Abstract

We demonstrate highly efficient evanescent coupling between a highly nonlinear chalcogenide glass two dimensional photonic crystal waveguide and a silica fiber nanowire. We achieve 98% insertion efficiency to the fundamental photonic crystal waveguide mode with a 3dB coupling bandwidth of 12nm, in good agreement with theory. This scheme provides a promising platform to realize low power nanocavity based all-optical switching and logic functions.

© 2006 Optical Society of America

1. Introduction

Two-dimensional (2D) photonic crystal (PhC) slabs have become a promising class of dielectric structure for micro- and nano-photonics. Their ability to control light at the wavelength scale [1–2] has already led to impressive demonstrations of various passive devices [3] and micro-lasers [4]. These achievements have been enabled by advanced technologies for patterning and etching materials such as silicon [5] or III-V semiconductors [6]. One of the promises of photonic crystals has been the realization of ultra-low power all-optical switches and logic via nonlinear high-Q nanocavities [7–9]. This has been highlighted by the recent demonstration in silicon photonic crystals of all-optical switching with <10 fJ pulse energies, and response times of <100 ps [10–11]. It is hoped that 2D PhC membranes will find utility in all-optical processors for ultra-fast and low power switching, optical logic gates, pulse regeneration, wavelength conversion, dispersion management and a variety of other applications [12–13].

Chalcogenide glasses are promising alternative nonlinear materials to silicon with which to realize all-optical photonic crystal devices. Whilst not possessing the mature fabrication techniques of silicon, chalcogenide glasses possess a number of significant advantages, such as high nonlinearity (n2 as high as 100-1000× that of silica), low linear absorption, low two-photon absorption [14–15] and the absence of the free-carrier effects that have posed a challenge to realizing ultrafast all-optical devices in silicon. In particular, the large refractive index of chalcogenide glasses (compared to other glasses) of 2.4 to 3.0 opens up the possibility of achieving compact nonlinear devices. In addition to reducing the switching power requirements, the pure Kerr-like nonlinearities offer the potential for near instantaneous response times (<100 fs) and are only limited by the resonator Q-factor. This compares favorably to carrier-based nonlinear effects, as exploited in silicon [10–11, 16] or III-V-based devices [17–18], which rely on dissipation to occur after switching, limiting the response time to tens of picoseconds.

We recently demonstrated chalcogenide glass photonic crystals fabricated by focused ion beam (FIB) milling [19–20]. In this paper we demonstrate more than 98% coupling efficiency to a two-dimensional photonic crystal waveguide (PCWG) in a chalcogenide membrane through the use of evanescent coupling via tapered optical fibre nanowires (Fig. 1). We observe coupling to both the fundamental and first higher order modes of the PCWG. The 3dB bandwidth of the coupling resonance to the fundamental mode is 12nm and the absolute coupling wavelength of 1550nm is in good agreement with theoretical results. This work is the result of recent advances in chalcogenide glass photonic crystal membrane fabrication by FIB milling [19–20], and the development of silica nanowire evanescent probing techniques [21], and represents an important step in the route to realizing low power nanocavity based all-optical switching in chalcogenide glass photonic crystals.

 

Fig. 1. (a) Schematic showing the coupling scheme of a PCWG and a tapered fiber, in this case backward coupling as explained in section 4. (b) Cross sectional view along YZ axis of the coupling mechanism between the taper and the PCWG. c) Cross sectional view normal to the direction of propagation.

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2. Device Fabrication

Full details of the fabrication process are briefly reviewed here and will be published elsewhere, see [19] for an earlier approach. A chalcogenide film of thickness 300nm, composed of AMTIR-1 glass (Ge33As12Se55 - refractive index ~2.7 @ 1.55 μm) was deposited by ultrafast pulsed laser deposition on a 50nm thick silicon nitride (Si3N4) membrane supported on a silicon substrate. The Si3N4 membrane was fabricated by wet etching the backside of a nitrided Si wafer. The Si3N4 initially 100nm thick was then accurately thinned to 50nm using Reactive Ion Etching. This resulted in a free-standing chalcogenide film on a thin (50nm) silicon nitride support film with an open aperture of approximately 130μm. Subsequently a thin Au coating was applied to both sides and a Ga+ FIB was used to mill cylindrical holes into the film from the back side (through the nitride). Consequently the beam first had to penetrate the relatively robust nitride layer before milling the softer glass, which greatly reduced the sculpting of the upper glass surface by the low intensity beam pedestal and resulted in nearly vertical sidewalls. The triangular lattice consisted of 550nm spaced holes of radius ~200nm (0.36×period). High-resolution scanned electron micrographs of a typical structure are shown in Fig. 2, taken at normal incidence imaged from the glass side. The final device under test was not imaged in this way because we have observed electron-induced refractive index changes in the past. Finally, the Au was wet etched and stripped for testing. The sidewall roughness can be very low in these structures, estimated to be <3 nm in our previous work [19]. The nearly cylindrical holes had sharp edges where they met the surface of the membrane. Figure 2 shows a PhC membrane waveguide consisting of a “W1” defect comprising a missing row of holes along the Γ-K direction. The waveguide under test consists of an open W1 with 160 holes removed (~90 μm). Since previous work we have added a drift correction scheme to greatly improve lattice periodicity in the device under test, to be published elsewhere.

 

Fig. 2. Scanned electron micrographs of a chalcogenide glass photonic crystal membrane fabricated by focused ion beam (FIB) milling of an AMTIR-1 chalcogenide glass film. left: film imaged at 0°. Right: picture of “W1” defect waveguide.

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3. Experiment

Coupling to waveguides and cavities with very small mode field dimensions is a challenge that has attracted significant attention. One approach to coupling is evanescent coupling via silica nanowires [21–28]. Reference [22] describes the first realization of evanescent coupling to a microcavity, which in this case was a relatively large mode volume glass microsphere cavity. Reference [23] represents the first realization of tapered fiber coupling to a wavelength-scale semiconductor microcavity, in this case, a photonic crystal defect microcavity. The distinction between references [22] and [23] are in the microcavity material (glass vs. silicon), geometry (microsphere vs. photonic crystal), and mode volumes (hundreds of cubic wavelengths vs. less than one cubic wavelength). Reference [25] is a recent demonstration of evanescent coupling from a taper utilized to pump an InP photonic crystal microlaser and to collect its light emission. Reference [26] theoretically discusses coupling to a photonic crystal waveguide, while reference [27] can be considered as the first experimental demonstration of taper-PCWG coupling and [21] and [29] present detailed experimental results on this topic. Coupling efficiencies of over 90% have been demonstrated in silicon based photonic crystal waveguides [28]. Here, we use this approach to demonstrate efficient coupling to chalcogenide glass based photonic crystal waveguides.

Figures 3 and 4 illustrate the principle of operation of this coupling scheme [26, 29]. Figure 3 shows the experimental configuration for coupling. Figure 4 shows both the photonic crystal waveguide dispersion relations calculated using a plane wave method (RSoft BandSolve) as well as that for the silica nanowire. Only TE-like modes (E field lying mainly in the slab) are included. The fiber taper is brought into close proximity with the photonic crystal waveguide, as illustrated in Fig. 3, such that the evanescent field overlaps with the waveguide mode field (see Fig. 1). Efficient coupling can occur in cases where phase matching between two modes that have appropriate transverse spatial overlap is accomplished. This occurs where the nanowire dispersion curve crosses the waveguide mode dispersion curve, as indicated by the dashed circles in Fig. 4, given by

βtaper=βPCWG,

where βtaper, βPCWG are the propagation constants of the taper mode and the photonic crystal waveguide mode respectively. Note that in this case the mode is coupled in to a waveguide mode with group velocity in the negative direction, i.e. undergoes a contra-directional coupling.

 

Fig. 3. (Top) Expimental measurement setup for evanescent coupling from silica nanowire to photonic crystal waveguide. (Bottom) Close up on the taper-PCWG alignment set up.

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Since the nanowire mode field must extend evanescently for some length outside the silica core, typical nanowire diameters need to be sub-micron. The fiber tapers are manufactured using a procedure developed previously [30] and applied to both standard SMF and microstructured optical fibre (MOF). In this work, the fiber taper is manufactured using a computer controlled taper rig whilst butane flame brushing the fiber (SMF-28) under controlled tension. The taper profiles are tailored by the appropriate choice of flame brushing profile, elongation and rate of elongation. Taper waist lengths are typically a few mm, with outside diameters down to 800nm being achieved. The fiber taper is then glued onto a glass slide. The mounted fiber is spliced to two SMF-28 fibers allowing the in-situ measurements. Tapers manufactured in this way present virtually no insertion loss. The finished fiber taper is aligned above and parallel to the photonic crystal waveguide using an automated nanopositioning facility. Both vertical and lateral positioning is imaged with two microscopes onto CCD cameras. Light is launched into the single mode fiber using a source consisting of four edge-emitting LEDs (Agilent EELED 83437A) covering the 1250–1700 nm bandwidth. In the taper region, light is adiabatically converted into the fundamental air-guided mode, allowing its evanescent tail to interact with the PCWG. The output end of the fiber is connected to an optical spectrum analyser (Agilent 86140B) where the transmission spectrum through the nanotaper is measured.

 

Fig. 4 (a) Dispersion diagram for the photonic crystal waveguides (red line) and the nanowire (blue line). Allowed bands of the surrounding photonic crystal are indicated by the shaded red region. Modes above the light line (grey line) that can couple to the continuum of radiative modes are not included. Dashed circle indicates modes for which phasematched coupling occurs. (b) Magnetic field profiles of the fundamental and first higher order PCWG modes.

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Since typical taper waist lengths are at least a few mm (limited on the short side by the requirement of having adiabatic transition regions) whereas photonic crystal membrane lengths are at most a few hundred microns, there is the possibility of evanescent coupling to the surrounding substrate region. For this reason we introduced a curvature in the taper waist, limiting the interaction region to the photonic crystal itself. Once the fiber is tapered, a bowing is induced by releasing the tension in the fiber (the movable clamps holding the taper are driven towards each other about 0.1 mm). The taper is then mounted onto a glass slide (Fig. 3) and embedded in epoxy resin. A curved shape is then induced by applying a small pressure on the taper while the resin is still curing. The curved tapers manufactured in this way do not suffer extra losses compared to straight tapers. The main limitation of testing with curved tapers, compared to straight tapers [21], is that the diameter of the taper at the interaction region, (controlling the propagation constant of the taper mode interacting with the PCWG mode) could not be tuned, preventing the experimental mapping of the PCWG band structure using a single taper. Figure 5 shows pictures of a typical nanowire taper loop with a loop diameter of 500μm.

 

Fig. 5. Picture of the curved microfiber used in the experiment. The reflection of the taper on the sample is clearly visible in the close up.

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4. Results and discussion

Figure 6 shows the transmission spectrum through the nanowire, with the nanowire placed at different separations from the PC waveguide, from >1.5 μm (red curve) to direct contact (black curve). The spectra have been normalized to transmission through the taper in the absence of the PCWG. Clearly, the coupling efficiency is extremely sensitive to the nanowire -waveguide separation. First, it is evident that off-resonance loss increases when the taper aproaches the PCWG, and increases with increasing wavelength. One source of this is related to scattering that occurs at the taper-PCWG interface which is expected to be both broadband and higher at longer wavelengths where the evanescent field expands. A second contribution to the broadband loss occurs because the input source is unpolarized. The taper mode can couple to TM-like modes. In this frequency range, the TM dispersion curve closely resembles the taper dispersion curve, which results in a broadband codirectional coupling. Since the TM-like modes of the PCWG are very lossy, this manifests as an overall 3dB broadband loss. We estimate the overall off resonance loss at around 6 dB in line with observations.

From Figure 6, resonances corresponding to coupling to both the fundamental W1 guided mode (TE0) and the first W1 higher order mode (TE1) can be identified. We found that the strength of the coupling to these modes was highly dependent on precise lateral positioning of the taper. When the taper is displaced away from the PCWG, these two resonances disappear confirming the coupling to localized modes (i.e to PCWG modes). Because TE0 is even and TE1 is odd in the in-plane direction (Fig. 4(b)), we should expect that only TE0 can couple to the taper mode when the taper is placed at the center of the PCWG. However, unless the taper is accurately placed at the center of the PCWG along the overall interaction length, the antisymmetric nature of the TE1 mode is difficult to confirm, especially when one considers the lateral extension of this mode (~ 800nm). Nevertheless, we found that the strength of the coupling to the TE1 mode was highly dependent on precise lateral positioning of the taper.

 

Fig. 6. Transmission spectrum of tapered nanowire, in close proximity to chalcogenide glass photonic crystal waveguide, showing resonant coupling. Red curve is for large (>1.5μm) fibre-waveguide separation. Blue curve for a 1 μm separation. Black curve is for direct contact. Transmission spectra have been normalized to the transmission through the taper in absence of the PCWG.

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The dotted lines in Fig. 6 indicate the resonant coupling wavelengths determined from mode dispersion relations calculated using a plane-wave method (Fig. 4). The strong narrow resonance near 1520nm is > 18 dB in depth, and reflects the resonant coupling to the fundamental TE0 mode of the PCWG, in relatively good agreement with the dispersion diagram prediction for the absolute wavelength. The residual difference of ~ 20nm arises from measurement uncertainty in the PC air hole radius as well as effects due to the thin silicon nitride layer and chalcogenide material dispersion, neither of which are taken into account in the modeling. The resonance depth of 18dB corresponds to more than 98% coupling efficiency, which is comparable to the best coupling efficiencies reported to date [28].

The 3dB width of this resonance is ~ 12nm. It is known [31] that the 3 dB bandwidth for a contradirectional coupler is approximately

Δλ=2λres2κπ(nPCWG+ntaper),

where λres is the resonant wavelength, κ the coupling coefficient and nPCWG and ntaper are the group index values respectively of the PCWG and the taper. From Fig. 4, we estimate nPCWG and ntaper to 30 and 1.3 respectively, yielding a coupling coefficient κ ~ 0.24 μm-1. Contradirectional coupling is also characterized [21,31–32] by a transmission function of the form:

T=1tanh2(κLc),

where Lc is the length of the taper/PCWG coupler. Given a transmission of 2% and a coupling coefficient κ ~ 0.24 μm-1, the deduced coupling length is ~ 10 μm. The large broad resonance (~25nm) near 1420nm results from coupling to the first higher order mode (TE1) of the W-1 waveguide which is antisymmetric in the in-plane direction and is in good agreement with theory. Table 1 summarizes the experimental results.

Tables Icon

Table 1. Experimental evanescent coupling results

5. Conclusions

In conclusion, we have demonstrated 98% coupling efficiency to a chalcogenide glass planar photonic crystal defect waveguide, fabricated by focused ion beam milling. We achieve good agreement with theoretical calculations of the coupling resonant wavelength and observe coupling to higher order photonic crystal modes. These results are on par with the best reported results in silicon photonic crystals and represent the first demonstration of coupling to PhCs made from highly nonlinear glass. This work represents a significant step in the drive towards Kerr nonlinearity based all-optical switching in photonic crystal nanocavities.

Acknowledgments

This work was produced with the assistance of the Australian Research Council (ARC). CUDOS (the Centre for Ultrahigh-bandwidth Devices for Optical Systems) is an ARC Centre of Excellence. We thank Andrei Rode for depositing the film, Maryla Krolikowska for preparation of the membranes, and ANU Electron Microscopy Unit for use of the FIB.

References and links

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef]   [PubMed]  

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987). [CrossRef]   [PubMed]  

3. S. Noda and T. Baba, Roadmap on photonic crystals (Springer, 2003).

4. C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001). [CrossRef]  

5. S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927. [CrossRef]   [PubMed]  

6. X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001). [CrossRef]  

7. E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000). [CrossRef]  

8. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]  

9. M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003). [CrossRef]  

10. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678 [CrossRef]   [PubMed]  

11. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kurarmochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 19 (2005). [CrossRef]  

12. R. E. Slusher and B. J. Eggleton, Nonlinear photonic crystals (Springer, Berlin, 2003).

13. M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004). [CrossRef]   [PubMed]  

14. Y. Ruan, W. Li, R. Jarvis, N. Madsen, A. Rode, and B. Luther-Davies, “Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching,” Opt. Express 12, 5140–5145 (2004), http://www.opticsexpress.org/abstract. cfm?URI=OPEX-12-21-5140 [CrossRef]   [PubMed]  

15. V. G. Ta’eed, M. Shokook-Saremi, L B. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Integrated all-optical pulse regenerator in chalcogenide waveguides,” Opt. Lett. 30, 2900–2902 (2005). [CrossRef]   [PubMed]  

16. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801 [CrossRef]   [PubMed]  

17. F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004). [CrossRef]  

18. F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005). [CrossRef]  

19. D. Freeman, S. Madden, and B. Luther-Davies, “Fabrication of planar photonic crystals in a chalcogenide glass using a focused ion beam,” Opt. Express 13, 3079–3086 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3079 [CrossRef]   [PubMed]  

20. C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, “Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes,” Opt. Express 14, 369–376 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-1-369 [CrossRef]   [PubMed]  

21. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004). [CrossRef]  

22. J. Knight, G. Cheung, F. Jacques, and T. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef]   [PubMed]  

23. K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004). [CrossRef]  

24. K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005). [CrossRef]  

25. I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005). [CrossRef]  

26. W. Kuang, C. Kim, A. Stapleton, and J. D. O’Brien, “Grating-assisted coupling of optical fibers and photonic crystal waveguides,” Opt. Lett. 27, 1604–1607 (2002). [CrossRef]  

27. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003). [CrossRef]  

28. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output optical fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004). [CrossRef]   [PubMed]  

29. P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003). [CrossRef]  

30. Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12, 3209–3217 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3209 [CrossRef]   [PubMed]  

31. D. Marcuse, “Bandwith of forward and backward coupling directional couplers,” J. Lightwave Technol. 51773–1777 (1987). [CrossRef]  

32. M. Qiu and M. Swillo, “Contra-directional coupling between two-dimensional photonic crystal waveguides,” Phot. and Nanostructures (2003).

References

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).
    [Crossref] [PubMed]
  3. S. Noda and T. Baba, Roadmap on photonic crystals (Springer, 2003).
  4. C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
    [Crossref]
  5. S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927.
    [Crossref] [PubMed]
  6. X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
    [Crossref]
  7. E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000).
    [Crossref]
  8. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
    [Crossref]
  9. M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
    [Crossref]
  10. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678
    [Crossref] [PubMed]
  11. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kurarmochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 19 (2005).
    [Crossref]
  12. R. E. Slusher and B. J. Eggleton, Nonlinear photonic crystals (Springer, Berlin, 2003).
  13. M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
    [Crossref] [PubMed]
  14. Y. Ruan, W. Li, R. Jarvis, N. Madsen, A. Rode, and B. Luther-Davies, “Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching,” Opt. Express 12, 5140–5145 (2004), http://www.opticsexpress.org/abstract. cfm?URI=OPEX-12-21-5140
    [Crossref] [PubMed]
  15. V. G. Ta’eed, M. Shokook-Saremi, L B. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Integrated all-optical pulse regenerator in chalcogenide waveguides,” Opt. Lett. 30, 2900–2902 (2005).
    [Crossref] [PubMed]
  16. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801
    [Crossref] [PubMed]
  17. F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
    [Crossref]
  18. F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
    [Crossref]
  19. D. Freeman, S. Madden, and B. Luther-Davies, “Fabrication of planar photonic crystals in a chalcogenide glass using a focused ion beam,” Opt. Express 13, 3079–3086 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3079
    [Crossref] [PubMed]
  20. C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, “Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes,” Opt. Express 14, 369–376 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-1-369
    [Crossref] [PubMed]
  21. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004).
    [Crossref]
  22. J. Knight, G. Cheung, F. Jacques, and T. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997).
    [Crossref] [PubMed]
  23. K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
    [Crossref]
  24. K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005).
    [Crossref]
  25. I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
    [Crossref]
  26. W. Kuang, C. Kim, A. Stapleton, and J. D. O’Brien, “Grating-assisted coupling of optical fibers and photonic crystal waveguides,” Opt. Lett. 27, 1604–1607 (2002).
    [Crossref]
  27. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003).
    [Crossref]
  28. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output optical fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004).
    [Crossref] [PubMed]
  29. P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
    [Crossref]
  30. Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12, 3209–3217 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3209
    [Crossref] [PubMed]
  31. D. Marcuse, “Bandwith of forward and backward coupling directional couplers,” J. Lightwave Technol. 51773–1777 (1987).
    [Crossref]
  32. M. Qiu and M. Swillo, “Contra-directional coupling between two-dimensional photonic crystal waveguides,” Phot. and Nanostructures (2003).

2006 (1)

2005 (8)

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801
[Crossref] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678
[Crossref] [PubMed]

D. Freeman, S. Madden, and B. Luther-Davies, “Fabrication of planar photonic crystals in a chalcogenide glass using a focused ion beam,” Opt. Express 13, 3079–3086 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3079
[Crossref] [PubMed]

V. G. Ta’eed, M. Shokook-Saremi, L B. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Integrated all-optical pulse regenerator in chalcogenide waveguides,” Opt. Lett. 30, 2900–2902 (2005).
[Crossref] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kurarmochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 19 (2005).
[Crossref]

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005).
[Crossref]

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

2004 (7)

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004).
[Crossref]

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output optical fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004).
[Crossref] [PubMed]

Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12, 3209–3217 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3209
[Crossref] [PubMed]

Y. Ruan, W. Li, R. Jarvis, N. Madsen, A. Rode, and B. Luther-Davies, “Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching,” Opt. Express 12, 5140–5145 (2004), http://www.opticsexpress.org/abstract. cfm?URI=OPEX-12-21-5140
[Crossref] [PubMed]

2003 (4)

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[Crossref]

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927.
[Crossref] [PubMed]

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003).
[Crossref]

2002 (2)

W. Kuang, C. Kim, A. Stapleton, and J. D. O’Brien, “Grating-assisted coupling of optical fibers and photonic crystal waveguides,” Opt. Lett. 27, 1604–1607 (2002).
[Crossref]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[Crossref]

2001 (2)

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

2000 (1)

E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000).
[Crossref]

1997 (1)

1987 (3)

D. Marcuse, “Bandwith of forward and backward coupling directional couplers,” J. Lightwave Technol. 51773–1777 (1987).
[Crossref]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).
[Crossref] [PubMed]

Aspar, B.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Baba, T.

S. Noda and T. Baba, Roadmap on photonic crystals (Springer, 2003).

Barclay, P. E.

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005).
[Crossref]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801
[Crossref] [PubMed]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output optical fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004).
[Crossref] [PubMed]

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003).
[Crossref]

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[Crossref]

Birks, T.

Bolger, J. A.

Borselli, M.

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005).
[Crossref]

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output optical fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004).
[Crossref] [PubMed]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003).
[Crossref]

Cassagne, D.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

Centeno, E.

E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000).
[Crossref]

Cheung, G.

Cojocaru, C.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

Cojocaru, Crina

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

Eggleton, B. J.

Fan, S.

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

Felbacq, D.

E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000).
[Crossref]

Fink, Y.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[Crossref]

Freeman, D.

Fu, L B.

Gendry, M.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Grillet, C.

C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, “Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes,” Opt. Express 14, 369–376 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-1-369
[Crossref] [PubMed]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

Hollinger, G.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Hwang, I.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

Ibanescu, M.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[Crossref]

Jacques, F.

Jalaguier, E.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Jarvis, R.

Joannopoulos, J. D.

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[Crossref]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).
[Crossref] [PubMed]

Johnson, S. G.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[Crossref]

Jouanin, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

Kim, C.

Kim, S.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

Kira, G.

Knight, J.

Kuang, W.

Kuramochi, E.

Kurarmochi, E.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kurarmochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 19 (2005).
[Crossref]

Lee, S.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

Lee, Y.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

Letartre, X.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

Levenson, A.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

Li, W.

Littler, I. C. M.

Lizé, Y. K.

Luther-Davies, B.

Madden, S.

Madsen, N.

Mägi, E. C.

Marcuse, D.

D. Marcuse, “Bandwith of forward and backward coupling directional couplers,” J. Lightwave Technol. 51773–1777 (1987).
[Crossref]

McNab, S. J.

McPhedran, R.

Mitsugi, S.

Moll, N.

Monat, C.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Monnier, P.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

Moss, D. J.

Noda, S.

S. Noda and T. Baba, Roadmap on photonic crystals (Springer, 2003).

Notomi, M.

O’Brien, J. D.

Painter, O.

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801
[Crossref] [PubMed]

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005).
[Crossref]

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output optical fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004).
[Crossref] [PubMed]

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003).
[Crossref]

Pocas, S.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Qiu, M.

M. Qiu and M. Swillo, “Contra-directional coupling between two-dimensional photonic crystal waveguides,” Phot. and Nanostructures (2003).

Raineri, F.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

Raj, R.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

Regreny, P.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Rochette, M.

Rode, A.

Rojo-Romeo, P.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

Ruan, Y.

Seassal, C.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

Shinya, A.

Shokook-Saremi, M.

Slusher, R. E.

R. E. Slusher and B. J. Eggleton, Nonlinear photonic crystals (Springer, Berlin, 2003).

Soljacic, M.

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[Crossref]

Srinivasan, K.

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005).
[Crossref]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801
[Crossref] [PubMed]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output optical fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004).
[Crossref] [PubMed]

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003).
[Crossref]

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[Crossref]

Stapleton, A.

Steel, M. J.

Steinvurzel, P.

Swillo, M.

M. Qiu and M. Swillo, “Contra-directional coupling between two-dimensional photonic crystal waveguides,” Phot. and Nanostructures (2003).

Ta’eed, V. G.

Tanabe, T.

Vassor d’Yerville, M. Le

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

Viktorovitch, P.

F. Raineri, C. Cojocaru, R. Raj, P. Monnier, A. Levenson, C. Seassal, X. Letartre, and P. Viktorovitch, “Tuning a two-dimensional photonic crystal resonance via optical carrier injection,” Opt. Lett. 30, 010064 (2005).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

Vlasov, Y. A.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

Yang, J.

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

Yanik, M. F.

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

Appl. Phys. Lett. (5)

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes” Appl. Phys. Lett. 79, 2312 (2001).
[Crossref]

F. Raineri, Crina Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal” Appl. Phys. Lett. 85, 1880 (2004).
[Crossref]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers,” Appl. Phys. Lett. 85, 4 (2004).
[Crossref]

I. Hwang, S. Kim, J. Yang, S. Kim, S. Lee, and Y. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[Crossref]

Electron. Lett. (2)

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Experimental demonstration of evanescent coupling from optical fiber tapers to photonic crystal waveguides,” Electron. Lett. 39, 842 (2003).
[Crossref]

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 μm,” Electron. Lett. 37, 764 (2001).
[Crossref]

IEEE J. Sel. Areas Commun. (1)

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “An optical-fiber based probe for photonic crystal microcavities,” IEEE J. Sel. Areas Commun. 23, 1321–1329 (2005).
[Crossref]

J. Lightwave Technol. (1)

D. Marcuse, “Bandwith of forward and backward coupling directional couplers,” J. Lightwave Technol. 51773–1777 (1987).
[Crossref]

J. Opt. Soc. Am. B (1)

Nature Materials (1)

M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[Crossref] [PubMed]

Opt. Express (7)

Y. Ruan, W. Li, R. Jarvis, N. Madsen, A. Rode, and B. Luther-Davies, “Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching,” Opt. Express 12, 5140–5145 (2004), http://www.opticsexpress.org/abstract. cfm?URI=OPEX-12-21-5140
[Crossref] [PubMed]

D. Freeman, S. Madden, and B. Luther-Davies, “Fabrication of planar photonic crystals in a chalcogenide glass using a focused ion beam,” Opt. Express 13, 3079–3086 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3079
[Crossref] [PubMed]

C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, “Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes,” Opt. Express 14, 369–376 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-1-369
[Crossref] [PubMed]

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927–2939 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2927.
[Crossref] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678
[Crossref] [PubMed]

Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12, 3209–3217 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3209
[Crossref] [PubMed]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801
[Crossref] [PubMed]

Opt. Lett. (6)

Phys. Rev. B (2)

E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000).
[Crossref]

K. Srinivasan, P. E. Barclay, M. Borselli, and O. Painter, “Optical-fiber based measurement of an ultra-small volume high-Q photonic crystal microcavity,” Phys. Rev. B 70, 081306(R) (2004).
[Crossref]

Phys. Rev. E (1)

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002).
[Crossref]

Phys. Rev. Lett. (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).
[Crossref] [PubMed]

Other (3)

S. Noda and T. Baba, Roadmap on photonic crystals (Springer, 2003).

R. E. Slusher and B. J. Eggleton, Nonlinear photonic crystals (Springer, Berlin, 2003).

M. Qiu and M. Swillo, “Contra-directional coupling between two-dimensional photonic crystal waveguides,” Phot. and Nanostructures (2003).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic showing the coupling scheme of a PCWG and a tapered fiber, in this case backward coupling as explained in section 4. (b) Cross sectional view along YZ axis of the coupling mechanism between the taper and the PCWG. c) Cross sectional view normal to the direction of propagation.

Fig. 2.
Fig. 2.

Scanned electron micrographs of a chalcogenide glass photonic crystal membrane fabricated by focused ion beam (FIB) milling of an AMTIR-1 chalcogenide glass film. left: film imaged at 0°. Right: picture of “W1” defect waveguide.

Fig. 3.
Fig. 3.

(Top) Expimental measurement setup for evanescent coupling from silica nanowire to photonic crystal waveguide. (Bottom) Close up on the taper-PCWG alignment set up.

Fig. 4
Fig. 4

(a) Dispersion diagram for the photonic crystal waveguides (red line) and the nanowire (blue line). Allowed bands of the surrounding photonic crystal are indicated by the shaded red region. Modes above the light line (grey line) that can couple to the continuum of radiative modes are not included. Dashed circle indicates modes for which phasematched coupling occurs. (b) Magnetic field profiles of the fundamental and first higher order PCWG modes.

Fig. 5.
Fig. 5.

Picture of the curved microfiber used in the experiment. The reflection of the taper on the sample is clearly visible in the close up.

Fig. 6.
Fig. 6.

Transmission spectrum of tapered nanowire, in close proximity to chalcogenide glass photonic crystal waveguide, showing resonant coupling. Red curve is for large (>1.5μm) fibre-waveguide separation. Blue curve for a 1 μm separation. Black curve is for direct contact. Transmission spectra have been normalized to the transmission through the taper in absence of the PCWG.

Tables (1)

Tables Icon

Table 1. Experimental evanescent coupling results

Equations (3)

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β taper = β PCWG ,
Δ λ = 2 λ res 2 κ π ( n PCWG + n taper ) ,
T = 1 tanh 2 ( κL c ) ,

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