Soliton-effect optical pulse compression in CMOS-compatible ultra-silicon-rich nitride waveguides

Optical pulse compression provides an avenue for short pulse generation beyond that possible through mode-locking alone. Its applications are many and diverse, spanning from optical metrology^1,2 and biology^3,4 to supercontinuum generation^5,6 and telecommunications.⁷ Temporal pulse compression may be implemented using single-stage and two-stage compression schemes. In the latter, new frequencies are first generated through nonlinear effects such as self-phase modulation, before anomalous group velocity dispersion is applied in the second stage to temporally synchronize all frequency components. Single-stage temporal compression schemes rely on solitons. Soliton-effect compression occurs when an input pulse simultaneously undergoes self-phase modulation (SPM) and anomalous group velocity dispersion (GVD) as it propagates throughout the device.^8,9 Therefore, soliton-effect pulse compressors may be compact and easily implemented in integrated photonic crystal waveguides,^10,11 integrated spiral nanowire waveguides,¹² and glass rod nanowires.¹³ For a fundamental soliton, the SPM and GVD effects counterbalance each other such that the fundamental soliton propagates undistorted. For high-order solitons, the temporal and spectral pulse profile evolves periodically with the soliton period, z₀. High-order solitons experience an initial narrowing at the beginning of each soliton period. With appropriate design of the waveguide geometry and length to coincide with this narrowing phase, strong soliton-effect temporal compression can be achieved. The degree of compression depends on the soliton number, N, which in turn depends on the input peak power, nonlinear length, and dispersive length.⁸ 

In this manuscript, we demonstrate on-chip, soliton-effect subpicosecond pulse compression in an ultra-silicon-rich nitride (USRN) waveguide. USRN is a backend CMOS-compatible platform that has a high nonlinearity (n₂) of 2.8 × 10⁻¹³ cm²/W, ∼100 times larger than that in stoichiometric silicon nitride (2.4 × 10⁻¹⁵ cm²/W),^14,15 a relatively large bandgap of 2.1 eV,¹⁴ and negligible two-photon absorption (TPA) at a wavelength of 1550 nm.^16–20 The TPA coefficient has been characterized to be negligible at wavelengths longer than 1200 nm.²¹ Using the USRN platform, wideband supercontinuum,¹⁷ high gain optical parametric amplification in photonic waveguides,¹⁴ and enhanced nonlinearity in photonic crystal waveguides^20,22 have been demonstrated. The large linear index (3.1 at 1550 nm) allows tightly confined modes with a small effective area to be realized, enabling large nonlinear parameters to be realized. We experimentally observe 8.7× compression of 2 ps pulses at 1550 nm using picojoule pulse energies. The strong observed temporal compression is supported by calculations of the nonlinear Schrödinger equation to be largely attributed to the large nonlinearity and TPA -free nature of the USRN waveguides at 1550 nm.

Nonlinear pulse propagation dynamics are well described by the nonlinear Schrödinger equation (NLSE),

where α is the loss coefficient, A and ω₀ are the slowly varying envelope and carrier frequency, respectively, z and T are the propagation and temporal coordinates, respectively, β₂ is the GVD coefficient, and γ is the nonlinear parameter. T exists in a moving frame defined as T = t − β₁z due to the removal of the temporal walk-off induced by the group velocity (1/β₁).⁸ To obtain accurate theoretical results, the short length of the output coupling fiber is accounted for in this calculation.

Frequently encountered quantities in soliton theory include the nonlinear length, L_nl = 1/γP_c (where P_c is the peak power of the pulse), and the dispersion length, L_d = T₀²/|β₂| [where T₀ = T_{FHWM_}/1.76 (for sech² pulse), and T_{FHWM_} is the input pulse full width at half-maximum]. These two quantities determine the soliton order through the following relationship: $N2=LdLNL$⁠. Consequently, it follows that for a waveguide with β₂ that is small and negative, a high-order soliton may form. Another characteristic of high-order soliton is their ability to temporally and spectrally evolve periodically along the propagation length with a soliton period, z₀ = πL_d/2. The larger the soliton order, N, the greater the potential for high compression, especially when engineering the propagation length to coincide with the soliton evolution state where the temporal pulse width is narrowest. For N ≥ 10, the optimal length, z_opt = 1.6z₀/N, resulting in the optimal compression factor (F_c = N/1.6).⁸ If the input pulse passes through the waveguide, the pulse is initially temporally compressed to a fraction of its original pulse width via the high-order soliton effect even if the waveguide length is not z_opt.²³ Figure 1 shows the temporal evolution of a pulse as a function of the input pulse energy and propagation length, where the waveguide length <z_opt.

The theoretical output intensity profiles along the interaction length and input pulse energy are calculated using the NLSE and presented in Figs. 1(a) and 1(b), respectively. In both figures, the time scale is normalized to the initial pulse width T₀, where T₀ is defined $TFWHM1.76$ for sech² pulses (TFHWM=full-width at half maximum pulse width). A few main observations may be made from the theoretical calculations. First, Fig. 1(a) shows the pulse evolution as it propagates through the USRN waveguide at a fixed pulse energy of 16.3 pJ. It is observed that at a fixed pulse energy, there exists an optimum propagation length at which the pulse has the highest compression. For the USRN waveguide, a pulse energy of 16.3 pJ results in an optimum propagation length of ∼3.5 mm. Beyond the optimal propagation length, the pulse starts to develop pedestals that cause some of the energy to reside outside of the main pulse lobe. Second, it is observed from Fig. 1(b) that when the USRN waveguide length is fixed at 7 mm, the optimal pulse energy is 16 pJ–20 pJ. At these pulse energies, the pulse is strongly compressed with most of its energy being carried in the main lobe. As the input pulse energy is increased beyond 23 pJ, it is observed that the pulse pedestals increase considerably in amplitude. Beyond this pulse energy, the compression factor changes minimally. Therefore, Fig. 1 indicates that optimized temporal compression occurs at a pulse energy of ∼16 pJ, beyond which it saturates with an observed increase in pulse pedestals.

Fabrication of the USRN waveguides is performed by first depositing 330 nm of USRN film using inductively coupled chemical vapor deposition on a 10 µm thermal oxide on a silicon substrate. Electron-beam lithography is used to pattern the waveguides before dry etching and plasma enhanced chemical vapor deposition of the SiO₂ overcladding. The 7-mm-long USRN waveguide is designed to possess a submicron core (height of 330 nm and width of 450 nm) for single-mode operation, anomalous dispersion, and a large nonlinear parameter. The USRN refractive index (n) and absorption coefficient (κ) were previously measured by Fourier-transform infrared spectroscopy to be 3.1 and ∼0, respectively, at the 1550 nm wavelength.¹⁷ The group index (n_g) is 3.82 at the wavelength of interest. The GVD coefficient (β₂) is anomalous between 1240 nm-1580 nm, with a value of −0.17 ps²/m at 1550 nm as shown in Fig. 2(a). The third order dispersion (TOD) coefficient (β₃) is calculated to be −0.0071 ps³/m at 1550 nm. γ is calculated as a function of the waveguide width for a height of 330 nm [Fig. 2(b)]. For a waveguide height of 330 nm and width of 450 nm, the effective mode area (A_eff), defined as $∫−∞∞∫−∞∞F(x,y)2dxdy2∫−∞∞∫−∞∞F(x,y)4dxdy$⁠, where F(x, y) is a modal distribution for fundamental TE mode, is calculated to be 0.26 µm² at 1550 nm, resulting in a γ of 440 W⁻¹/m. The inset shows the electric field profile of the waveguide mode.

To study the pulse compression dynamics, a 2 ps pulsed laser at a repetition rate of 20 MHz and a central wavelength of 1550 nm is used. The optical pulses are adjusted for TE-polarization before coupling into the USRN waveguide using a tapered lensed fiber. The spectral and temporal profiles of the output are measured using an optical spectrum analyzer and autocorrelator, respectively. Fiber-waveguide coupling losses and waveguide propagation losses are 7 dB per facet and 3 dB/cm, respectively. The intensity autocorrelation traces and the corresponding spectra of the output pulses are measured as a function of coupled pulse energy (E_c) as shown in Fig. 3(a). As a result of the large nonlinearity in the USRN waveguide, the pulse undergoes significant SPM-induced broadening with high spectral symmetry [Fig. 3(a)]. The spectral bandwidth of the output at the −3 dB level broadens to 13 nm at maximum E_c, which is ∼10× broader than that of the input pulse.

Simultaneously, the anomalous GVD in the waveguide facilitates temporal compression of the optical pulses as shown in Fig. 3(b). The temporal evolution of the pulse as a function of input pulse energy is measured using an autocorrelator. The measured autocorrelation trace width is observed to decrease to 360 fs as E_c increases to 22.4 pJ [Fig. 3(b)]. The temporal pulse width (FWHM) is obtained by applying the deconvolution factor (1.54 for sech² pulse) to the autocorrelation trace width. The measured minimum pulse width of 230 fs is achieved at maximum E_c, corresponding to a compression factor of 8.7×. The presence of pedestals in the experimentally measured temporal trace is a characteristic of soliton-effect compression.²³ 

T_FHWM measured using the autocorrelator as a function of E_c (black circles) is shown in Fig. 4(a), alongside the theoretically calculated values (red line). T_FHWM is observed to decrease as E_c increases and flattens at a value of ∼230 fs at high E_c. T_FHWM is almost identical for E_c values between 16.3 pJ and 22.4 pJ, implying that the minimum T_FWHM is achieved experimentally at E_c ∼ 16 pJ. When E_c is >12 pJ, T_FWHM decreases below 300 fs. The theoretical curves also exhibit a flattening in the compressed pulse width at input pulse energies exceeding 16 pJ. As shown in Fig. 1(b), significant compression is observed at E_c > 16 pJ together with the formation of pulse pedestals that become more severe as E_c increases. This indicates that the flattening in compression arises in part from the presence of side lobes that exist at high input pulse energy. The experiment agrees well with theoretical calculations as shown in Fig. 4(a).

In addition, we quantify the compression factor as a function of E_c. The compression factor (F_c), defined as the ratio of T_FHWM of the input pulse to that of the compressed pulse,⁸ is measured to be 8.7× at the maximum E_c as shown in Fig. 4(b). Good agreement between experimental measurements and theoretical calculations is achieved, with similar trends observed and maximum F_c achieved for E_c ∼ 16 pJ for both curves.

The theoretical input pulse energy where the main lobe of the pulse narrows significantly is shown in Fig. 1(b) to be similar to that observed in the experiment [Fig. 4(a)], indicating that the experiment agrees with the theory in terms of temporal evolution as a function of input pulse energy. Figure 5 shows a comparison of output theoretical and experimental pulse traces for E_c = 16.3 pJ along with the input pulse. Experimental pulse traces (green hollow circles) are plotted after applying a sech² deconvolution on autocorrelation traces. The inset shows that the measured input pulse and main lobe of the output pulses (gray hollow circle) agree well with sech² pulse profiles (red dashed line). In addition, experimental and theoretical (blue solid line) traces of the compressed pulse show good agreement. The theoretical T_FWHM is estimated to be ∼280 fs, which is close to the experimentally measured T_FWHM.

To confirm that the compression effect is derived solely from the USRN device, a control experiment whereby pulses with E_c = 16.3 pJ undergo the same temporal characterization setup but without coupling into the USRN waveguide is performed. The measured output temporal profile is shown as the pink solid line in Fig. 5. It is observed that there is no compression in the control experiment, confirming that the strong pulse compression originates from the high-order soliton effect in the USRN device. The time-bandwidth product (TBP) of the input laser pulses is ∼0.33, which is close to that for an ideal hyperbolic secant. The TBP of the compressed pulse is 0.39, beyond the 5% variation in the Fourier limit of hyperbolic secant pulses (TBP ∼ 0.315),¹⁰ implying that the output pulse is slightly chirped.

Next, we analyze the compressed pulse quality. The ratio of the output peak power (P_peak,out) to input coupled peak power (P_peak,in) is measured as a function of E_c and shown in Fig. 6(a). The output peak power is calculated as P_peak,out = $(f×Pavg)/(R∫−∞+∞Ptdt)$⁠, where P_avg is the measured average power, f is the fraction of the energy in main lobe to total energy, R is the repetition rate of the input laser (20 MHz), and P(t) is the normalized pulse intensity assuming a sech² pulse.²⁴ While calculating the ratio of output to input peak power, P_peak,out is normalized to the measured propagation and coupling losses. From Fig. 6(a), it is observed that the ratio of the output to input peak power increases as E_c is increased up to a value of 16.3 pJ and achieves its maximum when 16.3 pJ ≤ E_c ≤ 20.3 pJ, corresponding to the minimum T_FWHM of 230 fs. At the maximum E_c of 22.4 pJ, the ratio decreases because of the increase of energy carried in sidelobes. In addition, the degree of increase in P_peak,in is higher than that in P_peak,out at the maximum E_c because the temporal pulse width is saturated, and $∫−∞+∞Ptdt$ is the same for E_c ≥ 16.3 pJ. The theoretical curve (red solid line) is also shown in Fig. 6(a). It is observed that there is good agreement between the experimental data and simulations. The experiment follows the same trend having the same maximum P_peak,out/P_peak,in at E_c ∼ 16 pJ. Figure 6(a) reveals that the output pulse is maximally compressed and possesses a large value of P_peak,out/P_peak,in for E_c ∼ 16 pJ. This is physically interpreted as the pulse acquiring a significantly larger peak power compared to precompression.

The compression efficiency is also characterized by the quality factor (Q_c), defined as P_n/F_c, where P_n is the output peak power of the compressed pulse normalized to the peak power of the input pulse.⁸ Q_c is a measure of how much energy contributes to the component of the compressed pulse. The output pulses possess pedestals, which is a characteristic of the soliton-effect. Therefore, the output peak power of the compressed pulse is measured in two different ways: (i) The total normalized output peak power is assumed to be P_n, and (ii) the normalized output peak power in the main lobe of the pulse is assumed to be P_n. In this way, the Q_c measured by total output peak power (solid square dots) and output peak power (solid triangle dots) in the main lobe of the pulse is measured as a function of E_c as shown in Fig. 6(b). Q_c decreases as E_c increases because Q_c generally decreases as the soliton number becomes large. This trend arises because the soliton order is linearly proportional to the square of input coupled peak power.²³ It implies that not all of the input pulse energy contributes to the main lobe of the compressed pulse due to pedestals that are characteristic of solitons. Q_c remains relatively unchanged because f and T_FWHM are almost similar when 16.3 pJ ≤ E_c ≤ 22.4 pJ. Q_c measured in terms of (i) the total output peak power and (ii) the peak power in the main lobe saturates at 0.25 and 0.12, respectively. Theoretical calculations of Q_c (orange and purple solid lines) plotted alongside the experimental data in Fig. 6(b) are observed to agree well with the experiments.

Soliton-effect pulse compression depends largely on the interplay between dispersive and nonlinear effects that are described by N. The TOD length (T₀²/|β₃|) of the USRN waveguide is ∼180 m. Consequently, TOD effects that can cause pulse asymmetry are negligible. L_d is estimated to be ∼7 m, which is much larger than L_nl of 0.2 mm at E_c = 22.4 pJ (at minimum T_FHWM), resulting in N ∼ 190. For the experimental conditions in this manuscript, the soliton period, z₀ ∼ 11 m. For N ≥ 10, the optimal length, z_opt, is estimated to be 92 mm, approximately 13× larger than the waveguide length of 7 mm. Theoretically, F_c may be as large as ∼120 when using a USRN waveguide with a length equivalent to z_opt.⁸ Furthermore, on-chip photonic nanowire waveguides in general have anomalous GVD < −1 ps²/m, implying that the presence of high N values is inevitable.²⁵ As the pulse is temporally compressed from the initial propagation in the presence of the high-order soliton-effect, the compression ratio is still significant at a low pulse energy of ∼16 pJ, even if the USRN waveguide does not meet the length z_opt compared with other references as shown in Table I. Comparing with other platforms as shown in Table I, our USRN pulse compressor leverages a nanowire waveguide, which is less complex to implement compared to GaInP and silicon photonic crystal waveguides in terms of both design and processing. Because of the large optical nonlinearity and Kerr nonlinearity figure of merit (FOM) in USRN waveguides, relatively short lengths and modest pulse energies may be employed to achieve significant compression.

Aside from considerations of the compression factor, practical applications also consider factors such as pulse quality and energy efficiency. In an ideal scenario, the majority of the compressed pulse energy should reside within the main lobe of the pulse, with minimum energy accorded to pedestals. The quality factor of the pulse provides an indicator as to how energy efficient the compression process is. Two approaches to improving the quality factor may be explored: (i) Current waveguide losses are 3 dB/cm, implying 2.1 dB of loss in the 7 mm waveguide. Therefore, a reduction in the waveguide losses to ∼1 dB/cm could improve Q_c by ∼40%. (ii) It is also well-known that soliton-effect pulse compression leads to pulse pedestals, due to imperfect matching of the instantaneous frequency vs time profile from self-phase modulation and dispersive effects. To further increase Q_c, approaches to reduce pulse pedestals through pulse shaping techniques could be investigated.

As a result of the aforementioned intricacies of physics underlying soliton formation, not many demonstrations of on-chip photonic waveguide-based soliton-effect temporal pulse compression have been reported. Soliton-based pulse compression has been demonstrated on a chip on a few different platforms and devices. Photonic crystal waveguides have large anomalous group velocity dispersion on the blue side of the band edge, with magnitudes that can be 1000× larger than that in on-chip waveguides. Consequently, seed pulses with larger temporal widths may fulfill soliton formation requirements in terms of the relative contributions of dispersion and nonlinearity. Photonic crystal waveguide-based soliton compression has been demonstrated with compression factors of 5.4× and 2.3× in GaInP and crystalline silicon, respectively.^10,11 InGaP does not have two-photon absorption at 1550 nm and may be heterogeneously integrated with silicon substrates,^26,27 while crystalline silicon is CMOS-compatible but limited by two-photon and free-carrier absorption. Another drawback of photonic crystal waveguide-based compressors is their larger propagation losses that are on the order of few decibels per millimeter compared with few decibels per centimeter in on-chip photonic waveguides.

A two-stage silicon-based pulse compression scheme composed of a 6-mm silicon waveguide followed by an anomalously dispersive grating was previously reported to enable 7× compression of 7 ps pulses.²⁴ More recently, Bragg solitons on the USRN platform have been demonstrated to achieve 5.7× compression of 5 ps pulses as well as soliton fission.²² These demonstrations of pulse compression functionalities are impressive in their own right and leverage fundamentally different device physics. In the soliton-effect compression demonstrated in this manuscript, we utilized a photonic nanowire waveguide with less process and design complexity and achieved larger compression factors than those in the two references. A key advantage of our pulse compression scheme here over the silicon-based 2-stage compressor is the absence of two-photon absorption.

We have demonstrated subpicosecond soliton-effect pulse compression using on-chip USRN photonic waveguides. 2 ps pulses centered at 1550 nm undergo strong temporal compression to 230 fs at an input pulse energy of 16.3 pJ, corresponding to a maximum compression factor of 8.7×. The experimental T_FWHM as a function of E_c and pulse evolution agrees well with numerical calculations based on the nonlinear Schrödinger equation and confirms that the strong demonstrated compression originates from the high nonlinearity and negligible TPA in the USRN waveguides. The presence of pedestals at high E_c is evident of soliton-effect compression that leads to saturation in the compression factor, as also evidenced by the significantly larger L_d than L_nl. Our study here demonstrates strong temporal compression at low energies, achieved with an on-chip, dispersion, and nonlinearity engineered CMOS-compatible photonic nanowire platform. Through further design optimization, better compression factors and pulse quality leveraging the USRN nanowire waveguide may be achieved in the future toward applications in biomedicine, imaging, and optical metrology. This demonstration represents the strongest on-chip photonic waveguide-based soliton-effect temporal compression, in a compact, CMOS-compatible platform.

This work was supported by the National Research Foundation Competitive Research Grant, MOE ACRF Tier 2 grant, SUTD–MIT International Design center and the Digital Manufacturing and Design Grant. The authors acknowledge the National Research Foundation, Prime Minister’s Office, Singapore, under its Medium Sized Centre Program. This work is a collaboration project between SUTD and IME (A^*STAR).