Nonlinear light propagation in chalcogenide photonic crystal slow light waveguides

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 × 10 Wm, 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 selfphase modulation and four-wave mixing, which are assisted by lowdispersion slow light. ©2010 Optical Society of America OCIS codes: (230.5298) Photonic crystals; (230.4320) Nonlinear optical devices; (160.2750) Glass and other amorphous materials; (230.3120) Integrated optics devices. References and links 1. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. 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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). #134309 $15.00 USD Received 31 Aug 2010; revised 22 Sep 2010; accepted 23 Sep 2010; published 6 Dec 2010 (C) 2010 OSA 6 December 2010 / Vol. 18, No. 2


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], they generally require high operating power and/or long device length due to limited material nonlinearities.Figure 1 summarizes the operating power and the lengths of various nonlinear devices.Fiberbased 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 [2,3].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-cmlong As 2 S 3 chalcogenide glass rib waveguide at an input power of less than 1 W [4]. 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][6][7][8].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 [9,10].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].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].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, Sand 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 [13,14] and ultrahigh-speed third-order nonlinear response (< 100 fs) without carrier effects.
iii) Their films can be fabricated at low temperature (< 400°C) [17][18][19], 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][21][22].
PCWs are formed by introducing a single line-defect into air-bridge photonic crystal slab, which consists of two-dimensionally periodic array of airholes in a triangular lattice.Their small modal cross-section and low group velocity υ g of light, namely slow light, can enhance the optical intensity in the waveguides [23].In particular, low dispersion slow light (we call it LD slow light) is obtained in optimized structures, and the nonlinearity is enhanced through the spatial compression of short optical pulses.In fact, the enhancement of SPM, TPA, FWM and third harmonic generation has been observed in Si slow-light PCWs [24][25][26][27] and GaAs, AlGaAs and GaInP ones [12,[28][29][30].
Challenges to fabricating ChG photonic crystals have been reported with various ChGs and fabrication process, such as the combination of Ge 33 As 12 Se 55 with focused ion beam milling [31], that with e-beam lithography and chemically assisted ion beam etching [32], As 2 S 3 with holographic lithography and wet etching [33], and As 2 S 3 and Ge 20 As 20 Se 14 Te 46 with direct laser writing [34,35].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-As 2 Se 3 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].This material is known to have n 2 of 9.0 × 10 17 m 2 /W at λ = 1.05 μm [37], which is the highest value ever reported for ChGs.Therefore, Ag-As 2 Se 3 and LD slowlight PCW can be one of the most powerful combination toward the present purpose.
In this paper, we comprehensively discuss the Ag-As 2 Se 3 PCW in both high and low υ g regimes.We first show the design of lattice-shifted PCWs (LS-PCWs) suitable for LD slowlight generation [25].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.

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-As 2 Se 3 ChG LS-PCW is calculated by using three-dimensional finite-deference time-domain method with periodic boundaries.We assume the material index of Ag-As 2 Se 3 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 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 summarizes the minimum n g , Δλ giving 0 -10% change in n g , and the normalized delay-bandwidth product n g Δλ/λ giving the slow-light performance [23].The n g Δλ/λ varies from 0.33 -0.14, which is almost similar to Si-PCWs' [25].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].Therefore, we targeted n g and Δλ at s/a = 0.48 in Table 1.

Fabrication
In the fabrication of Ag-As 2 Se 3 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-As 2 Se 3 and InP.Since the melting point and vapor pressure are different between Ag and As 2 Se 3 , we cannot directly deposit Ag-As 2 Se 3 using thermal evaporation of ternary source.Therefore, we evaporate 300-nm-thick As 2 Se 3 at 0.2 nm/s, followed by 10-nm-thick Ag at 0.01 nm/s.from halogen lamp for 30 min.Unlike thermal diffusion, Ag distributes almost uniformly in depth [40], and on this condition, Ag concentration becomes 5 at.%.The PCW pattern is formed by using e-beam lithography with ~500-nm-thick positive resist (ZEON ZEP-520A) charge-dissipating agent (Showa-Denko Espacer-300Z) and 50 kV e-beam writer (Elionix ELS7500-EX).The pattern is transferred to the Ag-As 2 Se 3 layer using ICP etching with CF 4 : CHF 3 = 4: 1 gas mixture.The main etching gas is CF 4 , while CHF 3 is used to deposit a thin polymer layer for protecting airhole sidewalls against neutral radicals in the plasma.It should be noted, however, that the excess deposition degrades the uniformity of airholes.To find a good balance, we optimized flow rates of these gases.The detail of the results is shown in the next section.To remove the resist after the etching, the substrate is boiled in a resist remover (ZEON ZDMAC) and cleaned in ultra-sonic bath.Finally, waveguide facets are formed by cleavage, and the air-bridge slab is formed by HF etching of Ti at room temperature and HCl: H 2 O = 4: 1 etching of InP at 4 °C.

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 shows the results of normal PCWs (s = 0).It is seen from the comparison between (a) and (b) that CHF 3 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 CHF 3 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 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], 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].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 g Δλ/λ ~0.24) at s/a = 0.33, n g ~20 with Δλ ~15 nm (n g Δλ/λ ~0.19) at s/a = 0.43 and n g ~35 with Δλ ~4 nm (n g Δλ/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].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].

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 λ p (1.53 and 1.56 μm in the high and low υ g regimes, respectively) with desired FWHM bandwidth Δλ p (2.0 nm corresponding to a FWHM pulse width τ p = 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, τ p 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.

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

A. Two-photon absorption
To evaluate TPA, sub-ps pulses from the laser are amplified by EDFA, appropriately attenuated, and coupled to the LS-PCW.To avoid the SPM in the EDFA and fibers, P fiber is set below 200 W, corresponding to P in < 2 W. Figure 6 compares the input/output response between the high and low υ g regimes.Neglecting the data fluctuation, almost linear response is observed for both of them.In Si LS-PCWs having the same modal cross-section and length, the saturation of output power appears at P in > 0.3 W in the low υ g regime with n g ~30 [25].On the other hand, TPA is negligible in this ChG PCW.We also observe that, at P in > 2 W, the input facet is damaged such that the line defect nearby the facet is chipped off.Since Ag-As 2 Se 3 is transparent and the TPA is negligible at λ ~1.55 μm, we can consider multi-photon absorption, absorption of higher order harmonics and photo-induced mechanical stress as reasons.

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 shows the pulse spectra at different λ p in a normal PCW (different sample from that for Fig. 4(a)).At λ p < 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 λ p is close to the bandedge, 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 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].The symmetric spectrum in the ChG LS-PCW indicates the pure third-order nonlinearity without carrier effects induced by TPA.
Let us verify the result more quantitatively.In this experiment, P in required for 1.5π phase change is reduced to half when n g is increased from 10 to 20.The nonlinear phase shift Δ NL is expressed as where A eff and L eff are the effective modal area and the effective length at 1/e power decay, respectively.In Eq. ( 1), n g 2 , A eff and L eff can be altered by exploiting LS-PCW.In the experiment, n g 2 increased from 10 2 to 20 2 , corresponding to 4-fold enhancement.According to the cross-sectional mode analysis, A eff also increases from 0.17 to 0.26 μm 2 , leading 0.65fold reduction.Also, L eff decreases from 0.23 mm (α = 14 dB/mm) to 0.17 dB/mm), indicating 0.74-fold reduction.In total, 1.9-fold reduction of P in is estimated, which is in good agreement with the experimental result.
We also estimated the nonlinear parameter γ eff = Δ NL /P in L eff , to be 2.3 × 10 4 and 6.3 × 10 4 W 1 m 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, γ eff is expressed as γ eff = (n g 2 /A eff ) (2πn 2 /λ p ).If the same enhancement and reduction as mentioned above are assumed, 2.6-fold enhancement is evaluated in γ eff .To the best of our knowledge, this γ eff is 200 times larger than 307 W 1 m 1 for Si wire waveguide [43] 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-As 2 Se 3 is deduced from γ eff to be as high as ~8 × 10 17 m 2 /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 As 2 Se 3 to three fold higher [37].For As 2 Se 3 , n 2 = 2.3 × 10 17 m 2 /W has been measured at λ = 1.55 μm [15].According to the above effect of the Ag doping, 6.9 × 10 17 m 2 /W is expected for Ag-As 2 Se 3 , 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 λ p .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. Two idlers are generated from the original signal and pump light.Conversion efficiencies from the signal to the longwavelength-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

Conclusion
We reported the design, fabrication process and characterization of Ag-As 2 Se 3 chalcogenide photonic crystal waveguides.To demonstrate the nonlinearity enhancement due to lowdispersion 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 × 10 4 W 1 m 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 slowlight 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.

Fig. 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.

Fig. 7 .
Fig. 7. Change of pulse spectrum caused by SPM near the photonic band-edge in normal ChG PCW.