Wideband nonlinear spectral broadening in ultra-short ultra - silicon rich nitride waveguides

CMOS-compatible nonlinear optics platforms with high Kerr nonlinearity facilitate the generation of broadband spectra based on self-phase modulation. Our ultra – silicon rich nitride (USRN) platform is designed to have a large nonlinear refractive index and low nonlinear losses at 1.55 μm for the facilitation of wideband spectral broadening. We investigate the ultrafast spectral characteristics of USRN waveguides with 1-mm-length, which have high nonlinear parameters (γ ∼ 550 W−1/m) and anomalous dispersion at 1.55 μm wavelength of input light. USRN add-drop ring resonators broaden output spectra by a factor of 2 compared with the bandwidth of input fs laser with the highest quality factors of 11000 and 15000. Two – fold self phase modulation induced spectral broadening is observed using waveguides only 430 μm in length, whereas a quadrupling of the output bandwidth is observed with USRN waveguides with a 1-mm-length. A broadening factor of around 3 per 1 mm length is achieved in the USRN waveguides, a value which is comparatively larger than many other CMOS-compatible platforms.

nitride, which is generally characterized by a refractive index < 2.2 23,24 and according to Miller's rule, concomitantly lower nonlinear refractive index.
In this paper, we study ultra -silicon rich nitride (USRN) waveguides for their ability to acquire nonlinear phase using ultra -short lengths. The USRN material 25,26 is distinguished from the typical silicon rich nitride platform as it is characterized by a much larger linear refractive index (n = 3.1), much larger nonlinear parameters (∼ 550 W −1 /m vs. a few W −1 /m) though both have a sufficiently large band gap to eliminate TPA at the 1.55 μ m wavelength. The ultrafast spectral characteristics of USRN waveguide structures are investigated. Using the broad spectrum generated with the short waveguide lengths, quality -factors (Q-factors) of a ring resonator are characterized over a wavelength range of almost 200 nm, outside of that typically available using an erbium -based amplified spontaneous emission source. The output spectra at pass ports of USRN ring resonators using a femtosecond fiber source are examined to understand how the resonator Q-factors and spectral bandwidth change. In addition, the short waveguides with a 1-mm-length scale are sufficiently short to be well below the dispersion length and therefore, nonlinear dynamics are predominantly governed by the waveguide's nonlinearity.

Results
Our USRN film is composed of approximately 2:1 of Si:N ratio that is much more silicon rich than stoichiometric silicon nitride (Si:N = 3:4). USRN waveguides which are 600 nm wide and 300 nm thick possess anomalous waveguide dispersion of around 200 ps/nm/km at 1.55 μm. Waveguides used in this experiment have a length of ∼ 1 mm. Using the previously measured n 2 value of the film 25 , the nonlinear parameter for this waveguide is calculated to be ∼ 550 W −1 /m. This implies a dispersive length (L D ) of 32 cm and a nonlinear length (L NL ) of < 0.19 mm for peak powers > 10 W. Given that the L D is much longer and the L NL is much shorter than the physical waveguide length, the pulse dynamics will be dominated by the nonlinearity rather than dispersion in the waveguide. The large energy bandgap (E g ∼ 2.1 eV) is also enough to eliminate TPA of the laser centered at 1.55 μ m (∼ 0.8 eV) 16 . Figure 1(a) depicts the schematic of the experimental setup to observe output spectra of USRN waveguides. Figure 1(b) shows a scanning electron micrograph of the fabricated USRN waveguide. We use a 500 fs fiber laser centered at 1.55 μ m with 20MHz of repetition rate to generate broadened spectra dominated by SPM, which induces temporal variations of the ultrafast pulse intensity. The quasi-TE mode was coupled into the USRN waveguides via tapered lensed fiber. The spectra of output TE signals were observed through optical spectrum analyzer. We use two different structures of USRN waveguides (a bus waveguide with a single ring resonator and a short-length waveguide) to detect the characteristics of their spectral broadening and Q-factor using femtosecond pulses.
First, we investigate the output spectra from the pass ports of two USRN add-drop ring resonators (USRN_ RR1 and USRN_RR2) waveguides as shown in Fig. 2. USRN_RR1 and USRN_RR2 possessing a 20 μ m ring radius both were fabricated to have gaps of 150 nm and 100 nm gap between ring and bus waveguide, respectively. The length of the bus waveguide is 430 μ m for USRN_RR1 and 650 μ m for USRN_RR2.
The transmission spectra at each pass port are present with the number of resonant peaks as shown in Fig. 2(a). The spectral bandwidth of the input pulse entering the waveguides is measured to be approximately 60 nm at the − 30 dB level. The bandwidth measured at the output of USRN_RR1 and RR2 was 110 nm and 130 nm respectively, representing 1.8 and 2.2 times broadening over the original pulse bandwidth. As expected, the output spectral width of USRN_RR2 is a larger because the longer bus waveguide length allows more nonlinear phase to be acquired (Qualitatively, the nonlinear phase acquired in the absence of any nonlinear losses, ϕ NL = γ .L eff .P peak , where L eff is the effective waveguide length and P peak is the peak power used). Two spectral side wings in Fig. 2(a) appear with around 1530 and 1590 nm of center wavelengths. The wings depict an evidence of nonlinear broadening because these are situated outside the region where the fs source possesses spectral content. Consequently, the side wings due to nonlinear spectral broadening facilitate an increase in the number of observable resonance peaks. Each resonance peak is quantified by the Q-factor, defined as center wavelength divided by full-width half maximum (FWHM) bandwidth of a signal (See Fig. 2(b)). The free spectral range (FSR), defined as the spacing in optical frequency between two successive transmission peaks, of two USRN_RR are around 5 nm and the observable resonance peaks span a wavelength range from 1480 to 1640 nm. It is observed that the Q-factor is the highest at the shortest wavelength (USRN_RR1 = 15000 and USRN_RR2 = 11000), and decreases linearly as the wavelength is longer. A greater extent of the optical field is evanescent at longer wavelengths, and consequently, light stored/resonating within the ring couples more easily into the bus waveguide. In line with the definition of Q-factor (= energy stored / energy dissipated per cycle), it follows that Q-factor decreases at longer wavelengths.
Next, we investigate the nonlinear spectral broadening properties of a USRN waveguide (USRN_SWG) with 1.2 mm length (∼ 2× that in the ring resonator with the 650 μ m bus waveguide). The output spectra of 500 fs pulses launched into USRN_SWG are observed as the input peak power (P peak ) is increased and the results are shown in Fig. 3. The output spectrum is observed to broaden as the P peak is increased from 26 W to 66 W. P peak denoted in the figure depicts the coupled input peak power compensated for waveguide loss (10 dB/cm) and output fiber-waveguide coupling loss (∼ 10 dB per facet). The spectra corresponding with P peak = 26 W, 40 W and 53 W are observed to be highly symmetric, therefore SPM-induced broadening is likely to be the dominant effect. Soliton effects and Cherenkov radiation for example is unlikely to be present at these length scales -It often facilitates the broadening of pulse spectra in the regime of supercontinuum, through dispersive wave  formation and consequently results in spectra which are asymmetric. At P peak = 66 W, the spectral envelope appears slightly asymmetric with different power levels between two wings located on either side of a 1.55-μ m spectral peak. The L NL calculated for P peak = 66 W is ∼ 3.0 × 10 −2 mm. The parameter N 2 (= L D /L NL ) is around 10000, in other words, N 2 ≫ 1. Therefore, it shows that SPM dominates over group velocity dispersion (GVD) for spectral broadening 27 . If we don't take into account dispersion effect due to dominantly large SPM effect, the asymmetric shapes can arise from the interplay of SPM and high order nonlinear effects. For ultrashort input pulses, self-steepening effect resulting from the intensity dependence of the group velocity occurs and it leads to an asymmetry in the SPM-broadened spectra 28 . Especially, self-steepening at the trailing edge of the pulse produces optical shock formation 29 . When loss is assumed to be zero for simplicity, the shock distance z s defined as ∼ 0.43L NL /s for hyperbolic secant pulse typical in a fiber laser (Where parameter s = 1/ω 0 T 0, ω 0 = angular frequency, T 0 = T FWHM /1.76 for hyperbolic secant pulse, T FWHM = 500 fs) 25 . The shock distance, z s at P peak = 66W is around 4 mm at 1.55 μ m, respectively. z s has same order of length with the waveguide length (= 1.2 mm), so self-steepening -induced asymmetric spectral shape might account for the slight asymmetry in the spectrally broadened pulse (see Fig. 3). In addition, SPM-broadening can be limited by the extent of propagation loss that is related with L eff 27 . The experimentally measured loss coefficient α wg is 2.30 cm −1 . L eff defined as (1 − exp(− α wg L))/ α wg is calculated to be 0.10 cm at a physical length L = 1.2 mm. The maximum achievable L eff (L eff(max) ) becomes 0.43 cm as L goes to infinity. The calculation shows that reducing the propagation loss to 1 dB/cm enables 10% increase in SPM-broadening parameter, ϕ NL owing to the increase of L eff value for same waveguide length and experimental condition.
The spectral bandwidth at − 30 dB level, Δ λ 30 dB , is also drawn as a function of input peak power in Fig. 4(a). The bandwidth increases linearly up to P peak ∼ 66 W with 2.3 nm/W of a slope. To investigate nonlinear loss including TPA effects on the USRN_SWG, output peak power (P out ) is measured as a function of P peak up to 100 W. P peak varies by using a digital variable attenuator and P out is calculated from measured average output power at output tapered fiber via the USRN waveguide. Variation of the reciprocal transmission as the input peak power is varied (P peak /P out versus P peak 30 ) allows us to extrapolate the presence of two photon absorption. P peak /P out is observed in Fig. 4(b) to be almost flat with a standard deviation of 0.78 and an average of 23, implying the absence of nonlinear loss at these power levels. Therefore, the linear increase in both the output bandwidth and power versus P peak indicates that USRN waveguide has relatively low nonlinear losses including TPA and free carrier effects up to P peak = 100 W. The spectral evolution of 500 fs pulses as a function of input peak power calculated using the Nonlinear Schrödinger equation is shown to increase linearly as P peak increases (see Fig. 4(c)). The 2 mm USRN_SWG at − 30 dB level as a function of input peak power (b) Measured value of P peak /P out vs. P peak . The flat profile obtained for P peak /P out as P peak is varied implies negligible nonlinear losses. (c) Evolution of the 500 fs pulses as a function of the input peak power.
Scientific RepoRts | 6:27120 | DOI: 10.1038/srep27120 calculation also reveals that the pulse spectrum spans from 1450-1700 nm at P peak ∼ 66 W, which corresponds well with the experimental result (See Fig. 3).
To see the effect of the spectral broadening on the waveguide length, we compared the output spectra as a function of waveguide length as shown in Fig. 5. Figure 5(a) shows measured spectra of 1.2-mm and 1.6-mm length USRN_SWG. Δ λ 30 dB of 1.2 and 1.6-mm USRN_SWG is around 230 and 270 nm, respectively which is 3.7 and 4.6 times larger than that of the fundamental input. The average measured output power was of 84 μ W and 88 μ W for 1.2-mm and 1.6-mm USRN_SWG, respectively. Δ λ 30 dB is also compared for USRN_RR1, USRN_RR2, USRN_SWG (1.2-mm-length) and USRN_SWG (1.6-mm-length). These 4 waveguides have different interaction lengths, so Δ λ 30 dB in terms of waveguide length can be plotted as shown in Fig. 5(b). If we adopt a linear fit into the graph, the slope is derived to around 150 nm/mm, implying that the bandwidth broadens by 150 nm per millimeter of USRN waveguide .
We define a length-dependent broadening factor, F b (= Δ λ out /(Δ λ in · L), mm −1 ) which takes into account the bandwidth ratio between input (Δ λ in ) and output pulses (Δ λ out ) per unit length in the waveguide (L). For USRN waveguides with lengths of 1.2 mm and 1.6 mm, the F b is 3.19 and 2.81 respectively. The comparison of F b between our USRN_SWG with other platforms measured at the telecommunication bands is listed in Table 1. The table includes other reports on both SPM and SCG spectral broadening with a few to hundreds mm of waveguide length. SPM-broadening is normally implemented with hundreds and thousands femtoseconds of pulse widths. F b is shown less than 0.1 excluding the silicon nitride waveguide (F b ∼ 0.36) 15 that is achieved due to relative short waveguide length. It indicates that the F b value on our waveguide is more than 30 times larger than other SPM-broadened data even though the broadened Silicon rib 31  spectra from our device is also dominated by SPM. Our USRN_SWGs have relatively the shortest length, but the highest F b (∼ 3) among SPM-induced waveguides. This is because γ in our demonstrated USRN waveguides is ~ 550 W −1 /m 25 which is large enough to induce spectral broadening even with lengths as short as 1 mm. Comparing the reports on SCG broadening listed in Table 1, F b is observed to be ≤ 1 except for that on ref. 42. We note further that in ref. 42, the longer length scales enable nonlinear effects in addition to pure self -phase modulation such as dispersive wave formation to help facilitate the spectral broadening. The Si 3 N 4 waveguide (ref. 42) depicts higher F b than other SCG-generated waveguides owing to engineering of two zero-GVD points and very small propagation losses (= 0.7 dB/cm) for coherent SCG. Despite these benefits to obtain the broad SCG spectrum, however, F b is ∼ 0.7 times smaller than those in our USRN-SWG. Furthermore, we only estimated the minimum (transform-limited) input spectral width at − 30 dB level on the Si 3 N 4 waveguide by time-bandwidth product assuming Sech 2 pulse, so F b value might in fact be smaller than what we expected. Frequency comb generation in a silicon nanophotonic wire waveguide reported in ref. 43 is characterized by an F b ∼ 0.24 because of the broad input spectral width even with an octave spanning. Based on Table 1, therefore, our USRN_SWG achieves high spectra-broadened efficiency even with ultra-short lengths because of a combination of large nonlinearity and negligible nonlinear losses. In addition, high powers can be used without TPA effects. Such TPA effects have been widely documented to occur at sub -watt powers in silicon waveguides.
Using the USRN waveguides with a length of 1 mm, an output bandwidth of around 200 nm centered at 1550 nm is achieved.

Discussions
When we consider the third order dispersion (TOD), TOD length, defined as L D ′ = T 0 3 /β 3 , is ∼ 0.3 m (β 3 = 68 ps 3 /km at 1.555 μ m) 25 . L D and L D ′ are about 0.3 m-4 orders of magnitude larger magnitude than L NL and 300 times larger than the waveguide length in USRN_SWG (∼ 1 mm). Consequently, we don't take into account dispersion effects in the broadened spectra. The asymmetric spectral shape as shown in Fig. 3 can be attributed to other nonlinear effects such as modulation instability as well as self-steepening effect because the waveguide's anomalous dispersion could trigger several nonlinear processes for extending the spectra. The spectral shape around 1.55-μ m-wavelength doesn't show significant phase shift as input peak power increase, but instead, the spectrum broadens with high order sidebands as shown in Fig. 3. Therefore, it is difficult to identify the nonlinear effects present by solely observing output spectral shapes. Through observations of the broadened spectra, their evolution and the length scales involved, self -phase modulation is likely to be the dominant effect contributing to the spectral broadening.

Conclusions
We have studied ultrafast wideband broadening of USRN waveguides which are around 1 mm in length. USRN add-drop ring resonators broaden the output spectra by a factor of around 2 compared with the bandwidth of the 500 fs input pulses. The Q-factors, which range from 1480 and 1680 nm, measured at pass ports of the resonators are examined to have the highest values of 11000 and 15000 according to the bus waveguide length with a free spectral range of 5 nm. In addition, short waveguides of 1.2 mm and 1.6 mm USRN_SWG facilitated broadening of the spectral bandwidth to 230 and 270 nm, corresponding to 3.8 and 4.5 times larger than that of the fundamental input, respectively. Owing to the high nonlinear parameter (γ ∼ 550 W −1 /m) and low TPA of USRN, the waveguides possess a higher F b (∼ 3) than that in other CMOS-compatible platforms. Therefore, we can obtain output bandwidths of 200 nm (0.2 octaves) centered at 1.55 using ultra-short USRN waveguides with 1 mm in length. Consequently, the demonstrated USRN waveguides could be well poised to enable CMOS-compatible nonlinear optical devices with much smaller footprints due to its short length and high nonlinearity, and find applications in wideband and multi-wavelength generation at the telecommunications wavelength.

Measurements.
A 500 fs fiber laser centered around 1.55 μ m with 20 MHz repetition rate was used as a fundamental source. The laser polarization maintains with quasi TE mode, linearly horizontal-polarized by using in-line fiber polarization controller. The polarization-maintained input light was coupled into USRN waveguides via tapered lensed fiber. Output TE signals were also coupled into the same type of polarization maintaining tapered fiber and their spectra were observed through optical spectrum analyzer.
Device fabrication. Fabrication of the waveguides was performed by first depositing 300 nm of ultra -silicon rich nitride films using inductively coupled chemical vapor deposition. In order to minimize N -H bonds which are known to cause materials losses close to 1.55 μ m, precursor gases used were SiH 4 and N 2 . The gas flow ratio of SiH 4 :N 2 used to deposit the films in this work was ∼ 2:1. The deposition temperature used was 250 °C. The waveguides were then defined using electron -beam lithography followed by reactive ion etching. Finally, 2 μ m of SiO 2 overcladding was deposited using plasma enhanced chemical vapor deposition.