Milliwatt-level fiber-coupled laser power from photonic crystal band-edge laser

doi:10.1364/OE.19.002105

Milliwatt-level fiber-coupled laser power from photonic crystal band-edge laser

Sunghwan Kim, Sungmo Ahn, Jeongkug Lee, Heonsu Jeon, Philippe Regreny, Christian Seassal, Emmanuel Augendre, and Lea Di Cioccio »View Author Affiliations

Optics Express, Vol. 19, Issue 3, pp. 2105-2110 (2011)
http://dx.doi.org/10.1364/OE.19.002105

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– Abstract
1. Introduction
2. Design and fabrication
3. Measurements
4. Differential quantum efficiency versus pattern size
5. Conclusions
– References and links

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Abstract

We report unprecedentedly high output powers measured from large area two-dimensional square-lattice photonic-crystal band-edge lasers (BELs), patterned by holographic lithography. In order to ensure mechanical rigidity, the BELs were fabricated in an InP-based epilayer bonded onto a fused silica substrate beforehand. The BEL devices, employing the surface-emitting Γ-point monopole band-edge mode, provide a fiber-coupled single mode output power as high as 2.6 mW and an external differential quantum efficiency of ~4%. The results of a three-dimensional finite-difference time-domain simulation agree with the experimental observation that the large BELs are beneficial for achieving both high power output and high differential quantum efficiency.

1. Introduction

Compound semiconductors that incorporate photonic crystal (PC) structures have created a new paradigm for fabricating compact coherent light sources. In particular, substantial efforts have been devoted to the development of efficient PC lasers, in which the lasing mechanism relies on strongly confining photons inside a nano-scale cavity [1

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim I, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef] [PubMed]

], or on the gain enhancement at photonic band-edge modes [2

H. Y. Ryu, S. H. Kwon, Y. J. Lee, Y. H. Lee, and J. S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476 (2002). [CrossRef]

]. As far as output power is concerned, however, PC lasers have yielded only modest results to date. On the contrary, optical powers greater than 50 μW are typically required for an on-chip photonic receiver operated at a high speed (10 GHz) and a low bit-error rate (10⁻¹²) [3

S. J. Koester, C. L. Schow, L. Schares, G. Dehlinger, J. D. Schaub, F. E. Doany, and R. A. John, “Ge-on-SOI-Detector/Si-CMOS-Amplifier Receivers for High-Performance Optical-Communication Applications,” J. Lightwave Technol. 25(1), 46–57 (2007). [CrossRef]

]. Recently, a few research groups have achieved powers in that level with different PC laser systems: an array of coupled cavity lasers [4

H. Altug and J. Vucković, “Photonic crystal nanocavity array laser,” Opt. Express 13(22), 8819–8828 (2005). [CrossRef] [PubMed]

], a line cavity edge-emitting laser [5

L. Lu, A. Mock, E. H. Hwang, J. O’Brien, and P. D. Dapkus, “High-peak-power efficient edge-emitting photonic crystal nanocavity lasers,” Opt. Lett. 34(17), 2646–2648 (2009). [CrossRef] [PubMed]

], or a surface-emitting band-edge laser [6

S. Kim, J. Lee, H. Jeon, and H. J. Kim, “Fiber-coupled surface-emitting photonic crystal bandedge laser for biochemical sensor applications,” Appl. Phys. Lett. 94(13), 133503 (2009). [CrossRef]

Here we report the operation of a PC laser with an unprecedentedly high mW-level fiber-coupled output. To achieve the high laser power output, we used a band-edge mode (not a cavity mode) that is spatially extended over a large area. Since the band-edge mode relies on a perfectly periodic PC pattern, we used laser-holographic lithography (LHL) method to fabricate the band-edge lasers (BELs) over a large area (typically 1×1 cm²). Unlike electron-beam lithography, intrinsically an extremely low-throughput process, the LHL method has shown to be useful for fabricating PCs or PC lasers with a high throughput [7

C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. H. Jang, Y. S. Park, and J. C. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 (2005). [CrossRef]

, 8

S. Ahn, S. Kim, and H. Jeon, “Single-defect photonic crystal cavity laser fabricated by a combination of laser holography and focused ion beam lithography,” Appl. Phys. Lett. 96(13), 131101 (2010). [CrossRef]

2. Design and fabrication

Figure 1(a) shows the schematic diagram of the PC BEL used in this study. An InP-based multiple quantum well (MQW) slab was grown by molecular beam epitaxy. It is nominally 230-nm-thick, consists of four InAsP MQWs separated by InP barriers, and has a central emission wavelength of ~1550 nm. Underneath the MQW layer, an InGaAs etch-stop layer was grown for selective chemical etching. The first step in the fabrication process was to bond the InP wafer onto a fused silica substrate, with the InAsP/InP MQW layer facing down. Then, the InP substrate and InGaAs etch-stop layer were selectively removed in dilute HCl and FeCl₃ solutions, respectively [9

C. Seassal, C. Monat, J. Mouette, E. Touraille, B. B. Bakir, H. T. Hattori, J.-L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP bonded membrane photonics components and circuits: toward 2.5 dimensional micro-nano-photonics,” IEEE J. Sel. Top. Quantum Electron. 11(2), 395–407 (2005). [CrossRef]

]. A 50-nm-thick silicon nitride hard mask layer was deposited onto the bonded epilayer by plasma-enhanced chemical vapor deposition. In order to generate a square-lattice air-hole array pattern, the two-beam LHL process was applied twice, with the sample rotated by 90° before the second exposure. More details about the LHL process are given in Ref. 8

. Reactive-ion etching was then performed to transfer the PC patterns into the hard mask layer and subsequently into the InAsP MQW layer. A photographic image and a scanning electron microscope (SEM) image of a fabricated BEL device are shown in Figs. 1(b) and 1(c). Note that the blue-color features in the photograph, produced by diffraction in the square-lattice PC pattern, are uniformly distributed over ~1 cm², indicating the ability of the LHL process to produce patterns over a large area. The SEM image demonstrates the high quality of the PC patterns generated by LHL.

Fig. 1 (a) Schematic diagram of the square-lattice PC BEL bonded onto fused silica substrate. (b) Photograph and (c) SEM image of the fabricated PC BEL. The blue-color features in the photograph are due to diffraction by the square-lattice PC pattern of the BEL structure.

We employed a Γ-point band-edge because its surface emission characteristics are ideal for direct fiber coupling. Figure 2 shows the band structure calculated by the three-dimensional (3D) plane-wave-expansion (PWE) method. In this calculation, we assumed the refractive indices of the InP slab and of the fused silica substrate to be 3.17 and 1.45, respectively. Three distinct band-edges appear at the Brillouin zone center (the Γ-point), which correspond to the monopole, quadrupole, and dipole modes. The insets in the figure show the magnetic field profiles for the three band-edge modes, which were calculated by the 3D finite-difference time-domain (FDTD) method. From the band structure which was calculated for the hole radius of r = 0.2a, we determined the lattice constant to be a = 610 nm so that the monopole mode overlaps with the gain peak of the MQWs. We intended the monopole mode to lase because it has the highest quality factor among the three Γ-point band edges [10

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13(8), 2869–2880 (2005). [CrossRef] [PubMed]

Fig. 2 Photonic band structure diagram of the wafer-bonded square-lattice PC structure. Insets are the magnetic-field profiles for three Γ-point band-edge modes.

3. Measurements

We built a compact PC BEL system by coupling the device to a 1×2 wavelength-division-multiplexing (WDM) coupler with a single butt-end fiber tip, as shown in Fig. 3(a) . The BEL device was optically excited using a 980-nm laser diode in pulsed mode (20-ns pulse width and 1% duty cycle). Unlike our previous study [6

S. Kim, J. Lee, H. Jeon, and H. J. Kim, “Fiber-coupled surface-emitting photonic crystal bandedge laser for biochemical sensor applications,” Appl. Phys. Lett. 94(13), 133503 (2009). [CrossRef]

], we used a multimode WDM fiber coupler (Fiberer Corporation, China) composed of a fiber with a 50-μm core diameter for pumping over a large area, in order to achieve a high output power. The optical excitation of the BEL and light collection of the BEL output were accomplished simultaneously by the butt-end multimode fiber tip. The fiber tip was brought to the sample until a gentle physical contact was made. The combination of a large fiber core diameter (50-μm) and a small distance between fiber tip and the device surface (< 10-μm) ensured a high fiber coupling efficiency. A narrow beam divergence angle of the Γ-point BEL also helped keeping the high fiber coupling efficiency [9

]. From an independent but direct reflectance measurement of gold mirror using the same fiber coupling setup, we could estimate the fiber coupling efficiency to be greater than 90%, which was also confirmed by numerical model calculations. The BEL emission was then fed into either an optical power meter or an optical spectrum analyzer for characterization. Figure 3(b) shows the lasing spectrum of the BEL device. In addition to the sharp lasing peak at ~1510 nm, the emission spectrum exhibits two more distinct modes at shorter wavelengths. From the comparison with the calculated band-edge positions (Fig. 2), we can assign the dipole, quadrupole, and monopole modes to the peaks at 1410 nm, 1470 nm, and 1510 nm, respectively. Thus we can conclude that the BEL lased in a single mode (specifically at the monopole band-edge mode, as we intended), with the side-mode-suppression ratio greater than 40 dB.

Fig. 3 (a) Schematic diagram of the butt-end fiber coupling setup with a 1 × 2 multimode WDM fiber coupler. (b) Lasing spectrum of the PC BEL. L-L curves of the PC BEL for (c) the low excitation level and (d) the entire excitation range.

The measured relationship between light-in and light-out (L-L) is shown in Fig. 3: (c) for low excitation levels and (d) for the entire excitation range. The excitation power at the laser threshold is ~8 mW in terms of power incident on the MQWs, rather than the power absorbed by the MQWs. The fiber-coupled BEL output power was as high as ~2.6 mW, which was limited by the maximum pump power available (~400 mW). To our knowledge, this laser output far exceeds the achievement of any kind of PC lasers reported to date, excluding surface-modulated grating based lasers [11

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293(5532), 1123–1125 (2001). [CrossRef] [PubMed]

4. Differential quantum efficiency versus pattern size

The differential external quantum efficiency (η_DQE ), which indicates the overall combined efficiency of both pumping and photon harvesting, is defined as

η_{D Q E} = \frac{Δ N_{o u t}}{Δ N_{i n}} = \frac{Δ P_{o u t} / ℏ ω_{B E L}}{Δ P_{i n} / ℏ ω_{p}} = \frac{Δ P_{o u t}}{Δ P_{i n}} \cdot \frac{λ_{B E L}}{λ_{p}},

(1)

where N_in is the number of pump-laser photons that are fed into the system per unit time interval, and N_out is the number of BEL photons that are coupled to the fiber per unit time interval; ω_p (λ_p ) and ω_BEL (λ_BEL ) are the frequencies (wavelengths) of the pump laser and BEL, respectively; and ℏ is the reduced Planck’s constant. Assuming that 20% of the pump power is absorbed by the MQWs [12

L. J. Martínez, B. Alén, I. Prieto, J. F. Galisteo-López, M. Galli, L. C. Andreani, C. Seassal, P. Viktorovitch, and P. A. Postigo, “Two-dimensional surface emitting photonic crystal laser with hybrid triangular-graphite structure,” Opt. Express 17(17), 15043–15051 (2009). [CrossRef] [PubMed]

], we obtain η_DQE ≈ 4% by substituting the experimental values (measured at the output power of ~1 mW) into Eq. (1). In contrast, when the L-L measurement was repeated with a single mode fiber coupler (with a core diameter of only 9 μm), η_DQE is only 1.3%, i.e. much smaller than the 4% obtained for the multimode fiber coupler. This dependence of η_DQE on the pump area can be understood qualitatively as follows. In principle, all the band-edge photons within an infinitely large PC structure can be completely coupled out in the vertical direction. On the contrary, a band-edge mode in a finite-size PC structure suffers from lateral loss and therefore only a fraction of band-edge photons can be coupled out to free space [12

]. Therefore, using a multimode fiber (or pumping over a large area) is crucial for achieving a high power output with a BEL. It should be noted that, although our BELs have an effectively infinite size (~ 1 cm²) as far as the patterned area is concerned, they are nonetheless finite in reality, since the MQWs outside the pumped area behave as absorbers. There may also be other reasons for the reduction in differential quantum efficiency when employing a single mode fiber, such as mode mismatch and diffraction loss, which degrade light coupling to fiber.

The 3D FDTD method was used to simulate the BEL performance, using a MEEP package developed at MIT [13

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31(20), 2972–2974 (2006). [CrossRef] [PubMed]

]. The magnetic-field intensity profiles of the monopole BEL mode are shown in Figs. 4(a) and 4(b), which clearly demonstrate that more photons are lost laterally than are extracted in the vertical direction. The simulations indicate that lateral loss decreases monotonically with increasing PC pattern size. To analyze this quantitatively, we calculated the quality factor of the BEL as a function of the pattern size. We can also estimate the η_DQE using the theoretical equation [14

M. H. Shih, W. Kuang, T. Yang, M. Bagheri, Z. J. Wei, S. J. Choi, L. Lu, J. D. O’Brien, and P. D. Dapkus, “Experimental characterization of the optical loss of sapphire-bonded photonic crystal laser cavities,” IEEE Photon. Technol. Lett. 18(3), 535–537 (2006). [CrossRef]

Fig. 4 Intensity profiles of the vertical magnetic field at the center of the slab, calculated by the 3D FDTD method over (a) the xy-plane and (b) the xz-plane. (c) Quality factors (Q_v, Q_t) and their ratio Q_t/Q_v plotted as a function of the lateral size of PC pattern.

η_{D Q E} = \frac{Q_{v}^{- 1}}{Q_{t}^{- 1}} \cdot \frac{1}{{(n_{S i O_{2}} / n_{a i r})}^{3} + 1} \cdot η_{i} \cdot η_{c} .

(2)

The total quality factor, Q_t , is composed of the vertical and lateral quality factors, Q_v and Q_l : Q_t ⁻¹ = Q_v ⁻¹ + Q_l ⁻¹. The ratio of refractive indices n_SiO2 and n_air accounts for differences in the speed of light in fused silica and in air in the vertically asymmetric BEL structure, and η_i and η_c are the internal quantum efficiency and the fiber coupling efficiency, respectively. Figure 4(c) displays how the quality factors (Q_v and Q_t ) and their ratio Q_t /Q_v change with increasing PC pattern size. As the lateral length of the PC increases, Q_v , Q_t , and Q_t /Q_v all increase accordingly. These simulation results imply that Q_l increases faster than Q_v . As a consequence, η_DQE increases with the PC pattern size, consistent with the previous qualitative but intuitive argument. Assuming approximate values η_i ≈ 80% and η_c ≈ 90%, Eq. (2) gives η_DQE ≈ 5.3%, in reasonable agreement with the experimental value, 4%.

5. Conclusions

In conclusion, we have fabricated large-area square-lattice PC BELs using laser-holographic lithography and demonstrated their output power to be as high as 2.6 mW at room temperature. For stable laser operation over a large area, the BELs are bonded onto a fused silica substrate. A high external differential quantum efficiency of ~4% was obtained from a BEL of ~50 μm in diameter. We also investigated the properties of the BELs using the 3D FDTD method. Experimental and simulation results are in agreement, in the sense that the differential quantum efficiency increases in proportion to the BEL size.

Acknowledgments

This study was supported by the Mid-career Researcher Program funded by the National Research Foundation (2010-0014470), and by the World-Class University (WCU) Project funded by the Ministry of Education, Science & Technology of Korea (R31-2009-100320). This work was partly performed in the frame of the French-Korean LIA “Center for Photonics and Nanostructure.”

References and links

1.	O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim I, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef] [PubMed]
2.	H. Y. Ryu, S. H. Kwon, Y. J. Lee, Y. H. Lee, and J. S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476 (2002). [CrossRef]
3.	S. J. Koester, C. L. Schow, L. Schares, G. Dehlinger, J. D. Schaub, F. E. Doany, and R. A. John, “Ge-on-SOI-Detector/Si-CMOS-Amplifier Receivers for High-Performance Optical-Communication Applications,” J. Lightwave Technol. 25(1), 46–57 (2007). [CrossRef]
4.	H. Altug and J. Vucković, “Photonic crystal nanocavity array laser,” Opt. Express 13(22), 8819–8828 (2005). [CrossRef] [PubMed]
5.	L. Lu, A. Mock, E. H. Hwang, J. O’Brien, and P. D. Dapkus, “High-peak-power efficient edge-emitting photonic crystal nanocavity lasers,” Opt. Lett. 34(17), 2646–2648 (2009). [CrossRef] [PubMed]
6.	S. Kim, J. Lee, H. Jeon, and H. J. Kim, “Fiber-coupled surface-emitting photonic crystal bandedge laser for biochemical sensor applications,” Appl. Phys. Lett. 94(13), 133503 (2009). [CrossRef]
7.	C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. H. Jang, Y. S. Park, and J. C. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 (2005). [CrossRef]
8.	S. Ahn, S. Kim, and H. Jeon, “Single-defect photonic crystal cavity laser fabricated by a combination of laser holography and focused ion beam lithography,” Appl. Phys. Lett. 96(13), 131101 (2010). [CrossRef]
9.	C. Seassal, C. Monat, J. Mouette, E. Touraille, B. B. Bakir, H. T. Hattori, J.-L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP bonded membrane photonics components and circuits: toward 2.5 dimensional micro-nano-photonics,” IEEE J. Sel. Top. Quantum Electron. 11(2), 395–407 (2005). [CrossRef]
10.	M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13(8), 2869–2880 (2005). [CrossRef] [PubMed]
11.	S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293(5532), 1123–1125 (2001). [CrossRef] [PubMed]
12.	L. J. Martínez, B. Alén, I. Prieto, J. F. Galisteo-López, M. Galli, L. C. Andreani, C. Seassal, P. Viktorovitch, and P. A. Postigo, “Two-dimensional surface emitting photonic crystal laser with hybrid triangular-graphite structure,” Opt. Express 17(17), 15043–15051 (2009). [CrossRef] [PubMed]
13.	A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31(20), 2972–2974 (2006). [CrossRef] [PubMed]
14.	M. H. Shih, W. Kuang, T. Yang, M. Bagheri, Z. J. Wei, S. J. Choi, L. Lu, J. D. O’Brien, and P. D. Dapkus, “Experimental characterization of the optical loss of sapphire-bonded photonic crystal laser cavities,” IEEE Photon. Technol. Lett. 18(3), 535–537 (2006). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(110.4235) Imaging systems : Nanolithography
(230.5298) Optical devices : Photonic crystals

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 14, 2010
Revised Manuscript: January 3, 2011
Manuscript Accepted: January 3, 2011
Published: January 20, 2011

Citation
Sunghwan Kim, Sungmo Ahn, Jeongkug Lee, Heonsu Jeon, Philippe Regreny, Christian Seassal, Emmanuel Augendre, and Lea Di Cioccio, "Milliwatt-level fiber-coupled laser power from photonic crystal band-edge laser," Opt. Express 19, 2105-2110 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2105

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References

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-Gap defect mode laser,” Science 284(5421), 1819–1821 (1999). [CrossRef] [PubMed]
H. Y. Ryu, S. H. Kwon, Y. J. Lee, Y. H. Lee, and J. S. Kim, “Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs,” Appl. Phys. Lett. 80(19), 3476 (2002). [CrossRef]
S. J. Koester, C. L. Schow, L. Schares, G. Dehlinger, J. D. Schaub, F. E. Doany, and R. A. John, “Ge-on-SOI-Detector/Si-CMOS-Amplifier Receivers for High-Performance Optical-Communication Applications,” J. Lightwave Technol. 25(1), 46–57 (2007). [CrossRef]
H. Altug and J. Vucković, “Photonic crystal nanocavity array laser,” Opt. Express 13(22), 8819–8828 (2005). [CrossRef] [PubMed]
L. Lu, A. Mock, E. H. Hwang, J. O’Brien, and P. D. Dapkus, “High-peak-power efficient edge-emitting photonic crystal nanocavity lasers,” Opt. Lett. 34(17), 2646–2648 (2009). [CrossRef] [PubMed]
S. Kim, J. Lee, H. Jeon, and H. J. Kim, “Fiber-coupled surface-emitting photonic crystal bandedge laser for biochemical sensor applications,” Appl. Phys. Lett. 94(13), 133503 (2009). [CrossRef]
C.-O. Cho, J. Jeong, J. Lee, H. Jeon, I. Kim, D. H. Jang, Y. S. Park, and J. C. Woo, “Photonic crystal band edge laser array with a holographically generated square-lattice pattern,” Appl. Phys. Lett. 87(16), 161102 (2005). [CrossRef]
S. Ahn, S. Kim, and H. Jeon, “Single-defect photonic crystal cavity laser fabricated by a combination of laser holography and focused ion beam lithography,” Appl. Phys. Lett. 96(13), 131101 (2010). [CrossRef]
C. Seassal, C. Monat, J. Mouette, E. Touraille, B. B. Bakir, H. T. Hattori, J.-L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP bonded membrane photonics components and circuits: toward 2.5 dimensional micro-nano-photonics,” IEEE J. Sel. Top. Quantum Electron. 11(2), 395–407 (2005). [CrossRef]
M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13(8), 2869–2880 (2005). [CrossRef] [PubMed]
S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293(5532), 1123–1125 (2001). [CrossRef] [PubMed]
L. J. Martínez, B. Alén, I. Prieto, J. F. Galisteo-López, M. Galli, L. C. Andreani, C. Seassal, P. Viktorovitch, and P. A. Postigo, “Two-dimensional surface emitting photonic crystal laser with hybrid triangular-graphite structure,” Opt. Express 17(17), 15043–15051 (2009). [CrossRef] [PubMed]
A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett. 31(20), 2972–2974 (2006). [CrossRef] [PubMed]
M. H. Shih, W. Kuang, T. Yang, M. Bagheri, Z. J. Wei, S. J. Choi, L. Lu, J. D. O’Brien, and P. D. Dapkus, “Experimental characterization of the optical loss of sapphire-bonded photonic crystal laser cavities,” IEEE Photon. Technol. Lett. 18(3), 535–537 (2006). [CrossRef]

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