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Abstract
We propose a method of supercontinuum light generation enhanced by multimode excitation in a precisely dispersion-engineered deuterated SiN (SiN:D) waveguide. Although a regularly designed SiN-based nonlinear optical waveguide exhibits anomalous dispersion with the fundamental and first-order multimode operation, the center-symmetric light pumping at the input edge has so far inhibited the full potential of the nonlinearity of SiN-based materials. On the basis of numerical analysis and simulation for the SiN:D waveguide, we intentionally applied spatial position offsets to excite the fundamental and higher-order modes to realize bandwidth broadening with flatness. Using this method, we achieved an SNR improvement of up to 18 dB at a wavelength of 0.6 µm with an offset of about 1 µm in the Y-axis direction and found that the contribution was related to the presence of dispersive waves due to the excitation of TE10, and TE01 modes.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Si, which has been a major electronic material for a long time, has seen remarkable progress as an “optical” functional material in recent years [1,2]. Thanks to the industrial-based ecosystem of Si-CMOS process technologies, Si photonics has provided low-cost, high-density, and high-performance integrated circuits for a variety of optical communications and sensing applications [3,4,5]. Furthermore, since Si-based materials have very large nonlinearity with strong optical mode confinement, they have recently opened up new research fields such as entangled photon sources for quantum communications [6,7] and optical frequency comb (OFC) generators for metrology [8,9], spectroscopy [10,11], as well as ultrahigh-capacity optical communications [12,13]. One of the major nonlinear effects in Si-based materials is supercontinuum light generation (SCG), which is known as a kind of OFCs. This type of broadband light with excellent coherence can be produced by coupling ultrashort pulses of picoseconds or less into high-confinement nonlinear waveguides and fibers [14,15,16,17,18]. Among the many Si-based nonlinear materials, silicon nitride (SiN) exhibits excellent optical properties in the ultraviolet (UV) to mid-infrared (MIR) bands, and the concern about multiphoton absorption due to the pump pulse in the optical communications wavelength band is negligible. The ease of waveguide fabrication and the fact that propagation loss can be reduced by nearly an order of magnitude compared to Si waveguides are also significant advantages for inducing nonlinear phenomena [19,20,21,22]. However, SiN devices are already well optimized in terms of the material composition [23,24] and waveguide geometry [25,26], so the ways to further extend the spectral bandwidth are limited. Recently, multimode excitation has been proposed to overcome this situation. In the past, there were some studies on multimode excitation using optical fibers with large silica or liquid core (e.g., step-index [27,28], and graded-index profiles [29,30]), but the control of mode number by excitation and its contribution has not been investigated. The only application to SiN was reported by quasi-phase matching (QPM) method [31]. They used periodic modulation of the SiN waveguide structure to selectively launch a few modes up to TE20 with discrete QPM-dispersive waves (DWs).
In this paper, we propose a very simple and effective way to obtain a sufficiently wide bandwidth even with low-energy excitation on a SiN platform. By manipulating the spatial incidence position of the pump light with a precision of a few hundreds of nanometers, we can control the number of modes and nonlinear contribution in the core of a dispersion-engineered deuterated SiN (SiN:D) waveguide. As a result, a smooth and flat-top SCG spectrum from the UV to NIR bands and beyond is expected. The final goal of the broadband SCG is to stabilize our electro-optic modulated (EO) OFCs [9] with feedback control of the carrier-envelope offset (CEO) signal on an integrated platform. By combining our existing direct f-3f [32] and unique 2f-3f self-reference interferometers (SRIs) [33,34] with the efficient SCG device, we would be able to stabilize OFCs with a pump pulse energy as low as 0.3 nJ, which will lead to the realization of an “optical RF synthesizer” that can generate arbitrary frequencies from the sub-PHz to kHz bands originating from the optical frequencies [35].
2. Device design
A schematic of the dispersion-engineered SiN:D waveguide device is illustrated in Fig. 1. A pair of adiabatic spot-size converters (SSCs) are formed at the edge of the straight dispersion-engineered waveguide. A cross-sectional SEM image of the device is shown on the right in Fig. 1, in which the SiN:D core and Si handle substrate are highlighted with false color. To extract an accurate material dispersion relation, we started with the angular resolved ellipsometry characterization of the deposited SiN:D thin film. At a wavelength of 0.63 µm, the refractive index n of 1.87 was obtained. The full range of the dispersion over the refractive index ranging from 0.3 to 2.5 µm is shown in Fig. 2(a). Here, we superimposed the calculated effective refractive indices ${n_{eff}}$ obtained by a mode solver (Photon Design, FIMMWAVE) for the quasi-transverse electric (TE)-polarized fundamental mode (TE00) and higher-order modes (TE10, TE01). The cross-section of the waveguide was designed to be 1300 nm × 1000 nm to control the dispersion relation within the anomalous regime. The corresponding dispersion parameter D curves, given as $D ={-} ({c/\lambda } )\cdot ({{d^2}{n_{eff}}/d{\lambda^2}} ),$ are shown in Fig. 2(b). A SiO2 planarized top-cladding design was employed to further decrease the mode confinement, and increase the absolute anomalous dispersion D value, which can maintain the nonlinear propagation distance short. This structure can also interact with materials with extremely high nonlinearities, such as graphene on a Si photonic platform, which has been reported from our group [36].
Fig. 1. Device design schematic and cross-sectional SEM image with top-planarized SiN:D waveguide (scale bar: 1 µm; SiN:D core and Si substrate are shown with false color).
Fig. 2. (a) Measured material dispersion of 100-nm-thick SiN:D film from 0.3 to 2.5 µm (dashed line) and calculated effective refractive indices ${n_{eff}}$ with electrical field distribution for TE-polarized fundamental (TE00) and higher-order modes (TE10, TE01). (b) Calculated dispersion parameter D curves for each mode.
A key feature of our device design is the use of the contributions of TE10 and TE01 modes to enhance the SCG in short wavelength ranges, in addition to the expansion of the anomalous dispersion band by the TE00 mode. To realize such multiple modes-mixing state, the spatial position of the incident pump light is intentionally changed along the X- or Y-axis. The simulated evolution of the mode coupling efficiency from TE00 to TE00 (TE00/TE00), TE10 (TE00/TE10), and TE01 (TE00/TE01), and the integrated value of the three modes (TE00/TE00 + 10 + 01) are shown in Figs. 3(a) and (b). Note that the separation symbol of “ / “ indicates before and after the mode coupling.
Fig. 3. Results of mode-coupling calculation results of between incident TE00 mode and TE00, TE10, and TE01 modes with position offsets along (a) X-, and (b) Y-axes. Dotted lines indicate integrated efficiency of all modes. Note that Y: 0, and –1000 nm are located on the top, and bottom of the waveguide core.
In this simulation, the modes overlap efficiency and intermodal mixing evolution in the 300 µm-long SSC tapered structure (cf. liner variation of the waveguide width from 500 to 1300 nm) were essentially considered. However, when the SSC distance is short, as in this case, a spatial position offset has a strong influence on the excitation efficiencies of higher-order modes. This phenomenon has been confirmed in our eigenmode expansion (EME) simulations, which indicate that the TE00 mode field at the 500-nm-wide SSC tip is no longer a single-peak distribution if the offset is significant (e.g. over a few hundred nm), but a hybridized “TE00 + leaky” mode exists in both the SiN:D core and lower BOX layer. Unfortunately, the calculation of such TE00-based leaky mode cannot be well defined, so that a rigorous simulation with an FDTD method would be the best way to gain the absolute coupling efficiency from an objective lens to the dispersion-engineered region with high-order modes. On the other hand, the device scale for the full-scale simulation is too large at present. Thus, we assume that the leaky TE00 mode supported by the SSC tip (with arbitrary spatial offset if necessary) is now directly coupling to the dispersion-engineered section with a width of 1300 nm, to excite all TE00, TE10 and TE01 modes. This simplified approach is a realistic solution and saves enormous computational resources. Of course, the absolute coupling efficiencies shown in Fig. 3 are not in perfect agreement with experimental results.
The horizontal axes are shown with spatial position offsets along the X- and Y-axes, respectively. The coupling efficiency of the TE00 mode is reduced by the X-axis offset, while the TE00 + 10 + 01 efficiency is recovered to a certain amount by the TE00/TE10 coupling. Similarly, the TE00/TE01 coupling also contributes to the increase in the total efficiency on the Y-axis, but note that its shape is now asymmetric with respect to the offset change. The asymmetric distribution of the coupling efficiency is due to the large shift of the optical mode toward the -Y direction caused by the air-top cladding confinement [see the mode profile in the inset of Fig. 2(a)].
In principle, SCG can be promoted by utilizing strong light-matter interactions with self-phase modulation (SPM), four-wave mixing (FWM), stimulated Raman scattering (SRS), and soliton fission. To maintain the huge peak intensity within a short pulse duration, anomalous dispersion design through the confinement structure and material selection is an important guideline. In the case of higher-order solitons, the SPM initially dominates, but it quickly catches up by the group velocity dispersion (GVD), causing a periodic evolution along the device interaction length. Eventually, these perturbations break up the pulse propagating as a high-order solitons into its constituent fundamental solitons (i.e. soliton fission). At this moment, the energy of the higher-order soliton waves is segmented, resulting in a wide range of spectra on the frequency axis. Another essential design guideline to extend the SCG bandwidth is to activate the DWs with phase-matching conditions. When a fundamental soliton pulse is perturbed by higher-order dispersion, a part of the pulse energy is transferred to the DWs at specific frequencies. These frequencies are determined by the phase-matching conditions due to the nature of the soliton pulse rather than the well-recognized FWM process. The frequency-dependent optical phases for the DWs $\phi ({{\omega_{DW}}} )$ and soliton pulse $\phi ({{\omega_s}} )$ after the propagation distance z (i.e., with a delay of $t = z/{v_g}$) satisfy the following Eqs. (1) and (2), respectively [37]:
Based on this relationship, we can estimate the wavelengths of DW generation. As shown in Fig. 2(b), any pumping light sources below 1.2 µm is essential to flatten the SCG spectrum by exciting the TE10 and TE01 modes (both must be in anomalous dispersion regime), and subsequent DWs production. According to our spectral evolution simulations (see “4. Simulation, measurement, and discussion” for the details), a new virtual light source below 1.2 µm can indeed be created by the SPM effect of the TE00 mode (interaction length up to the beginning 2.5 mm), which is originally excited at 1.55 µm. This excitation scheme is defined as “cascaded pumping”.
In order to investigate the DWs production wavelengths via the cascaded pumping, we carried out a calculation under an assumption that the pump wavelength is continuously distributed ranging 1.00–1.55 µm. Expected phase-matching conditions with various pump wavelengths for TE00, TE10, and TE01 modes are shown in Figs. 4(a)-(c). In most cases, the DW generation wavelengths ($\mathrm{\Delta }\beta = 0$) are observed at two locations, in the VIS and MIR bands, respectively. In the case of the fundamental TE00 mode, the DW wavelengths in both the VIS and MIR bands tend to redshift gradually by sweeping the pump wavelength from 1.55 to 1.00 µm. In addition, regardless of the pump wavelength, the DW wavelengths in the VIS band are all in the range of 0.55–0.8 µm, indicating that the contribution of the SCG effect was small. The DW generation bands and their trend are quite different for the higher-order TE10 and TE01 modes case since the dispersion curves are apparently steeper and blue-shifted. As a result, multiple new DWs observed near the phase-matching wavelengths of 0.4–0.65 µm are generated, which contribute to the broadening and smoothing of the SCG at the device end. The DW generation points ($\mathrm{\Delta }\beta = 0$) of all the propagation modes against the pump wavelength variation are summarized in Fig. 4(d). Compared to the SCG with the fundamental TE00 mode alone, we can gain new bandwidth in the range of the UV to VIS bands by controlling the higher-order modes.
Fig. 4. (a)-(c) Calculated phase-matching condition $\mathrm{\Delta }\beta $ and dispersion parameter D of TE00, TE10, and TE01 modes. Red and green shaded areas indicate $\mathrm{\Delta }\beta $ less than ±5 mm-1. (d) Expected peak wavelengths of DW generation ($\mathrm{\Delta }\beta = 0$) caused by effects of sequential pump light transition. Blue shaded area corresponds to DW generation originated from TE10, and TE01 modes.
3. Sample preparation
In the sample preparation, the SiN:D film was formed by electron-cyclotron-resonance plasma-enhanced chemical vapor deposition (ECR-PECVD) at 200°C. Since a source gas of deuterated silane (SiD4) was used with N2 instead of conventional gases such as SiH4 or NH3, the SiN:D film contains no hydrogen, which avoids the strong optical absorption at the pump wavelength due to second-order N-H harmonic vibrations (see Ref. [38] for the detailed properties and composition analysis). For the fabrication, after the deposition of a 1-µm-thick SiN:D film on a 3-µm-thick thermal oxide Si wafer, a resist masked pattern was defined by electron-beam lithography. Then, the waveguide pattern was transferred by reactive ion etching. Once the SiN:D waveguide core had been fully embedded by the SiO2 cladding with the ECR-CVD, the top SiO2 layer was finally planarized by chemical mechanical polishing to maximize the anomalous dispersion. An SEM cross-sectional view of the fabricated waveguide device has been shown in Fig. 1. The device interaction length in this fabrication was fixed at 5 mm, which was determined from the following numerical analysis.
4. Simulation, measurement, and discussion
Before starting the experimental evaluation of the device, we simulated the SCG spectrum for the fundamental TE00 mode by the nonlinear Schrödinger equation (NLSE) associated with the split-step Fourier method. The purpose of this modeling was to see how well the spectrum would perform without considering the multimode excitation. The assumed calculation conditions were a coupled pump energy of 422 pJ with a pulse duration of 74 fs, a nonlinear refractive index n2 of 2.4 × 10−19 m2/W, and a propagation loss of 0.5 dB/cm. Figure 5(a) shows the calculated SCG spectrum for the TE00 mode, in which the incident pump pulse (dotted line) is broadened by more than 2.3 octaves after 5-mm-long propagation. Stimulated Raman scattering response is ignored in this simulation due to the material properties of SiN. The soliton order N [37] can be expressed as ${N^2} = \gamma {P_0}T_0^2/|{{\beta_2}} |$, where the Kerr nonlinearity $\gamma $ is $0.79\; {\textrm{W}^{ - 1}}{\textrm{m}^{ - 1}}$, the pulse duration ${T_0}$ is $74$ fs, and the second-order dispersion parameter ${\beta _2}$ is $- 0.07\; \textrm{p}{\textrm{s}^2}/\textrm{m}$ at the pump wavelength of 1.56 µm. Thus, the value of N before the soliton fission state is estimated to be 16 at the maximum input power. In fact, more than 10 small peaks have been observed in the simulated SCG spectrum. The DWs in the VIS and MIR bands can be clearly seen at wavelengths of 0.6–0.7 and 2.4–2.7 µm. The consistency of the two different approaches—analysis of the phase-matching conditions for the DWs and simulation of the short pulse evolution governed by the NLSE—is this thus completely confirmed.
Fig. 5. (a) Simulated SCG spectra for fundamental mode with center-symmetric pumping after 5-mm propagation. The incident pump pulse (center wavelength λ: 1.56 µm) is indicated by a dotted grey line. DWs in VIS and MIR bands exist around 0.6–0.7 and 2.4–2.7 µm. (b) and (c) Experimental SCG spectra with various spatial offset modulation along X- and Y-axes, respectively, where “near TE00 center” corresponds to the approximate center-symmetric excitation position for the TE00 mode (i.e., Y: 0 nm is located on top of the SiN core). (d) SCG spectra magnified for visible range 0.55–0.8 µm. (e) Far-field photograph of output SCG.
In the device characterization, a commercialized passively mode-locked Er-doped fiber laser with a repetition rate of 250 MHz was used as the pump source. We experimentally confirmed that the pulse duration was 74 fs, which matches with a Lorentz-function shape. A TE-polarized laser beam from the fiber laser was collimated by a lens, and then launched into the SiN:D waveguide’s SSC by using an aspherical lens in free space (NA: 0.55, MFD: ∼2.5 µm). Both the collimating and aspheric lenses were mounted on the same XYZ piezo stage, so that the focusing spot size was always maintained without variation. The coupling efficiency between the incident beam and SSC was estimated to be about 32%, which agrees with the mode-overlapping simulation result. This value results in a maximum pump energy of 422 pJ that can be coupled into the waveguide. The output SC light was corrected through a multimode fiber, and two types of optical spectrum analyzers were used to measure the wavelength range from 0.32 to 1.70 µm. Here, we attempted to excite the multiple modes by precisely modulating the spatial position of the incident focusing beam. With the multi-axis differential micrometer stages controlled with internal piezoelectric actuators, we introduced the spatial position offsets in the X- and Y-axes with a resolution of 267 nm/V to examine the SCG spectrum variation. We used a 3-axis Piezo Flexure stage (NanoMax 312, Thorlabs, Inc.) with a compatible controller (MDT693B). Since this stage has a positional resolution of 20 nm, we estimate that the controller is capable of 267 ± 10 nm of adjustment per 1 V. Thus, we acquired the experimental SCG spectra in the offset range of −1335 – + 1335 nm in 267-nm steps for both axes. Typical spectra among them are depicted in Figs. 5(b) and (c) for the X- and Y-axes, respectively. Note that if the X-axis position is at 0 nm, it means that the pump light is coupling with the maximum electrical field of the TE00 mode. However, the same condition corresponds to around –534 nm on the Y-axis because the center position is shifted downward significantly due to the asymmetric refractive index distribution of the SiN:D waveguide structure. This is clear when examining the mode-coupling results in Fig. 3 and the mode field distribution in the inset of Fig. 2(a). As for the measurement procedures, we first determined the mode center as “Y: −534 nm” by minimizing the device’s insertion loss, and then added an offset in steps of 267 nm/V. During the initial waveguide alignment, the pump power was squeezed as low as possible to suppress the optical nonlinearity.
Several selected SCG spectra magnified for visible range 0.55–0.8 µm are indicated in Fig. 5(d). On both the X- and Y-axes, a considerably deep notch response (∼ −50 dB in intensity) is observed at the wavelength of around 0.6 µm under the near central excitation condition for the TE00 mode (X: 0 nm, Y: −534 nm), which corresponds to the boundary area between the responses of DWs, and a continuous spectrum is formed by the SPM and soliton fission effects. In contrast, when an offset condition with ±801 nm was applied to the X-axis, the DW’s main peak around 0.55 µm was split and reduced, while a wide-ranging improvement in output intensity of ∼13 dB was found for the waves longer than 0.6 µm. In the same manner, in the Y-axis direction, gradually increasing the offset produced the smoothest SCG spectra at −1068 and +534 nm, respectively. These results are in good agreement with the calculated offset parameters required for the coexistence and generation of multiple modes as studied in the device design section, so we can expect that the meaningful signal enhancement of the SCG is achieved by the sequential interaction of TE00, TE10 and TE01 with multiple anomalous dispersion curves. As a proof of the existence of higher-order modes, we observed the SSC output port and captured the image as a far-field profile, as displayed in Fig. 5(e). Here, the offset value was set to one of the smoothest conditions of the SCG spectrum (X: −801 nm). It can be seen that the two bright spots are located in parallel due to the higher-order modes, overlap around as the fundamental mode.
We further analyzed the SCG light intensity transition in the VIS to NIR region by adding the spatial position offsets for X- and Y-axes, respectively. As shown in Figs. 6(a) and (b), the probing wavelengths were set to 0.4–1.0 µm in 0.2-µm steps, as well as to 0.55 µm, at which the original DWs peaks were dominated by the fundamental TE00 mode. First, focusing on the wavelength at 0.55 µm, we find that the maximum peak intensity is distributed around the offset value of 0 nm on the X-axis, and between 0 and –1000 nm on the Y-axis. This discrepancy can be simply explained by the partial overlapping of the peaks of the TE00 and TE01 on the Y-axis, as observed in the theoretical calculation in Figs. 3(a) and (b). Next, we consider the other wavelength bands. The output intensity is now significantly enhanced when the offset condition with the multimode excitation. Compared to the conventional excitation state suitable for TE00 mode, the SCG enhancement reaches 5–10 dB at the wavelengths of 0.4 and 0.8 µm, and up to 18 dB at 0.6 µm. Our interpretation of this phenomenon is that the original DW energy concentrated around 0.55 µm is being dispersed to the surrounding frequencies by the generation of multiple modes. As a result, it contributes to the broadening and smoothing of the SCG. When compared to the discrete phase-matching condition induced by QPM-DWs method [31], the spectral smoothness and overall SNR in the VIS and NIR regions are remarkably improved, even though our SiN:D waveguide is limited to just three modes. As an example of numerical comparison, the signal variation in the wavelength range of 0.6–1.2 µm was found to be ∼7 dB in our proposal while it was more than 20 dB for the QPM-DWs. Another important feature is the simplicity of our method, which does not need any periodic sub-micron structures.
Fig. 6. Extracted SCG light intensity at specific wavelengths by varying spatial position offsets along (a) X- and (b) Y-axes. The monitoring wavelengths are set to two groups: 0.4–1.0 µm in 0.2-µm steps, and 0.55 µm (corresponding to DWs induced by TE00 mode), to ascertain the impacts of the multiple modes.
Discussions so far have focused on the consideration of intramodal phase-mismatch condition with the cascaded pumping process. However, several recent studies have revealed that intermodal FWM processes [39,40,41] can also occur, in which waves of one mode are scattered by strong pump pulses of the other modes. This process can also contribute to the spectral broadening of the SCG light. In particular, the intermodal FWM effect from a TE00 mode to TE10 and TE01 modes should be negligibly small because of the large dispersion discrepancies, the interaction between TE10 and TE01 can help the signal enhancement in the visible range. From a practical point of view, the coherence state is one of the key evaluation criteria for realizing an excellent OFCs generator. When we launched the higher-order modes with an offset of Y: –1068 nm, the CEO signals can be detected in both f-2f external interferometer and f-3f SRI setups [32], which offers preliminary evidence of a good coherence state even in the visible range. We shall confirm the feasibility over a wide range spectrum as a part of our future work.
5. Conclusion
In conclusion, by taking advantage of our existing excellent SiN:D waveguide integration platform, we have presented an effective method for smoothing the SCG spectrum with simultaneous excitations of the fundamental TE00 and higher-order TE10 and TE01 modes. After a theoretical treatment from several different points of view, including a mode excitation analysis and search for phase-matching conditions of DWs, we experimentally demonstrated the feasibility of the proposed method by controlling the spatial position offset at the pump input facet. Using the SiN:D waveguide device with an interaction length of 5 mm, we found an enhancement of up to 18 dB in SCG intensity at a wavelength of 0.6 µm with an offset of about −1 µm along the Y-axis direction. Overall, an increase in the SNR was obtained in the spectral range of 0.4 to 1.0 µm, resulting in a broadband and flat-top SCG spectrum. We are convinced that the demonstration and analysis of the multimode excitation can contribute to the bandwidth broadening and smoothing of the SCG spectrum even at low energy excitation.
Funding
Ministry of Education, Culture, Sports, Science and Technology (LEADERs); Japan Society for the Promotion of Science (19H02156, 19K15054, 20H00357).
Acknowledgments
The authors would like to thank to R. Sato, M. Motoki, and Y. Sutoh for their technical support.
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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