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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 19 — Sep. 12, 2011
  • pp: 18272–18282
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Modal loss mechanism of micro-structured VCSELs studied using full vector FDTD method

Du-Ho Jo, Ngoc Hai Vu, Jin-Tae Kim, and In-Kag Hwang  »View Author Affiliations


Optics Express, Vol. 19, Issue 19, pp. 18272-18282 (2011)
http://dx.doi.org/10.1364/OE.19.018272


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Abstract

Modal properties of vertical cavity surface-emitting lasers (VCSELs) with holey structures are studied using a finite difference time domain (FDTD) method. We investigate loss behavior with respect to the variation of structural parameters, and explain the loss mechanism of VCSELs. We also propose an effective method to estimate the modal loss based on mode profiles obtained using FDTD simulation. Our results could provide an important guideline for optimization of the microstructures of high-power single-mode VCSELs.

© 2011 OSA

1. Introduction

Vertical cavity surface-emitting lasers (VCSELs) have unique and useful features such as low cost, low power consumption, and a small footprint. They are now key devices in local area and metropolitan networks. Consumer applications, such as laser mice and laser printers, have also grown recently.

In several applications, single transverse mode operation is highly desirable for stable output intensity and high speed modulation. For this reason, various methods have been proposed and demonstrated to obtain the high power single mode in VCSELs. As described in the literature, single-mode VCSELs have been fabricated mainly using two different techniques. One technique is to make the device small enough to support only the fundamental mode, where the best results have been achieved using oxide-confined VCSELs [1

1. S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73(5), 596–598 (1998). [CrossRef]

]. However, the disadvantage of this approach is low output power due to the small active volume. The other technique is to use mode-selective loss in a larger multimode device. Metal apertures [2

2. J. Hashizume and F. Koyama, “Plasmon-enhancement of optical near-field of metal nanoaperture surface-emitting laser,” Appl. Phys. Lett. 84(17), 3226–3228 (2004). [CrossRef]

], anti-resonant reflecting elements [3

3. D. Zhou and L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(12), 1599–1606 (2002). [CrossRef]

], air hole structures [4

4. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photonic-crystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82(19), 3182–3184 (2003). [CrossRef]

], or high-contrast gratings [5

5. C. J. Chang-Hasnain, Y. Zhou, M. C. Y. Huang, and C. Chase, “High-contrast grating VCSELs,” IEEE J. Sel. Top. Quantum Electron. 15(3), 869–878 (2009). [CrossRef]

] are introduced on top of the surface to selectively induce a large loss for the higher-order modes. Fairly good results have been reported by many groups.

Numerical analyses of modes in VCSELs have been performed using a wide variety of techniques including the effective index method [6

6. G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20(13), 1483–1485 (1995). [CrossRef] [PubMed]

,7

7. W. C. Ng, Y. Liu, B. Klein, and K. Hess, “Improved Effective Index Method for Oxide-Conned VCSEL Mode Analysis,” Proc. SPIE 4646, 168–175 (2002). [CrossRef]

], the beam propagation method [8

8. N. N. Elkin, A. P. Napartovich, V. N. Troshchieva, D. V. Vysotsky, T.-W. Lee, S. C. Hagness, N.-H. Kim, L. Bao, and L. J. Mawst, “Antiresonant reflecting optical waveguide-type vertical-cavity surface emitting lasers: comparison of full-vector finite-difference time-domain and 3-D bidirectional beam propagation methods,” J. Lightwave Technol. 24(4), 1834–1842 (2006). [CrossRef]

], the plane wave admittance method [9

9. M. Dems, T. Czyszanowski, and K. Panajotov, “Numerical analysis of high Q-factor photonic-crystal VCSELs with plane-wave admittance method,” Opt. Quantum Electron. 39(4-6), 419–426 (2007). [CrossRef]

], and the finite difference time domain (FDTD) method [8

8. N. N. Elkin, A. P. Napartovich, V. N. Troshchieva, D. V. Vysotsky, T.-W. Lee, S. C. Hagness, N.-H. Kim, L. Bao, and L. J. Mawst, “Antiresonant reflecting optical waveguide-type vertical-cavity surface emitting lasers: comparison of full-vector finite-difference time-domain and 3-D bidirectional beam propagation methods,” J. Lightwave Technol. 24(4), 1834–1842 (2006). [CrossRef]

,10

10. G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface emitting lasers,” Appl. Phys. Lett. 73(6), 726–728 (1998). [CrossRef]

,11

11. K. Morito, D. Mori, E. Mizuta, and T. Baba, “Full 3D FDTD analysis of modal characteristics in VCSELs with holey structure,” Proc. SPIE 5722, 191–200 (2005). [CrossRef]

]. In this work, the full-vector three-dimensional (3-D) FDTD technique was used to analyze micro-structured VCSELs. Compared to other techniques, the FDTD method is a simple and straightforward algorithm for solving time-dependent electromagnetic problems. The algorithm requires minimal assumptions and approximations, and thus provides fairly reliable results. With this approach, it is possible to directly examine the electric field distribution at each time step, which helps to determine the physical mechanism of the device behavior.

2. 3-D FDTD Model for Micro-Structured VCSEL

In our FDTD method, the VCSEL structure in the computational domain was surrounded by a perfectly matched layer (PML) with a thickness of 400 to 600 nm to absorb any outgoing waves. The spatial resolution, or the dimensions of the grids, determines the computation time and the accuracy of finite difference approximations. We determined the optimal resolutions that yielded reliable accuracy with reasonable computation time to be Δx = Δy = 0.1 μm and Δz = 0.02 μm in our VCSEL structure (Δx, Δy, and Δz are the dimensions of one grid). The small grid size along the z-axis was selected because light propagated along the z-axis, and a large variation of both the optical phase and the amplitude of the laser modes appeared.

3. Excitation of the Resonant Modes using Magnetic Field Parity

When a single dipole source is used to generate optical waves inside the computation structure, multiple resonant modes are exited at the same time, as shown by the black curves in Fig. 3
Fig. 3 Mode spectra obtained using Hz parity for selective excitation of (a) LP01, (b) LP11, and (c) LP21. The black curves show the original mode spectrum with no parity applied.
. However, to obtain mode-specific properties, the excitation of only one particular mode is required. In this case, the large number of modes densely located in a spectrum makes single mode excitation a difficult and time-consuming task. The problem can be effectively solved when using the symmetry relation of the mode to be excited. Mirror symmetry conditions or parities can be applied when the cavity structure under consideration has mirror symmetries as our VCSELs. In this study, parity was applied to the z component of the magnetic field (Hz component) with respect to the x- and y-axes. Table 1

Table 1. Conditions for selective excitation of LP modes

table-icon
View This Table
shows the parity of three different modes in the format of (i, j), where 1/-1 denotes even/odd symmetry with respect to each axis. The z-axis parity was not used since the VCSEL structure did not have symmetry along the z axis. In each case, the dipole source was located where the mode intensity was relatively high for effective excitation of the corresponding mode. Here, the transverse modes of the VCSEL are named LPlm (linearly polarized mode) form, which is typically used for optical waveguides.

Figure 3 shows three different mode spectra obtained when the parities of Table 1 were applied. Note that only a part of the original resonant peaks (shown as black curves) was selectively excited as the parity conditions were applied. Excitation of any single mode can be performed much more easily due to the low density of the mode spectra. Successful excitation of single mode is verified by purely exponential decay of field amplitude with no fluctuation. The longest wavelength or lowest frequency peak in each result corresponds to the LP01, LP11, and LP21 modes, respectively. Each mode was excited with a dipole source with a narrow spectral band, and the resulting intensity distributions are shown in Figs. 4(a)-(c)
Fig. 4 Modal intensity distributions of (a) LP01, (b) LP11, (c) LP21, and the Hz fields of (d) LP01, (e) LP11, and (f) LP21 in the xy-plane obtained from the FDTD computation with proper parity conditions.
. The mode pattern is in good agreement with those from waveguide theory. Figures 4(d)-(f) show the Hz field components of the modes, which explicitly contain the parities applied. When the parity condition was applied in our FDTD simulation, the computation was performed only for a quarter of the structure instead of the full structure. Therefore, the use of parity in mode excitation decreases the spectral density, and also reduces the memory requirement and computation time of each run.

4. Optical Loss Mechanism for Micro-Structured VCSEL

4.1. Variation of modal losses depending on oxide aperture size

To understand these phenomena, we plotted the optical intensity distributions of the LP01 and LP11 modes in a cross-section of the yz-plane, as shown in Fig. 6
Fig. 6 Modal intensity profiles in side view for two different oxide aperture diameters. (a) Oxide aperture size = 10 μm, and (b) oxide aperture size = 14 μm.
. The color bar denotes the optical intensity on a log scale. The figure shows two main loss channels: the optical transmission through the top DBR (the top DBR has fewer layers than the bottom DBR), and optical leakage (or scattering) through air holes. An animation built with multiple shots of field profiles taken at successive times clearly shows that the optical wave inside the air holes was a propagating wave, whereas the optical wave inside the cavity was a standing wave [13

13. N. H. Vu, B.-C. Jeon, D.-H. Jo, and I.-K. Hwang, “Management of computational errors in a finite-difference time-domain method for photonic crystal fibers,” J. Kor. Phys. Soc. 55(4), 1335–1343 (2009). [CrossRef]

]. When the oxide aperture was small enough and no leakage loss occurred, both the LP01 and LP11 modes experienced the same loss of 2.9x10−4; this corresponds to the top DBR loss.

For high quality single mode lasing, a large difference between the LP01 and LP11 loss is preferred. Low loss for the LP01 mode is also important for a low threshold. To achieve high output power of the VCSEL, the ratio of DBR loss to total loss should be considered since the leakage loss does not contribute to a laser emission with a Gaussian profile. Based on this reasoning, a desirable cavity structure is, roughly speaking, one with a large value of (LP11 loss – LP01 loss)/(LP01 loss). In this sense, the large oxide aperture is preferred, as shown in Fig. 5. However, since the oxide aperture diameter also plays a role as a current channel and significantly affects the threshold current, we selected a relatively small diameter of 8 μm for this study.

4.2. Variation of modal losses depending on air hole pitch

4.3. Variation of modal losses depending on air hole depth

The underlying mechanism was found when observing the field profiles shown in Fig. 10
Fig. 10 Modal intensity profiles in side view for different etch depths: (a) 1 μm, (b) 1.8 μm, (c) 2.6 μm, and (d) 3.4 μm.
. When the depth increased from 1 to 1.8 μm, the hole induced a larger loss while retaining the overall distributions of the modes, which is similar to the change from (b) to (a) in Fig. 8. However, when the depth increased to 3 and 3.4 μm, a dramatic change occurred in the mode profiles. The lateral mode size shrank to greatly reduce the leakage loss. This means that the air holes started to act both as an optical enclosure and as a loss element when the hole was deep enough.

To investigate this effect in detail, we plotted the mode size as a function of hole depth as shown in Fig. 11
Fig. 11 Mode size and reflection loss of DBR under an etched hole.
. The mode size was defined by the positions where the optical intensity dropped by 1/e at the level of the oxide layer. The mode size of 4 μm, which was determined by the oxide aperture, was retained until the depth increased to 1.8 μm. It started to shrink after 1.8 um, and reached the bottom line at a hole depth of 3.0 μm. In the final stage, the mode was well confined in the GaAs-air waveguide, as shown in Fig. 10 (d). We do not yet understand why the mode size changed significantly at a depth of 1.0 to 1.4 μm.

5. Estimation of Modal Loss Based on Mode Intensity Profile

First, we assumed that the leakage loss was proportional to the optical energy density integrated over the bottom surface of the holes as described by Eq. (1). Integration over the oxide layer was used to represent the total optical energy of the mode since the maximum energy density is found there.

modal   loss=leakagepowertotalenergyopticalenergyatholesurfacesopticalenergyatoxidelayer=hole|E|2dAoxide|E|2dA
(1)

5. Conclusion

Acknowledgments

This work was supported by Regional Innovation Center for Photonic Materials and Devices at Chonnam National University under grant R12-2002-054, and by a Korea Research Foundation grant funded by the Korean government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-331-C00115).

References and links

1.

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73(5), 596–598 (1998). [CrossRef]

2.

J. Hashizume and F. Koyama, “Plasmon-enhancement of optical near-field of metal nanoaperture surface-emitting laser,” Appl. Phys. Lett. 84(17), 3226–3228 (2004). [CrossRef]

3.

D. Zhou and L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 38(12), 1599–1606 (2002). [CrossRef]

4.

D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photonic-crystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett. 82(19), 3182–3184 (2003). [CrossRef]

5.

C. J. Chang-Hasnain, Y. Zhou, M. C. Y. Huang, and C. Chase, “High-contrast grating VCSELs,” IEEE J. Sel. Top. Quantum Electron. 15(3), 869–878 (2009). [CrossRef]

6.

G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20(13), 1483–1485 (1995). [CrossRef] [PubMed]

7.

W. C. Ng, Y. Liu, B. Klein, and K. Hess, “Improved Effective Index Method for Oxide-Conned VCSEL Mode Analysis,” Proc. SPIE 4646, 168–175 (2002). [CrossRef]

8.

N. N. Elkin, A. P. Napartovich, V. N. Troshchieva, D. V. Vysotsky, T.-W. Lee, S. C. Hagness, N.-H. Kim, L. Bao, and L. J. Mawst, “Antiresonant reflecting optical waveguide-type vertical-cavity surface emitting lasers: comparison of full-vector finite-difference time-domain and 3-D bidirectional beam propagation methods,” J. Lightwave Technol. 24(4), 1834–1842 (2006). [CrossRef]

9.

M. Dems, T. Czyszanowski, and K. Panajotov, “Numerical analysis of high Q-factor photonic-crystal VCSELs with plane-wave admittance method,” Opt. Quantum Electron. 39(4-6), 419–426 (2007). [CrossRef]

10.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface emitting lasers,” Appl. Phys. Lett. 73(6), 726–728 (1998). [CrossRef]

11.

K. Morito, D. Mori, E. Mizuta, and T. Baba, “Full 3D FDTD analysis of modal characteristics in VCSELs with holey structure,” Proc. SPIE 5722, 191–200 (2005). [CrossRef]

12.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite- Difference Time-Domain Method (Artech House 2005).

13.

N. H. Vu, B.-C. Jeon, D.-H. Jo, and I.-K. Hwang, “Management of computational errors in a finite-difference time-domain method for photonic crystal fibers,” J. Kor. Phys. Soc. 55(4), 1335–1343 (2009). [CrossRef]

14.

J. H. Baek, D. S. Song, I. K. Hwang, H. H. Lee, Y. H. Lee, Y. G. Ju, T. Kondo, T. Miyamoto, and F. Koyama, “Transverse mode control by etch-depth tuning in 1120-nm GaInAs/GaAs photonic crystal vertical-cavity surface-emitting lasers,” Opt. Express 12(5), 859–867 (2004). [CrossRef] [PubMed]

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication
(140.3945) Lasers and laser optics : Microcavities
(140.7260) Lasers and laser optics : Vertical cavity surface emitting lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 5, 2011
Revised Manuscript: August 18, 2011
Manuscript Accepted: August 21, 2011
Published: September 2, 2011

Citation
Du-Ho Jo, Ngoc Hai Vu, Jin-Tae Kim, and In-Kag Hwang, "Modal loss mechanism of micro-structured VCSELs studied using full vector FDTD method," Opt. Express 19, 18272-18282 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18272


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References

  1. S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett.73(5), 596–598 (1998). [CrossRef]
  2. J. Hashizume and F. Koyama, “Plasmon-enhancement of optical near-field of metal nanoaperture surface-emitting laser,” Appl. Phys. Lett.84(17), 3226–3228 (2004). [CrossRef]
  3. D. Zhou and L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.38(12), 1599–1606 (2002). [CrossRef]
  4. D. S. Song, Y. J. Lee, H. W. Choi, and Y. H. Lee, “Polarization-controlled, single-transverse-mode, photonic-crystal, vertical-cavity, surface-emitting lasers,” Appl. Phys. Lett.82(19), 3182–3184 (2003). [CrossRef]
  5. C. J. Chang-Hasnain, Y. Zhou, M. C. Y. Huang, and C. Chase, “High-contrast grating VCSELs,” IEEE J. Sel. Top. Quantum Electron.15(3), 869–878 (2009). [CrossRef]
  6. G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett.20(13), 1483–1485 (1995). [CrossRef] [PubMed]
  7. W. C. Ng, Y. Liu, B. Klein, and K. Hess, “Improved Effective Index Method for Oxide-Conned VCSEL Mode Analysis,” Proc. SPIE4646, 168–175 (2002). [CrossRef]
  8. N. N. Elkin, A. P. Napartovich, V. N. Troshchieva, D. V. Vysotsky, T.-W. Lee, S. C. Hagness, N.-H. Kim, L. Bao, and L. J. Mawst, “Antiresonant reflecting optical waveguide-type vertical-cavity surface emitting lasers: comparison of full-vector finite-difference time-domain and 3-D bidirectional beam propagation methods,” J. Lightwave Technol.24(4), 1834–1842 (2006). [CrossRef]
  9. M. Dems, T. Czyszanowski, and K. Panajotov, “Numerical analysis of high Q-factor photonic-crystal VCSELs with plane-wave admittance method,” Opt. Quantum Electron.39(4-6), 419–426 (2007). [CrossRef]
  10. G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface emitting lasers,” Appl. Phys. Lett.73(6), 726–728 (1998). [CrossRef]
  11. K. Morito, D. Mori, E. Mizuta, and T. Baba, “Full 3D FDTD analysis of modal characteristics in VCSELs with holey structure,” Proc. SPIE5722, 191–200 (2005). [CrossRef]
  12. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite- Difference Time-Domain Method (Artech House 2005).
  13. N. H. Vu, B.-C. Jeon, D.-H. Jo, and I.-K. Hwang, “Management of computational errors in a finite-difference time-domain method for photonic crystal fibers,” J. Kor. Phys. Soc.55(4), 1335–1343 (2009). [CrossRef]
  14. J. H. Baek, D. S. Song, I. K. Hwang, H. H. Lee, Y. H. Lee, Y. G. Ju, T. Kondo, T. Miyamoto, and F. Koyama, “Transverse mode control by etch-depth tuning in 1120-nm GaInAs/GaAs photonic crystal vertical-cavity surface-emitting lasers,” Opt. Express12(5), 859–867 (2004). [CrossRef] [PubMed]

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