivities and (b) phases of a single SWG as varying the duty factor (A→C) and the period (C→E).

Fig. 5.
Fig. 5.

(a). Phase responses of the SWG VCSEL and (b) resonant wavelengths shown in the DBR stopband as the duty factor (A→C) and the period (C→E) are varied.

Fig. 6.
Fig. 6.

(a). Reflectivities and (b) phases of a single Phc slab as the radius of the air hole is adjusted (A→B→C), and the lattice constant is varied (D→C→E).

Fig. 7.
Fig. 7.

(a). Phase responses of the Phc VCSEL and (b) resonant wavelengths shown in the stopband under varying r (A→B→C) and a (D→C→E).

Fig. 8.
Fig. 8.

(a. Tuning slopes of the three different VCSEL structures according to air gap variation in the cavity and (b) corresponding cavity Qs at resonances.

Fig. 9.
Fig. 9.

Resonance tuning by (a) SWG duty factor (α), (b) SWG period (Λ), (c) Phc radius of the air hole (r) and (d) Phc lattice constant (a).

Fig. 10.
Fig. 10.

Cavity Qs at resonances for the SWG and Phc VCSEL, lithographically (α, Λ, r, a) tuned.

Tables (4)

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Table 1. Resonant Wavelengths Estimated by Three Different Methods, and Corresponding Cavity Qs.

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Table 2. Resonant Wavelengths Estimated by Two Different Methods, and Corresponding Cavity Qs.

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Table 3. Resonant Wavelengths Estimated by Two Different Methods, and Corresponding Cavity Qs

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Table 4. Three different VCSEL structures aimed at the 850nm resonant wavelength

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