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Abstract
This article proposes and numerically demonstrates a widely tunable on-chip Raman soliton source based on a cascaded As2Se3 waveguide. The cascaded sub-waveguides (input and output) with varying widths act as nonlinear devices, while a tapered waveguide is arranged between them to achieve low-loss transmission. The input waveguide provides anomalous dispersion in the near-infrared band, thereby enabling the 1.96 µm source for Raman soliton self-frequency shift (SSFS) pumping. The output waveguide exhibits large anomalous dispersion and good mode confinement in the mid-infrared band thus supporting further SSFS process. A 2.29∼4.57 µm tunable Raman source is theoretically realized in this on-chip platform. This work presents a simple and easy-to-implement strategy to extend the tuning range of on-chip sources. Notably, to the best of our knowledge, this is the first demonstration of the cascading strategy for SSFS process in an on-chip platform. The proposed tunable source has great potential in integrated spectroscopy, gas sensing, and LiDAR applications.
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1. Introduction
Tunable ultrafast lasers operating in the mid-infrared (IR) region hold significant applications in spectroscopy, gas sensing, and LiDAR [1,2]. Two nonlinear frequency conversion techniques, namely optical parametric chirp pulse amplification (OPCPA) and Raman soliton self-frequency shift (SSFS) [3,4], have found application in tunable mid-IR ultrashort pulse generation. The OPCPA method converts a short-wavelength pump pulse to a mid-IR signal via second-order nonlinear effects providing advantages such as large gain bandwidth and small thermal effect. However, this method requires expensive but frail nonlinear crystal and precise dispersion management, making the implementation rather difficult. Moreover, OPCPA's intrinsic cyclic dynamic limits the pump-to-signal conversion efficiency [5]. In contrast, the Raman SSFS, utilizing the third-order nonlinear effect, provides continuous redshift of wavelength, offering easy implementation, broad spectral tunability, and high conversion efficiency. In the past few decades, SSFS based mid-IR sources have been widely investigated [6–9]. However, the demonstrations of such sources have predominantly been limited to fiber platforms, hindering their integration into on-chip platforms where they hold great potential for various applications.
The on-chip platform exhibits advantages of high compactness, low energy consuming, and flexible dispersion engineering, making it very suitable for SSFS generation. Recent developments in chip-based nonlinear photonics offer the prospect of realizing highly compact, robust and fully integrated SSFS-based tunable ultrafast sources [10–13]. Raman SSFS process in on-chip platform has been first observed in dissipative Kerr combs within a Si3N4 resonant cavity [14]. Nevertheless, due to the low nonlinear coefficient and Raman response of Si3N4 materials, the SSFS induced redshift is merely 20 nm. In contrast, chalcogenide materials exhibit strong nonlinear Kerr effect and Raman response [15], and low transmission loss in mid-IR, making them ideal platforms for SSFS generation. Recently, tunable ultrafast Raman source based on Ge28Sb12Se60 chalcogenide glass waveguides was experimentally demonstrated [16]. However, limited by the anomalous dispersion range, the tuning range of this source is only ∼230 nm. It is important to note that SSFS can only generate in the anomalous dispersion region. Extending the anomalous dispersion range in waveguides typically involve increasing the waveguide size [17–20]. However, when the waveguide size is enlarged, the first zero dispersion wavelength (ZDW) undergoes a redshift [17–20]. As a result, longer wavelength ultrafast lasers would be needed for pumping. Unfortunately, the development level of mid-IR ultrafast lasers lags significantly behind that of near-infrared lasers [21–23]. To solve this contradiction, a near-infrared source pumped on-chip SSFS scheme with ultra-wide frequency shift range needs to be proposed.
In this article, we proposed and numerically demonstrated an octave-tunable, ultrafast Raman soliton source, by employing a cascaded rib As2Se3 chalcogenide waveguide. The cascaded waveguide consists of three sub-waveguides with engineered dispersion, namely, input waveguide, tapered waveguide, and output waveguide. The input waveguide provides anomalous dispersion in the near-infrared band, thereby enabling the 1.96 µm pump source for SSFS generation. The tapered waveguide transmits the light from input waveguide to the output waveguide losslessly. The output waveguide exhibits large anomalous dispersion and mode confinement in the mid-IR band, which extends the SSFS range. As a result, a Raman SSFS-based 2.29∼4.57 µm tunable source is theoretically realized in an on-chip platform. By optimizing the waveguide length, the longest output Raman soliton wavelength reaches 4.7 µm. The proposed tunable source almost achieves wavelength coverage of an atmospheric transparent window (3∼5 µm), which has great potentials in on-chip LiDAR applications and spectroscopic sensors. Moreover, this work, to the best of our knowledge, is the first demonstration of the cascading strategy for SSFS process in on-chip platform, which provides a simple and feasible approach to extend the tuning range of on-chip Raman sources.
2. Numerical models and theories
In order to enhance mode confinement and avoid SiO2 absorption in the mid-IR band, we employ a suspended rib waveguide as shown in Fig. 1(a) as the basic platform. The suspended rib As2Se3 waveguide has been demonstrated for supercontinuum generation in Ref. [20,24], which is robust and mechanical feasible. As depicted in Fig. 1(b), an excellent quasi-TE mode confinement of the 4 µm mid-infrared light was achieved with the waveguide size of 2 × 0.8 × 0.2 µm (Width × Height × Slab thickness), while the 1 × 0.8 × 0.2 µm waveguide completely leaked the mid-IR light. Group velocity dispersion (GVD) is a crucial parameter in nonlinear photonics as solitons can only be generated under anomalous dispersion regime. Therefore, we used Lumerical Mode to calculate the GVD of the suspended waveguide. The materials Sellmeier coefficients were obtained from Ref. [25]. In the calculation, the height (H) and slab thickness (S) were kept constant as 0.8 µm and 0.2 µm, respectively, and the width (W) was adjusted from 1 to 2.4 µm. The results, plotted in Fig. 1(c), demonstrated that the first zero-dispersion wavelength redshifts with an increasing waveguide width, while the anomalous dispersion range extends with an increasing width. As a consequence, a challenge for a large range SSFS lies in the intrinsic contradiction between short-wave pumping (via decreasing the width) and large tuning range (via increasing the width).
Fig. 1. (a) The schematic diagram of the suspended rib As2Se3 waveguide. (b) Electric field of the fundamental quasi-TE mode at 4 µm. (c) The simulated GVD characteristics of the suspended waveguide with varying width. (d) The structure of the cascaded waveguide. (e) The GVD curve of the waveguides W1 and W3.
We designed a cascaded As2Se3 waveguide, depicted in Fig. 1(d), which is comprised of three segments. The input waveguide (W1) has a width of 1 µm while the output waveguide (W3) possesses a width of 2 µm. The middle waveguide (W2) is a tapered waveguide whose width varies linearly from 1 to 2 µm, and it is used to couple light from the input waveguide W1 to the output waveguide W3 with low transmission loss. All the waveguides have the same heights and slab thicknesses of 0.8 µm and 0.2 µm, respectively. Such cascaded waveguide structure can be easily realized by a specific mask design. The GVD characteristics of W1 and W3 are plotted in Fig. 1(e). At the pump wavelength of 1.96 µm, the waveguide W1 exhibits a large anomalous dispersion, which is suitable for SSFS generation. At the wavelength beyond 3.5 µm, the mode confinement of waveguide W1 decreases dramatically, and its dispersion evolves into normal dispersion. As for the waveguide W3, it maintains large anomalous dispersion and high mode confinement at wavelengths beyond 3.5 µm (see Fig. 1(b)), which can support the SSFS on the 4∼5 µm band. The transmittance of 3.5 µm mid-IR light of the tapered waveguide W2 was calculated using Lumerical EME solver, which is plotted in Fig. 2(a). It can be seen that when the taper length beyond 4 microns, the mid-IR light can be transmitted from W1 to W3 without additional loss (transmittance > 0.99). The nonlinear coefficient γ, which characterizes the intensity of waveguide nonlinearity, can be calculated using the formula: γ = (2πn2)/λAeff, where n2 is the nonlinear refractive index of As2Se3-based chalcogenide glass (2.4 × 10−17 m2/W) [25], and Aeff represents the effective mode field area that is dependent on wavelength. Figure 2(b) plots the γ values of waveguides W1 and W3. At shorter wavelengths, the waveguide W1 exhibits a higher γ value. But as the wavelength increases to around 3400 nm, the γ value of waveguide W3 becomes higher. This is because the waveguide W1 leaks the mid-IR light, increasing the mode field area and resulting in a lower γ value. For the tapered waveguide W2, we use the nonlinear coefficient and GVD of its intermediate cross-section to approximate the whole taper, which is feasible due to the very short tapered length of 5 microns. The overall cascading SSFS scheme is depicted in Fig. 2(c). Driven by the SSFS effect in W1 waveguide, the input pulse is initially redshifted to 3.5 µm, which is limited by the anomalous dispersion range and the lower mode confinement of waveguide W1. The tapered waveguide W2 enables lossless mode field conversion, and the waveguide W3 provides mid-IR mode confinement ability and large anomalous dispersion to support further SSFS process.
Fig. 2. (a) The transmittance of the tapered waveguide with varying length. (b) The nonlinear coefficients γ and loss of waveguides W1 and W3. (c) The schematic diagram of the cascading strategy for extending the SSFS range.
The evolution of the fundamental TE mode in the proposed cascaded waveguide can be modeled by the generalized nonlinear Schrödinger equation (GNLSE):
In which fR represents the fractional contribution to nonlinear response. hR(t) is the delayed Raman response, which can be calculated using the damped oscillations described in Eq. (3). For As2Se3 material, fR = 0.148, τ1 = 23 fs, τ2 = 164.5 fs [20].
The split-step Fourier transformation method and fourth-order Runge–Kutta numerical method is used to solve the GNLSE. The pump pulses at 1960nm with the width of 60 fs are modeled as a Gauss field profile during the simulation, which was used for chalcogenide waveguide SSFS simulation in Ref. [17]. During the simulations, 0.8 µm step length, 216 discretization points, and up to the 12th order of dispersion coefficients are adopted to ensure the calculation accuracy.
3. Results and discussions
To investigate the SSFS process in the cascaded waveguide, we firstly conducted simulations of the nonlinear evolution of pulses in a cascaded waveguide with lengths of L1 (4 mm), L2 (5 µm), and L3 (12 mm) (See Fig. 2(c)). For the W1 waveguide, the frequency and time domain characteristics of the soliton pulse are presented on the left side of Fig. 3(a) and (b). The pump threshold is as low as 2.4 pJ, corresponding to a generated soliton wavelength of 2.14 µm. As the input pulse energy (PE) is increased to 240 pJ, the Raman soliton continuously redshifts to 3.56 µm. Further increasing the pump energy to 300 pJ does not result in a continued redshift, which is limited by the second ZDW and a dramatic increased loss in the longer wavelength. The frequency and time domain spectra after the pulse propagating the cascaded waveguide are depicted on the right side of Fig. 3(a) and (b). For an input pulse with 2.4 pJ energy, the output 2.14 µm Raman soliton from waveguide W1 is further redshifted to 2.29 µm. Due to a relatively small GVD value at 2.14 µm (∼40 ps/nm/km) of waveguide W3, the output spectrum resembles a supercontinuum. With input PE increased to 240 pJ, the soliton envelope becomes clear, and the wavelength is further redshifted from 3.56 to 4.51 µm. When the input PE is further increased to 300 pJ, the output soliton wavelength from W3 is further shifted to 4.57 µm. The additional 60 nm wavelength shift is due to the increased PE of the input 3.56 µm Raman soliton. The SSFS induced wavelength shifts after W1 and the overall cascaded waveguide are plotted in Fig. 4. For different PE intervals, the wavelength shift velocity is different, and the overall trend is gradually slowing down. This is caused by the decreased nonlinear coefficient and the increased loss. The velocity variation in a small PE range can be attribute to the competition between the fundamental-order soliton and the higher-order solitons [17]. Through waveguide cascading, we achieved an additional redshift of ∼1 µm along with an expanded turning range from 1.42 µm (2.14∼3.56 µm) to 2.28 µm (2.29∼4.57 µm).
Fig. 3. (a) Spectral and (b) temporal evolution of the Raman soliton as the pump pulse energy increases from 2.4 to 300 pJ.
The dynamics of spectral and temporal evolution in the cascaded waveguide, under 300 pJ pump energy, are depicted in Fig. 5(a) and (b). In waveguide W1, the input pulse is firstly broadened through nonlinear self-phase modulation (SPM). Then it splits and forms a Raman soliton branch and a blue-shifted Cherenkov branch, with total photon momentum preservation. After the pulse is propagated for 4 mm in the waveguide W1, the Raman soliton redshifts to ∼3.56 µm. The soliton pulse characteristics are shown in Fig. 5(c) and (d), the spectral full-width at half-maximum (FWHM) is 102 nm and a sech2 fit of temporal curve indicates a pulse duration of 67 fs. The calculated pump-to-soliton conversion efficiency, defined as the energy ratio of the 1st order Raman soliton pulse to the input pulse, is 13.4%. The low conversion efficiency is attribute to the high waveguide loss and ultrahigh soliton number N of ∼51 in the waveguide W1($N = \sqrt {\mathrm{\gamma }{\textrm{P}_0}{\textrm{T}_0}^2/|{{\beta_2}} |} $) [28]. Subsequently, the pulse envelope containing the Raman soliton propagated through the tapered waveguide W2 into the waveguide W3. The original soliton equilibrium between SPM and dispersion is broken at first. After transmitting a critical length of 500 microns, the Raman soliton reforms at 4 µm, and continuously redshifts to 4.57 µm. The output soliton pulse characteristics are presented in Fig. 5(e) and (f), revealing a spectral FWHM and sech2-fitted pulse duration of 152 nm and 69 fs, respectively. The overall pump-to-soliton efficiency of the cascaded waveguide stands at 8.5%. Notably, the conversion efficiency between solitons, defined as the energy ratio of the output 4.57 µm Raman soliton pulse to the 3.56 µm Raman soliton pulse, amounts to 63.4%. This high efficiency arises from a reduced soliton number N of 4.6 and low loss in waveguide W3, indicating the feasibility and efficiency of extending the SSFS range by waveguides cascading.
Fig. 5. Dynamics of (a) spectral and (b) temporal Raman SSFS evolution as the pulse propagates along a 16 mm long cascaded waveguide under 300 pJ pump energy. (c) Spectral and (d) temporal pulse characteristics of the fundamental soliton output from W1. (e) Spectral and (f) temporal pulse characteristics of the fundamental soliton output from W3.
The simulations of mid-IR femtosecond lasers direct pumping the waveguide W3 were conducted. The waveguide length is fixed as 16 mm, which is the same as the cascaded waveguide (4 + 12 mm). The pulses with the same duration of 60 fs and different center wavelength of 2.4, 2.6, 2.8 and 3 µm are inputted into this waveguide. With the input PE increased to 300 pJ, their wavelength tuning range is plotted in Fig. 6(a). We can obtain that the 1.96 µm pumped cascaded waveguide exhibits the largest wavelength tuning range. Moreover, the tuning range completely covers the 2.4∼2.8 µm pumping scheme. It is worth mentioning that compared with these 2.4∼3 µm ultrafast lasers, 1.96 µm near-infrared femtosecond laser is the most economical, mature and accessible pump source.
Fig. 6. (a) Comparison of the SSFS range under 0∼300 pJ PE with different pump source. (b) Center wavelength of output Raman soliton and (c) dynamics of spectral evolution of cascaded waveguides with different length L1 under 300 pJ PE.
The waveguide length is a critical parameter for SSFS process. In general, the amount of wavelength shift is positively correlated with the length of the waveguide. However, in the proposed cascading scheme, the output wavelength and waveguide length are not entirely positively correlated. This is caused by the significant loss of waveguide W1. Although an increase in length L1 provides a greater wavelength shift, it also reduces the pulse energy that is input into the waveguides W2 and W3. Herein, the effect of length L1 on the SSFS process has been numerically investigated. In the simulations, the total length was kept constant at 16 mm, and the length L1 was increased from 2 mm to 5 mm in 0.5 mm steps, corresponding to a decreased length L3 from 14 mm to 11 mm. The output wavelength and spectral dynamics of cascaded waveguide with varying length are plotted in Fig. 6(b) and (c), respectively. We can obtain that with a 300 pJ PE, the longest output wavelength of 4.7 µm can be obtained at the cascaded waveguide with 2.5 mm L1. Below this length, waveguide W1 cannot support sufficient Raman SSFS, while above this length, transmission loss becomes the primary limiting factor for the frequency shift.
Table 1 provides a detailed comparison of SSFS-based tunable sources. In the fiber platform, experimentally and theoretically achieved maximum wavelengths are 7.2 µm and 4.8 µm, respectively. Both of the demonstrations using ultrafast mid-IR pump sources (4.1 and 2.8 µm), which poses challenges to the implementation of the SSFS system. Compared with the fiber-based platform, the on-chip platform exhibits advantages of high compactness, low energy consuming, and the most important, flexible dispersion engineering, making it very suitable for SSFS generation. While relevant demonstrations are still generally in the theoretical stage, the maturity of chalcogenide wafer preparation technology and growing demands for on-chip tunable sources suggest that this technology will make significant progress in the next few years. Among different on-chip SSFS schemes available, our proposed cascading strategy is notable for offering the largest wavelength tunability and the longest wavelength, which has great potential in the on-chip SSFS system optimization.
Table 1. Comparison of Raman SSFS-based mid-IR sources
4. Conclusion
In summary, we numerically demonstrated a novel cascaded strategy for extending the SSFS range in the chalcogenide waveguide. The cascaded waveguide allows near-infrared pump source for exciting mid-IR SSFS process thus reducing the pumping cost and making the system easier to implement. As a result, a 2.29∼4.57 µm octave tunable Raman source is theoretically realized in an on-chip platform by 1.96 µm femtosecond source pumping. Moreover, the center wavelength of the Raman soliton can further redshift to 4.7 µm by optimizing the waveguide length. To the best of our knowledge, this is the longest wavelength achieved in various near-infrared source pumped Raman SSFS scheme. This work presents a simple and feasible approach to extend the tuning range of mid-IR on-chip SSFS-based sources. The extended range almost achieves wavelength coverage of an atmospheric transparent window (3∼5 µm), which has great potential in highly integrated spectroscopic sensors and LiDAR applications.
Funding
Sichuan Province Science and Technology Support Program (2023NSFSC033, 2023NSFSC1964); Fundamental Research Funds for the Central Universities (ZYGX2019Z012, ZYGX2020KYQD003, ZYGX2021YGCX014); National Natural Science Foundation of China (61421002, 62005040, U20A20210).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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