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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 27039–27044
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High-Q width modulated photonic crystal stack mode-gap cavity and its application to refractive index sensing

Kaiyuan Yao and Yaocheng Shi  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 27039-27044 (2012)
http://dx.doi.org/10.1364/OE.20.027039


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Abstract

An optical sensor based on One-Dimensional photonic crystal (1D PhC) stack mode-gap cavity has been designed, fabricated and characterized. By introducing quadratically modulated width tapering structure, a waveguide coupled 1D PhC stack mode-gap cavity with calculated Q-factor 1.74 × 107 and an effective mode volume 1.48(λ/nSi)3 has been designed. This cavity has been used for sensing applications by immersing into water-ethanol mixture of different volume concentrations. Transmission measurement shows a quality factor as high as 27, 000 can be achieved for the cavity immersed in analytes. A sensitivity of 269nm/RIU has been demonstrated.

© 2012 OSA

1. Introduction

Optical microcavities like microring [1

1. J. Hu and D. Dai, “Cascaded-ring optical sensor with enhanced sensitivity by using suspended Si-nanowires,” Photon. Technol. Lett. 23(13), 842–844 (2011). [CrossRef]

, 2

2. J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16(6), 4296–4301 (2008). [CrossRef] [PubMed]

], microtoroids [3

3. A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-Q Microcavities,” Opt. Lett. 31(12), 1896–1898 (2006). [CrossRef] [PubMed]

, 4

4. H. K. Hunt and A. M. Armani, “Label-free biological and chemical sensors,” Nanoscale 2(9), 1544–1559 (2010). [CrossRef] [PubMed]

] and photonic crystal (PhC) cavities [5

5. R. V. Nair and R. Vijaya, “Photonic crystal sensors: An overview,” Prog. Quantum Electron. 34(3), 89–134 (2010). [CrossRef]

] have been widely and intensely researched for label-free biochemical sensing. In typical sensing applications, the shift of resonant wavelength for the microcavities induced by the change of background refractive index is used for analyzing samples. Therefore the detection limit of such sensors is determined by the Q-factor of the cavity mode and its sensitivity (nm/RIU) by the overlap between the light field and the background analytes. PhC cavities have attracted increasing attention owing to the advantage of high Q-factor, wavelength-dimension sensing area and strong light-matter interaction. Two-dimensional (2D) PhC cavities with Q-factor as high as 2 × 106 have been experimentally achieved [6

6. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010). [CrossRef]

]. Thus, various kinds of micro-sensor based on PhCs have been demonstrated [7

7. B. Wang, M. A. Dündar, R. Nötzel, F. Karouta, S. He, and R. W. van der Heijden, “Photonic crystal slot nanobeam slow light waveguides for refractive index sensing,” Appl. Phys. Lett. 97(15), 151105 (2010). [CrossRef]

10

10. Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, Sindy, K. Y. Tang, R. Illic, and M. Lončar, “Ultrasensitive on-chip photonic crystal nanobeam sensor using optical bistability,” Quantum Electronics and Laser Science Conference (QELS) Baltimore, Maryland, May 1, (2011).

].

Recently there has been much interest in PhC cavities realized in free standing nanobeams patterned with a one-dimensional lattice of holes [11

11. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009). [CrossRef]

17

17. Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19(19), 18529–18542 (2011). [CrossRef] [PubMed]

]. Such one-dimensional (1D) nanobeam PhC cavities have been demonstrated with experimental Q-factor over 105 [11

11. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009). [CrossRef]

, 13

13. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16(15), 11095–11102 (2008). [CrossRef] [PubMed]

], which is comparable to most 2D PhC cavities and much higher than air-slot cavities. In additional, the structural simplicity and small footprint inherent in 1D PhC cavities make them easier to be densely assembled for on-chip integration.

However, there are two intrinsic problems with PhC cavities for refractive index sensing. Firstly, the overlap of the light field with analytes (low-index) is always insufficient because the major part of light field is confined within the high-index area. The sensitivity of a silicon air-hole nanobeam sensor is only 83 nm/RIU [10

10. Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, Sindy, K. Y. Tang, R. Illic, and M. Lončar, “Ultrasensitive on-chip photonic crystal nanobeam sensor using optical bistability,” Quantum Electronics and Laser Science Conference (QELS) Baltimore, Maryland, May 1, (2011).

]. This is usually due to the small percentage of void space in PhC cavities, especially for 1D PhC cavities. Secondly, the high-index membrane material (silicon, etc.) cuts the void space into different pieces, such as isolated air-holes, and blocks the flow of sample fluids [8

8. T. Xu, N. Zhu, M. Y.-C. Xu, L. Wosinski, J. S. Aitchison, and H. E. Ruda, “Pillar-array based optical sensor,” Opt. Express 18(6), 5420–5425 (2010). [CrossRef] [PubMed]

].

In the present paper, an optical sensor based on 1D PhC stack mode-gap cavity has been designed, fabricated and characterized. Firstly, 1D PhC stack mode-gap cavity has been designed. Then, we analyze the dependence of the quality factor and the sensitivity of the cavity on the geometric parameters of the cavity. Finally, the cavity has been fabricated and the peak wavelength shift with volume concentrations for the water-ethanol mixture was recorded and analyzed.

2. Device design and analysis

Several designs of 1D PhC cavity with ultrahigh Q/V have been reported, such as nanobeam cavity [11

11. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009). [CrossRef]

] and mode-gap cavity [13

13. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16(15), 11095–11102 (2008). [CrossRef] [PubMed]

]. Instead of modifying the holes periodicity and/or size, B.-H. Ahn et al used an adiabatic parabolic tapering of the width of the nanobeam cavity to demonstrate an on-chip laser in a InGaAsP slab [12

12. B.-H. Ahn, J.-H. Kang, M.-K. Kim, J.-H. Song, B. Min, K.-S. Kim, and Y.-H. Lee, “One-dimensional parabolic-beam photonic crystal laser,” Opt. Express 18(6), 5654–5660 (2010). [CrossRef] [PubMed]

]. Figure 1(a)
Fig. 1 (a) Schematics of width-modulated stack cavity, in which a = 400 nm, Wx = 0.3a and Wy quadratically modulated from Wy(0) = 2.5a in the center to Wy(20) = 5.0a on both sides; (b) Intensity profile (|Ey|2) calculated by 3D FDTD method; (c) Zoomed in picture of the framed part in (a) with annotations; (d) TE band structure of the mode-gap waveguides with Wy = 2.5a (red) and Wy = 5.0a (blue). The black dot indicates the resonant frequency.
shows the schematic for the 1D PhC stack mode-gap cavity considered in our work. It consists of a simple periodic array of dielectric blocks in analytes. This array has a true 1D PBG on the x axis. The widths (Wy (i)) of the dielectric blocks are quadratically modulated (Wy(i) = Wy(0) + i2(Wy(imax)-Wy(0))/imax2, from the center to both sides, i increases from 0 to imax) in order to introduce a defect into the photonic bandgap (PBG) (Fig. 1(d)). Compared to the cavity proposed by M. Notomi et al. in [13

13. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16(15), 11095–11102 (2008). [CrossRef] [PubMed]

, 14

14. E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y.-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18(15), 15859–15869 (2010). [CrossRef] [PubMed]

], we modulate Wy instead of Wx. By such modulation, the area of the void space in the center of the cavity can be greatly increased. In addition, only a limited variation can be achieved when modulating Wx, because Wx should not be too small regarding the fabrication limitation. All these considerations are intended for the goal of higher sensitivity and make the fabrication easy.

Silicon-on-Insulator platform is considered in our work. The refractive index of the silicon stack and the silica insulator layer are 3.46, 1.44 respectively. The thickness of the silicon layer and the insulating layer are 220 nm and 2 μm, respectively. The lateral size of the silicon block (Wx) is chosen to be 0.3a so that the sample fluid can easily infiltrate into the void space between silicon blocks and effectively interact with the light field. The simulation is performed with commercial finite difference time domain (FDTD) software (Lumerical FDTD Solutions). The cavity was optimized using the deterministic high-Q design method introduced by Q. Quan [17

17. Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19(19), 18529–18542 (2011). [CrossRef] [PubMed]

]. Figure 1(b) shows the intensity profile (|Ey|2) calculated by 3D FDTD method. The calculated Q-factor is 1.74 × 107 (evaluated according to the decay of electromagnetic energy as a function of time) and the effective mode volume is 1.48(λ/nSi)3 (defined as V=dVε|E|2/[ε|E|2]max). Although the peak energy density is still confined in silicon, a large part of electric field (about 35%) locates in the void space which enables more interaction with analytes. The percentage of electric field in the void space can be further increased by varying Wx and Wy(0). Figure 1(d) shows the TE band diagram, also calculated by 3D FDTD method. The defect mode locates close to the center of the bandgap.

For the application in an optical sensor, cavities with high Q-factors and high sensitivity are preferred. Thus, the dependence of sensitivity and Q-factor on the key geometric parameters is systematically studied. Here sensitivity is defined as the shift of resonation wavelength when the background refractive index changes by one refractive index unit (RIU). The value of sensitivity and Q-factor vary with Wx and Wy(0) are given in Figs. 2(a)
Fig. 2 Influence of (a) Wx, (b) Wy(0) and (c) number of Gaussian mirror segments (NG) on the Q-factor and sensitivity of width-modulated stack cavity sensor;(d) Wavelength shift and variance of Q-factor over different background refractive indices.
and 2(b). From Fig. 2, we can find that the cavities with smaller Wx and Wy(0) give higher sensitivity. This can be easily understood since more percent of electric field energy locates in the void space for the cavities with smaller Wx / Wy(0). However, a moderate Q-factor must be maintained in this optimization. Figure 2(a) shows that Q-factor remains high enough when Wx is larger than 0.3a but will drop sharply if Wx is further reduced.When Wx is large enough (>0.3a in this case), the electric field can be well confined by the robust silicon stacks. However, it will too narrow to confine the electric field if Wx is further reduced (from 0.3a to 0 in this case), thus Q-factor will drop then. From Fig. 2(b), we can find that the highest theoretical Q-factor can be achieved when Wy(0) = 2.5a. This is reasonable since the resonant mode locates around the center of photonic bandgap at this value. Thus, Wx ad Wy(0) are set to be 0.3a and 2.5a respectively, considering the trade-off between sensitivity and Q-factor.

The number of Gaussian mirrors segments (NG) on either side of the stack cavity will also influence the sensitivity and Q-factor. From Fig. 2(c), we can find that Q-factor increases exponentially by adding more Gaussian mirrors when NG<20. Meanwhile mode volume and footprint of the stack cavity sensor will also be inevitably increased. However, sensitivity remains almost unchanged for different NG. This is significant that the Q-factor, mode volume and footprint of the stack cavity sensor can be flexibly tailored to different requirements without sacrificing sensitivity. To achieve a high Q-factor while keep a reasonable footprint, we choose NG = 20 in our work.

From the above analysis, the final parameters for the cavity are: Wx = 0.3a, Wy(0) = 2.5a, NG = 20. The resonant wavelength and Q-factor for the cavity vary with the refractive indices of the covering analytes is given in Fig. 2(d). From Fig. 2(d), we can find that the Q-factor maintains a high value over a wide range of background refractive index, indicating a very large sensing range of the device. This is especially advantageous compared to the microring based sensors whose sensing range is inevitably limited by the free spectrum range (FSR).

3. Fabrication and optical measurement

We fabricated and characterized the stack cavity sensor. The device was fabricated on a SOI wafer (SOITEC Inc.) with a silicon layer of 220 nm and insulating layer of 2 μm. The geometric parameters for the cavity are: a = 400 nm, Wx = 126 nm, Wy(0) = 1017 nm, Wy(20) = 2012 nm, the width for input/output waveguide is 2 μm. The pattern was defined on a positive electron beam resist film (PMMA 950K) of 310 nm thickness with an e-beam lithography tool (Raith 150 II) using 20kV acceleration voltage. Then the pattern was transferred to the 220 nm SOI device layer by inductively coupled plasma (ICP) etcher using a gas mixture of SF6 and C4F8. The resist was then removed with acetone in ultrasonic cleaner followed by an ashing process. In order to measure the transmission spectrum, we used the grating coupler approach for coupling from input/output waveguides to fibers. The grating couplers are fabricated on both the input and output waveguide by another overlay exposure followed by a shallow etching (70 nm). Scanning electron microscope (SEM) of the fabricated device is shown in Fig. 3
Fig. 3 Scanning electron microscope (SEM) image of the fabricated stack cavity sensor.
.

Besides, the sensing performance of stack cavity sensor may be slightly influenced by ambient temperature. This is because the resonating wavelength is mostly determined by the refractive indices of the device layer (silicon) and analytes (water-ethanol mixture in this experiment), and in turn these refractive indices varies slightly with temperature. To evaluate such effect, a temperature dependent measurement is carried out with minimized input power to eliminate the thermo-optic effect due to optical power heating [14

14. E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y.-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18(15), 15859–15869 (2010). [CrossRef] [PubMed]

]. The chip is heated by a thermo resistor and the temperature is controlled by tuning the applied voltage. The wavelength drift induced by temperature is shown in Fig. 4(d). There will be a blue shift of approximately 0.025 nm when the ambient temperature is increased by 1 °C. Owing to the good linearity of the wavelength drift with temperature, the thermal drift can be conveniently compensated by a reference cavity sensor if necessary.

4. Conclusion

In this paper, we have demonstrated an ultra-sensitive optical sensor based on 1D-PhC stack mode-gap cavity. A Q-factor as high as 27,000 was measured. The confined mode has a large percent of electric field energy locating in the void space and has large interaction with the analytes. The parameters for the cavity are optimized to achieve a high sensitivity while keeping a high Q-factor. We fabricated the stack cavity sensor and characterized in solutions of different concentration to confirm the numerical results. The measurement shows a sensitivity of 269nm/RIU. In additional, the sensing range of the proposed sensor is quite large since there is no limitation of FSR. Considering the benefits of high Q-factor, high sensitivity, large sensing range and small sensing area, we believe that this device will be a promising candidate in on-chip biochemical sensing.

Acknowledgments

This project was partially supported by the National Nature Science Foundation of China (No. 60907018), and also supported by the Fundamental Research Funds for the Central Universities.

References and links

1.

J. Hu and D. Dai, “Cascaded-ring optical sensor with enhanced sensitivity by using suspended Si-nanowires,” Photon. Technol. Lett. 23(13), 842–844 (2011). [CrossRef]

2.

J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16(6), 4296–4301 (2008). [CrossRef] [PubMed]

3.

A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-Q Microcavities,” Opt. Lett. 31(12), 1896–1898 (2006). [CrossRef] [PubMed]

4.

H. K. Hunt and A. M. Armani, “Label-free biological and chemical sensors,” Nanoscale 2(9), 1544–1559 (2010). [CrossRef] [PubMed]

5.

R. V. Nair and R. Vijaya, “Photonic crystal sensors: An overview,” Prog. Quantum Electron. 34(3), 89–134 (2010). [CrossRef]

6.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010). [CrossRef]

7.

B. Wang, M. A. Dündar, R. Nötzel, F. Karouta, S. He, and R. W. van der Heijden, “Photonic crystal slot nanobeam slow light waveguides for refractive index sensing,” Appl. Phys. Lett. 97(15), 151105 (2010). [CrossRef]

8.

T. Xu, N. Zhu, M. Y.-C. Xu, L. Wosinski, J. S. Aitchison, and H. E. Ruda, “Pillar-array based optical sensor,” Opt. Express 18(6), 5420–5425 (2010). [CrossRef] [PubMed]

9.

M. G. Scullion, A. Di Falco, and T. F. Krauss, “Slotted photonic crystal cavities with integrated microfluidics for biosensing applications,” Biosens. Bioelectron. 27(1), 101–105 (2011). [CrossRef] [PubMed]

10.

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, Sindy, K. Y. Tang, R. Illic, and M. Lončar, “Ultrasensitive on-chip photonic crystal nanobeam sensor using optical bistability,” Quantum Electronics and Laser Science Conference (QELS) Baltimore, Maryland, May 1, (2011).

11.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009). [CrossRef]

12.

B.-H. Ahn, J.-H. Kang, M.-K. Kim, J.-H. Song, B. Min, K.-S. Kim, and Y.-H. Lee, “One-dimensional parabolic-beam photonic crystal laser,” Opt. Express 18(6), 5654–5660 (2010). [CrossRef] [PubMed]

13.

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16(15), 11095–11102 (2008). [CrossRef] [PubMed]

14.

E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y.-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18(15), 15859–15869 (2010). [CrossRef] [PubMed]

15.

B. C. Richards, J. Hendrickson, J. D. Olitzky, R. Gibson, M. Gehl, K. Kieu, U. K. Khankhoje, A. Homyk, A. Scherer, J.-Y. Kim, Y.-H. Lee, G. Khitrova, and H. M. Gibbs, “Characterization of 1D photonic crystal nanobeam cavities using curved microfiber,” Opt. Express 18(20), 20558–20564 (2010). [CrossRef] [PubMed]

16.

Y. Gong, B. Ellis, G. Shambat, T. Sarmiento, J. S. Harris, and J. Vuckovic, “Nanobeam photonic crystal cavity quantum dot laser,” Opt. Express 18(9), 8781–8789 (2010). [CrossRef] [PubMed]

17.

Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19(19), 18529–18542 (2011). [CrossRef] [PubMed]

18.

CRC Handbook of Chemistry and Physics, ed. David R. Lide (92nd Edition Internet Version 2012).

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: August 28, 2012
Revised Manuscript: November 10, 2012
Manuscript Accepted: November 10, 2012
Published: November 15, 2012

Citation
Kaiyuan Yao and Yaocheng Shi, "High-Q width modulated photonic crystal stack mode-gap cavity and its application to refractive index sensing," Opt. Express 20, 27039-27044 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27039


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References

  1. J. Hu and D. Dai, “Cascaded-ring optical sensor with enhanced sensitivity by using suspended Si-nanowires,” Photon. Technol. Lett.23(13), 842–844 (2011). [CrossRef]
  2. J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express16(6), 4296–4301 (2008). [CrossRef] [PubMed]
  3. A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-Q Microcavities,” Opt. Lett.31(12), 1896–1898 (2006). [CrossRef] [PubMed]
  4. H. K. Hunt and A. M. Armani, “Label-free biological and chemical sensors,” Nanoscale2(9), 1544–1559 (2010). [CrossRef] [PubMed]
  5. R. V. Nair and R. Vijaya, “Photonic crystal sensors: An overview,” Prog. Quantum Electron.34(3), 89–134 (2010). [CrossRef]
  6. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73(9), 096501 (2010). [CrossRef]
  7. B. Wang, M. A. Dündar, R. Nötzel, F. Karouta, S. He, and R. W. van der Heijden, “Photonic crystal slot nanobeam slow light waveguides for refractive index sensing,” Appl. Phys. Lett.97(15), 151105 (2010). [CrossRef]
  8. T. Xu, N. Zhu, M. Y.-C. Xu, L. Wosinski, J. S. Aitchison, and H. E. Ruda, “Pillar-array based optical sensor,” Opt. Express18(6), 5420–5425 (2010). [CrossRef] [PubMed]
  9. M. G. Scullion, A. Di Falco, and T. F. Krauss, “Slotted photonic crystal cavities with integrated microfluidics for biosensing applications,” Biosens. Bioelectron.27(1), 101–105 (2011). [CrossRef] [PubMed]
  10. Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, Sindy, K. Y. Tang, R. Illic, and M. Lončar, “Ultrasensitive on-chip photonic crystal nanobeam sensor using optical bistability,” Quantum Electronics and Laser Science Conference (QELS) Baltimore, Maryland, May 1, (2011).
  11. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett.94(12), 121106 (2009). [CrossRef]
  12. B.-H. Ahn, J.-H. Kang, M.-K. Kim, J.-H. Song, B. Min, K.-S. Kim, and Y.-H. Lee, “One-dimensional parabolic-beam photonic crystal laser,” Opt. Express18(6), 5654–5660 (2010). [CrossRef] [PubMed]
  13. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express16(15), 11095–11102 (2008). [CrossRef] [PubMed]
  14. E. Kuramochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y.-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express18(15), 15859–15869 (2010). [CrossRef] [PubMed]
  15. B. C. Richards, J. Hendrickson, J. D. Olitzky, R. Gibson, M. Gehl, K. Kieu, U. K. Khankhoje, A. Homyk, A. Scherer, J.-Y. Kim, Y.-H. Lee, G. Khitrova, and H. M. Gibbs, “Characterization of 1D photonic crystal nanobeam cavities using curved microfiber,” Opt. Express18(20), 20558–20564 (2010). [CrossRef] [PubMed]
  16. Y. Gong, B. Ellis, G. Shambat, T. Sarmiento, J. S. Harris, and J. Vuckovic, “Nanobeam photonic crystal cavity quantum dot laser,” Opt. Express18(9), 8781–8789 (2010). [CrossRef] [PubMed]
  17. Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express19(19), 18529–18542 (2011). [CrossRef] [PubMed]
  18. CRC Handbook of Chemistry and Physics, ed. David R. Lide (92nd Edition Internet Version 2012).

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