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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 25 — Dec. 6, 2010
  • pp: 26461–26468
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Square lattice photonic crystal surface mode lasers

Tsan-Wen Lu, Shao-Ping Lu, Li-Hsun Chiu, and Po-Tsung Lee  »View Author Affiliations


Optics Express, Vol. 18, Issue 25, pp. 26461-26468 (2010)
http://dx.doi.org/10.1364/OE.18.026461


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Abstract

In this report, we propose a square lattice photonic crystal hetero-slab-edge microcavity design. In numerical simulations, three surface modes in this microcavity are investigated and optimized by tuning the slab-edge termination τ and gradual mirror layer. High simulated quality (Q) factor of 2.3 × 105 and small mode volume of 0.105 μm3 are obtained from microcavity with τ = 0.80. In experiments, we obtain and identify different surface modes lasing. The surface mode in the second photonic band gap shows a very-low threshold of 140 μW and high Q factor of 5,500, which could be an avenue to low-threshold optical lasers and highly sensitive sensor applications with efficient light-matter interactions.

© 2010 OSA

1. Introduction

In this report, even though the square-PhC has weaker PBG effect than that of the triangular-PhC, we show that high Q surface modes can be created in a square-PhC slab-edge based on our proposed mode gap confinement mechanism, which has not been studied and demonstrated yet. We investigate and optimize different surface modes in square-PhC slab-edge microcavities with reduced cavity sizes and different facets τ in simulations, which provides a guideline for achieving high Q and low threshold surface modes lasing.

In experiments, we optimize the fabrication process by proximity correction for electron-beam lithography, which enables us to precisely obtain the desired parameters of the slab-edge microcavities. In measurements, high Q and low threshold surface modes lasing actions at different slab-edge terminations are obtained and identified.

2. Surface modes in square-PhC microcavity

For a 2D square-PhC dielectric slab with air cladding shown in Fig. 1(a)
Fig. 1 (a) (top) Scheme of 2D truncated square-PhC slab and (bottom) the definition of slab-edge termination parameter τ. (b) The simulated TE-like band diagram (right) and transmission spectrum (left) of 2D square-PhC slab by 3D PWE and FDTD methods.
, the air hole radius (r) over lattice constant (a) (r/a) ratio, slab thickness, and refractive index are set to be 0.38, 220 nm, and 3.4, respectively. The simulated transverse-electric-like (TE-like) band diagram of square-PhC dielectric slab by 3D plane-wave expansion (PWE) method is shown in Fig. 1(b). The 1st-PBG is ranged from 0.33 to 0.36 in normalized frequency (a/λ), which is confirmed by 3D finite-difference time-domain (FDTD) simulated transmission spectrum also shown in Fig. 1(b). The 1st-PBG corresponds to a spectral width of 100 nm when a = 500 nm, which could not provide sufficient confinement for surface modes at certain slab-edge terminations. Thus, besides the 1st-PBG, in our following design, we will also use the 2nd-PBG with larger spectral width from 0.38 to 0.43, as shown in Fig. 1(b).

The surface wave can exist at the 2D truncated PhC slab-edge shown in Fig. 1(a) by the PBG and TIR confinements. To well confine the surface wave in a slab-edge segment with finite length, we had designed a hetero-slab-edge (HSE) interface with mode gap effect. For a given square-PhC slab-edge τC shown in Fig. 2(a)
Fig. 2 (a) Scheme of square-PhC slab-edges τC and τC. The air holes at slab-edge τC are shifted and shrunk, which leads to the decreased frequency of surface mode and a mode gap region denoted by the shadow region in (b) is formed. (b) The surface mode dispersion curves under different Δr/a. The r/a ratio difference between slab-edges τC and τC is defined as Δr/a. (c) Scheme of square-PhC HSE interface that forms mirror layers, including the outer mirror τC and gradual mirror τG, while the slab-edge τC is served as the cavity region.
, we can obtain a slab-edge τC with decreased surface mode frequency by shrinking and shifting the air holes at the slab-edge, as shown in Fig. 2(a). The r/a ratio difference between the slab-edges τC and τC’ is defined as Δr/a. The simulated surface mode dispersion curves under different Δr/a are shown in Fig. 2(b). For the decreased surface mode frequency of slab-edge τC, a mode gap represented by the shadow region in Fig. 2(b) will form owing to the surface mode frequency difference between the slab-edges τC and τC. In the slab-edge τC, the surface mode with frequency inside the mode gap is forbidden to propagate in slab-edge τC. Thus, we can use the slab-edge τC’ as a mirror layer for slab-edge τC to form a microcavity, as shown in Fig. 2(c). To reduce the scattering loss between the cavity τC and the outer mirror region τC [17

17. Y. Tanaka, T. Asano, and S. Noda, “Design of Photonic Crystal Nanocavity with Q-factor of ~109,” J. Lightwave Technol. 26(11), 1532–1539 (2008). [CrossRef]

], we design a gradual mirror region τG, where the air-hole r/a ratio at slab-edge is linearly changed, as shown in Fig. 2(c). The initial parameters are as follows: (1) The r/a ratio and length of the cavity τC are 0.38 and 6a. (2) The Δr/a ratio is chosen as 0.03. (3) The length of gradual mirror τG is 5a.

According to above parameters, we vary the slab-edge termination parameter τ (as defined in Fig. 1(a)) of cavity τC from 0 to 0.90. By 3D FDTD simulations, we find three high Q surface modes under different τ, which are denoted as the DD1-, DD2-, and DD3- modes. The surface modes we investigate here are all 0th-order fundamental modes. The first and second letters stand for the mode behaviors in the air and PhC regions, respectively. We use the letters D and E to mean Decay and Extended [18

18. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 2008).

]. The simulated Q factors and mode volumes (V) of the three surface modes under different τ are shown in Figs. 3(a)
Fig. 3 The simulated Q factors and mode volumes of the 0th-order (a) DD1-, (b) DD2-, and (c) DD3-modes under different τ. The Δr/a is fixed at 0.03.
3(c). The DD1- and DD3-modes both lie inside the 2nd-PBG and high Q factors of 1.0 × 105 and 9.1 × 104 can be obtained when τ = 0.10 and 0.80, respectively. However, we find the mode volume of the DD3-mode (~0.117 μm3) is smaller than that of the DD1-mode (~0.204 μm3), which shows a higher Q/V value of DD3-mode and is beneficial for laser source in quantum electron dynamic devices and photonic integrated circuits. Thus, in the following experiments, we will focus on the DD3-mode. At τ = 0.80, we optimize the Q factor of the DD3-mode in HSE microcavity by varying Δr/a from 0.02 to 0.18. The simulated Q factors and mode volumes under different Δr/a are shown in Fig. 4(a)
Fig. 4 (a) The simulated Q factor and mode volume of the DD3-mode under fixed τ of 0.80 and different Δr/a from 0.02 to 0.18. High Q factor and small mode volume of 2.3 × 105 and 0.105 μm3 are obtained when Δr/a = 0.09. (b) The simulated Ex- and Ey-fields of the DD3-mode in microcavity with τ = 0.80 and Δr/a = 0.09, which are even and odd symmetric to the y-axis (dash line).
. When Δr/a = 0.09, we obtain a high Q factor of 2.3 × 105 and a small V of 0.105 μm3 (close to one wavelength cubic). It is worthy to note the surface mode volume is very small even the cavity size is quite large (6a), which originates from its feature of highly concentrated field at the surface. The simulated electric field components (Ex and Ey) of the DD3-mode are shown in Fig. 4(b). We can observe that the electric field concentrates at the surface of the microcavity region and very small field fraction extends into the square-PhC, which reveals good confinement by the 2nd-PBG effect. In addition, in Fig. 4(b), the Ex- and Ey-fields are even and odd symmetric to the y-axis (dash line in Fig. 4(b)), respectively. That means the Ey far-field will be cancelled and implies the Ex far-field emission contributes more to the emissions inside the collectable radiation angle [19

19. S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73(23), 235117 (2006). [CrossRef]

], for example, ± 30°, when the emission is collected by an objective lens with numerical aperture of 0.5.

Furthermore, the DD2-mode inside the 1st-PBG reaches its highest Q factor of 6.4 × 104 and smallest mode volume of 0.203 μm3 at τ = 0.35. We then optimize the DD2-mode by varying Δr/a from 0.01 to 0.07 at τ = 0.35. The simulated Q factors and mode volumes under different Δr/a are shown in Fig. 5(a)
Fig. 5 (a) The simulated Q factor and mode volume of the DD2-mode under fixed τ of 0.35 and different Δr/a from 0.01 to 0.07. (b) The simulated Ex-fields of the DD2-mode in microcavities with τ = 0.35 (top) and 0.40 (bottom) and (c) their Ex-field distributions along the dash line in (b).
. When Δr/a = 0.02, we obtain a high Q factor of 8.0 × 104 and the simulated Ex-field distribution is shown in Fig. 5(b), where we can observe the Ex-field extends more into the square-PhC than that of the DD3-mode shown in Fig. 4(b). This is caused by the insufficient 1st-PBG confinement, which makes the DD2-mode become a DE-like mode. This could be responsible for its lower Q factor and larger mode volume than those of the DD3-mode. This phenomenon becomes more significant when τ increases to be 0.40 or decreases to be 0.30, where the Q factor appreciably decreases and the mode volume increases, respectively, as shown in Fig. 3(b). The simulated Ex-field of the DD2-mode in microcavity with τ = 0.40 is also shown in Fig. 5(b). The Ex-field distributions of the DD2-mode in microcavities with τ = 0.35 and 0.40 along the dash line shown in Fig. 5(b) are shown in Fig. 5(c). Clearly, the Ex-field of the DD2-mode at τ = 0.40 extends more into the square-PhC region, as shown by the shadow region in Fig. 5(c).

Thus, comparing the DD2-mode with the DD3-mode, we can conclude the 2nd-PBG of square-PhC can provide more efficient confinement than the 1st-PBG, which leads to high Q factor and small mode volume of surface mode.

3. Surface modes lasing actions

In fabrication, the epitaxial structure consisted of four 10 nm compressively strained InGaAsP multi-quantum-wells (MQWs) with 220 nm thickness is prepared. The measured photoluminescence (PL) centered at 1530 nm is shown in Fig. 6(a)
Fig. 6 (a) The measured PL spectrum of the InGaAsP MQWs. (b) SEM pictures of the fabricated slab-edges with different τ from 0 to 0.90. (c) Top- and (d) tilted-view SEM pictures of the square-PhC HSE microcavity with τ = 0.40. (e) The zoom-in SEM pictures of cavity τC, gradual mirror τG, and outer mirror τC', which show the well-controlled Δr/a of 0.02.
. The MQWs is deposited a silicon nitride hard mask and spin-coated electron-beam resist in sequence. The square-PhC patterns are defined by electron-beam lithography on the resist layer. After a series of reactive ion etching and inductively coupled plasma etching, the square-PhC slab is formed by HCl selective wet-etching process. Designing the patterns with proper proximity corrections for electron-beam lithography is very important, which assures that we can fabricate the optimized τ and Δr/a ratio obtained in simulation, and keep the r/a ratio uniform near the slab-edge of the fabricated devices. Scanning electron microscope (SEM) pictures of the fabricated slab-edges with τ = 0 to 0.90 are shown in Fig. 6(b). However, there would be very slight r/a ratio difference between the PhC patterns near and far away from the slab-edge. Top- and tilted-view SEM pictures of the square-PhC HSE microcavity are shown in Figs. 6(c) and 6(d). From the zoom-in SEM pictures of cavity τC, gradual mirror τG, and outer mirror τC shown in Fig. 6(e), the fabricated a, τ, r/a and Δr/a ratios are estimated to be 520 nm, 0.40, 0.38, and 0.02, respectively.

According to the optimized results in simulation, the square-PhC HSE microcavity with fabricated a = 620 nm, r/a = 0.38, Δr/a = 0.09, and τ = 0.80 shown as the insets in Fig. 7(a)
Fig. 7 (a) L-L curve and (b) lasing spectrum in dB scale of the DD3-mode from microcavity with τ = 0.80 and Δr/a = 0.09. The zoom-in SEM pictures of the measured microcavity and the spectrum below threshold are shown as the insets of (a) and (b). (c) Lasing wavelengths of the DD3-mode under different τ from 0.70 to 0.85 (top), which agree with 3D FDTD simulation results (bottom) quite well.
is optically pumped by 20 ns pulse with 0.6% duty cycle at room temperature. The measured light-in light-out (L-L) curve and lasing spectrum in dB scale at 1556 nm are shown in Figs. 7(a) and 7(b), which show a very low threshold of 140 μW and side-mode suppression-ratio larger than 25 dB. The spectrum at 0.7 times threshold shown as the inset of Fig. 7(b) shows the measured line-width of 0.28 nm, which corresponds to a high estimated Q factor of 5,500. The localization property of surface mode in HSE microcavity can be easily confirmed by moving the excitation laser spot from microcavity to square-PhC and outer mirror regions, respectively, and no lasing action is observed when pumping these regions. To further confirm the surface mode lasing, lasing spectra of the DD3-mode at different τ from 0.70 to 0.85 are obtained and shown in the top of Fig. 7(c). The measured normalized frequencies agree with the 3D FDTD simulated results, as shown in the bottom of Fig. 7(c).

We also measure the HSE microcavity with fabricated a = 520 nm, r/a = 0.38, Δr/a = 0.02, and τ = 0.35, shown as the inset of Fig. 8(a)
Fig. 8 (a) The measured lasing spectra from the HSE microcavity with τ = 0.35 when pumping (top) the cavity and (bottom) the central square-PhC regions. Lasing actions of the 0th-, 1st-order DD2-modes and BE-mode can be observed when pumping the cavity, while only BE-mode lasing can be observed when pumping the central square-PhC. The zoom-in SEM picture of the measured HSE microcavity with τ = 0.35 is also shown as inset. (b) Comparisons between the 3D FDTD simulated and measured frequencies of the 0th-order DD2- and BE-modes.
. From the measured spectrum in the top of Fig. 8(a), we observe three lasing peaks at 1480, 1505, and 1576 nm. The first two peaks areidentified as 0th- and 1st-order DD2-modes, by comparing with 3D FDTD simulation results. The 0th-order DD2-mode is the mode we discuss and optimize in Fig. 3(b). Furthermore, we believe the lasing peak at 1576 nm comes from the band-edge (BE) mode at M-point of the 1st-band (M1). When the excitation laser spot is moved to the central square-PhC region denoted in Fig. 6(d), this peak can still be obtained while there is no DD2-mode lasing observed, as shown in the bottom of Fig. 8(a) under 5 times the pump power used to obtain the top lasing spectrum of Fig. 8(a). This shows the field localization and extension features of the DD2- and BE-modes, respectively. This also implies the PhC slab-edge presented here could efficiently lead out the emission of the BE slab modes confined inside the PhC slab. The wavelength shift of the BE-mode in Fig. 8(a) is attributed to the slightly shrunk r/a ratio of central square-PhC because of the proximity effect during electron-beam lithography. Moreover, the BE-mode can be further confirmed by its almost-constant frequency when τ is varied from 0.30 to 0.40, as shown in Fig. 8(b). In contrast, the 0th-order DD2-mode frequency decreases with increased τ from 0.30 to 0.40. Both of them agree with the 3D FDTD simulated results shown in Fig. 8(b). Thus, we can confirm the lasing modes come from the DD2- and BE-modes, respectively.

4. Summary

In this report, we propose a square-PhC HSE microcavity, which sustains different surface modes at different slab-edge terminations τ. Via 3D FDTD simulation, three different surface modes are investigated, including the DD1- (τ = 0.80 - 0.20) and DD3-modes (τ = 0.60 - 0.85) in the 2nd-PBG, and the DD2-mode (τ = 0.30 - 0.45) in the 1st-PBG. By optimizing τ and gradual-mirror parameter Δr/a, we obtain a high Q factor of 2.3 × 105 and small mode volume of 0.105 μm3 from the DD3-mode at τ = 0.80 and Δr/a = 0.09. In experiments, via designed proximity corrections in electron-beam lithography, we can well-control the desired fabricated τ, Δr/a ratio, and keep the r/a ratio uniform near the slab-edge of the fabricated devices. We obtain the DD2- and DD3-mode lasing actions from the HSE microcavities with τ = 0.35 and 0.80. These two modes are identified by wavelength shifts under different τ, which differentiates them from the BE-mode at M1-point extracted by PhC slab-edge with invariant wavelength. The DD3-mode lasing shows a very low threshold of 140 μW and high measured Q factor of 5,500. Due to the feature of surface mode field concentrated at surface, we believe this microcavity design with surface mode could be an avenue to low-threshold optical laser and highly sensitive optical sensor applications with efficient light-matter interactions.

Acknowledgements

This work is supported by Taiwan’s National Science Council (NSC) under contract number NSC-98-2221-E-009-015-MY2. The authors would like to thank the help from Center for Nano Science and Technology (CNST) of National Chiao Tung University, Taiwan.

References and links

1.

P. Yeh, Optical Waves in Layered Media, (Wiley, New York, 2005).

2.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991). [CrossRef] [PubMed]

3.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18(7), 528–530 (1993). [CrossRef] [PubMed]

4.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]

5.

W. Ṡmigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75(20), 205430 (2007). [CrossRef]

6.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92(9), 092114 (2008). [CrossRef]

7.

H. C. Chen, K. K. Tsia, and A. W. Poon, “Surface modes in two-dimensional photonic crystal slabs with a flat dielectric margin,” Opt. Express 14(16), 7368–7377 (2006). [CrossRef] [PubMed]

8.

Yu. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95(9), 4538–4544 (2004). [CrossRef]

9.

V. S. Volkov, S. I. Bozhevolnyi, L. H. Frandsen, and M. Kristensen, “Direct observation of surface mode excitation and slow light coupling in photonic crystal waveguides,” Nano Lett. 7(8), 2341–2345 (2007). [CrossRef] [PubMed]

10.

S. Xiao and M. Qiu, “Optical microcavities based on surface modes in two-dimensional photonic crystals and silicon-on-insulator photonic crystals,” J. Opt. Soc. Am. B 24(5), 1225–1229 (2007). [CrossRef]

11.

Z. Zhang, M. Dainese, L. Wosinski, S. Xiao, M. Qiu, M. Swillo, and U. Andersson, “Optical filter based on two-dimensional photonic crystal surface-mode cavity in amorphous silicon-on-silica structure,” Appl. Phys. Lett. 90(4), 041108 (2007). [CrossRef]

12.

J. Wang, Y. Song, W. Yan, and M. Qiu, “High-Q photonic crystal surface-mode cavities on crystalline SOI structures,” Opt. Commun. 283(11), 2461–2464 (2010). [CrossRef]

13.

J. K. Yang, S. H. Kim, G. H. Kim, H. G. Park, Y. H. Lee, and S. B. Kim, “Slab-edge modes in two-dimensional photonic crystals,” Appl. Phys. Lett. 84(16), 3016–3018 (2004). [CrossRef]

14.

T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “Photonic crystal hetero-slab-edge microcavity with high quality factor surface mode for index sensing,” Appl. Phys. Lett. 94(14), 141110 (2009). [CrossRef]

15.

V. N. Konopsky and E. V. Alieva, “A biosensor based on photonic crystal surface waves with an independent registration of the liquid refractive index,” Biosens. Bioelectron. 25(5), 1212–1216 (2010). [CrossRef]

16.

T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “High-index sensitivity of surface mode in photonic crystal hetero-slab-edge microcavity,” Opt. Lett. 35(9), 1452–1454 (2010). [CrossRef] [PubMed]

17.

Y. Tanaka, T. Asano, and S. Noda, “Design of Photonic Crystal Nanocavity with Q-factor of ~109,” J. Lightwave Technol. 26(11), 1532–1539 (2008). [CrossRef]

18.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 2008).

19.

S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73(23), 235117 (2006). [CrossRef]

OCIS Codes
(140.5960) Lasers and laser optics : Semiconductor lasers
(140.3945) Lasers and laser optics : Microcavities
(230.5298) Optical devices : Photonic crystals

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 15, 2010
Revised Manuscript: October 27, 2010
Manuscript Accepted: November 22, 2010
Published: December 2, 2010

Citation
Tsan-Wen Lu, Shao-Ping Lu, Li-Hsun Chiu, and Po-Tsung Lee, "Square lattice photonic crystal surface mode lasers," Opt. Express 18, 26461-26468 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-25-26461


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References

  1. P. Yeh, Optical Waves in Layered Media, (Wiley, New York, 2005).
  2. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991). [CrossRef] [PubMed]
  3. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Opt. Lett. 18(7), 528–530 (1993). [CrossRef] [PubMed]
  4. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]
  5. W. Ṡmigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75(20), 205430 (2007). [CrossRef]
  6. H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92(9), 092114 (2008). [CrossRef]
  7. H. C. Chen, K. K. Tsia, and A. W. Poon, “Surface modes in two-dimensional photonic crystal slabs with a flat dielectric margin,” Opt. Express 14(16), 7368–7377 (2006). [CrossRef] [PubMed]
  8. Yu. A. Vlasov, N. Moll, and S. J. McNab, “Mode mixing in asymmetric double-trench photonic crystal waveguides,” J. Appl. Phys. 95(9), 4538–4544 (2004). [CrossRef]
  9. V. S. Volkov, S. I. Bozhevolnyi, L. H. Frandsen, and M. Kristensen, “Direct observation of surface mode excitation and slow light coupling in photonic crystal waveguides,” Nano Lett. 7(8), 2341–2345 (2007). [CrossRef] [PubMed]
  10. S. Xiao and M. Qiu, “Optical microcavities based on surface modes in two-dimensional photonic crystals and silicon-on-insulator photonic crystals,” J. Opt. Soc. Am. B 24(5), 1225–1229 (2007). [CrossRef]
  11. Z. Zhang, M. Dainese, L. Wosinski, S. Xiao, M. Qiu, M. Swillo, and U. Andersson, “Optical filter based on two-dimensional photonic crystal surface-mode cavity in amorphous silicon-on-silica structure,” Appl. Phys. Lett. 90(4), 041108 (2007). [CrossRef]
  12. J. Wang, Y. Song, W. Yan, and M. Qiu, “High-Q photonic crystal surface-mode cavities on crystalline SOI structures,” Opt. Commun. 283(11), 2461–2464 (2010). [CrossRef]
  13. J. K. Yang, S. H. Kim, G. H. Kim, H. G. Park, Y. H. Lee, and S. B. Kim, “Slab-edge modes in two-dimensional photonic crystals,” Appl. Phys. Lett. 84(16), 3016–3018 (2004). [CrossRef]
  14. T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “Photonic crystal hetero-slab-edge microcavity with high quality factor surface mode for index sensing,” Appl. Phys. Lett. 94(14), 141110 (2009). [CrossRef]
  15. V. N. Konopsky and E. V. Alieva, “A biosensor based on photonic crystal surface waves with an independent registration of the liquid refractive index,” Biosens. Bioelectron. 25(5), 1212–1216 (2010). [CrossRef]
  16. T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “High-index sensitivity of surface mode in photonic crystal hetero-slab-edge microcavity,” Opt. Lett. 35(9), 1452–1454 (2010). [CrossRef] [PubMed]
  17. Y. Tanaka, T. Asano, and S. Noda, “Design of Photonic Crystal Nanocavity with Q-factor of ~109,” J. Lightwave Technol. 26(11), 1532–1539 (2008). [CrossRef]
  18. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 2008).
  19. S. H. Kim, S. K. Kim, and Y. H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73(23), 235117 (2006). [CrossRef]

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