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Abstract
Bragg-soliton dynamics in a 2-stage ultra-silicon-rich-nitride (USRN) chip-based device, consisting of a cladding-apodized modulated Bragg grating (CMBG) stage and a USRN channel waveguide stage, is studied and optimized for enhanced supercontinuum generation. We observe that the enhancement is strongly dependent on the Bragg-soliton effect temporal compression developing in the CMBG stage, which is linked to both device and input pulse parameters. With the optimal parameter combination, a supercontinuum spanning 610 nm at the −30 dB level is experimentally demonstrated in the 2-stage USRN device, representing a 5× enhancement compared to that in a reference waveguide. Good agreement is obtained between the experimentally measured supercontinuum and simulations based on the generalized nonlinear Schrödinger equation and is consistent with design rules based on Bragg soliton compression. This device provides an encouraging path to generate supercontinuum in compact chip-based platforms, which does not need ultrashort, femtosecond scale pulses, greatly relaxing the pulse width and pulse power requirement.
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1. Introduction
Supercontinuum generation (SCG), an interesting nonlinear photonic process that is the basis of broadband light sources, has been widely investigated ever since its first demonstration in the 1970s [1], developing over the years to span applications in optical frequency combs [2,3], microscopy [4], and metrology [5]. It is well known that broadband SCG in optical waveguides depends on the strong nonlinearity and dispersion profiles that are favorable for efficient spectral broadening effects, relying on the interplay of well understood nonlinear propagation effects, such as self-phase modulation (SPM), soliton fission, and dispersive wave generation. A strong optical nonlinearity facilitates the generation of new frequencies, and the ability to tailor dispersion is critical for various aspects of SCG.
One direction of exploration for maximizing the optical nonlinearity for SCG has involved studies into on-chip platforms, offering significant reductions in footprint and possibilities for tailoring the dispersion by the design of the waveguide geometry, including Si [6–10], amorphous Si [11,12], Si3N4 [13–15], lithium niobate [16], tantala [17], and AlGaAs [18,19]. Among the platforms mentioned above, Si is the most popular because of its compatibility with the traditional CMOS process but its small bandgap (1.12 eV) causes unfavorable two-photon absorption (TPA) at near-infrared wavelengths. In Si3N4-chip based devices, the TPA can be neglected, however, the spectral broadening at low power levels in these devices is limited because of its low Kerr nonlinearity (∼2.4 × 10–15 cm2 W–1) [20]. Though AlGaAs has a high Kerr nonlinearity (on the order of 10−13 cm2 W−1) [21] and lacks TPA at telecommunication wavelengths, it’s not CMOS-compatible, making it less straightforward to be integrated with CMOS-based electronics.
In contrast, ultra-silicon-rich-nitride (USRN: Si7N3) offers very desirable properties for on-chip SCG, in that (i) it has a large bandgap (2.1 eV), thus eliminating TPA in telecommunication wavelengths [22–24]; (ii) it holds a high Kerr nonlinearity of 2.8 × 10–13 cm2 W–1 [22,25], 100 times larger than that of Si3N4, which is essential for enhanced nonlinear effects; (iii) it is CMOS-compatible and therefore can be easily integrated with electronics; and (iv) its linear refractive index at 1550 nm is 3.1 (measured using Fourier Transform Infrared Spectroscopy), creating a large refractive index contrast with the SiO2 cladding (1.44), resulting in tight light confinement in the waveguide core area [22,26], making it easy to engineer both the sign and the magnitude of the waveguide dispersion by tuning the waveguide geometry.
The second key ingredient involved in the SCG process is dispersion, which is of great significance in the generation and evolution of SCG [27]. Various techniques have been introduced that yield enhancement in the supercontinuum, for example, waveguide dispersion profiles that are flat and low over a broad wavelength range [28,29], situating the pump close to the zero-dispersion wavelength [30], or even dispersion profiles that possess more than one zero-dispersion wavelengths to facilitate the expanded supercontinuum bandwidth via dispersive wave generation on both sides of the spectrum [31,32]. Wideband supercontinuum generation has been demonstrated in a As2S3 chalcogenide, benefitting from an anomalous dispersion at near-infrared wavelengths by tuning its transverse waveguide dimensions [33]. A 2-octave broadband supercontinuum in tapered fibers has been demonstrated, taking advantage of the carefully engineered dispersion spectra by immersing the tapered fiber in heavy water [34]. Enhanced supercontinuum generation in highly nonlinear fibers has also been demonstrated to benefit from a well-tailored dispersion distribution induced through UV exposure, which can be used to increase the core refractive index step, leading to a nonuniform dispersion distribution along the length of the continuum fiber, thereby altering the supercontinuum generation properties [35,36].
A different approach to enhance SCG involves harnessing dispersion induced by resonant structures, such as on-chip Bragg gratings [37]. Indeed, our previous work has shown that the strong Bragg grating induced dispersion at wavelengths near the blue-edge of the stopband of a nonlinear Bragg grating may cause Bragg soliton compression [38] that leads to considerable enhancements in the generated output spectrum [37,39,40]. In that the dispersion is strongly frequency-dependent, tuning the pulse-stopband detuning allows control of the Bragg soliton dynamics, including the pulse compression ratio which allows for variations in the output bandwidth. Importantly, circumventing the need for ultra-short, sub-picosecond pulses is availed by this approach, and pulses on the picosecond time scale may be used for SCG. In our previous work, a 4.3× spectral enhancement was demonstrated in a 7-mm long device, including a CMBG stage of 1 mm and a waveguide staged of 6 mm, using picosecond pump pulses of 1.7 ps pulses with a peak power of 5.5 W [37], but the generated spectrum was limited to 340 nm due to the roughly selected device dimensions and pulse conditions which were not optimized to maximize the Bragg-soliton effects induced spectral enhancement.
Following our initial demonstration, in this work, we examine the critical design parameters required to fully harness the Bragg soliton dynamics for the enhancement of the supercontinuum generation. Our study reveals that judicious design of the nonlinear grating is critical for optimal supercontinuum enhancement conferred by Bragg soliton dynamics. We unveil the underlying physics which lead to this enhancement, discussed with respect to the temporal properties of the pulse evolution and Bragg soliton self-compression, linked to the Bragg grating induced dispersion. The numerical study provides insights into optimized designs, with which we experimentally demonstrate a supercontinuum spanning 610 nm with 1.9 ps pulses and a low peak power of 4.4 W. The spectral bandwidth of the generated supercontinuum in this device is ∼5× larger than that in a reference waveguide of the same total length and cross-section [41]. We further analyze the impacts of the CMBG length, the waveguide width, and the input pulse conditions in the enhancement of the generated spectrum. This work showcases an avenue for low-power, low-cost on-chip SCG sources using picosecond pulses.
2. Principle and design
2.1 Design and numerical simulation
The principles for the enhanced spectral broadening in our 2-stage device, consisting of a cladding-apodized modulated Bragg grating (CMBG) and a channel waveguide, can be briefly described as follows. The initial input pulses undergo soliton-effect temporal compression in the CMBG stage, resulting in augmented pulse peak power at the end of the CMBG. Subsequently, the pulses continue to propagate in the concatenated waveguide stage and experience enhanced nonlinear effects, leading to further spectral broadening. Therefore, a considerably wider spectrum is obtained at the end of the waveguide stage. Ideal operation would entail a CMBG length, a waveguide width, and initial pulse conditions which lead to maximum temporal compression at the CMBG output.
The schematic of our 2-stage USRN device is plotted in Fig. 1(a), including a CMBG stage and a waveguide stage, both are 300 nm high, where the CMBG stage contains a central channel waveguide and some pillars seated nearby, where Lapod and Λ are the apodization length and the grating pitch, respectively. The gaps between the central waveguide and the pillars get smaller from the two ends to the center of the CMBG, based on a raised cosine function [39,40], where G1 and Gapod denote the gaps at the center and the two ends of the CMBG, respectively. The apodization scheme is applied to engineer the mode effective refractive index, while the grating pitch has an effect on the stopband position for the grating.
Fig. 1. (a) Schematic of the 2-stage USRN device, including the CMBG stage and the waveguide stage, where Lapod is the apodization length, Λ is the grating pitch, G1 and Gapod are the gaps between the pillars and the central waveguide at the center and the two ends of the CMBG, respectively. (b) Measured transmission (red line) and the group index ng (blue line) of the 2-stage USRN device, showing the position of the input wavelength used in the SCG experiment. (see also Ref. [41]).
The stopband of our device is designed to be centered near 1565 nm (grating pitch Λ = 325 nm), which can be seen in the measured transmission spectrum (red line) plotted in Fig. 1(b). We also measured the group index (ng) of our device and plot the results in Fig. 1(b) as the blue line. As shown in Fig. 1(b), in the SCG measurement, we used pulses with a center wavelength of 1553 nm, 12 nm away from the center of the stopband, lying in a region with both large dispersion and high transmission, which is of great importance for spectral broadening in nonlinear media.
The pulse dynamics in the 2-stage USRN device can be numerically studied according to the Generalized Nonlinear Schrödinger Equation (GNLSE) shown in Eq. (1) [27,42], which is solved with the split-step Fourier method,
In line with the 2-stage USRN device, the simulation is split into 2 stages, where parameters related to the CMBG are used for the 1st stage simulation, and parameters related to the channel waveguide are utilized for the 2nd stage simulation. In the 1st stage simulation, the dispersion coefficients are extracted from the experimentally measured values for the Bragg grating, the linear loss, α = 13 dB/cm, a value extracted from cut-back measurements. The propagation length is set as the CMBG length, and the effective nonlinear parameter γeff is defined as γeff = (ω0n2)/(cAeff) × (ng/n0)2, where ω0 is the frequency of the initial input pulse, c is the light speed in the vacuum, ng is the group index, n0 is the refractive index of the USRN material, and Aeff is the effective mode area. For the simulation parameters for the 2nd stage, the dispersion coefficients are calculated using the finite element method, the linear loss, α is 3.5 dB/cm obtained experimentally, the propagation length is the same as the waveguide length (Lwg = 6.0 mm), and γeff = (ω0n2)/(cAeff).
2.2 Device parameter and initial pulse conditions optimization for SCG enhancement
To study the optimal device dimensions and initial pulse conditions which lead to the widest output spectrum at the end of the 2-stage device, we simulate the pulse evolution as a function of CMBG length, using pulses with different pulse widths (full-width at half-maximum, TFWHM) and peak power (P0). We first simulate the pulse dynamics as a function of pulse peak power in several 2-stage devices with the same waveguide width of 600 nm but different CMBG lengths, using 1.9 ps pulses centered at 1553 nm. The results are plotted in Fig. 2. From Fig. 2, we observe that a relatively wide spectrum is generated when LCMBG = 0.5 mm or 0.8 mm and when the peak power lies within 4.0 W–5.0 W. To find an optimal CMBG length, we further simulate the 30 dB bandwidth of the generated supercontinuum at the end of the 2-stage device, using 1.9 ps, 4.4 W pulses. The simulated 30 dB bandwidth varying with LCMBG is plotted in Fig. 3, which shows an optimal CMBG length of ∼0.7 mm.
Fig. 2. Simulated pulse dynamics varying with the pulse peak power in several 2-stage devices with the same waveguide width of 600 nm but different CMBG lengths, using 1.9 ps pulses.
Fig. 3. Simulated 30 dB bandwidth as a function of CMBG length, at the end of the 2-stage device with a width of 600 nm using 1.9 ps, 4.4W pulses.
For the example of 1.9 ps, 4.4 W pulses centered at 1553 nm, the soliton order, N, can be obtained according to the equation, N2 = LD /LNL, where LD is the dispersion length, and LNL denotes nonlinear length [27,38,42,43]. LNL = (γeff P0)–1, where γeff is the effective nonlinear parameter in the CMBG stage and P0 is the peak power coupled into the grating. LD = T02 / |β2|, where T0 = TFWHM /1.76 and β2 = – 0.783 ps2/mm, is the 2nd order dispersion coefficient at 1553 nm, a value highly dependent on the blue-detuning between the pulse wavelength and the grating stopband [38,43,44]. By calculation, LNL = 0.16 mm, LD = 1.48 mm, and N = 3.04. There are a few key length scales pertinent to the observation of Bragg soliton dynamics, including the soliton period (z0), the soliton fission length (Lfission), and the soliton self-compression distance (LSCD), where z0 indicates the typical length scale over which solitons can change their shapes, Lfission refers to the length needed to initiate soliton fission, and the soliton self-compression distance LSCD is the position at which the extent of soliton pulse compression reaches the maximum. Among these length scales, LSCD is of great significance, showing the position where the pulse width reaches the minimum. These length scales can be obtained using equations z0 = π/2 × LD, Lfission ∼ LD /N, and LSCD ≈ 0.71× Lfission [45]. By calculation, z0 = 2.3 mm, Lfission = 0.49 mm, and LSCD = 0.35 mm. In the regime where LCMBG is larger than Lfission, soliton fission can be initiated, and in the regime where LCMBG is close to LSCD, considerable soliton compression may happen, both can lead to spectral enhancement.
Consequently, a CMBG length of 0.2 mm is shorter than Lfission (0.49 mm), indicating that soliton fission has not been initiated, resulting in an output spectrum (Fig. 2(a)) with small overall broadening. In contrast, a CMBG length of 0.5 mm is larger than Lfission and close to LSCD (0.35 mm), implying the occurrence of soliton fission and considerable soliton compression. Consequently, we can see a noticeable increase in the output pulse spectrum in Fig. 2(b). For CMBG length up to 0.8 mm, the increase in peak power leads to a monotonic increase in the extent of spectral broadening, shown in Fig. 2(c). As the input peak power increases, Lfission and LSCD decrease, becoming increasingly smaller than the CMBG lengths between 1.0 mm to 3.0 mm, resulting in an output spectrum that iteratively broadens and narrows with the increasing peak power. This can be seen in Fig. 2 (d)–(f).
As LSCD approaches LCMBG, the Bragg soliton effect induced temporal compression developing in the first stage increases, resulting in a strong spectral broadening in the second stage. The analysis outlined above can be validated using simulations: the simulated temporal profile, pulse peak power, and temporal compression factor (CF) at the end of the CMBG stage for 2-stage USRN devices with different CMBG lengths, using 1.9 ps, 4.4 W pulses are respectively shown in Fig. 4 (a), Fig. 4(b) and Fig. 4(c), where the CF is defined by CF = (TFWHM of the pulse at the input of the 1st stage) / (TFWHM of the pulse at the end of the 1st stage). From Fig. 4(a), we cannot see soliton fission when the CMBG length is less than 0.5 mm. When LCMBG exceeds 0.5 mm, soliton fission occurs and gradually intensifies. In Fig. 4(c), we can observe significant temporal compression when LCMBG lies within 0.5 mm–1.0 mm. Using the simulated raw data plotted in Fig. 4(c), an analytical equation between CF and LCMBG can be obtained via piecewise data fitting, as shown in Eq. (2):
Fig. 4. Simulated temporal profile (a), pulse peak power (b), and temporal compression factor (c) as a function of CMBG length at the end of the CMBG stage, using 1.9 ps, 4.4 W pulses. (d) Calculated CF as a function of pulse peak power at the end of the CMBG stage with a CMBG length of 0.5 mm, using 1.9 ps pulses.
According to Eq. (2), the maximum temporal compression occurs when LCMBG ≈ 0.7 mm. We notice that there is a discrepancy between the simulated position (LCMBG ≈ 0.7 mm) and the theoretical predicted position (LSCD ≈ 0.35 mm) where the maximum temporal compression happens. We note that the prediction of the self-compression distance formulated by Chen et al. [45] is most accurate when N >> 1. In our case, LD and LNL are on the same order, thus we obtain a relatively small value of N = 3.04. Nevertheless, we note that the theoretically predicted position for maximum temporal compression is close to the value predicted by the simulation, providing an additional design guide for the 2-stage device. Referring to Fig. 4 (b), after considering the propagation loss, the pulse peak power at the end of the CMBG stage is optimal when LCMBG lies within 0.5 mm–0.8 mm. Considering the benefit of a smaller footprint in the integrated circuits and the lower overall insertion loss of a shorter grating, we choose 0.5 mm in our device design, a case where both considerable temporal compression and spectral broadening occur. In addition, we note that the write-field in the electron-beam lithography process is 500 µm by 500 µm. Therefore, setting the CMBG length to 0.5 mm advantageously allows us to eliminate any stitching errors between write fields within the grating.
For the case where the CMBG length is 0.5 mm, we simulated the temporal compression factor when the pulse peak power varies using 1.9 ps pulses. The results are plotted in Fig. 4(d). An analytical equation between CF and P0 is obtained via data fitting, as shown in Eq. (3):
To determine the ideal initial pulse peak power to use, considering the important design goal of generating the enhanced SCG at low powers, we consider the figure of merit, CF/P0, such that the compression factor and pulse power are both taken into account. For P0 between 4.4 W to 5.5 W, CF/ P0 is the largest, possessing a value of 0.69 W-1. Consequently, we adopt a pulse peak power of 4.4 W.
Figure 5(a) plots the output spectrum using 4.4 W pulses when the CMBG length varies. Between 0.5 mm to 0.8 mm, the input pulse narrows considerably at the end of the CMBG stage, leading to considerably enhanced spectra at the end of the 2-stage device. Beyond these lengths, we observe that the output pulse spectrum decreases quickly. The soliton order at this pulse peak power is 3.04. When considering the soliton period of 2.3 mm, the high-order Bragg soliton undergoes an initial temporal compression, periodic splitting into constituents, and restoration. CMBG lengths much larger than the soliton period is not optimal for harnessing the critical region of strong temporal compression. Consequently, weak spectral broadening is observed for CMBG lengths from 1.0 mm to 3.0 mm.
Fig. 5. (a) Simulated output spectrum at the end of the 2-stage USRN devices with different CMBG lengths and a waveguide width of 600 nm, using 1.9 ps, 4.4 W pulses. (b) Simulated output spectrum at the end of the 2-stage USRN devices with different waveguide widths and a CMBG length of 0.5 mm, using 1.9 ps, 4.4 W pulses. (c) Simulated output spectrum at the end of the optimal 2-stage USRN device, using pulses with different pulse widths and a peak power of 4.4 W. Simulated spectral evolution in the optimal 2-stage USRN device(d), and in the reference waveguide (e), using 1.9 ps, 4.4 W pulses.
For a fixed CMBG length of 0.5 mm, we simulate the pulse dynamics in the 2-stage USRN devices, the widths of which are varied from 500 nm to 800 nm, using 1.9 ps, 4.4 W pulses. In each of these simulations, the waveguide dispersion is calculated by performing a Taylor-series expansion of the propagation constant β(ω), where β(ω) = neff(ω)ω/c and neff(ω) is calculated using a finite element algorithm. The results are shown in Fig. 5(b), from which we can tell that the best waveguide width is 600 nm, because of its smallest effective mode area as well as a negative 2nd-order dispersion coefficient, which contributes to larger nonlinear effects and stronger spectral broadening. By comparing Fig. 5(a) and Fig. 5(b), we also notice that the influence of the CMBG length on the spectral broadening enhancement is much stronger than that from the waveguide width. Therefore, a judiciously selected CMBG length is most important in our 2-stage USRN device design. Based on the numerical calculations and discussion above, we choose an optimal design for the 2-stage USRN device having a CMBG length of 0.5 mm, a waveguide length of 6.0 mm, a waveguide width of 600 nm, and a height of 300 nm. In the following content of this work, we use the term, optimal 2-stage USRN device for conciseness.
To obtain an optimal initial input pulse width, we simulate the pulse dynamics in the optimal 2-stage USRN device, using pulses with a pulse width varying from 1 ps to 9 ps and a peak power of 4.4 W. The results are plotted in Fig. 5(c). From Fig. 5(c), the optimal spectral broadening is observed when the pulse width is ∼1.9 ps. For wider pulse widths, the output spectrum narrows quickly. This is because both Lfission and LSCD increase with pulse width, even exceeding the CMBG length, which is not favorable for the Bragg soliton dynamics. For instance, at the same peak power of 4.4 W, for 5 ps pulses, Lfission = 1.3 mm and LSCD = 0.92 mm, whereas for 9 ps pulses, Lfission = 2.35 mm and LSCD = 1.67 mm. In both cases, Lfission and LSCD exceed and get further away from the CMBG length of 0.5 mm. Consequently, the degree of spectral broadening decreases because of the short interaction length for the Bragg solitons to form and compress. Based on what is discussed above, the optimal initial pulse possesses a pulse width of 1.9 ps, a peak power of 4.4 W, and a center wavelength of 1553 nm.
To clearly attribute the spectral enhancement to the Bragg soliton temporal compression in the optimal 2-stage USRN device, we simulate the pulse evolution in the optimal 2-stage USRN device and a reference USRN channel waveguide that is 6.5-mm long, 600-mm wide, and 300-nm high, using 1.9 ps, 4.4 W pulses. The results are shown in Fig. 5(d)–(e). From Fig. 5(d)–(e), we observe that great enhancement in the spectral bandwidth is developed in the optimal 2-stage USRN device in comparison to the reference waveguide. Spectral broadening in the reference waveguide occurs largely from SPM of the 1.9 ps pulse that does not encounter any peak power enhancement or Bragg-induced temporal narrowing.
Figure 6 shows the simulated temporal and spectral profiles at the beginning of the CMBG stage, the end of the CMBG stage, and the end of the waveguide stage of the optimal 2-stage USRN device, using 1.9 ps, 4.4 W pulses. From Fig. 6(a), temporal compression occurs in the 1st stage, and the TFWHM of pulses at the end of the 1st stage is compressed to be around 0.61 ps. A compression factor (CF) of ∼3.1 is obtained. Considering a linear loss of 0.65 dB (13 dB/cm*0.5 mm) in the CMBG stage, the peak power of pulses at the end of the 1st stage is around 11.8 W, enhanced by ∼2.7× with regard to the input peak power of 4.4 W. Because of the temporal compression occurring in the 1st stage, the pulse peak power entering the 2nd stage of our device is strongly enhanced, resulting in much stronger nonlinear effects in the waveguide stage, and finally leading to a much wider spectrum at the end of the 2nd stage. From Fig. 6(b), strong spectral broadening happens in the 2nd stage of our device.
Fig. 6. Simulated temporal profile (a) and spectral profile (b) at the input of the 1st stage (bottom lines), the end of the 1st stage (middle lines), and the end of the 2nd stage (top lines) of the optimal 2-stage USRN device, using 1.9 ps, 4.4 W pulses.
The aforementioned conditions are favorable for the enhancement of supercontinuum. However, changes in the pulse condition, for example in the input pulse width while maintaining similar input powers might not result in a similar enhancement. We simulate the dynamics of wider pulses (5 ps and 9 ps pulses) with the same peak power of 4.4 W in the optimal 2-stage USRN device and plot the results in Fig. 7. From the temporal profiles shown in Fig. 7, negligible temporal compression occurs in the 1st stage when using 5 ps and 9 ps pulses, corresponding to a CF value of 1.01 and 1.08, respectively. Consequently, there is no augmentation in the peak power of the pulses prior to them entering the waveguide stage. In other words, the pulse power is not high enough to lead to sufficient nonlinear effects in the waveguide stage. As a result, much narrower spectra are obtained at the end of the 2-stage device.
Fig. 7. Simulated temporal (a,b), and spectral (c,d) profiles at the input of the 1st stage, the end of the 1st stage, and the end of the 2nd stage of the optimal 2-stage USRN device, using 5 ps and 9 ps pulses with a peak power of 4.4W.
3. Device fabrication and SCG experimental demonstration
The study of the device parameters and their impact on the output spectrum allows an optimized 2-stage device to be designed, which we proceed to fabricate. Our device is fabricated on top of a 10-µm SiO2 layer residing on the Si substrate, where the USRN film deposition is first conducted via inductively coupled chemical vapor deposition at 250 °C, followed by the grating-waveguide structure definition using electron-beam lithography. Next, the pattern is transferred to the USRN layer using inductively coupled plasma etching. A 2-µm SiO2 upper cladding layer is deposited using atomic layer deposition and plasma-enhanced vapor deposition.
The experimental setup used for the SCG measurement in the optimal 2-stage USRN device is shown in Fig. 8(a). We use a mode-locked femtosecond fiber laser to launch 1.9 ps pulses. These pulses have a repetition rate of 20 MHz. The laser is followed by an optical attenuator to tune the pulse power required in the measurement. Before coupling into the optimal 2-stage USRN device, the pulses are adjusted to be quasi-TE polarized. Two optical spectrum analyzers (OSAs) that cover different wavelength ranges are utilized to monitor the output spectrum. One of them is from 1000 nm to 1750 nm, and the other is from 1600 nm to 2000 nm. The 1.9 ps pulses are tuned to have a center wavelength of 1553 nm, near the blue-side edge of the grating stopband, a region with both strong dispersion and high transmission.
Fig. 8. (a) Experimental setup used for the spectral broadening characterization, where the blue lines are polarization-maintaining (PM) fibers, where OA: optical attenuator, DUT: device under test, OSA: optical spectrum analyzer. (b) Measured output spectra of the optimal 2-stage USRN device at various input peak powers using 1.9 ps pulses. (c) Measured output spectrum of the optimal 2-stage USRN device and the reference waveguide using 1.9 ps pulses with a power of 4.4 W, together with the laser source. (see also Ref. [41]).
Figure 8(b) shows the measured supercontinuum in the optimal 2-stage USRN device at several input peak powers using 1.9 ps. From Fig. 8(b), we observe that the spectrum broadens rapidly with increasing power. When the input peak power is 4.4 W, a supercontinuum spanning from 1237 nm to 1847 nm is generated, possessing a bandwidth of 610 nm at the –30 dB level. The corresponding bandwidth at the –40 dB level is 702 nm, ranging from 1186 nm to 1888 nm.
The output spectrum in the reference USRN waveguide is also measured using the same input pulses. The generated supercontinuum in both the optimal 2-stage USRN device and the reference waveguide are plotted in Fig. 8(c), together with the laser source, from which we see a significantly enhanced spectrum in the optimal 2-stage USRN device. To quantitively describe the enhancement effect, we introduce the enhancement factor (EF), defined as EF = (30 dB bandwidth obtained in the optimal 2-stage USRN device) / (30 dB bandwidth obtained in the reference waveguide), and an EF ≈ 5 is obtained.
We also perform the measurement using temporally wider pulses. The experimentally measured spectra in the optimal 2-stage USRN device and the reference waveguide, together with the laser source when using 5 ps pulses and 9 ps pulses with a peak power of 4.4 W, are shown in Fig. 9. As shown in Fig. 9, the generated spectra in the optimal 2-stage device are almost identical to that of the reference waveguide, with negligible enhancement occurring in the optimal 2-stage USRN device. For these wider pulse widths, the extent of Bragg soliton effect compression occurring at a peak power of 4.4 W is negligible.
Fig. 9. Measured output spectra in the optimal 2-stage USRN device and the reference waveguide, together with the laser source, when using 5 ps pulses (a) and 9 ps pulses (b) with a peak power of 4.4 W.
4. Discussion and conclusions
Several recently reported on-chip SCG work are listed in Table 1, in which we can see 1.9 ps pulses are used in this work, with a pulse width significantly wider than those used in other platforms, where femtosecond scale pulses are used. In addition, the on-chip peak power reported in this work is as low as 4.4 W, much smaller than pulse powers used in Si (360 W and 37 W) [6,7], Amorphous Si (17 W) [11], Si3N4 (6,560 W and 380 W) [13,14], Lithium Niobate (4.0 KW) [16], AlGaAs (36 W) [18], and As2S3 (68 W) [33]. Previous demonstrations of SCG in the USRN platform [26] utilized a 7-mm-long waveguide. In that work, a SCG with a bandwidth of 600 nm at the −30 dB level was generated using a peak power of 140 W. In this work, we carefully design the dimensions of the 2-stage device (the CMBG length and the waveguide width), and the initial pulse conditions (the pulse width, the center wavelength, and the peak power) based on numerical calculations, to obtain an optimal Bragg-soliton effect spectral enhancement. Based on the simulation results, the CMBG length and the pulse width are the two most important factors that impact spectral broadening. A CMBG length of 0.5 mm, a waveguide width of 600 nm, a pulse width of 1.9 ps, and a pulse peak power of 4.4 W, is analyzed to be optimal. Using the optimal design, we experimentally demonstrated the SCG in the 2-stage USRN device. The 2-stage configuration used in this work generated a slightly wider SCG with significantly lower power (30×), 4× wider pulse width, and 14% smaller device footprint, showcasing the efficiency of the Bragg soliton dynamics in enhancing the generated supercontinuum spectrum.
Table 1. SCG demonstration in various on-chip platforms
We note further the impacts of fabrication related biases in the optical properties of the device. In the CMBG stage, Gapod is a factor that affects the effectiveness of apodization, and errors in Gapod or the profile in which the gap width varies along the grating length will cause more oscillations in the group delay and the transmission spectrum. Any fabrication induced bias results in a larger (smaller) G1, and this will cause an increase (decrease) in the coupling coefficient as well as the bandwidth of the stopband. A sidewall that is not perfectly vertical could induce a smaller effective index, which would concomitantly result in a smaller effective index and blue-shift in the stopband. We note in our device that the main fabrication induced bias comes from the grating pitch. Based on the Bragg condition, ${\lambda _B} = 2{n_{eff}} \cdot \Lambda $, where the grating pitch $\Lambda $ = 325 nm and neff is calculated to be 2.393, the theoretical Bragg wavelength should be at 1555 nm. There is a marginal red-shift in the measured Bragg wavelength of 1565 nm.
In the future, greater enhancements to the generated supercontinuum may be achieved by incorporating multiple alternating sections of CMBGs and waveguides. Optimally designing each CMBG section to achieve the strongest temporal compression prior to entering a subsequent waveguide stage would allow the Bragg soliton effects to significantly enhance the generated supercontinuum in several stages. Similar, but non-identical phenomena have been studied in purely waveguide-based supercontinuum generated using waveguide sections of different dispersion profiles [46–49]. In Ref. 46 for example, strong low noise spectral broadening and temporal compression are first achieved in normal dispersion highly nonlinear fiber prior to wideband supercontinuum in a silicon nitride waveguide with anomalous dispersion. Ref. 47 on the other hand, adopts varying dispersive sections to extend the supercontinuum by inducing a continuous shift in the location of the dispersive wave. The two-stage device here offers greater degrees of freedom in accessing both normal and anomalous dispersion of varying magnitudes while further providing a slow light scaling in the nonlinear parameter. Both of these effects may be advantageously combined with a multi-stage CMBG-waveguide system to achieve far greater supercontinuum enhancement.
To sum up, the work reported here relaxes the requirement for pulse width and pulse power used for SCG, providing an encouraging path to generate supercontinuum that doesn’t need ultrashort, femtosecond scale pulses.
Funding
Ministry of Education - Singapore (ACRF Tier 2 Grant); Agency for Science, Technology and Research (RIE2025 MTC IRG Grant); Agency for Science, Technology and Research.
Acknowledgments
Funding from the Ministry of Education ACRF Tier 2 Grant, A*STAR RIE2025 MTC IRG Grant, and A*STAR is gratefully acknowledged. Portions of this work were presented at the OptoElectronics and Communications Conference (OECC) and International Conference on Photonics in Switching and Computing (PSC) in 2022, “Bragg-Soliton Enhanced Supercontinuum in an Ultra-Silicon-Rich-Nitride Grating”.
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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