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

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  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]

2009 (2)

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]

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]

2007 (1)

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]

2006 (1)

2005 (1)

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]

2004 (2)

2003 (1)

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]

2002 (2)

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]

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]

1998 (2)

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]

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]

1995 (1)

Baba, T.

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]

Babic, D. I.

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]

Baek, J. H.

Bao, L.

Barnes, D. C.

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]

Chang-Hasnain, C. J.

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]

Chase, C.

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]

Choi, H. W.

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]

Choquette, K. D.

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]

Chuang, S. L.

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]

Corzine, S. W.

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]

Czyszanowski, T.

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]

Dems, M.

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]

Elkin, N. N.

Geib, K. M.

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]

Hadley, G. R.

Hagness, S. C.

Hashizume, J.

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]

Hegarty, S. P.

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]

Hess, K.

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]

Hou, H. Q.

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]

Huang, M. C. Y.

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]

Huyet, G.

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]

Hwang, I. K.

Hwang, I.-K.

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]

Jeon, B.-C.

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]

Jo, D.-H.

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]

Ju, Y. G.

Kim, N.-H.

Klein, B.

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]

Kondo, T.

Koyama, F.

Lee, H. H.

Lee, T.-W.

Lee, Y. H.

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]

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]

Lee, Y. J.

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]

Liu, G.

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]

Liu, Y.

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]

Mawst, L. J.

McInerney, J. G.

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]

Miyamoto, T.

Mizuta, E.

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]

Mori, D.

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]

Morito, K.

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]

Napartovich, A. P.

Ng, W. C.

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]

Panajotov, K.

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]

Seurin, J.-F.

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]

Song, D. S.

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]

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]

Tan, M.

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]

Tiouririne, T. N.

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]

Troshchieva, V. N.

Vu, N. H.

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]

Vysotsky, D. V.

Zhou, D.

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]

Zhou, Y.

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]

Appl. Phys. Lett. (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]

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]

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]

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]

IEEE J. Quantum Electron. (1)

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]

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

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]

J. Kor. Phys. Soc. (1)

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]

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

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]

Proc. SPIE (2)

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]

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]

Other (1)

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

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Figures (13)

Fig. 1
Fig. 1

Schematic of micro-structured VCSEL structure.

Fig. 2
Fig. 2

Output structure of micro-structured VCSEL. (a) Side view, (b) top view, and (c) cross sectional view at an oxide layer

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.

Fig. 4
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.

Fig. 5
Fig. 5

Modal loss and resonant wavelength versus the oxide aperture diameter.

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.

Fig. 7
Fig. 7

Dependence of loss and resonant wavelength on the hole pitch.

Fig. 8
Fig. 8

Modal intensity profiles in side view for two values of Λ: (a) Λ = 4 μm, and (b) Λ = 5 μm.

Fig. 9
Fig. 9

Dependence of loss and resonant wavelength on hole etching depth.

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.

Fig. 11
Fig. 11

Mode size and reflection loss of DBR under an etched hole.

Fig. 12
Fig. 12

Comparison of actual leakage loss and the loss estimated from the mode profile for various hole pitch values.

Fig. 13
Fig. 13

Comparison of actual leakage loss and the loss estimated from the mode profile for the various hole depths.

Tables (1)

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Table 1 Conditions for selective excitation of LP modes

Equations (1)

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modal   loss = l e a k a g e p o w e r t o t a l e n e r g y o p t i c a l e n e r g y a t h o l e s u r f a c e s o p t i c a l e n e r g y a t o x i d e l a y e r = h o l e | E | 2 d A o x i d e | E | 2 d A

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