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Abstract
We measure the transmission of near-infrared ps pulses through single CdTe nanowires. Benefitting from the strong light confinement and large effective nonlinearity of these nanowires, a significant spectral broadening of ∼ 5 nm and nonlinear phase shift of a few π due to self-phase modulation (SPM) is observed experimentally at coupled peak power of a dozen W with a propagating length down to several hundred µms. A nonlinear-index coefficient (n2) as high as (9.5 ± 1.4) × 10−17 m2/W at 1550 nm is extracted from transmission spectra, corresponding to a nonlinear parameter (γ) of ∼ 1050 W−1m−1. The simulations indicate a spectral broadening more than 1.5 µm in single nanowire when pumped by fs pulses in anomalous dispersion regime. The obtained results suggest that, CdTe nanowire is promising in developing ultracompact nonlinear optical devices for microphotonic circuits.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Benefitting from a number of interesting properties including low propagating loss, tight optical confinement and highly tunable dispersion, photonic nanowires have been proved an excellent platform for nonlinear optical effects [1–3]. In past decades, continuous efforts have been paid on nonlinear photonic nanowires for both scientific studies and technological applications [4–7]. In particular, SPM, one of the main effects dominating the propagation of short laser pulses through optical waveguides, has been studied both theoretically and experimentally in a variety of nanowires (e.g., silica, chalcogenide glasses, Ta2O5, silicon, ZnO and InGaAsP) [8–13]. Meanwhile, a variety of SPM-based devices (e.g., supercontinuum laser sources, wavelength converters, signal regenerators, optical switches) have been demonstrated for applications ranging from optical sensing to optical communication [2,14–17].
For device applications, higher compactness and energy efficiency are always desired, especially for on-chip photonic circuits such as optical communication and interconnection [18–20]. Typically, in waveguide structures, with input energy down to 1-pJ/pulse level or less, a propagating length from a few mm to several cm is usually necessary for generating noticeable SPM-induced spectral broadening [9,11,13,21–23]. To reduce the footprint at similar power level, e.g., several hundred µms with input energy less than 1 pJ/pulse, high-index nanowire waveguides with much higher optical confinement (and thus much larger effective nonlinearity) become the possible candidates [1,2].
Among various high-index materials for nanowires, CdTe has been attracting continuous attentions as a promising optical material [24–27] owing to its favorable properties including high refractive index (e.g., ∼ 2.74 at wavelength of 1550 nm), ultra-broad intrinsic transparency window over infrared spectral range (from ∼ 1 to 25 µm), excellent photovoltaic property and nonlinear optical property. Previously, CdTe nanowires and microwires have been reported for optical waveguiding in spectral region from ∼ 1 to 9 µm [28,29]. It is worth to mention that, benefitting from their large second-order nonlinear coefficient (e.g., 109 pm/V at wavelength of 1064 nm) and nonlinear-index coefficient (e.g., over 5×10−17 m2/W at wavelength of 1550 nm, which is about 5–10 times larger than silicon) [30,31], these nanowires have been used for nonlinear optical applications such as transverse-second-harmonic-generation based single-nanowire optical correlation with pusle energy down to 2 fJ/pulse [32].
In this work, we demonstrate SPM effect in a single CdTe nanowire using ps pump pulses. The n2, which can be extracted from the transmission spectra in experiment, is measured to be (1.3 ± 0.7) × 10−17 m2/W, (3.9 ± 1.3) × 10−17 m2/W and (9.5 ± 1.4) × 10−17 m2/W at wavelength of 1064 nm, 1310 nm and 1550 nm, respectively. Taking advantage of the high material nonlinearity and strong optical confinement, noticeable SPM-induced spectral broadening (∼ 0.4 nm) is observed with coupled peak power down to ∼ 0.4 W (corresponding to an input energy of about 400 fJ/pulse) with a propagating length down to 640 µm. The effects of two-photon absorption (TPA) and free carriers on nonlinear process are studied both theoretically and experimentally, which suggest a significant suppression of TPA and free-carrier effects on SPM process inside CdTe nanowires at high coupled peak power.
2. Nanowire fabrication and experimental setup
Monocrystalline CdTe nanowires with diameter from hundreds of nms to several µms were synthesized using a thermal evaporation process [32,33]. The highly uniform diameter and excellent surface smoothness (Fig. 1(a)) ensure the low waveguiding loss within infrared spectral range [29]. To demonstrate the SPM effect, a single CdTe nanowire was placed on a MgF2 substrate (Fig. 1(b)). The pump pulses from a 1550-nm-wavelength laser source (MERCURY 1550-100-PM, Polaronyx Inc.; pulse width, 1 ps; repetition 80 MHz) were evanescently coupled into the nanowire using a fiber taper, and coupled out using another fiber taper after propagating along the nanowire for a certain length. The transmission spectra were then measured using a spectrometer (AQ6315, Yokogawa Inc.).
Fig. 1. (a) Scanning electron microscope image of an 800-nm-diameter CdTe nanowire (scale bar, 2 µm). (b) Schematic diagram of the experiment. The inset is the optical microscope image of an 800 nm-diameter CdTe nanowire with a length of 640 µm, which was placed on a MgF2 substrate (scale bar, 200 µm). 1550 nm-wavelength pulses were coupled into the nanowire through a fiber taper.
3. Results and discussions
3.1 Nonlinear-index coefficient
The power-dependent transmission spectra of an 800-nm-diameter CdTe nanowire with length of 640 µm is shown in Fig. 2(a). Under low-power pump (e.g., peak power of 0.6 W and 2.8 W), the transmitted intensity increases with an increasing coupled peak power. Compared with transmission spectrum with input fiber only, the spectra only differ in the transmitted intensity but not in spectral shape and position. As coupled peak power further increases, significant spectral broadening (e.g., ∼ 5 nm at 5 dB crosstalk level for 16.7 W) are observed. Figure 2(b) shows the relationship between coupled input power and spectral broadening measured at different crosstalk level. It shows that, the spectral broadening increases with an increasing input power.
Fig. 2. (a) Transmission spectra of an 800-nm-diameter CdTe nanowire with length of 640 µm as a function of coupled peak power. Inset, calculated power density profile of the fundamental mode of an 800-nm-diameter CdTe nanowire guiding a 1550-nm-wavelength light on a MgF2 subtrate. (b) SPM-induced spectral broadening measured at 5 dB and 10 dB crosstalk level.
A noticeable spectral broadening of ∼ 0.4 nm at 5 dB crosstalk level is obtained with coupled peak power down to ∼ 0.4 W, corresponding to an input energy of ∼ 400 fJ/pulse and a coupled peak power intensity of ∼ 1.1 × 108 W/cm2. Meanwhile, compared with other longer micro-waveguides reported in previous works (as shown in Table 1), the CdTe nanowires exhibited a comparable input energy for nonlinear phase shift of a few π [9,11,12,21]. Considering the relatively small propagating length used in our experiment, the results indicate a much strong nonlinear effect in CdTe nanowire than other typical micro-waveguides.
Table 1. Key parameters of SPM in different optical nanowires.
In addition to the spectral broadening, a multipeak structure in the transmission spectra is also observed (as shown in Fig. 2(a)), which arises from the phase interference caused by the time dependent SPM-induced frequency chirp [34]. The nonlinear phase shift $\phi $ is given by [9,34]
where M is the number of peaks in the broadened spectra, and the nonlinear-index coefficient n2 is given by [34] where Aeff is the effective mode area, P is the coupled peak power, Leff is the effective length of the waveguide.As shown in Fig. 2(a), a nonlinear phase shift of 3.5 ± 0.5 π is obtained at coupled peak power of 16.7 W, corresponding to an input energy of 16.7 pJ/pulse. From Eq. (2), we get a nonlinear-index coefficient at 1550-nm wavelength of (9.5 ± 1.4) × 10−17 m2/W, which is one to two order of magnitude larger than silicon and typical chalcogenide glasses (e.g., As2S3, As2Se3, AlGaAs) [8,9,35,36].
The normalized power density and nonlinear parameter of different nanowires were calculated (as shown in Fig. 3), indicating a much larger γ (e.g., ∼ 1050 W−1m−1 for an 800-nm-diameter nanowire at 1550-nm wavelength, which is ∼7 times larger than Si nanowire with sectional dimension of 0.5×0.3 µm) of CdTe nanowires. Benefitting from the large nonlinearity, CdTe nanowire shows a much shorter nonlinear length (Ln = cAeff/Pn2ω) compared with other typical nanowires with a same mode area and coupled peak power. For example, for a CdTe nanowire with diameter of 800 nm (corresponding to a mode area of 0.37 µm2), Ln is calculated to be ∼ 60 µm at coupled peak power of 16.7 W. While for silicon nanowire with same mode area, the Ln is larger than 300 µm at the same coupled peak power.
Fig. 3. Calculated normalized power density (black triangle) and calculated nonlinear parameter (red square) of different nanowires. Corresponding profiles of fundamental mode are shown above. The ZnO and CdTe nanowire has a hexagonal across section with a side-to-side diameter of 0.8 µm. The As2S3 nanowire has a circle across section with a diameter of 0.8 µm. The Si nanowire has a rectangular across section with size of 0.5×0.3 µm. The pumping wavelength is 1550 nm.(Scar bar, 500 nm)
3.2 TPA and free-carrier effects
With a bandgap of ∼ 1.5 eV (∼ 800 nm in wavelength), 1550 nm-wavelength input pulses may induce TPA and free-carrier effects inside the nanowire [24]. The propagation of an optical pulse through nanowire is governed by [37]
The carrier density is then given by
Nonlinear shifts as a function of coupled peak power are shown in Fig. 4. As coupled peak power increases, the reduction of nonlinear phase shift caused by TPA and FCD increases. For example, at coupled peak power of 10 W, there is a TPA-induce reduction of ∼0.33π and FCD-induced reduction (Δ$\varPhi$=2πLeffΔn/λ) of ∼0.13π. The results suggest that, the SPM-induced nonlinear phase shift can be severely suppressed by TPA and FCD effect at high coupled peak power.
Fig. 4. (a) Transmission spectra with different nonlinear phase shifts. The arrows denote the position of side wings. (b) Nonlinear phase shift as a function of coupled peak power. The square denotes experimental data. The black line denotes the case in absent of TPA and free-carrier effects. The blue dash line denotes the case include the effect of TPA only. The red dot line denotes the case include the effect of TPA and free-carrier dispersion (FCD).
The output peak power as a function of coupled peak power is also measured (Fig. 5(a)). At low coupled peak powers (e.g., < 7 W), the output power exhibits a linear increase. When the coupled power exceeds 7 W, the output power shows a nonlinear relationship with increasing input power and saturation with coupled peak power larger than 20 W. Considering that the SPM is an energy-conserving process, the saturation in transmission is rather explained by TPA and free-carrier absorption inside the nanowire. The transmission is simulated using a numerical modeling including the effect of TPA (denoted by red line in Fig. 5a) [37,38], which agrees fairly well with the experimental data measured at low coupled peak power (< 15 W). The deviation between theoretical prediction and experimental results at high coupled peak power (> 15 W) can be explained by the neglection of free carriers effects in theoretical calculation [1]. A blueshift due to free-carrier induced phase shift is also observed experimentally (Fig. 5(b)) [1,15,39]. As coupled peak power increases from 0.6 W to 2.8 W, the peak wavelength has shifted by about 0.5 nm. The obtained results suggest a significant influence of TPA and free-carrier effects on SPM process inside CdTe nanowires.
Fig. 5. (a) Measured output peak power (black squares) as a function of coupled peak power. The red line denotes the theoretical prediction which includes the effect of TPA, and the black line shows the result in the absence of TPA. Free-carrier effects are not included in the theoretical model. (b) Transmission spectra of an 800-nm-diameter CdTe nanowire with coupled peak power from 0.6 W to 7.1 W. Inset shows the coupled peak power depended peak wavelength (black squares) and central wavelength measured at 5 dB cross talk level (red dots).
3.3 Wavelength dependent nonlinearity
n2 at different wavelength are also measured, and the dispersion property of n2 within measured spectral range is studied experimentally. n2 of (1.3 ± 0.7) × 10−17 m2/W and (3.9 ± 1.3) × 10−17 m2/W at wavelength of 1064 nm and 1310 nm respectively are obtained using ultrashort pulses from a Ti:sapphire femtosecond laser source (Coherent, Inc.; pulse width, 200 fs; repetition rate, 76.5 MHz).
Using a Kramers-Kronig analysis, β and n2 can be predicted by [40]
The calculated β and n2 is shown in Fig. 6. The n2 obtained experimentally, which agrees well with the calculated curve, shows a negative dispersion property within measured spectral range. Considering a two-photon absorption (TPA) edge of ∼ 0.75 eV (corresponding to a wavelength of ∼ 1650 nm) for CdTe, the obtained dispersion of n2 can be explained by a nonlinear Kramers-Kronig relation between the real and imaginary part of the third-order susceptibility (χ(3)) [40].
Fig. 6. Calculated two-photon absorption coefficient and nonlinear-index coefficient of CdTe at different wavelength. The black square denotes n2 obtained from experimental data.
3.4 Supercontinuum generation base on single CdTe nanowire
By solving generalized nonlinear Schrödinger equation [41], we have also studied supercontinuum generation in a 500-nm-diameter single CdTe nanowire theoretically. 1550-nm-wavelength pulses with duration of 100 fs are used in the simulation. Benefitting from the large dispersion (∼ 2500 ps/(nm·km) at 1550 nm) (Fig. 7(a)) and nonlinear parameter (∼ 2000 W−1m−1) [22,42] of the nanowire, a spectral broadening wider than 1 µm is obtained at peak power of 10 W with propagating length less than 1 mm (Fig. 7(c)), indicating the great possibility for developing ultracompact and integratable supercontinuum laser sources using this kind of nanowires.
Fig. 7. (a) Calculate dispersion of a 500-nm-diameter CdTe nanowire, denoting two zero dispersion wavelengths at ∼ 1200 nm and 1800nm respectively. (b) Simulated spectral evolution and temporal evolution along the nanowire at a coupled peak power of 10 W. The pulse width used in the simulation is 100 fs. (c) Simulated transmission spectra of the nanowire with different length at coupled peak power of 10 W.
4. Conclusion
In summary, we have demonstrated SPM effect of ps pulses in single CdTe nanowires. The noticeable spectral broadening is observed at coupled peak power down to 0.4 W, corresponding to input energy of ∼ 400 fJ/pulse. Nonlinear-index coefficients at different wavelength within near infrared spectral range are extracted from experimental data (e.g., n2 is measured to be (9.5 ± 1.4) × 10−17 m2/W at 1550 nm). Supercontinuum generation in a single CdTe nanowire is also studied theoretically, which shows that, using 100-fs 10-W-peak-power pulses, a spectral broadening wider than 1 µm can be obtained in a CdTe nanowire shorter than 1 mm. Our results suggest that, these nanowires are promising in developing ultracompact nonlinear optical devices for future on-chip microphotonic circuits.
Funding
National Natural Science Foundation of China (11527901, 61475140, 61635009); Fundamental Research Funds for the Central Universities.
Acknowledgments
The authors thank Yixiao Gao, Jue Gong, Dawei Cai, Wei Wang, Xian Chen and Yanru Zhou for their helpful discussion in experiment preparation.
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