We have fabricated 630 × 500nm nanowires from Ge11.5As24Se64.5 chalcogenide glass by electron beam lithography (EBL) and inductively coupled plasma (ICP) etching. The loss of the nanowire was measured to be 2.6dB/cm for the fundamental TM mode. The nonlinear coefficient (γ) was determined to be ≈136 ± 7W−1m−1 at 1550nm by both CW four-wave-mixing (FWM) and modeling. Supercontinuum (SC) was produced in an 18mm long nanowire pumped by 1ps pulses with peak power of 25W.
© 2010 Optical Society of America
All-optical signal processing in highly nonlinear waveguides is currently a subject of considerable interest because it enables single channel data rates in a telecommunications network to far exceed those imposed by the limited bandwidth of electronics. Bandwidths of several THz have been demonstrated for optical processing in short, highly nonlinear, dispersion-engineered waveguides based on Kerr nonlinear materials [1,2]. Because of the short device lengths the available bandwidth is generally orders of magnitude larger than can be achieved using alternative nonlinear waveguides such as highly nonlinear fiber.
Waveguide nonlinear devices based on four wave mixing (FWM) or cross phase modulation (XPM) have proven effective for functions such as wavelength conversion [3–8]; mid-span spectral inversion ; parametric amplification [10,11]; de-multiplexing ; RF spectral analysis [13,14] regeneration [15–17] and impairment monitoring . Many of these optical devices require a nonlinear phase shift, Δφ = γPLeff ≈1, where P is the pulse power, γ = 2πn2/λAeff is the nonlinear parameter, Leff is the effective length of the device determined by losses and Aeff the mode area in the waveguide. The operating bandwidth is determined by the phase-mis-match (ΔβLeff≈2β2Δω2Leff<π) and pulse walk-off, where β2 is the second order dispersion in the waveguide. β2 needs to be small as should the device length to obtain the maximum bandwidth. This implies the need for an extremely large nonlinear coefficient, γ, and the use of dispersion engineering to compensate the large normal material dispersion common to highly nonlinear waveguide materials.
To achieve these goals nanowire waveguides fabricated in Kerr nonlinear materials have attracted increasing attention. To date most nanowires have been made from silicon with reported values up to γ ≈ 150W−1m−1 . However, silicon has some disadvantage for high-speed nonlinear optical signal processing since in 1550nm bands it is affected by two-photon (TPA) and free carrier absorption (FCA) that degrade performance . Thus, we have focused on the use of chalcogenide glasses for all-optical processing since they have as high or higher a nonlinear index as silicon but negligible TPA and FCA [20–23].
A large number of nonlinear optical processing demonstrations have successfully used dispersion engineered low index contrast rib waveguides made from As2S3 chalcogenide glasses [12–14,18] albeit having a modest γ of 10W−1m−1. In an effort to increase n 2 we recently reported studies of glasses in the Ge-As-Se chalcogenide glass system to identify compositions with a combination of high nonlinearity, low optical loss and the requisite stability for all-optical processing [22,24]. In order to further increase γ we have now combined glasses with enhanced nonlinearity with designs for nanowires with small mode areas and that provide small dispersion in the telecommunications c-band.
In this paper, therefore, we report the fabrication and characterization of nanowires made from Ge11.5As24Se64.5 glasses by electron beam lithography (EBL) and dry etching. The loss was measured to be as low as 2.6dB/cm for fundamental TM mode. The nonlinear coefficient was measured to be 136 ± 7W−1m−1 by continuous wave (CW) FWM for the TM mode at 1550nm. These nanowires could be used to generate super-continuum spanning from 1200 to beyond 1700nm using 1550nm pump pulses with 25W peak power and 1ps duration provided the waveguide dispersion was anomalous and sufficiently large. We analyzed SC generation by the split-step Fourier method confirming that it was mainly controlled by second order of dispersion that determines the soliton fission length for the nanowires.
The Ge11.5As24Se64.5 is one of a small family of Ge-As-Se glass compositions that have favourable properties for all-optical processing [22,24]. It is known that the physical properties of ternary chalcogenides vary significantly as a function of their mean coordination number (MCN = the sum of the products of the valency times the atomic abundance of the constituent atoms) and that MCN can be used to categorize the basic properties of the glass network [25–27]. In the case of Ge-As-Se glasses we have found that their linear and nonlinear refractive indices, optical losses, elastic properties, etc, all vary strongly with MCN. Ge11.5As24Se64.5, for which MCN = 2.45, lies in the so-called “intermediate” phase (IP) which lies between the “floppy” and “stressed-rigid” glass networks. Of particular significance is that films produced by thermal evaporation in this region have similar properties to those of bulk glasses – an unusual behaviour for films made from ternary chalcogenides. This is illustrated in Fig. 1 where we plot the bandgap of bulk and as-deposited films obained from Tauc plots as a function of MCN. As is evident, for most values of MCN the evaporated films have a significantly smaller bandgap than the bulk glasses and this translates to a substantially higher refractive index. This is because different chemical bonds form in the non-equilibrium conditions existing when a vapour condenses onto a cold substrate. Furthermore, as shown in Fig. 1(b) when annealed at temperatures up to their glass transition temperatures, the bandgap of films with MCN close to 2.48 do not change significantly whereas those with higher (or lower) MCN generally evolve in response to thermally induced changes in their chemical bonds . Thus, the physical properties of compositions such as Ge11.5As24Se64.5 are relatively stable, and this is important for all-optical processing where any change, for example, in refractive index can result is a variation in important waveguide properties such as dispersion.
Compared with As2S3 glass, which has been our workhorse for all-optical devices to date, Ge11.5As24Se64.5 has a higher linear refractive index (2.66 compared with 2.43) which leads to better mode confinement and, as would be expected from Miller’s rule , a higher nonlinear index, n 2 (8.6×10 −14cm2/W c.f. 3×10−14cm2/W for As2S3 at 1500nm ). No TPA could be detected during z-scan measurements made on bulk Ge11.5As24Se64.5 samples, however, the figure of merit, FOM = n2/α2λ, where α2 is the two photon absorption coefficient, has been found to be ≈60 from measurements of the power-dependence of the transmission for Ge11.5As24Se64.5 rib waveguides .
3. Nanowire design, fabrication and testing
Chalcogenide glasses generally have a smaller material dispersion than silicon. As a result, nanowires engineered for zero dispersion by offsetting waveguide against material dispersion, are generally larger than those fabricated from silicon and can be few-moded. To reduce the number of higher order modes we, therefore chose to reduce the index contrast by applying a polymer cladding (refractive index 1.51). Using the empirical relationship reported in , this core-cladding combination would achieve the minimum mode area of 0.24µm2 to achieve the highest nonlinear response: ≈2.5 times the optimum area of an air-clad silicon nanowire. The mode indices were determined more accurately using a FDTD mode solver  and the effective area Aeff calculated by the method described in . Figures 2(a) and 2(b) show the dispersion D in ps/nm/km for a 630nm wide nanowire (corresponding to the width of the structure that was fabricated) as a function of waveguide height and wavelength for both the fundamental TM and TE modes. The solid line shows the locus of the zero-dispersion points with regions to the right and above this line being in the anomalous regime. As is evident from Fig. 2(a) ≈465nm thick film provides zero-dispersion for the TE mode at 1550nm, whilst for TM mode the waveguide needs to be slightly thinner at ≈455nm. We chose a design made from a 500nm thick film for which the dispersion parameters were predicted to be ≈125ps/nm/km and ≈66ps/nm/km at 1550nm for the fundamental TM and TE modes respectively. The predicted nonlinear coefficient (γ) varied with wavelength from a high of ≈152.5W−1m−1 for TE mode at the bottom of the S-band to a low of 122W−1m−1 for TM mode at the top of the L-band.
It is apparent from Fig. 2 that there scope to engineer the dispersion to obtain similar values for both TE and TM modes at 1550nm and this occurs for a nanowire ≈590nm thick. In fact this nanowire design is close to case where the TE and TM modes become degenerate which could be implemented by choosing the cladding index to match that of fused silica and making a nanowire with a square cross-section. This should be relatively easy to achieve and illustrates an advantage of using polymer or glass clad glass high index nanowires compared with air-clad structures.
Nanowires were fabricated using the following process. First a 500nm thick Ge11.5As24Se64.5 film was deposited by thermal evaporation onto a silicon wafer with 2µm thick thermal oxide as the substrate. Since most chalcogenide glasses are chemically sensitive to alkaline developers, we chose a 200nm thick PMMA film spin-coated onto the glass layer as an electron beam resist. E-beam lithography was used to pattern the PMMA using the fixed beam moving stage (FBMS) method. In this approach the electron beam was used to expose ≈2µm wide “claddings” on either side of a 650nm wide waveguide as the stage was moved orthogonal to the scanning direction to produce the pattern required for the waveguide. FBMS eliminates stitching errors between the different writing fields that can be present in conventional field-scanning EBL and allowed the production of long nanowires with relatively low optical losses. After development of the PMMA, the glass was fully etched using CHF3 plasma in an Oxford Instruments ICP-100 RIE system. This was followed by an oxygen plasma etch to remove the remaining PMMA from the top of waveguide. Figure 3(a) shows the waveguide profile after the etching process and shows that the waveguide was well defined with smooth and near vertical sidewalls and was 630nm wide and 500nm high. After resist stripping a thin (5nm) layer of Al2O3 was deposited by atomic layer deposition (ALD). This has been found to both improve the adhesion of polymer cladding and also passivate the glass surface and this has been found to improve the damage resistance of chalcogenide waveguides at high average optical powers. Following ALD a polysiloxane Inorganic Polymer Glass (IPG™) cladding from RPO Inc. was spin-coated onto the waveguide and cured with UV light following which the end facets were prepared by hand cleaving.
The losses of the waveguide were determined by the cut-back method as show in Fig. 3(b). The values for TM and TE modes were measured to be 2.6dB/cm and 3.2dB/cm respectively with the higher losses for the TE mode originating from its greater sensitivity to the roughness of the etched side-walls. Lensed fibers with a mode-field area of ≈5µm2 were used to couple light into and out of the nanowires and this resulted in a total coupling losses of −7.5dB per facet due mostly to the large mismatch with the fundamental mode of the waveguide whose area was ≈0.27µm2.
To determine the accuracy of our design we first determined the nonlinear parameter γ of TM mode by CW FWM as shown in Fig. 4(a). In order to eliminate any effect of dispersion on the measurement, the pump and signal were chosen close to each other at 1550.8nm and 1552.6nm, respectively. These were combined in a wavelength division multiplexer (WDM) with additional filtering used to eliminate the amplified spontaneous emission produced by the erbium-doped fiber amplifiers (EDFAs) at the wavelengths (1549nm and 1554.4nm) generated by FWM between the two inputs. The pump and signal beam powers coupled into the waveguide were <35mW and <2.8mW respectively limited by the powers available from the amplifiers. Polarization controllers were used to adjust both pump and signal to either the TM or TE mode which could be determined by imaging the output of the waveguide onto an InGaAs camera through a Wollaston prism which created a split image which could be used to monitor the powers in the TE and TM polarizations. A power meter was used to monitor the input power and the output spectrum was monitored using an optical spectrum analyzer (OSA).
The nonlinear coefficient could be calculated though the idler conversion efficiency according to equation:
where Pp is the input power, α is the linear propagation loss and η is the efficiency of conversion from signal to idler at the output. The effective length Leff accounts for group velocity dispersion and is given by:
where Δβ is the phase mismatch term due to second order dispersion β2. In the experiment, the idler conversion efficiency was measured using the OSA at the output of a 16mm long nanowire as shown in Fig. 4(c). We confirmed that the conversion varied as the square of the pump power as shown Fig. 4(b) and showed no evidence of saturation effects which could invalidate the use of (1). By measuring the power at the lensed fiber; the coupling losses; the propagation losses and relative output powers, we calculated the nonlinear coefficient to be 136 ± 7W−1m−1 at 1550nm – consistent with the predicted value of 135W−1m−1. This represents a value almost equal to that achieved in silicon nanowires .
4. Supercontiuum generation
Whilst we were unable to directly measure the dispersion of the nanowires, we could obtain information from spectral broadening produced by passing short 1ps duration pulses from a mode-locked fiber laser through a 18mm long nanowire. After taking coupling losses into account, we were able to couple pulses with a maximum power of 25W into the nanowires. At close to this power, supercontinuum (SC) was generated for the TM mode but only spectral broadening due to self-phase modulation (SPM) was observed in the case of the TE mode (Fig. 5). This confirmed that the dispersion for the TM mode was indeed anomalous as predicted. Since soliton fission is essential for SC generation in waveguides such as these, the difference in the output spectra between the two polarization could have been due to the differences in dispersion evident in Fig. 2(c). Smaller dispersion leads to larger soliton fission length that would raise the threshold for SC generation for the TE mode.
To analyze this possibility, we used the split-step Fourier method to solve the nonlinear Schrödinger equation (NLSE):
where A is the electric field amplitude, α is the linear loss of the waveguide. βm is the mth order dispersion, α2 = 9.3 × 10−14m/W is the two-photon absorption coefficient and γ is nonlinear coefficient of 136W−1m−1 for the nanowire. R(t) = (1−fR)σ(t) + fRhR(t) is the response function, including the Raman contribution hR which was deduced from the measured Raman spectrum via the Kramers-Kronig relations with fR being the fractional contribution.
Using the dispersion values calculated from the FDTD mode solver, the experimentally confirmed values for γ and measured losses, we obtained a very good match between simulated spectra and the experiment as shown in Fig. 6(a) and Fig. 6(b) suggesting that the actual waveguide dispersion is consistent with the predicted values. To confirm that magnitude of the dispersion was the main factor leading to the difference in spectra between TE and TM modes, we set the losses for both polarization to be the same and compared simulations of the evolution of the spectra as a function of pulse power for the two polarization. Figures 6(c) and 6(d) confirm that for TE mode about 30% higher peak power was required to reach the threshold for SC generation and that the dispersion for TE mode was too small to allow soliton fission at 25W in agreement with our observations. According to these simulations the SC spectrum extended over 1000nm from 1200 to 2200nm although the region beyond 1700nm could not be measured with our optical spectrum analyzer.
5. Discussion and Conclusions
We have successfully fabricated dispersion engineered chalcogenide nanowires from Ge11.5As24Se64.5 chalcogenide glass films that have the highest nonlinear coefficient yet reported for a disersion-engineered glass nanowire although an extreme value of γ = 2.6×104 W−1m−1 has been reported for a Ag-As2Se3 photonic crystal with a moderate group index of 10 . The reported sensitivity of the nonlinearity of Ag-As2Se3 to pulse duration and intensity , however, suggest that this composition is unlikely to be suitable for all-optical processing of high bit rate signals where devices need to be exposed to continuous power densities of >10MW/cm2. Prior to this work the largest reported value of γ for a chalcogenide nanowire was 93.4W−1m−1 for a taper made from As2Se3 fiber . The value measured here using CW FWM was 136 ± 7W−1m−1 at 1550nm in agreement with calculations. This value is close to the maximum achievable using a cladding with index of ≈1.51 although values about 20% higher can be obtained by reducing the cladding index to 1.45 and using a smaller waveguide with square cross-section, which also corresponds to a polarization independent design. With air as a cladding values close to 190W−1m−1 are predicted. However, increasing γ may move the design into a region of increasing normal dispersion (Figs. 2(a), 2(b)). This is not a serious problem for all-optical processing based on FWM since the bandwidth Δω≈(1/√(2Leff|β2|)) is still in the 100nm range for cm-long devices even if |β2| rises to a few hundred ps2/km. This means operation across the complete telecommunications s-, c-, and l-bands should still be achieved.
It is worth noting that in the aim of these experiments was to measure the nonlinear coefficient so the conversion efficiency, which was less than −30dB, was not intended to be high enough for optical processing and was limited by the power that could be coupled into the waveguides. Eliminating the facet losses of −7.5dB would allow higher powers to be coupled which should lead to 1–2 orders of magnitude improvement in the conversion efficiency. Modeling has shown that the facet losses could be reduced to ≈−0.4dB using inverse tapers overlaid with SU8 waveguides mode-matched to high-NA optical fiber. In this design it is convenient to taper the film thickness by using a mask during deposition rather than the nanowire width which is the common approach using silicon. We will implement this solution in future devices which should allow the ultimate limits on the conversion to be determined.
Whilst we were unable to measure the waveguide dispersion directly, we compared the spectra produced by propagating 1ps duration pulses with a peak power of 25W through the nanowires with the prediction of simulations. We found that measured spectra were in good agreement using our calculated values of dispersion. In particular when power was launched in the TM mode a supercontinuum spanning from 1200nm to beyond 1700nm was produced whereas for the TE mode only SPM occurred. Whilst the dispersion is anomalous for both polarizations, it is smaller for the TE mode which results in a larger soliton fission length and consequently a higher threshold for supercontinuum generation for this polarization. The simulations showed that the threshold power for supercontinuum generation for TE excitaiton was above 20% above that available in our experiments.
The optical losses in these nanowires were as low as 2 0.6dB/cm – comparable with values achieved in Si nanowires with a similar nonlinear parameter. Because the index contrast of these polymer clad nanowires is about half that generally used with Si nanowires there appears scope to reduce these losses through improved processing to reduce side-wall roughness. Finally we note that the absence of two photon and free carrier absorption in these nanowires makes them a very good basic for all-optical processing at extreme bit rates of advanced modulation formats.
The support of the Australian Research Council through its Centres of Excellence program is gratefully acknowledged.
References and links
1. See. e.g. M. D. Pelusi, V. G. Ta’eed, L. B. Fu, E. Magi, M. R. E. Lamont, S. Madden, D. Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Applications of highly-nonlinear chalcogenide glass devices tailored for high-speed all-optical signal processing,” IEEE J. Sel. Top. Quantum Electron. 14(3), 529–539 (2008). [CrossRef]
3. Y. H. Kuo, H. S. Rong, V. Sih, S. B. Xu, M. Paniccia, and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14(24), 11721–11726 (2006). [CrossRef] [PubMed]
4. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007). [CrossRef] [PubMed]
5. F. Luan, M. D. Pelusi, M. R. E. Lamont, D. Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Dispersion engineered As(2)S(3) planar waveguides for broadband four-wave mixing based wavelength conversion of 40 Gb/s signals,” Opt. Express 17(5), 3514–3520 (2009). [CrossRef] [PubMed]
6. B. G. Lee, A. Biberman, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Demonstration of Broadband Wavelength Conversion at 40 Gb/s in Silicon Waveguides,” IEEE Photon. Technol. Lett. 21(3), 182–184 (2009). [CrossRef]
7. M. D. Pelusi, F. Luan, S. Madden, D. Y. Choi, D. A. Bulla, B. Luther-Davies, and B. J. Eggleton, “Wavelength Conversion of High-Speed Phase and Intensity Modulated Signals Using a Highly Nonlinear Chalcogenide Glass Chip,” IEEE Photon. Technol. Lett. 22(1), 3–5 (2010). [CrossRef]
8. A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010). [CrossRef] [PubMed]
9. S. Ayotte, H. S. Rong, S. B. Xu, O. Cohen, and M. J. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32(16), 2393–2395 (2007). [CrossRef] [PubMed]
10. M. R. E. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, X. Gai, and B. J. Eggleton, “Net-gain from a parametric amplifier on a chalcogenide optical chip,” Opt. Express 16(25), 20374–20381 (2008). [CrossRef] [PubMed]
11. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006). [CrossRef] [PubMed]
12. M. Galili, J. Xu, H. C. H. Mulvad, L. K. Oxenløwe, A. T. Clausen, P. Jeppesen, B. Luther-Davis, S. Madden, A. Rode, D. Y. Choi, M. Pelusi, F. Luan, and B. J. Eggleton, “Breakthrough switching speed with an all-optical chalcogenide glass chip: 640 Gbit/s demultiplexing,” Opt. Express 17(4), 2182–2187 (2009). [CrossRef] [PubMed]
13. M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009). [CrossRef]
14. M. D. Pelusi, T. D. Vo, F. Luan, S. J. Madden, D. Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Terahertz bandwidth RF spectrum analysis of femtosecond pulses using a chalcogenide chip,” Opt. Express 17(11), 9314–9322 (2009). [CrossRef] [PubMed]
15. 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]
17. V. G. Ta’eed, M. Shokooh-Saremi, L. B. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. L. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(3), 360–370 (2006). [CrossRef]
18. T. D. Vo, M. D. Pelusi, J. Schröder, F. Luan, S. J. Madden, D. Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Simultaneous multi-impairment monitoring of 640 Gb/s signals using photonic chip based RF spectrum analyzer,” Opt. Express 18(4), 3938–3945 (2010). [CrossRef] [PubMed]
20. C. Quemard, F. Smektala, V. Couderc, A. Barthelemy, and J. Lucas, “Chalcogenide Glasses with High Nonlinear Optical Properties for Telecommunications,” J. Phys. Chem. Solids 62(8), 1435–1440 (2001). [CrossRef]
21. J. M. Harbold, F. O. 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]
22. A. Prasad, C. J. Zha, R. P. Wang, A. Smith, S. Madden, and B. Luther-Davies, “Properties of GexAsySe1-x-y glasses for all-optical signal processing,” Opt. Express 16(4), 2804–2815 (2008). [CrossRef] [PubMed]
23. J. T. Gopinath, M. Sojacic, E. P. Ippen, V. N. Fuflyingin, W. A. King, and M. Shurgailn, “Third Order Nonlinearities in Ge-As-Se-based Glasses for Telecommunications Applications,” J. Appl. Phys. 96(11), 6931–6933 (2004). [CrossRef]
24. 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. (Berl.) 96(3), 615–625 (2009).
25. J. C. Phillips, “Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys,” J. Non-Cryst. Solids 34(2), 153–181 (1979). [CrossRef]
26. P. Boolchand, D. G. Georgiev, and B. Goodman, “Discovery of the Intermediate Phase in Chalcogenide Glasses,” J. Optoelectron. Adv. Mater. 3, 703–720 (2001).
28. C. C. Wang, “Empirical Relation Between the Linear and the Third Order Nonlinear Optical Susceptibilities,” Phys. Rev. B 2(6), 2045–2048 (1970). [CrossRef]
29. A. Prasad, “Ge-As-Se chalcogenide glasses for all-optical signal processing” PhD thesis, Australian National University, 2010.
30. P. Lusse, P. Stuwe, J. Schule, and H.-G. Unger, “Analysis of Vectorial Mode Fields in Optical Waveguides by a New Finite Difference Method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]
31. K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express 17(25), 22393–22400 (2009). [CrossRef]
32. 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]
33. D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33(7), 660–662 (2008). [CrossRef] [PubMed]
34. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15(10), 5976–5990 (2007). [CrossRef] [PubMed]