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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 25 — Dec. 6, 2010
  • pp: 26675–26685
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Nonlinear light propagation in chalcogenide photonic crystal slow light waveguides

Keijiro Suzuki and Toshihiko Baba  »View Author Affiliations


Optics Express, Vol. 18, Issue 25, pp. 26675-26685 (2010)
http://dx.doi.org/10.1364/OE.18.026675


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Abstract

Optical nonlinearity can be enhanced by the combination of highly nonlinear chalcogenide glass and photonic crystal waveguides (PCWs) providing strong optical confinement and slow-light effects. In a Ag-As2Se3 chalcogenide PCW, the effective nonlinear parameter γeff reaches 6.3 × 104 W−1m−1, which is 200 times larger than that in Si photonic wire waveguides. In this paper, we report the detailed design, fabrication process, and the linear and nonlinear characteristics of this waveguide at silica fiber communication wavelengths. We show that the waveguide exhibits negligible two-photon absorption, and also high-efficiency self-phase modulation and four-wave mixing, which are assisted by low-dispersion slow light.

© 2010 OSA

1. Introduction

In recent years, optical network traffic and its electrical power consumption have increased very rapidly. To deal with future growth, more advanced transmission systems, particularly photonic routers, are anticipated. Wavelength routing has been studied as one of the candidate solutions, but it requires highly efficient wavelength convertors. Although cross-phase modulation and four-wave mixing (FWM) are promising techniques [1

1. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]

], they generally require high operating power and/or long device length due to limited material nonlinearities. Figure 1
Fig. 1 Relation of operating power and device length for optical nonlinearity such as SPM (1.5 π nonlinear phase shift) and FWM in various material waveguides. Circles, square, and triangle denote ChG, Si, and III-V materials, respectively.
summarizes the operating power and the lengths of various nonlinear devices. Fiber-based devices are easy to fabricate and evaluate. However, low power density in their large core is disadvantageous for nonlinearities, and so it must be compensated by a device length longer than centimeters [2

2. R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004). [CrossRef]

,3

3. M. D. Pelusi, F. Luan, E. Magi, M. R. Lamont, D. J. Moss, B. J. Eggleton, J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “High bit rate all-optical signal processing in a fiber photonic wire,” Opt. Express 16(15), 11506–11512 (2008). [CrossRef] [PubMed]

]. On-chip optical waveguides, on the other hand, are advantageous for enhancing the power density, shortening the device, and integration with other components. FWM induced by third-order nonlinearity has been observed in a 6-cm-long As2S3 chalcogenide glass rib waveguide at an input power of less than 1 W [4

4. F. Luan, M. D. Pelusi, M. R. E. Lamont, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Dispersion engineered As2S3 planar waveguides for broadband four-wave mixing based wavelength conversion of 40 Gb/s signals,” Opt. Express 17(5), 3514–3520 (2009). [CrossRef] [PubMed]

]. Various nonlinearities have also been demonstrated for Si photonic wire waveguides. This type of waveguide can particularly enhance the power density, due to its strong optical confinement into the high index contrast tiny core [5

5. H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44(9A), 6541–6545 (2005). [CrossRef]

8

8. I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express 14(25), 12380–12387 (2006). [CrossRef] [PubMed]

]. In Si-based waveguides, however, the nonlinearity mainly arises from carrier effects generated by two-photon absorption (TPA), which results in a high loss and a response time limited by the carrier lifetime. Although FWM was observed at several hundreds of mW where the TPA was negligible, a long waveguide of 5 cm was necessary [9

9. H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006). [CrossRef] [PubMed]

,10

10. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005). [CrossRef] [PubMed]

]. In 600-μm-long AlGaAs wire waveguides whose aluminum content was increased to suppress the TPA at silica-fiber communication wavelengths, e.g. λ ~1.55 μm, the self-phase modulation (SPM) was observed at a 30 W input power [11

11. G. A. Siviloglou, S. Suntsov, R. El-Ganainy, R. Iwanow, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, D. Modotto, A. Locatelli, C. De Angelis, F. Pozzi, C. R. Stanley, and M. Sorel, “Enhanced third-order nonlinear effects in optical AlGaAs nanowires,” Opt. Express 14(20), 9377–9384 (2006). [CrossRef] [PubMed]

]. The same material was also processed into photonic crystal waveguides (PCWs), and the power required for the same SPM was reduced to 3.5 W by exploiting slow-light effects [12

12. K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009). [CrossRef] [PubMed]

]. Thus, we can expect slow-light PCWs made of highly nonlinear materials without TPA to be a suitable platform of nonlinear devices satisfying low-power operation, short length and carrier-free high-speed response.

When chalcogenide glasses (ChGs) are used as base materials for nonlinear devices at λ ~1.55 μm, S- and Se-based glasses mixed with As and/or Ge are often employed. They have the following attractive properties:

  • i) These ChGs have a broad transparent window from λ = 0.8 – 20 μm [13

    13. R. G. DeCorby, N. Ponnampalam, M. M. Pai, H. T. Nguyen, P. K. Dwivedi, T. J. Clement, C. J. Haugen, J. N. McMullin, and S. O. Kasap, “High index contrast waveguides in chalcogenide glass and polymer,” IEEE J. Sel. Top. Quantum Electron. 11(2), 539–546 (2005). [CrossRef]

    ,14

    14. V. K. Tikhomirov, D. Furniss, A. B. Seddon, J. A. Savage, P. D. Mason, D. A. Orchard, and K. L. Lewis, “Glass formation in the Te-enriched part of the quaternary Ge-As-Se-Te system and its implication for mid-infrared optical fibres,” Infrared Phys. Technol. 45(2), 115–123 (2004). [CrossRef]

    ] and ultrahigh-speed third-order nonlinear response (< 100 fs) without carrier effects.
  • ii) They exhibit a large third-order nonlinear index n 2 simultaneously with low TPA coefficient β at λ ~1.55 μm. The nonlinear figure of merit FOM (≡ n 2/βλ) is 11 for bulk As2Se3 [15

    15. J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27(2), 119–121 (2002). [CrossRef]

    ], while 0.4 for bulk Si [16

    16. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

    ].
  • iii) Their films can be fabricated at low temperature (< 400°C) [17

    17. A. Zakery, and S. R. Elliott, Optical Nonlinearities in Chalcogenide Glasses and their Applications (Springer, New York, 2007).

    19

    19. S. Song, J. Dua, and C. B. Arnold, “Influence of annealing conditions on the optical and structural properties of spin-coated As2S3 chalcogenide glass thin films,” Opt. Express 18(6), 5472–5480 (2010). [CrossRef] [PubMed]

    ], which is compatible to back-end process in Si-photonics.
  • iv) Illuminated by light around the absorption edge, some photo-induced phenomena occur. One of these, photodarkening, can be used for the fabrication and post-tuning of devices [20

    20. T. G. Robinson, R. G. DeCorby, J. N. McMullin, C. J. Haugen, S. O. Kasap, and D. Tonchev, “Strong Bragg gratings photoinduced by 633-nm illumination in evaporated As2Se3 thin films,” Opt. Lett. 28(6), 459–461 (2003). [CrossRef] [PubMed]

    22

    22. D. Freeman, C. Grillet, M. W. Lee, C. L. C. Smith, Y. Ruan, A. Rode, M. Krolikowska, S. Tomljenovic-Hanic, C. M. De Sterke, M. J. Steel, B. Luther-Davies, S. Madden, D. J. Moss, Y. H. Lee, and B. J. Eggleton, “Chalcogenide glass photonic crystals,” Photon. Nanostructures 6(1), 3–11 (2008). [CrossRef]

    ].

Challenges to fabricating ChG photonic crystals have been reported with various ChGs and fabrication process, such as the combination of Ge33As12Se55 with focused ion beam milling [31

31. 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(8), 3079–3086 (2005). [CrossRef] [PubMed]

], that with e-beam lithography and chemically assisted ion beam etching [32

32. Y. Ruan, M.-K. Kim, Y.-H. Lee, B. Luther-Davies, and A. Rode, “Fabrication of high-Q chalcogenide photonic crystal resonators by e-beam lithography,” Appl. Phys. Lett. 90(7), 071102 (2007). [CrossRef]

], As2S3 with holographic lithography and wet etching [33

33. A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Two dimensional photonic band gap pattering in thin chalcogenide glassy films,” Thin Solid Films 488(1–2), 185–188 (2005). [CrossRef]

], and As2S3 and Ge20As20Se14Te46 with direct laser writing [34

34. A. Popescu, S. Miclos, D. Savastru, R. Savastru, M. Ciobanu, M. Popescu, A. Lorinczi, F. Sava, A. Velea, F. Jipa, and M. Zamfirescu, “Direct laser writing of two-dimensional photonic structures in amorphous As2S3 thin films,” J. Optoelectron. Adv. Mater. 11(11), 1874–1880 (2009).

,35

35. K. Paivasaari, V. K. Tikhomirov, and J. Turunen, “High refractive index chalcogenide glass for photonic crystal applications,” Opt. Express 15(5), 2336–2340 (2007). [CrossRef] [PubMed]

]. In general, however, it is not straightforward to form waveguide facets and vertical airholes of photonic crystals because of the softness of ChGs, which makes optical characterizations challenging. Previously, we fabricated Ag-As2Se3 PCWs using e-beam lithography and inductively coupled plasma (ICP) etching, and reported their linear and nonlinear characteristics, for the first time, although they were limited in the high υ g regime [36

36. K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express 17(25), 22393–22400 (2009). [CrossRef]

]. This material is known to have n 2 of 9.0 × 10−17 m2/W at λ = 1.05 μm [37

37. K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, “Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching,” Opt. Lett. 29(3), 265–267 (2004). [CrossRef] [PubMed]

], which is the highest value ever reported for ChGs. Therefore, Ag-As2Se3 and LD slow-light PCW can be one of the most powerful combination toward the present purpose.

In this paper, we comprehensively discuss the Ag-As2Se3 PCW in both high and low υ g regimes. We first show the design of lattice-shifted PCWs (LS-PCWs) suitable for LD slow-light generation [25

25. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

]. We have developed this type of waveguide for Si. In this study, we optimized it for the ChG through the photonic band analysis. Next, we describe the fabrication process in detail, which enables us to observe the clear propagation characteristics against continuous light and short pulses in the linear regime. Finally, we present the nonlinear characteristics such as TPA, SPM and FWM against short pulse pumping, discuss their dependency on slow light and compare with those in Si waveguides.

2. Design

In the LS-PCW, the third rows of airholes from the line defect are shifted parallel to the line defect. The photonic band diagram of the Ag-As2Se3 ChG LS-PCW is calculated by using three-dimensional finite-deference time-domain method with periodic boundaries. We assume the material index of Ag-As2Se3 to be 2.85, which was deduced from the fitting of calculated band-edge wavelengths with experimental ones. We set the slab thickness as 300 nm to satisfy the single mode condition in the vertical direction and to obtain sufficient mechanical strength. Compared with Si (n ~3.5) PCWs, the small material index shifts the guided mode band to higher frequencies. Considering our measurement facilities shown later, we targeted the light propagation at λ ~1.55 μm, and chose a large lattice constant of a = 480 nm and a small normalized airhole diameter of 2r/a = 0.55.

Figure 2
Fig. 2 Photonic band diagram of Ag-As2Se3 LS-PCW. Inset shows scanning electron micrograph (SEM) of fabricated ChG LS-PCW.
shows the calculated results for different normalized shifts s/a. At s/a = 0, a round shape photonic band sandwiched by air light line and band-edge is observed. Increasing s/a, this band is raised by slab mode bands at lower frequencies, and the LD slow-light band characterized by a gentle slope (low υ g) and nearly straight part (low dispersion) appears. When s/a is relatively small, the group index n g (≡ c/υ g = c(dk/dω), c: light speed in vacuum) giving the slowdown factor and the bandwidth Δλ of LD slow-light are large and narrow, respectively. As s/a increases, n g decreases and Δλ broadens due to the essential constraint of slow light, and the flat band appears on the high frequency side. As s/a increases further, the flat band is almost fixed and the band-edge shifts to high frequency side. Consequently, n g increases and Δλ narrows again. In each LD slow-light band, n g takes its minimum around the center wavelength. Table 1

Table 1. Calculated group index, bandwidth and normalized delay-bandwidth product of Ag-As2Se3 LS-PCW.

table-icon
View This Table
summarizes the minimum n g, Δλ giving 0 – 10% change in n g, and the normalized delay-bandwidth product n gΔλ/λ giving the slow-light performance [23

23. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

]. The n gΔλ/λ varies from 0.33 – 0.14, which is almost similar to Si-PCWs’ [25

25. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

]. Larger n g enhances the nonlinearity more, but narrower Δλ restricts the observation of SPM and FWM. In addition, the extrinsic loss caused by structural disordering becomes severe at n g > 30 [38

38. L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007). [CrossRef] [PubMed]

]. Therefore, we targeted n g and Δλ at s/a = 0.48 in Table 1.

3. Fabrication

In the fabrication of Ag-As2Se3 PCW, we employ InP substrate for easy formation of waveguide facets by cleavage. First, 10-nm-thick Ti is thermally evaporated on the substrate at a deposition rate of 0.01 nm/s. This film is used for improving the adhesion of Ag-As2Se3 and InP. Since the melting point and vapor pressure are different between Ag and As2Se3, we cannot directly deposit Ag-As2Se3 using thermal evaporation of ternary source. Therefore, we evaporate 300-nm-thick As2Se3 at 0.2 nm/s, followed by 10-nm-thick Ag at 0.01 nm/s. To form Ag-As2Se3, they are interfused by photodoping technique [39

39. T. Wágner, V. Perina, A. Mackova, E. Rauhala, A. Seppala, M. Vleck, S. O. Kasap, M. Vlcek, and M. Frumar, “The tailoring of the composition of Ag-As-S amorphous films using photo-induced solid state reaction between Ag and As30S70 films,” Solid State Ion. 141(1), 387–395 (2001). [CrossRef]

], i.e. illuminating light from halogen lamp for 30 min. Unlike thermal diffusion, Ag distributes almost uniformly in depth [40

40. K. Ogusu, S. Maeda, M. Kitao, H. Li, and M. Minakata, “Optical and structural properties of Ag(Cu)-As2Se3 chalcogenide films prepared by a photodoping,” J. Non-Cryst. Solids 347(1–3), 159–165 (2004). [CrossRef]

], and on this condition, Ag concentration becomes 5 at.%.

4. Linear characteristics

In all the measurements in this the following two sections, laser light is transverse-electric polarized, and coupled to the cleaved facet of 400-μm-long samples using microscope objectives. Output light is directly coupled to lensed fiber or fiber-coupled via another objective lenses. Light sources and other equipments are different between measurements.

A. Transmission spectra and etching condition

For the transmission spectrum in the linear regime, CW light from tunable laser is incident on the device. Output light is measured using optical power meter.

Let us discuss the dependence of the airhole cross-section and transmission spectrum on the gas flow rate in the ICP etching. Figure 3
Fig. 3 Transmission spectrum of fabricated ChG PCW and SEM image of airhole cross-section for different gas flow rates in the ICP etching. White bar in the SEM images show a length of 100 nm. (a) CF4: CHF3 = 5: 0 sccm. (b) 4: 1 sccm. (c) 40: 10 sccm.
shows the results of normal PCWs (s = 0). It is seen from the comparison between (a) and (b) that CHF3 effectively suppresses the side etching, flattens the sidewalls, and improves the uniformity of airhole diameter 2r. This greatly suppresses unwanted oscillation in the transmission spectrum, makes spectral drops at the air light line and band-edge clearer, and improves the transmissivity by more than 5 dB. When the fraction of CHF3 is increased while maintaining the total gas flow, excess deposition of the polymer degrades the sidewall angle and uniformity. (c) shows the results for the same gas fractions and higher total flow rate. Since the high flow rate suppresses the excess deposition, it makes the sidewall almost vertical, sharpens the spectral drop at the band-edge, and further improves the transmissivity. On this condition, the rms error in 2r is 4.4 nm, which is larger than 1.7 nm we evaluated for Si PCWs previously. Although we cannot increase gas flow rates any more in the current ICP machine, we expect a higher flow rate to provide better uniformity.

B. Transmission and group index spectra

Figure 4
Fig. 4 Transmission and n g spectra of fabricated ChG PCWs. (a) s/a = 0, 2r/a = 0.52, (b) 0.33, 0.53, (c) 0.43, 0.53 and (d) 0.47, 0.53. Light red color indicates LD slow-light band.
shows the transmission and n g spectra of LS-PCWs with different s and 2r. For the latter, n g is estimated using modulation phase-shift method [41

41. J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]

], where tunable laser light is modulated sinusoidally and the signal phase of output light is measured to estimate the group delay and n g.

  • (a) is the case without lattice shift (s = 0). It exhibits a typical spectrum of the PCW, in which n g increases near the band-edge. Ideally, the increase is very rapid and the final n g diverges to infinity. However, the maximum n g measured is 42, and the spectral width from 20 – 80% of the maximum is 1.5 nm, which is wider than 0.5 nm in Si-PCWs [25

    25. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

    ]. It reflects the disordering in airhole diameters 2r.
  • (b) - (d) are the cases with the lattice shift. They exhibit the LD slow light on the long wavelength side of the high υ g regime. A dip between them corresponds to the flat band in Fig. 2. Since a huge n g and drastic modal change occur at the flat band, the transmission loss is large and n g cannot be measured. The oscillation in the n g spectra is primarily caused by the Fabry-Perot resonance between waveguide facets. In the LD slow-light band shown by light red color, n g and Δλ change similarly to those listed in Table 1; n g ~15 with Δλ ~25 nm (n gΔλ/λ ~0.24) at s/a = 0.33, n g ~20 with Δλ ~15 nm (n gΔλ/λ ~0.19) at s/a = 0.43 and n g ~35 with Δλ ~4 nm (n gΔλ/λ ~0.09) at s/a = 0.47.

The loss of the 400-μm-long device at the high υ g regime was estimated to be 5.4 dB, suggesting 5.4 dB / 0.400 mm = 14 dB/mm propagation loss α [36

36. K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express 17(25), 22393–22400 (2009). [CrossRef]

]. In the LD slow-light regime, relative transmission of each sample decreases to 3, 3 and 7 dB lower than that for high υ g regime, respectively. From these results, we can deduce α at the LD slow-light band: α = 8.4 dB / 0.400 mm = 21 dB/mm at n g ~15 and 20; and α = 12.4 dB / 0.400 mm = 31 dB/mm at n g ~35, respectively. These increase in α reflect structural disordering of the fabricated devices as mentioned above [38

38. L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007). [CrossRef] [PubMed]

].

C. Pulse transmission

The dispersion of slow light is evaluated through the pulse transmission measurement. Here, sub-ps pulses from mode-locked fiber laser with a 40 MHz repetition are amplified and spectrally expanded using SPM in erbium-doped fiber amplifier (EDFA). They are filtered by tunable band-pass filter at desired center wavelength λp (1.53 and 1.56 μm in the high and low υ g regimes, respectively) with desired FWHM bandwidth Δλp (2.0 nm corresponding to a FWHM pulse width τp = 2.48 ps), and coupled to the same LS-PCW sample as for Fig. 4(b). The coupling loss from fiber to the waveguide is roughly 20 dB including lens loss. The pulse peak power before coupling, P fiber, and coupled power to the waveguide, P in, are set below 10 W and 0.10 W, respectively, so that we can neglect the SPM in the fiber after the filter and in the sample. The output pulse is observed using autocorrelator. As shown in Fig. 5
Fig. 5 Autocorrelation traces of input and output pulses for ChG LS-PCW.
, τp in the high and low υ g regimes are almost the same as the input one. The dispersion constant is no higher than 0.04 fs/nm/mm. Thus, we confirmed that the dispersion is negligible in the devices.

5. Nonlinear characteristics

In the nonlinear measurements, the same pulse laser and LS-PCW sample as for Fig. 5 are used.

A. Two-photon absorption

B. Self-phase modulation

The SPM in PCWs is characterized from the spectral change using the same setup as for Fig. 5 and optical spectral analyzer. Figure 7
Fig. 7 Change of pulse spectrum caused by SPM near the photonic band-edge in normal ChG PCW.
shows the pulse spectra at different λp in a normal PCW (different sample from that for Fig. 4(a)). At λp < 1.544 μm, different spectral shapes at the lowest P in = 0.5 W is mainly caused by irregular pulse spectrum generated by the SPM in the EDFA and/or oscillating transmission spectrum of the PCW. When λp is close to the band-edge, however, pedestal of the spectrum becomes evident, and the spectral shape changes rapidly with P in. It indicates that the SPM is enhanced by band-edge slow light. Besides, the asymmetric n g spectrum of the normal PCW might generate asymmetric spectrum of SPM.

Figure 8
Fig. 8 Spectral change through SPM in ChG LS-PCW in (a) high υ g regime (n g ~10) and (b) low υ g regime (n g ~20).
compares the spectral change between the high and low υ g regimes in the LS-PCW. In the high υ g regime, the spectral peak begins to split into two at P in > 0.4 W, and 1.5π nonlinear phase-shift shown by the center dip occurs at P in = 0.89 W. In the low υ g regime, on the other hand, the center dip is already observed at P in = 0.42 W, and additional peaks appear at higher P in, suggesting a larger phase shift of the SPM enhanced by LD slow light. Different from asymmetric spectral broadening in Fig. 7, Fig. 8 exhibits the relatively symmetric ones. It might reflect the flat n g spectrum of LS-PCW. It is also different from the case of Si LS-PCWs, i.e. the spectrum particularly broadens toward the short wavelength side due to carrier-plasma effect [42

42. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009). [CrossRef] [PubMed]

]. The symmetric spectrum in the ChG LS-PCW indicates the pure third-order nonlinearity without carrier effects induced by TPA.

We also estimated the nonlinear parameter γeff = ΔϕNL/P in L eff, to be 2.3 × 104 and 6.3 × 104 W−1m−1 in the high and low υ g regimes, respectively, indicating 2.7-fold enhancement due to LD slow-light. We can confirm the consistency of this value with that expected from structural parameters. Substituting Eq. (1) into above, γeff is expressed as γeff = (n g 2/A eff) (2πn 2p). If the same enhancement and reduction as mentioned above are assumed, 2.6-fold enhancement is evaluated in γeff. To the best of our knowledge, this γeff is 200 times larger than 307 W−1m−1 for Si wire waveguide [43

43. T. Vallaitis, S. Bogatscher, L. Alloatti, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, F. Diederich, C. Koos, W. Freude, and J. Leuthold, “Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries,” Opt. Express 17(20), 17357–17368 (2009). [CrossRef] [PubMed]

] and is the largest value for any types of nonlinear waveguides. This is the clear evidence that the ChG slow-light PCWs can be a promising platform for on-chip nonlinear devices.

Furthermore, n 2 of Ag-As2Se3 is deduced from γeff to be as high as ~8 × 10−17 m2/W. Although n 2 has not been reported for λ = 1.55 μm, we can reconfirm the result at λ = 1.05 μm that the Ag doping magnify n 2 of As2Se3 to three fold higher [37

37. K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, “Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching,” Opt. Lett. 29(3), 265–267 (2004). [CrossRef] [PubMed]

]. For As2Se3, n 2 = 2.3 × 10−17 m2/W has been measured at λ = 1.55 μm [15

15. J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27(2), 119–121 (2002). [CrossRef]

]. According to the above effect of the Ag doping, 6.9 × 10−17 m2/W is expected for Ag-As2Se3, which agrees roughly with the above experimental result.

C. Four-wave mixing

To observe the FWM for synchronized two pulses, an optical pulse after the first EDFA is divided into two, each of which are filtered at different λp. The timing of the two pulses are adjusted by optical delay line in either arm so that the autocorrelation trace of two pulses after multiplexing shows a clear beat pattern. The multiplexed pulses are launched into the device with P in below the SPM level, and the output spectrum is observed using optical spectrum analyzer. The spectra in two different regimes are shown in Fig. 9
Fig. 9 Observation of FWM in ChG LS-PCW in the (a) high υ g regime (n g ~5), (b) low υ g regime (n g ~15) and (c) low υ g regime (n g ~20).
. Two idlers are generated from the original signal and pump light. Conversion efficiencies from the signal to the long-wavelength-side idler are –22, –14 and –17 dB in the high and low υ g (n g ~15, 20) regimes, respectively, i.e. 8 dB improvement by the slow-light effect. Thus it is suggested in this experiment that wide bandwidth LD slow-light waveguide is more advantageous because we can selectively use minimum dispersion spectrum suitable for phase and group velocity matching.

6. Conclusion

We reported the design, fabrication process and characterization of Ag-As2Se3 chalcogenide photonic crystal waveguides. To demonstrate the nonlinearity enhancement due to low-dispersion slow light, we designed and fabricated the third-row lattice-shifted waveguides, and the slow light was confirmed from their group-index spectra and picosecond pulse transmission. We confirmed that two-photon absorption is negligible even with the slow-light enhancement. As for the self-phase modulation, symmetric spectral broadening and central dip were observed, suggesting a 1.5π phase shift. The input power required for this was reduced to half with the slow-light enhancement, which agrees well with theoretical estimates. It suggests a huge effective nonlinear parameter of 6.3 × 104 W−1m−1, which is, to our knowledge, the highest value for any nonlinear waveguides. The four-wave mixing was also demonstrated with a conversion efficiency improved from –22 to –14dB due to the slow-light effect. This result is plotted as a red circle in Fig. 1. This study has achieved the optical nonlinearity on highly balanced condition between lower operating power and shorter device length than any other materials and waveguides. Although there are still much room for improving the optical coupling and spectral flatness, these results clearly show its promising potential for high-efficiency and compact on-chip nonlinear devices with ultrafast response.

Acknowledgements

This work was supported from the JSPS Research Fellow-ships for Young Scientists.

References and links

1.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]

2.

R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004). [CrossRef]

3.

M. D. Pelusi, F. Luan, E. Magi, M. R. Lamont, D. J. Moss, B. J. Eggleton, J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “High bit rate all-optical signal processing in a fiber photonic wire,” Opt. Express 16(15), 11506–11512 (2008). [CrossRef] [PubMed]

4.

F. Luan, M. D. Pelusi, M. R. E. Lamont, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Dispersion engineered As2S3 planar waveguides for broadband four-wave mixing based wavelength conversion of 40 Gb/s signals,” Opt. Express 17(5), 3514–3520 (2009). [CrossRef] [PubMed]

5.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44(9A), 6541–6545 (2005). [CrossRef]

6.

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]

7.

K. Narayanan and S. F. Preble, “Optical nonlinearities in hydrogenated-amorphous silicon waveguides,” Opt. Express 18(9), 8998–9005 (2010). [CrossRef] [PubMed]

8.

I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express 14(25), 12380–12387 (2006). [CrossRef] [PubMed]

9.

H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006). [CrossRef] [PubMed]

10.

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005). [CrossRef] [PubMed]

11.

G. A. Siviloglou, S. Suntsov, R. El-Ganainy, R. Iwanow, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, D. Modotto, A. Locatelli, C. De Angelis, F. Pozzi, C. R. Stanley, and M. Sorel, “Enhanced third-order nonlinear effects in optical AlGaAs nanowires,” Opt. Express 14(20), 9377–9384 (2006). [CrossRef] [PubMed]

12.

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009). [CrossRef] [PubMed]

13.

R. G. DeCorby, N. Ponnampalam, M. M. Pai, H. T. Nguyen, P. K. Dwivedi, T. J. Clement, C. J. Haugen, J. N. McMullin, and S. O. Kasap, “High index contrast waveguides in chalcogenide glass and polymer,” IEEE J. Sel. Top. Quantum Electron. 11(2), 539–546 (2005). [CrossRef]

14.

V. K. Tikhomirov, D. Furniss, A. B. Seddon, J. A. Savage, P. D. Mason, D. A. Orchard, and K. L. Lewis, “Glass formation in the Te-enriched part of the quaternary Ge-As-Se-Te system and its implication for mid-infrared optical fibres,” Infrared Phys. Technol. 45(2), 115–123 (2004). [CrossRef]

15.

J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27(2), 119–121 (2002). [CrossRef]

16.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

17.

A. Zakery, and S. R. Elliott, Optical Nonlinearities in Chalcogenide Glasses and their Applications (Springer, New York, 2007).

18.

D. A. P. Bulla, R. P. Wang, A. Prasad, A. V. Rode, S. J. Madden, and B. Luther-Davies, “On the properties and stability of thermally evaporated Ge-As-Se thin films,” Appl. Phys., A Mater. Sci. Process. 96(3), 615–625 (2009). [CrossRef]

19.

S. Song, J. Dua, and C. B. Arnold, “Influence of annealing conditions on the optical and structural properties of spin-coated As2S3 chalcogenide glass thin films,” Opt. Express 18(6), 5472–5480 (2010). [CrossRef] [PubMed]

20.

T. G. Robinson, R. G. DeCorby, J. N. McMullin, C. J. Haugen, S. O. Kasap, and D. Tonchev, “Strong Bragg gratings photoinduced by 633-nm illumination in evaporated As2Se3 thin films,” Opt. Lett. 28(6), 459–461 (2003). [CrossRef] [PubMed]

21.

A. V. Rode, A. Zakery, M. Samoc, R. B. Charters, E. G. Gamaly, and B. Luther-Davies, “Laser-deposited As2S3 chalcogenide films for waveguide applications,” Appl. Surf. Sci. 197, 481–485 (2002). [CrossRef]

22.

D. Freeman, C. Grillet, M. W. Lee, C. L. C. Smith, Y. Ruan, A. Rode, M. Krolikowska, S. Tomljenovic-Hanic, C. M. De Sterke, M. J. Steel, B. Luther-Davies, S. Madden, D. J. Moss, Y. H. Lee, and B. J. Eggleton, “Chalcogenide glass photonic crystals,” Photon. Nanostructures 6(1), 3–11 (2008). [CrossRef]

23.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

24.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009). [CrossRef]

25.

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]

26.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 16(1), 344–356 (2010). [CrossRef]

27.

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18(15), 15484–15497 (2010). [CrossRef] [PubMed]

28.

V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, P. Colman, A. De Rossi, M. Santagiustina, C. G. Someda, and G. Vadalà, “Highly efficient four wave mixing in GaInP photonic crystal waveguides,” Opt. Lett. 35(9), 1440–1442 (2010). [CrossRef] [PubMed]

29.

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17(2), 552–557 (2009). [CrossRef] [PubMed]

30.

I. Cestier, V. Eckhouse, G. Eisenstein, S. Combrié, P. Colman, and A. De Rossi, “Resonance enhanced large third order nonlinear optical response in slow light GaInP photonic-crystal waveguides,” Opt. Express 18(6), 5746–5753 (2010). [CrossRef] [PubMed]

31.

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(8), 3079–3086 (2005). [CrossRef] [PubMed]

32.

Y. Ruan, M.-K. Kim, Y.-H. Lee, B. Luther-Davies, and A. Rode, “Fabrication of high-Q chalcogenide photonic crystal resonators by e-beam lithography,” Appl. Phys. Lett. 90(7), 071102 (2007). [CrossRef]

33.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Two dimensional photonic band gap pattering in thin chalcogenide glassy films,” Thin Solid Films 488(1–2), 185–188 (2005). [CrossRef]

34.

A. Popescu, S. Miclos, D. Savastru, R. Savastru, M. Ciobanu, M. Popescu, A. Lorinczi, F. Sava, A. Velea, F. Jipa, and M. Zamfirescu, “Direct laser writing of two-dimensional photonic structures in amorphous As2S3 thin films,” J. Optoelectron. Adv. Mater. 11(11), 1874–1880 (2009).

35.

K. Paivasaari, V. K. Tikhomirov, and J. Turunen, “High refractive index chalcogenide glass for photonic crystal applications,” Opt. Express 15(5), 2336–2340 (2007). [CrossRef] [PubMed]

36.

K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express 17(25), 22393–22400 (2009). [CrossRef]

37.

K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, “Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching,” Opt. Lett. 29(3), 265–267 (2004). [CrossRef] [PubMed]

38.

L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007). [CrossRef] [PubMed]

39.

T. Wágner, V. Perina, A. Mackova, E. Rauhala, A. Seppala, M. Vleck, S. O. Kasap, M. Vlcek, and M. Frumar, “The tailoring of the composition of Ag-As-S amorphous films using photo-induced solid state reaction between Ag and As30S70 films,” Solid State Ion. 141(1), 387–395 (2001). [CrossRef]

40.

K. Ogusu, S. Maeda, M. Kitao, H. Li, and M. Minakata, “Optical and structural properties of Ag(Cu)-As2Se3 chalcogenide films prepared by a photodoping,” J. Non-Cryst. Solids 347(1–3), 159–165 (2004). [CrossRef]

41.

J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]

42.

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009). [CrossRef] [PubMed]

43.

T. Vallaitis, S. Bogatscher, L. Alloatti, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, F. Diederich, C. Koos, W. Freude, and J. Leuthold, “Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries,” Opt. Express 17(20), 17357–17368 (2009). [CrossRef] [PubMed]

OCIS Codes
(160.2750) Materials : Glass and other amorphous materials
(230.3120) Optical devices : Integrated optics devices
(230.4320) Optical devices : Nonlinear optical devices
(230.5298) Optical devices : Photonic crystals

ToC Category:
Chalcogenide Glass

History
Original Manuscript: August 31, 2010
Revised Manuscript: September 22, 2010
Manuscript Accepted: September 23, 2010
Published: December 6, 2010

Virtual Issues
Chalcogenide Glass (2010) Optics Express

Citation
Keijiro Suzuki and Toshihiko Baba, "Nonlinear light propagation in chalcogenide photonic crystal slow light waveguides," Opt. Express 18, 26675-26685 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-25-26675


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References

  1. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]
  2. R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004). [CrossRef]
  3. M. D. Pelusi, F. Luan, E. Magi, M. R. Lamont, D. J. Moss, B. J. Eggleton, J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “High bit rate all-optical signal processing in a fiber photonic wire,” Opt. Express 16(15), 11506–11512 (2008). [CrossRef] [PubMed]
  4. F. Luan, M. D. Pelusi, M. R. E. Lamont, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Dispersion engineered As2S3 planar waveguides for broadband four-wave mixing based wavelength conversion of 40 Gb/s signals,” Opt. Express 17(5), 3514–3520 (2009). [CrossRef] [PubMed]
  5. H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44(9A), 6541–6545 (2005). [CrossRef]
  6. E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]
  7. K. Narayanan and S. F. Preble, “Optical nonlinearities in hydrogenated-amorphous silicon waveguides,” Opt. Express 18(9), 8998–9005 (2010). [CrossRef] [PubMed]
  8. I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express 14(25), 12380–12387 (2006). [CrossRef] [PubMed]
  9. H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006). [CrossRef] [PubMed]
  10. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005). [CrossRef] [PubMed]
  11. G. A. Siviloglou, S. Suntsov, R. El-Ganainy, R. Iwanow, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, D. Modotto, A. Locatelli, C. De Angelis, F. Pozzi, C. R. Stanley, and M. Sorel, “Enhanced third-order nonlinear effects in optical AlGaAs nanowires,” Opt. Express 14(20), 9377–9384 (2006). [CrossRef] [PubMed]
  12. K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009). [CrossRef] [PubMed]
  13. R. G. DeCorby, N. Ponnampalam, M. M. Pai, H. T. Nguyen, P. K. Dwivedi, T. J. Clement, C. J. Haugen, J. N. McMullin, and S. O. Kasap, “High index contrast waveguides in chalcogenide glass and polymer,” IEEE J. Sel. Top. Quantum Electron. 11(2), 539–546 (2005). [CrossRef]
  14. V. K. Tikhomirov, D. Furniss, A. B. Seddon, J. A. Savage, P. D. Mason, D. A. Orchard, and K. L. Lewis, “Glass formation in the Te-enriched part of the quaternary Ge-As-Se-Te system and its implication for mid-infrared optical fibres,” Infrared Phys. Technol. 45(2), 115–123 (2004). [CrossRef]
  15. J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27(2), 119–121 (2002). [CrossRef]
  16. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]
  17. A. Zakery, and S. R. Elliott, Optical Nonlinearities in Chalcogenide Glasses and their Applications (Springer, New York, 2007).
  18. D. A. P. Bulla, R. P. Wang, A. Prasad, A. V. Rode, S. J. Madden, and B. Luther-Davies, “On the properties and stability of thermally evaporated Ge-As-Se thin films,” Appl. Phys., A Mater. Sci. Process. 96(3), 615–625 (2009). [CrossRef]
  19. S. Song, J. Dua, and C. B. Arnold, “Influence of annealing conditions on the optical and structural properties of spin-coated As2S3 chalcogenide glass thin films,” Opt. Express 18(6), 5472–5480 (2010). [CrossRef] [PubMed]
  20. T. G. Robinson, R. G. DeCorby, J. N. McMullin, C. J. Haugen, S. O. Kasap, and D. Tonchev, “Strong Bragg gratings photoinduced by 633-nm illumination in evaporated As2Se3 thin films,” Opt. Lett. 28(6), 459–461 (2003). [CrossRef] [PubMed]
  21. A. V. Rode, A. Zakery, M. Samoc, R. B. Charters, E. G. Gamaly, and B. Luther-Davies, “Laser-deposited As2S3 chalcogenide films for waveguide applications,” Appl. Surf. Sci. 197, 481–485 (2002). [CrossRef]
  22. D. Freeman, C. Grillet, M. W. Lee, C. L. C. Smith, Y. Ruan, A. Rode, M. Krolikowska, S. Tomljenovic-Hanic, C. M. De Sterke, M. J. Steel, B. Luther-Davies, S. Madden, D. J. Moss, Y. H. Lee, and B. J. Eggleton, “Chalcogenide glass photonic crystals,” Photon. Nanostructures 6(1), 3–11 (2008). [CrossRef]
  23. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]
  24. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009). [CrossRef]
  25. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009). [CrossRef] [PubMed]
  26. C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Sel. Top. Quantum Electron. 16(1), 344–356 (2010). [CrossRef]
  27. J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18(15), 15484–15497 (2010). [CrossRef] [PubMed]
  28. V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, P. Colman, A. De Rossi, M. Santagiustina, C. G. Someda, and G. Vadalà, “Highly efficient four wave mixing in GaInP photonic crystal waveguides,” Opt. Lett. 35(9), 1440–1442 (2010). [CrossRef] [PubMed]
  29. A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17(2), 552–557 (2009). [CrossRef] [PubMed]
  30. I. Cestier, V. Eckhouse, G. Eisenstein, S. Combrié, P. Colman, and A. De Rossi, “Resonance enhanced large third order nonlinear optical response in slow light GaInP photonic-crystal waveguides,” Opt. Express 18(6), 5746–5753 (2010). [CrossRef] [PubMed]
  31. 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(8), 3079–3086 (2005). [CrossRef] [PubMed]
  32. Y. Ruan, M.-K. Kim, Y.-H. Lee, B. Luther-Davies, and A. Rode, “Fabrication of high-Q chalcogenide photonic crystal resonators by e-beam lithography,” Appl. Phys. Lett. 90(7), 071102 (2007). [CrossRef]
  33. A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Two dimensional photonic band gap pattering in thin chalcogenide glassy films,” Thin Solid Films 488(1–2), 185–188 (2005). [CrossRef]
  34. A. Popescu, S. Miclos, D. Savastru, R. Savastru, M. Ciobanu, M. Popescu, A. Lorinczi, F. Sava, A. Velea, F. Jipa, and M. Zamfirescu, “Direct laser writing of two-dimensional photonic structures in amorphous As2S3 thin films,” J. Optoelectron. Adv. Mater. 11(11), 1874–1880 (2009).
  35. K. Paivasaari, V. K. Tikhomirov, and J. Turunen, “High refractive index chalcogenide glass for photonic crystal applications,” Opt. Express 15(5), 2336–2340 (2007). [CrossRef] [PubMed]
  36. K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express 17(25), 22393–22400 (2009). [CrossRef]
  37. K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, “Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching,” Opt. Lett. 29(3), 265–267 (2004). [CrossRef] [PubMed]
  38. L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007). [CrossRef] [PubMed]
  39. T. Wágner, V. Perina, A. Mackova, E. Rauhala, A. Seppala, M. Vleck, S. O. Kasap, M. Vlcek, and M. Frumar, “The tailoring of the composition of Ag-As-S amorphous films using photo-induced solid state reaction between Ag and As30S70 films,” Solid State Ion. 141(1), 387–395 (2001). [CrossRef]
  40. K. Ogusu, S. Maeda, M. Kitao, H. Li, and M. Minakata, “Optical and structural properties of Ag(Cu)-As2Se3 chalcogenide films prepared by a photodoping,” J. Non-Cryst. Solids 347(1–3), 159–165 (2004). [CrossRef]
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