On-chip mid-IR octave-tunable Raman soliton laser

Zhao Li; Fengbo Han; Zhipeng Dong; Qingyang Du; Qingyang Du; Qingyang Du; Zhengqian Luo; Zhengqian Luo; Zhengqian Luo

doi:10.1364/OE.462425

1. Introduction

The past decade has witnessed the fast development in photonic chip-scale ultrafast lasers as well as their applications in communication, computation, metrology, and bio-chemical sensing [1–8]. Particularly, in molecular sensing, mid-IR spectroscopy has been regarded as the gold standard in identifying a molecule via their extremely high specificity in “fingerprinting” molecular vibration modes [9]. A broadband or continuously tunable mid-IR light source is thus essential. To date, the generation of a broadband mid-IR ultrafast laser mostly relies on nonlinear optical interactions. A parametric process, four wave mixing has been widely leveraged in the formation of Kerr frequency combs [9–19]. Kerr combs are highly stable and precise in comb teeth lines and pulse shape and applications in methane gas sensing has been recently demonstrated [9]. However, such process requires a mid-IR continuous wave laser as the pump source and the frequency locking of the pump source to the cavity resonance is rather challenging. Similarly, supercontinuum generation broadens an initial high-power femto-second (fs) pulse to over several octave-spanning white light source via high-order nonlinear interactions [20–28]. Nevertheless, the spectral shape of a supercontinuum is highly sensitive to environment conditions and the energy partition in a small wavelength window is limited, and thus this process is energy inefficient. A non-parametric process, Raman soliton self-frequency shift (SSFS) is yet another mechanism to acquire mid-IR ultrafast light source [29–31]. Based on intra-pulse Raman scattering, it gradually red-shift the center wavelength of a Raman soliton in a cascading manner. Ultimately, a continuously wavelength tunable light source is readily to be realized by simply adjusting the pump pulse power. Unlike Kerr comb, SSFS does not require a resonant cavity and thus is much easier to implement. In addition, the coherence and the energy conversion efficiency are orders of magnitude higher than supercontinuum generation, which made SSFS an ideal process to realize mid-IR light sources.

In this article, we theoretically investigated and proposed an octave-tunning mid-IR ultrafast soliton source. We chose Ge₂₈Sb₁₂Se₆₀ (GeSbSe) chalcogenide glass as the waveguide platform by fully taking advantage of its strong optical nonlinearity and broadband transparency in the mid-IR [32, 33]. In fact, our previous work has successfully demonstrated the first near-IR on-chip ultrafast laser source based on Raman SSFS, continuously tunable over 200 nm spectral range from 1589 to 1807 nm [34]. In this work, we expanded its spectral tuning range towards mid-IR and theoretically designed a suspended waveguide device that achieved an octave tuning from 1.96 µm to 3.98 µm. The threshold pump energy is merely 3 pJ, featuring an order of improvement than that in a chalcogenide glass fiber [35]. The effect of the initial chirp parameter of the pump pulse were also investigated. We find that a chirpless pump pulse is optimum in producing the longest tuning range. Our work envisioned a compact continuously tunable laser source for mid-IR high specificity spectroscopic sensing system.

2. Device design and dispersion engineering

Considering SiO₂ starts to absorb light beyond 3.5 µm, we chose Ge₂₃Sb₇S₇₀ (GeSbS), another commonly used IR chalcogenide glass, as our waveguide cladding material. We initially designed four different waveguide structures: a symmetrically cladded channel waveguide, a regular channel waveguide, a rib waveguide and a suspended rib waveguide, whose structures are schematically drawn in Fig. 1(a) inset. We simulated their TE guided mode profiles using Lumerical MODE, as shown in Fig. 1(b) to Fig. 1(e), respectively. Group velocity dispersion (GVD) curve of optimized waveguide geometry corresponding to these four structures were calculated and displayed in Fig. 1(a). Evidently, for symmetrically cladded waveguide (structure 1), the GVD stays in the normal dispersion region, thus unsuitable for SSFS generation. A positive anomalous GVD was found in the uncladed channel (structure 2), however, the second zero dispersion wavelength (ZDW) is merely slightly above 2.5 µm, limiting the SSFS range. It is interesting to find that having less modal confinement in the air cladding reduces the overall modal anomalous dispersion, as is evidenced in the GVD curve by adding a slab to form a rib waveguide (structure 3). Thus, we concluded that an all-air-cladded suspended structure (structure 4) is the optimum choice in such waveguide system for longest SSFS generation. It’s worth pointing out that this all-air-cladded suspended structure is mechanically feasible [36]. In addition, chalcogenide glasses have been made into flexible and stretchable photonic devices [37, 38], evidencing its robustness against small stresses. The GVD curve in Fig. 1(a) also illustrated that the suspended structure has the largest anomalous dispersion and the longest wavelength interval between the two ZDWs, both of which are essential to achieve longest possible SSFS shifting range. For the subsequent section, we focused on the optimization of the suspended waveguide geometry to achieve the largest SSFS tuning range.

Fig. 1. (a) Group velocity dispersion curve of waveguide structures 1-4, inset: schematically drawing of the four waveguide structures. (b)-(e): simulated modal electric field distributions of the fundamental quasi-TE mode.

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We performed a systematic study of the modal GVD by adjusting the waveguide widths, slab thicknesses and rib height to yield the largest SSFS tuning. The results were plotted in Fig. 2. Figure 2(a) showed the dispersion profiles with different waveguide slab thickness, at a fixed waveguide width and rib height. The black contours marked the trajectory of the ZDW points. It is obvious to learn that with decreasing slab thickness, both GVD and the ZDW separation increase. However, we want to emphasize that the slab is essential in keeping the integrity and robustness of the entire suspended structure. Therefore, we decided to choose the slab thickness to be 0.2 µm without risking structural collapsing. Next, we consider the rib height. Figure 2(b) plotted the effect of rib height on the GVD curve. The results clearly indicated an increased rib height yields larger GVD and ZDW separation. As is already demonstrated in the literature, where a suspended slab rib ratio of 1:4 was successfully fabricated [36]. We believe choosing a rib height of 0.8 µm is within its mechanical robustness tolerance range. Finally, the effect of waveguide width is displayed in Fig. 2(c). As the waveguide widens, the separation between the two ZDW point increases, yet the GVD value shrinks, demanding higher pump threshold power. We want to emphasize that it is essential to keep the pump laser wavelength lies in the anomalous dispersion to initiate SSFS process, we therefore adopted a waveguide width of 1.2 µm to keep the largest ZDW separation while maintaining reasonably high anomalous GVD at the pump wavelength. The ultimate device layout was presented in Fig. 2(d). It has a slab thickness of 0.2 µm, rib height of 0.8 µm and rib width of 1.2 µm. Such device was readily to be fabricated by previous established protocols with opening wet etch holes at the waveguide vicinity to undercut the oxide below [36].

Fig. 2. Dispersion contour plot of the suspended waveguide structure: (a) fixed waveguide width and rib height of 1.2 and 0.8 μm; (b) fixed waveguide width of 0.8 μm and slab thickness of 0.2 μm; (c) fixed rib height and slab thickness of 0.8 μm and 0.2 μm, respectively. The black contours indicate the trajectory of the zero dispersion points. (d) A 3D drawing illustrating the ultimate waveguide structure.

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3. Raman soliton self-frequency shift

3.1 Theory

Numerical simulations were performed on the fundamental TE mode propagation using the generalized nonlinear Schrödinger equation (GNLSE) to model the electric field envelope A (z, t) with the following expression [39]:

(1)$$\frac{{\partial A}}{{\partial z}} ={-} \frac{\alpha }{2}A + \sum\limits_{k \ge 2} {\frac{{{i^{k + 1}}}}{{k!}}} {\beta _k}\frac{{{\partial ^k}A}}{{\partial {t^k}}} + i\gamma \left( {1 + \frac{i}{{{\omega_0}}}\frac{\partial }{{\partial t}}} \right)\left( {A(z,t)\int_{ - \infty }^{ + \infty } R ({{t^\prime }} ){{|{A({z,t - {t^\prime }} )} |}^2}\textrm{d}{t^\prime }} \right)$$

In this wave equation, on the righthand side, the first term considers the propagation loss and the second term models all orders of dispersion effect on the pulse. The third term includes nonlinear light-matter interactions, here we primarily consider Kerr and Raman effects. A is the slowly varying amplitude of the pulse envelope, z is propagation distance, and t denotes relaxation time. α stands for the waveguide propagation loss. We adopted a 4 dB/cm α value from our previously reported work [34]. In addition, ω₀ is the center frequency of the input pulse, β_k is the k’s order dispersion coefficient, γ represents the nonlinear parameter, and R(t) denotes the nonlinear response function.

β_k here was determined by taking the k’s derivative of the propagation constant with respect to ω:

(2)$${\beta _k} = {\left( {\frac{{{\textrm{d}^k}\beta }}{{\textrm{d}{\omega^k}}}} \right)_{\omega = {\omega _0}}}({k = 0,1,2 \cdots } )$$

we considered in total of 9 orders of dispersion in our simulations to sufficiently approximate the true dispersion curve.

γ was calculated via:

(3)$$\gamma = \frac{{{\omega _0}{n_2}({{\omega_0}} )}}{{c{A_{\textrm{eff}}}({{\omega_0}} )}} = \frac{{2\pi {n_2}({{\omega_0}} )}}{{\lambda {A_{\textrm{eff}}}({{\omega_0}} )}}$$

A_eff is the effective modal area, c is velocity of light, and n₂ denotes the nonlinear refractive index. Both A_eff and n₂ are frequency dependent. For GeSbSe glass, n₂ is equal to 5.1×10⁻¹⁸ m²/W at 1960nm [40], and A_eff is acquired through integration over the modal field distribution:

(4)$${A_{\textrm{eff}}} = \frac{{{{\left( {\int\!\!\!\int {{{|{F({x,y} )} |}^2}\textrm{d}x\textrm{d}y} } \right)}^2}}}{{\int\!\!\!\int {{{|{F({x,y} )} |}^4}\textrm{d}x\textrm{d}y} }}$$

F (x, y) represents the transverse electric field amplitude of the fundamental TE mode.

The nonlinear response function R(t) includes both the electronic and vibrational (Raman) contributions. Assuming that the electronic contribution is nearly instantaneous, R(t) is then simplified to Eq. (5):

(5)$$R(t )= ({1 - {f_\textrm{R}}} )\delta (t )+ {f_R}{h_\textrm{R}}(t )$$

where f_R denotes the nonlinear polarization contribution from the delayed Raman response, δ(t) is the Dirac delta function. The Raman response function h_R(t) is responsible for the Raman gain. Adopting the damped oscillations model, h_R(t) is expressed by Eq. (6) [41]:

(6)$${h_\textrm{R}}(t )= \frac{{\tau _1^2 + \tau _2^2}}{{{\tau _1}\tau _2^2}}\exp \left( { - \frac{t}{{{\tau_2}}}} \right)\sin \left( {\frac{t}{{{\tau_1}}}} \right)\Theta (t )$$

τ₁ and τ₂ are the time constants related to material phonon vibration and atomic vibration frequencies, respectively, and Θ(t) represents the Heaviside step function. For GeSbSe, these parameter values are: f_R = 0.148, τ₁ = 23 fs, τ₂ = 164.5 fs [34, 42].

We substitute Eq. (5) into the integral of GNLSE:

(7)$$\begin{aligned} &\int_{ - \infty }^\infty R ({{t^\prime }} ){|{A({z,t - {t^\prime }} )} |^2}\textrm{d}{t^\prime } = \int_{ - \infty }^\infty {({({1 - {f_\textrm{R}}} )\delta (t) + {f_\textrm{R}}{h_\textrm{R}}(t)} )} {|{A({z,t - {t^\prime }} )} |^2}\textrm{d}{t^\prime }\\ &= ({1 - {f_\textrm{R}}} )|A(z,t){|^2} + {f_\textrm{R}}\int_{ - \infty }^\infty {{h_\textrm{R}}} ({{t^\prime }} ){|{A({z,t - {t^\prime }} )} |^2}\textrm{d}{t^\prime } \end{aligned}$$

Equation (7) transforms the complex integral into the convolution between h_R(t) and A (z, t), making the calculation of the nonlinear term possible to solve the convolution by the simple Fourier transform. The GNLSE is solved with the Split-Step Fourier Transformation Method using MATLAB script in our simulation.

3.2 Results and discussion

We performed the simulation with an initial central wavelength of 1960 nm and a Gaussian pulse shape with a width of 60 fs in the suspended GeSbSe chalcogenide glass waveguide. First, we considered three different pumping scenarios by locating the pump wavelength at the anomalous dispersion, zero dispersion and normal dispersion, respectively. We fixed the pump pulse wavelength and energy to be 1.96 μm and 60 pJ. By gradually increasing the waveguide width, its corresponding GVD parameter shifted from anomalous to normal dispersion. The generated spectral and time domain pulse characteristics were presented in Fig. 3(a) and (b). For the 1.2 μm wide waveguide, a clearly distinguishable soliton pulse was observed both spectrally and temporally at a center wavelength of 2983 nm. When waveguide width increased to 1.6 μm, a broadband supercontinuum was generated, while the 2.4 μm wide waveguide also produces a supercontinuum yet with narrower bandwidth and flatter spectral shape. The results confirms that an anomalous dispersion condition at the pump wavelength is critical for Raman SSFS processes.

Fig. 3. (a) Spectral and (b) temporal domain simulation results under the same pump pulse energy of 60 pJ in various waveguide width.

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Next, we focused on the influence of pump pulse energy on Raman SSFS. The optimized waveguide geometry was deployed in this simulation. As shown in Fig. 4, we observed SSFS start to progress at a pump energy of 3 pJ. When the pump pulse energy increased from 3 pJ to 180 pJ, the center wavelength of the primary Raman soliton continuously shifted towards long wavelength direction and stops at to 3980 nm. Further increase the pump energy to 300 pJ did not produce longer shifting range. This range is mainly limited by the second ZDWlocation. Meanwhile, it is interesting to find that a secondary soliton formed at 60 pJ pump energy and continuously shifted towards 3980 nm. We also observed a competition effect between the primary and secondary solitons, this competition could explain the reduced shifting speed of the primary soliton at 150 pJ and the sudden jump at 180 pJ. As pump pulse energy increases from 3 pJ to 150 pJ, the primary Raman soliton generation efficiency, defined as the energy ratio between the primary Raman soliton pulse to the total pulse energy, reduces from 78% to 31%. Then, when the pump energy further increases to 180 pJ, the corresponding efficiency improves to 40%. This variation of efficiency is another consequence from the competition.

Fig. 4. (a) Spectral and (b) temporal pulse evolution of the Raman soliton generated in the optimized structure as the pump pulse energy grows from 3 to 300 pJ.

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The spectral and temporal evolution dynamics under 180 pJ pump energy was simulated and plotted in Fig. 5. Once the pump was injected into the waveguide, the spectrum initially broadened through nonlinear self-phase modulation. After propagating pass the critical length of 0.5 mm, a distinct Raman soliton branch formed. Simultaneously, a blue shifted branch was also generated via Cherenkov radiation, conserving the total photon momentum. This phenomenon was also evidenced from the temporal evolution, where the Raman branch and Cherenkov branch dissociate and formed a stable pulse when exceeding the critical length. The Cherenkov branch quickly decays in intensity due to its dispersive nature. It worth pointing out that the SSFS process was mainly in effect in the first 10 mm waveguide. The cumulated chirping of the pulse reduced its peak power, prohibiting further SSFS. The long waveguide length purified such Raman soliton and increased the conversion efficiency.

Fig. 5. (a) Sepctral and (b) temporal Raman SSFS evolution dynamics as the pulse propagates along the 24 mm long waveguide under 180 pJ pump energy.

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Pulse characteristic study of a 180 pJ pump energy was presented in Fig. 6. Initially, the generated SSFS had a pulse duration of 18 fs. As it propagated through the waveguide, the pulse broadened in time domain progressively and reached 155 fs at a waveguide length of 24 mm. The individual pulse characteristic was displayed in Fig. 6(a) inset. It has a perfect sech² soliton temporal pulse shape and an 89 nm spectral width. Finally, the influence of the initial chirp parameter C on SSFS was also investigated. For linearly chirped Gaussian pulses, the chirp parameter C is the first derivative of the frequency chirp with respect to normalized time [43]. As shown in Fig. 6(b), it is conclusive that a chirp free pulse produces the longest SSFS.

Fig. 6. (a) Pulse duration of Raman soliton along the 24 mm waveguide. Inset: exemplary individual Raman soliton pulse characteristics. (b) Raman shift study in three different initial chirp parameters under the same waveguide geometry.

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Our simulation results clearly indicated the generation of a secondary soliton, which compromise the purity of Raman soliton source. Therefore, it is necessary to optimize the efficiency of Raman soliton source. Evidences has shown that the efficiency of SSFS can be improved by reducing the soliton number, thereby generating as few solitons as possible. A pump source generating shorter pulses or increasing the level of anomalous dispersion will reduce the soliton number [34, 44]. The comparison of mid-IR on-chip light emitter technologies is shown in Table 1. For both Kerr comb and supercontinuum generation, though they offer superior wavelength covering range, their wavelength partition is energy inefficient. We instead leverage soliton self-frequency shift to progressively red-shift pump pulse wavelength into mid-IR, allowing a highly efficient continuous tuning from 1.96 µm to 3.98 µm. Our proposed waveguide structure can be pumped using a home-built ultra-compact 1.96 μm mode-locked fiber laser as our previously demonstrated work [34]. With the integration of the developing on-chip mode-locking technology, we envision a fully on-chip tunable Mid-IR soliton source. Our work opens up a practical route toward a fully integrated, compact photonic chip-scale platform for mid-IR ultrafast optics. We believe that these initial envisions also herald a lot more thrilling applications in optical ranging, detection, spectroscopy and sensing.

Table 1. Comparison of mid-IR on-chip light emitter technologies

View Table

4. Conclusion

In conclusion, we systematically investigated Raman SSFS process for GeSbSe chalcogenide glass in the mid-IR. By fully exploit dispersion engineering, we proposed a suspended waveguide structure that yields over an octave tuning, from 1.96 µm to 3.98 µm, mid-IR soliton source. The threshold pump power is only 3 pJ. It is also found that a chirpless pump pulse gives the maximum SSFS. Our work envisions a practical solution to continuously tunable mid-IR ultrafast laser sources with possible applications towards sensing and spectroscopy.

Funding

Natural Science Foundation of Fujian Province (2022J02007); Shenzhen Science and Technology Innovation Program (JCYJ20210324115813037); National Science Fund for Distinguished Young Scholars (62022069); Fundamental Research Funds for the Central Universities (20720200068); National Key Research and Development Program of China (2020YFC2200400).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are available upon reasonable request from the corresponding authors.

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Technologies	Waveguide material	CW optical pumping	Wavelength range (µm)	Soliton pulse	Wavelength tunable	[References] year
Kerr frequency comb	Silicon	√	2.4-4.3	√	×	[13] 2016
	Silicon nitride	√	1.3-2.0	√	×	[18] 2017
	Silicon nitride	√	1.46-1.68	√	×	[19] 2022
Supercontinuum	Ge-rich SiGe	×	3-13	×	×	[20] 2020
	GeAsSe	×	2-10	×	×	[28] 2016
	Silicon	×	2-5	×	×	[36] 2018
SSFS	GeSbSe	×	1.96-3.98	√	√	This work

On-chip mid-IR octave-tunable Raman soliton laser

Abstract

1. Introduction

2. Device design and dispersion engineering

3. Raman soliton self-frequency shift

3.1 Theory

3.2 Results and discussion

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Tables (1)

Equations (7)

Optics Express