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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 21397–21403
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Design of ultrahigh-Q photoinduced cavities in defect-free photonic crystal slabs

Snjezana Tomljenovic-Hanic and C. Martijn de Sterke  »View Author Affiliations


Optics Express, Vol. 18, Issue 20, pp. 21397-21403 (2010)
http://dx.doi.org/10.1364/OE.18.021397


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Abstract

We demonstrate numerically that a cavity can be induced in a defect-free photonic crystal slab made of photosensitive material such as chalcogenide glass. A key advantage of the design is the possibility for complete post-processing in an otherwise defect-free structure, and the cavity can thus be formed anywhere in the photonic crystal. We demonstrate that high-Q cavities with Q~108 can be designed in this way. Since the high-Q mode can originate from an air-band, these cavities appear to be ideal candidates for sensing applications.

© 2010 OSA

1. Introduction

It is also possible to induce the cavity by changing the refractive index of the background material [13

13. S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007). [CrossRef] [PubMed]

]. This concept can be realized in photosensitive material-based PCSs such as chalcogenide glasses and polymers. For example the refractive index of chalcogenide glass can be changed by 1-8%, depending on the type of glass, when it is illuminated by light, typically in the visible part of the spectrum [14

14. A. Zakery and S. R. Elliot, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]

]. We showed earlier that ultrahigh-Q cavities, Q~106, can be designed in chalcogenide-based double-heterostructure (DH) type PCS cavities when the refractive index change has one-dimensional Gaussian profile in the waveguide direction [13

13. S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007). [CrossRef] [PubMed]

]. This was experimentally confirmed when a cavity with Q = 1.25 × 105 was formed in this way [15

15. M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]

].

In this paper we design a cavity by changing the refractive index in otherwise defect-free chalcogenide-based PCS structure. In contrast, DH type cavities require a photonic crystal slab with a waveguide, and the cavity’s position is therefore restricted. Post-processing in defect-free structure was recently demonstrated where the cavity was formed by using a relocatable fibre taper [16

16. J.-Y. Kim, M.-K. Kim, M.-K. Seo, S.-H. Kwon, J.-H. Shin, and Y.-H. Lee, “Two-dimensionally relocatable microfiber-coupled photonic crystal resonator,” Opt. Express 17(15), 13009–13016 (2009). [CrossRef] [PubMed]

] but in this case the cavity is induced only when the fiber taper is present. Even though there are many reversible and irreversible photoinduced effects of chalcogenide glass, in this paper we consider a permanent refractive index change [15

15. M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]

]. The sign and magnitude of this change depend on the glass composition and the processing history of the sample [14

14. A. Zakery and S. R. Elliot, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]

]. Positive or negative refractive index changes can be obtained depending on the wavelength, intensity and polarization of the light used [17

17. K. Shimakawa, A. Kolobov, and S. R. Elliott, “Photoinduced effects and metastability in amorphous semiconductors and insulators,” Adv. Phys. 44(6), 475–588 (1995). [CrossRef]

]. Our cavity design is similar to the recently proposed and experimentally demonstrated geometry-based design where the cavity is formed by changing the size of the holes [18

18. F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, “Confinement of band-edge modes in a photonic crystal slab,” Opt. Express 15(17), 10890–10902 (2007). [CrossRef] [PubMed]

,19

19. F. Bordas, C. Seassal, E. Dupuy, P. Regreny, M. Gendry, P. Viktorovitch, M. J. Steel, and A. Rahmani, “Room temperature low-threshold InAs/InP quantum dot single mode photonic crystal microlasers at 1.5 microm using cavity-confined slow light,” Opt. Express 17(7), 5439–5445 (2009). [CrossRef] [PubMed]

].

2. Model and method

In our design we start with the bulk PCS without any defect. We consider a finite PCS composed of a hexagonal array of cylindrical air holes in a chalcogenide slab with n = 2.7. The lattice constant is a, hole radius R = 0.29a and the slab thickness is h = 0.7a. The structure has 49 periods in the x-direction and 55 periods in the y-direction for dielectric band edge mode calculations. The structure used for the air band edge mode calculations is smaller: it has 37 periods in the x-direction and 41 periods in the y-direction. The domain size was reduced as a satisfactory convergence could not be obtained for the larger domain.

The cavity is induced by changing the refractive index of the chalcogenide glass. The exposed region with the induced refractive index change has a rotationally symmetric Gaussian profile (in the plane of the slab), with a full width at the half maximum d = ma, where m is an integer. It is centered on the middle of the slab, at the centre of a hole. If the refractive index is increased, the bands shift to lower frequencies, and the mode forming the top of the band gap (the air band-edge mode) enters the photonic band gap (PBG) of the unexposed structure at the M point. This results in a mode being localized to the exposed region—this region thus forms a cavity, see Fig. 1(a)
Fig. 1 The potential well induced by (a) a positive refractive index change and (b) a negative refractive index change; the dotted lines represent the frequencies of the localized modes considered here; the solid horizontal lines represent the air and dielectric band-edge respectively.
. If the refractive index is decreased, bands shift to higher frequencies and the mode at the bottom of the band (the dielectric band-edge mode) enters the PBG of the unexposed structure at the K point, also forming a cavity, see Fig. 1(b). We assume that the induced refractive index change does not vary in the vertical direction. This is justified by the experimental verification of a photo-induced high-Q cavity [15

15. M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]

]. Otherwise, even small refractive index variations in the vertical direction break the symmetry and degrade the cavity Q [20

20. Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air-holes,” Appl. Phys. Lett. 82(11), 1661 (2003). [CrossRef]

].

The cavities’ quality factors, Q, are calculated using three-dimensional finite-difference time-domain (FDTD) simulations, combined with harmonic analysis techniques to extract narrow spectral features [21

21. V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997). [CrossRef]

]. Numerical parameters for the calculations can be found in Refs. [4

4. S. Tomljenovic-Hanic, C. M. de Sterke, and M. J. Steel, “Design of high-Q cavities in photonic crystal slab heterostructures by air-holes infiltration,” Opt. Express 14(25), 12451–12456 (2006). [CrossRef] [PubMed]

,13

13. S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007). [CrossRef] [PubMed]

].

3. Results

As discussed in Section 2 if the refractive index of chalcogenide glass decreases (increases), a high-Q dielectric band-edge (air-band edge) mode can be induced. We investigate the band-edge mode for different, positive and negative, refractive index changes. The size of the exposed region is similar to the length of the photoinduced DH cavity region demonstrated experimentally [15

15. M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]

].

First we consider a negative refractive index change. In Fig. 2(a)
Fig. 2 Quality factor (squares) and resonant frequency (crosses) as a function of the refractive index change for the (a) dielectric and (b) air band-edge mode. The horizontal solid lines represent the band-edges. The cavity width is fixed at m = 6.
we show Q and the resonant mode frequency as a function of the refractive index change. The cavity size is fixed at m = 6. The quality factor increases from Q = 2.7 × 107 at Δn = 0.08 to Q = 2.1 × 108 at Δn = 0.12. In this part of the curve the total quality factor is limited by in-plane losses [18

18. F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, “Confinement of band-edge modes in a photonic crystal slab,” Opt. Express 15(17), 10890–10902 (2007). [CrossRef] [PubMed]

]. Further decrease of the refractive index decreases the quality factor, due to increased out-of-plane losses [18

18. F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, “Confinement of band-edge modes in a photonic crystal slab,” Opt. Express 15(17), 10890–10902 (2007). [CrossRef] [PubMed]

], but it still well exceeds 108. In fact, there is a large range of the refractive index changes, the entire range considered here, where the Q > 107. Figure 2 also shows the resonant mode frequency (crosses) and the dielectric band-edge (solid line). The resonant frequency changes almost linearly with the refractive index. The frequency corresponding to the optimal Q is similar to that of DH structure cavities [22

22. S. Tomljenovic-Hanic, and C. M. de Sterke, “High-Q cavity design in photonic crystal heterostructures,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technol., OSA Technical Digest, JTuA125 (2008).

].

There are two major electric field components, Ex and Ey. In Fig. 3(a)
Fig. 3 One of the major electric field components, Ex, in the plane for the dielectric band-edge mode (a) with the larger domain, and (b) magnified in the centre of the slab, (c) the Fourier transform of the field; (d) to (f) similar, but for the air band-edge mode. For both cavities m = 6 periods and Δn = 0.1
and 3(b) one of the major electric field component, Ex, is shown for the dielectric band edge mode (Δn<0), and in 3(d) and (e) for the air-band edge mode (Δn>0). The refractive index change for both cavities is |Δn| = 0.1. The field is symmetric out-of-plane, anti-symmetric in the x-direction and in the y-direction for both modes. The circles represent the holes. In Figs. 3(b) and 3(e) we magnified field plots in the middle of the structure. As expected the field is mainly concentrated in the dielectric for the dielectric band-edge mode and mainly in the holes for the air band-edge mode. Figure 3 shows that the electric field is strong at the edges of the air holes. Therefore any random fluctuation of air-holes radius and position may affect the Q-factors [23

23. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]

].

In Figs. 3(c) and 3(f) we show Fourier transforms of the field with a circle indicating the light-cone. The field within the leaky light-cone region is insignificant as required for high-Q cavity modes [24

24. D. Englund, I. Fushman, and J. Vucković, “General recipe for designing photonic crystal cavities,” Opt. Express 13(16), 5961–5975 (2005). [CrossRef] [PubMed]

]. Though the out-of-plane quality factor component is usually considered to be the limiting factor in the design of high-Q cavities, this is not completely true here. For both the dielectric and the air band edge-mode, the limiting factor can be in-plane losses. Therefore if the refractive index change is in the range considered here (Δn = [0.08, 0.12]), special care has to be taken when choosing the dimensions of the entire structure. If the PCS is not large enough in comparison to the cavity size, the in-plane component can be the limiting factor.

4. Application for sensing

The quality factors for the air band-edge mode are significantly larger than the quality factors for any other reported air modes, including point type cavities, DH type cavities, and band-edge mode cavities [25

25. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12(17), 3988–3995 (2004). [CrossRef] [PubMed]

,26

26. S. Tomljenovic-Hanic, A. Rahmani, M. J. Steel, and C. Martijn de Sterke, “Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors,” Opt. Express 17(17), 14552–14557 (2009). [CrossRef] [PubMed]

]. DH cavity is restricted to the high-index waveguide region and therefore high-Q air modes are hard to achieve. In the case of the design based on modulation of radius of air-holes, the radius is modulated gradually; in our design the refractive index change is truly continuous. Both high Q, and a large field overlap with the sample, f, are important for optical cavity-based sensing [26

26. S. Tomljenovic-Hanic, A. Rahmani, M. J. Steel, and C. Martijn de Sterke, “Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors,” Opt. Express 17(17), 14552–14557 (2009). [CrossRef] [PubMed]

,27

27. N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluid. Nanofluid. 4(1-2), 117–127 (2008). [CrossRef]

]. The resonant shift, obtained when the sample is added to a liquid in the holes, is proportional to the energy fraction f of the resonant mode field interacting with the sample. The smallest refractive index change which can be sensed by a cavity-based sensor corresponds to a frequency shift larger than approximately the resonance linewidth, which, in turn, is determined by the quality factor. The air modes typically have large f but small Q [26

26. S. Tomljenovic-Hanic, A. Rahmani, M. J. Steel, and C. Martijn de Sterke, “Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors,” Opt. Express 17(17), 14552–14557 (2009). [CrossRef] [PubMed]

,27

27. N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluid. Nanofluid. 4(1-2), 117–127 (2008). [CrossRef]

], in contrast to the air band-edge mode presented here.

We investigate this type of the cavity for sensing application in the same manner as in Ref. [26

26. S. Tomljenovic-Hanic, A. Rahmani, M. J. Steel, and C. Martijn de Sterke, “Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors,” Opt. Express 17(17), 14552–14557 (2009). [CrossRef] [PubMed]

] for the air band-edge mode with an increased refractive index Δn = 0.12. In the case of liquid-based sensing all holes are infiltrated with the fluid, in this example water with nf = 1.33. The Q of the cavity is decreased from Q = 5.0 × 106 to Q = 4.2 × 105. This is not surprising as the refractive index difference between the holes and the slab is significantly reduced. Then we add the sample to the liquid, which changes its refractive index, shifting the cavity’s resonant frequency. In Fig. 4
Fig. 4 Sensitivity of the air band-edge mode cavity, Δn = 0.12, m = 6 for gas sensing (crosses) and liquid-based sensing (squares) as a function of the refractive index change induced by the sample, Δns. The solid horizontal line represents the detection limit S = 0.5.
, we show the sensitivity versus the refractive index change caused by the presence of the sample. If we choose the detection limit to be S = 0.5 [26

26. S. Tomljenovic-Hanic, A. Rahmani, M. J. Steel, and C. Martijn de Sterke, “Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors,” Opt. Express 17(17), 14552–14557 (2009). [CrossRef] [PubMed]

], at which the frequency shift is half the resonance linewidth, the detection limit of the infiltrated cavity is Δns = 5.4 × 10−6 and for the gas sensing it is Δns = 4.7 × 10−7. Therefore, a high-Q mode can originate from the air-band. Since such modes have a large overlap between the field and the sample, these cavities can be considered as ideal candidates for sensing applications. Larger overlap of the field and the sample was only demonstrated for the slotted PC waveguides that incorporate a geometry-based DH cavity [28

28. A. Di Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009). [CrossRef]

] but with the Q decreasing from Q = 5 × 104 to Q = 4 × 103 when the slot is infiltrated. Even though there is another localized mode in the potential well, in practice the spacing between modes is larger than the small shift induced by the presence of a sample.

5. Discussion and conclusions

Though we here consider continuously varying Gaussian refractive index profiles, qualitatively similar results are obtained for other circularly symmetric cavities. For example, taking the refractive index to be step-like top hat function, a refractive index change of Δn = −0.09 and a radius of eight periods leads to a cavity with Q = 7 × 105 for the dielectric band-edge mode. The same but positive refractive index change results in a cavity with Q = 3 × 105 for the air band-edge mode. The somewhat lower Q values for step-like refractive index profiles is consistent with results for DH cavities [13

13. S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007). [CrossRef] [PubMed]

]. Therefore the range of parameters, cavity size and the refractive index change that enable a high-Q cavity is quite broad. Consequently, it is not crucial to control the size and the refractive index change precisely. Similar findings were reported for DH cavities where the refractive index change is induced across the waveguide [22

22. S. Tomljenovic-Hanic, and C. M. de Sterke, “High-Q cavity design in photonic crystal heterostructures,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technol., OSA Technical Digest, JTuA125 (2008).

]. This differs from point cavities which are extremely sensitive to the values of the optimal parameters [25

25. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12(17), 3988–3995 (2004). [CrossRef] [PubMed]

]. Unlike geometry based cavities, our design does not require changes in the geometry with a precision measured in nanometers [2

2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]

,3

3. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]

,25

25. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12(17), 3988–3995 (2004). [CrossRef] [PubMed]

].

The quality factors obtained here are larger than those reported in photoinduced DH cavities. However, the main advantage of the current design is that it can be completely achieved by post-processing in an otherwise defect free structure; the cavity can thus be formed anywhere in the structure. In contrast, DH type cavities require a photonic crystal slab with a waveguide, and the cavity’s position is therefore restricted. Contrary, the new geometry allows the formation of high-Q cavities based on air bands, which is a key advantage in sensor applications. Modal volumes tend to be larger than for point-cavity designs [25

25. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12(17), 3988–3995 (2004). [CrossRef] [PubMed]

] and DH [13

13. S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007). [CrossRef] [PubMed]

]. The volumes of the resonant modes for the dielectric and air band-edge mode are of the order of a few (λ/n)3. For example the modal volume for the dielectric mode changes from V = 4.1 (λ/n)3 at Δn = 0.08 to V = 2.7 (λ/n)3 at Δn = 0.16. For the air mode for the same range it changes from V = 3.5(λ/n)3 to V = 1.9(λ/n)3. However, the increase in the quality factor is much larger than the modal volume increase. Therefore the overall ratio Q/V, important in many applications, is similar for the band-edge and DH type cavities. The required refractive index change for the band edge cavity modes, Δn~0.1, is larger than for the DH cavities, where Δn~0.03 [13

13. S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007). [CrossRef] [PubMed]

,15

15. M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]

], which in practice may lead to additional losses due to increased absorption [29

29. P. Skafte-Pedersen, P. S. Nunes, S. S. Xiao, and N. A. Mortensen, “Material limitations on the detection limit in refractometry,” Sensors (Basel Switzerland) 9(11), 8382–8390 (2009). [CrossRef]

,30

30. S. Tomljenovic-Hanic, A. D. Greentree, C. M. de Sterke, and S. Prawer, “Flexible design of ultrahigh-Q microcavities in diamond-based photonic crystal slabs,” Opt. Express 17(8), 6465–6475 (2009). [CrossRef] [PubMed]

].

In conclusion, we have shown that cavities with Q as high as Q~108 can be designed in defect-free chalcogenide-based photonic crystal slabs. Both positive and negative refractive index change can result in ultrahigh-Q cavities. This new geometry also allows the formation of high-Q cavities based on air bands, which is a key advantage in sensor applications. Though we considered only chalcogenide-based PCS, in principle this design can be applied to the other photosensitive materials as well.

Acknowledgments

This work was produced with the assistance of the Australian Research Council (ARC) under the ARC Centres of Excellence Program and by an award under the Merit Allocation Scheme on the National Facility of the National Computational Infrastructure. STH is supported by the Australian Research Council (ARC) Australian Research Fellowship (DP1096288). We thank D. J. Moss for pointing out the possibility for post-tuning in chalcogenide structure and A. Rahmani for useful discussions.

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15.

M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]

16.

J.-Y. Kim, M.-K. Kim, M.-K. Seo, S.-H. Kwon, J.-H. Shin, and Y.-H. Lee, “Two-dimensionally relocatable microfiber-coupled photonic crystal resonator,” Opt. Express 17(15), 13009–13016 (2009). [CrossRef] [PubMed]

17.

K. Shimakawa, A. Kolobov, and S. R. Elliott, “Photoinduced effects and metastability in amorphous semiconductors and insulators,” Adv. Phys. 44(6), 475–588 (1995). [CrossRef]

18.

F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, “Confinement of band-edge modes in a photonic crystal slab,” Opt. Express 15(17), 10890–10902 (2007). [CrossRef] [PubMed]

19.

F. Bordas, C. Seassal, E. Dupuy, P. Regreny, M. Gendry, P. Viktorovitch, M. J. Steel, and A. Rahmani, “Room temperature low-threshold InAs/InP quantum dot single mode photonic crystal microlasers at 1.5 microm using cavity-confined slow light,” Opt. Express 17(7), 5439–5445 (2009). [CrossRef] [PubMed]

20.

Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air-holes,” Appl. Phys. Lett. 82(11), 1661 (2003). [CrossRef]

21.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997). [CrossRef]

22.

S. Tomljenovic-Hanic, and C. M. de Sterke, “High-Q cavity design in photonic crystal heterostructures,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technol., OSA Technical Digest, JTuA125 (2008).

23.

H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]

24.

D. Englund, I. Fushman, and J. Vucković, “General recipe for designing photonic crystal cavities,” Opt. Express 13(16), 5961–5975 (2005). [CrossRef] [PubMed]

25.

Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12(17), 3988–3995 (2004). [CrossRef] [PubMed]

26.

S. Tomljenovic-Hanic, A. Rahmani, M. J. Steel, and C. Martijn de Sterke, “Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors,” Opt. Express 17(17), 14552–14557 (2009). [CrossRef] [PubMed]

27.

N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluid. Nanofluid. 4(1-2), 117–127 (2008). [CrossRef]

28.

A. Di Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009). [CrossRef]

29.

P. Skafte-Pedersen, P. S. Nunes, S. S. Xiao, and N. A. Mortensen, “Material limitations on the detection limit in refractometry,” Sensors (Basel Switzerland) 9(11), 8382–8390 (2009). [CrossRef]

30.

S. Tomljenovic-Hanic, A. D. Greentree, C. M. de Sterke, and S. Prawer, “Flexible design of ultrahigh-Q microcavities in diamond-based photonic crystal slabs,” Opt. Express 17(8), 6465–6475 (2009). [CrossRef] [PubMed]

OCIS Codes
(230.5750) Optical devices : Resonators
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: July 19, 2010
Revised Manuscript: September 17, 2010
Manuscript Accepted: September 20, 2010
Published: September 23, 2010

Citation
Snjezana Tomljenovic-Hanic and C. Martijn de Sterke, "Design of ultrahigh-Q photoinduced cavities in defect-free photonic crystal slabs," Opt. Express 18, 21397-21403 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21397


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References

  1. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]
  2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]
  3. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]
  4. S. Tomljenovic-Hanic, C. M. de Sterke, and M. J. Steel, “Design of high-Q cavities in photonic crystal slab heterostructures by air-holes infiltration,” Opt. Express 14(25), 12451–12456 (2006). [CrossRef] [PubMed]
  5. U. Bog, C. L. C. Smith, M. W. Lee, S. Tomljenovic-Hanic, C. Grillet, C. Monat, L. O’Faolain, C. Karnutsch, T. F. Krauss, R. C. McPhedran, and B. J. Eggleton, “High-Q microfluidic cavities in silicon-based two-dimensional photonic crystal structures,” Opt. Lett. 33(19), 2206–2208 (2008). [CrossRef] [PubMed]
  6. F. Intonti, S. Vignolini, V. Turck, M. Colocci, P. Bettotti, L. Pavesi, S. L. Schweizer, R. Wehrspohn, and D. Wiersma, “Rewritable photonic circuits,” Appl. Phys. Lett. 89(21), 211117 (2006). [CrossRef]
  7. B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004). [CrossRef]
  8. R. van der Heijden, C. F. Carlstrom, J. A. P. Snijders, R. W. van der Heijden, F. Karouta, R. Notzel, H. W. M. Salemink, B. K. C. Kjellander, C. W. M. Bastiaansen, D. J. Broer, and E. van der Drift, “E van der Drift, “InP-based two-dimensional photonic crystals filled with polymers,” Appl. Phys. Lett. 88(16), 161112 (2006). [CrossRef]
  9. P. El-Kallassi, S. Balog, R. Houdré, L. Balet, L. Li, M. Francardi, A. Gerardino, A. Fiore, R. Ferrini, and L. Zuppiroli, “Local infiltration of planar photonic crystals with UV-curable polymers,” J. Opt. Soc. Am. B 25(10), 1562–1567 (2008). [CrossRef]
  10. S. Tomljenovic-Hanic, C. M. de Sterke, M. J. Steel, B. J. Eggleton, Y. Tanaka, and S. Noda, “High-Q cavities in multilayer photonic crystal slabs,” Opt. Express 15(25), 17248–17253 (2007). [CrossRef] [PubMed]
  11. S. Gardin, F. Bordas, X. Letartre, C. Seassal, A. Rahmani, R. Bozio, and P. Viktorovitch, “Microlasers based on effective index confined slow light modes in photonic crystal waveguides,” Opt. Express 16(9), 6331–6339 (2008). [CrossRef] [PubMed]
  12. M.-K. Seo, J. H. Kang, M.-K. Kim, B.-H. Ahn, J.-Y. Kim, K.-Y. Jeong, H.-G. Park, and Y.-H. Lee, “Wavelength-scale photonic-crystal laser formed by electron-beam-induced nano-block deposition,” Opt. Express 17(8), 6790–6798 (2009). [CrossRef] [PubMed]
  13. S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Opt. Lett. 32(5), 542–544 (2007). [CrossRef] [PubMed]
  14. A. Zakery and S. R. Elliot, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]
  15. M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, E. C. Mägi, D. J. Moss, B. J. Eggleton, X. Gai, S. Madden, D.-Y. Choi, D. A. P. Bulla, and B. Luther-Davies, “Photowritten high-Q cavities in two-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 34(23), 3671–3673 (2009). [CrossRef] [PubMed]
  16. J.-Y. Kim, M.-K. Kim, M.-K. Seo, S.-H. Kwon, J.-H. Shin, and Y.-H. Lee, “Two-dimensionally relocatable microfiber-coupled photonic crystal resonator,” Opt. Express 17(15), 13009–13016 (2009). [CrossRef] [PubMed]
  17. K. Shimakawa, A. Kolobov, and S. R. Elliott, “Photoinduced effects and metastability in amorphous semiconductors and insulators,” Adv. Phys. 44(6), 475–588 (1995). [CrossRef]
  18. F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, “Confinement of band-edge modes in a photonic crystal slab,” Opt. Express 15(17), 10890–10902 (2007). [CrossRef] [PubMed]
  19. F. Bordas, C. Seassal, E. Dupuy, P. Regreny, M. Gendry, P. Viktorovitch, M. J. Steel, and A. Rahmani, “Room temperature low-threshold InAs/InP quantum dot single mode photonic crystal microlasers at 1.5 microm using cavity-confined slow light,” Opt. Express 17(7), 5439–5445 (2009). [CrossRef] [PubMed]
  20. Y. Tanaka, T. Asano, Y. Akahane, B.-S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air-holes,” Appl. Phys. Lett. 82(11), 1661 (2003). [CrossRef]
  21. V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997). [CrossRef]
  22. S. Tomljenovic-Hanic and C. M. de Sterke, “High-Q cavity design in photonic crystal heterostructures,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technol., OSA Technical Digest, JTuA125 (2008).
  23. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]
  24. D. Englund, I. Fushman, and J. Vucković, “General recipe for designing photonic crystal cavities,” Opt. Express 13(16), 5961–5975 (2005). [CrossRef] [PubMed]
  25. Z. Zhang and M. Qiu, “Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs,” Opt. Express 12(17), 3988–3995 (2004). [CrossRef] [PubMed]
  26. S. Tomljenovic-Hanic, A. Rahmani, M. J. Steel, and C. Martijn de Sterke, “Comparison of the sensitivity of air and dielectric modes in photonic crystal slab sensors,” Opt. Express 17(17), 14552–14557 (2009). [CrossRef] [PubMed]
  27. N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluid. Nanofluid. 4(1-2), 117–127 (2008). [CrossRef]
  28. A. Di Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009). [CrossRef]
  29. P. Skafte-Pedersen, P. S. Nunes, S. S. Xiao, and N. A. Mortensen, “Material limitations on the detection limit in refractometry,” Sensors (Basel Switzerland) 9(11), 8382–8390 (2009). [CrossRef]
  30. S. Tomljenovic-Hanic, A. D. Greentree, C. M. de Sterke, and S. Prawer, “Flexible design of ultrahigh-Q microcavities in diamond-based photonic crystal slabs,” Opt. Express 17(8), 6465–6475 (2009). [CrossRef] [PubMed]

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