We report ultra-broadband supercontinuum generation in high-confinement Si3N4 integrated optical waveguides. The spectrum extends through the visible (from 470 nm) to the infrared spectral range (2130 nm) comprising a spectral bandwidth wider than 495 THz, which is the widest supercontinuum spectrum generated on a chip.
© 2015 Optical Society of America
Ultra-broadband optical spectra obtained by supercontinuum generation (SCG) have found wide-spread use in applications and fundamental research. Examples are optical coherence tomography , unraveling nonlinear dynamics [2–4], coherent spectroscopy , and frequency metrology . Of particular interest is extending SCG into the visible range and beyond, which has so far been possible only with bulk nonlinear media , tapered fibers [8, 9], photonic crystal fibers [10–12], and χ(2) nonlinear waveguides .
A major disadvantage of these approaches is their lack of CMOS compatibility, because CMOS compatibility allows for fabrication of devices in high volumes using established facilities and for photonic integration with electronic circuits . A well-known CMOS-compatible waveguide platform is provided in silicon photonics, where a large nonlinear coefficient (γ ≈ 300 W−1m−1) is available to overcome waveguide losses and provide highly efficient SCG [15, 16]. However, the small band gap of silicon, corresponding to about 1 µm wavelength, limits the wavelength range of supercontinua to the infrared. Another limit is that at the high intensities needed for ultra-broadband SCG, pump wavelengths shorter than 2 µm, such as in the 1.3 and 1.5 µm telecommunication bands, suffer from nonlinear losses occurring in silicon such as two-photon absorption and subsequent free-carrier absorption.
A most promising CMOS-compatible approach for extending on-chip SCG into the visible range is based on silica [17, 18] and silicon nitride [19–21] glass platforms, which offer excellent transparency down to the ultraviolet. Specifically, low-pressure chemical vapor deposition (LPCVD) of stoichiometric materials  offers highly reproducible fabrication with predefined material dispersion and extremely low-loss waveguides (¡ 0.1 dB/m) . For optimally exploiting the Kerr index of Si3N4, n2 = 2.4·10−19 m2/W , the optical mode can be tightly confined due to the high-contrast offered by the silicon nitride based glass platform, thereby offering an increased nonlinear coefficient (γ ≈ 1 W−1m−1). Additional advantages are the options available for integrating extended waveguide circuitries , as well as rare-earth-doped lasers .
The widest supercontinuum spectra obtained in CMOS-compatible platforms to date were generated with silicon nitride waveguides, using ultrashort pulses at 1.5 µm wavelength in a 1.4 cm long waveguide  and at 1.3 µm wavelength in a 4.3 cm long waveguide . The latter yielded some output at the edge of the visible range (¿ 665 nm). Improved engineering of the dispersion was proposed  and applied for further spectral broadening [20,28], however, for SCG, the output remained at wavelengths longer than 700 nm. Most recent experiments successfully extended the SCG towards the blue range  with a spectral bandwidth of 310 THz in a 1 cm long underetched waveguide. These results show that, to obtain shorter wavelength supercontinua on a chip, a shorter wavelength pump is required and, consequently, suitable dispersion for a shorter pump wavelength has to be provided.
Here, we report ultra-broadband supercontinuum generation in high-confinement stoichiometric Si3N4 integrated optical waveguides. The SCG extends from the blue wavelength range (470 nm) to the infrared spectral range (2130 nm). This range comprises a spectral bandwidth of more than 495 THz which is, to our knowledge, the widest supercontinuum ever generated on a chip. The generation of such a wide spectral bandwidth supercontinuum is made possible by our novel technique for reliable fabrication of high thickness (up to ~1 µm), crack-free waveguides using LPCVD [29, 30]. The increased waveguide dimensions are used to shift the zero dispersion wavelength (ZDW) to values as short as 1 µm for phase-matched excitation with a mode-locked 1064 nm Yb-fiber laser, thereby extending the short-wavelength edge of the supercontinuum and obtain ultra-broadband SCG at a propagation length as short as 5.5 mm.
2. Dispersion calculation
The scanning electron microscope (SEM) picture in Fig. 1(a) shows a typical example of the cross section of the waveguides used in this experiment with a Si3N4 waveguide core shown in red and a SiO2 cladding shown in blue. It can be seen that the lower part of the cross section has a rounded shape. For calculating the waveguide dispersion, this shape was taken into account in the form of step index profiles as found in the SEM images. The optical modes and their effective refractive indices were calculated using a finite element solver  for a wavelength range from 400 to 2500 nm. The calculated dispersion parameter, D, for the fundamental quasi-TM modes and waveguides with a height, h, of 1.0 µm and widths, w, of 0.70, 0.75, and 0.80 µm, respectively, is shown in Fig. 1(b). These particular dimensions were chosen so that light with a pump wavelength of 1064 nm, such as conveniently available from Yb-or Nd-doped lasers, experiences anomalous dispersion (D > 0), which is not the case for bulk Si3N4 (red dashed line). We note that increasing the waveguide width (from 0.70 µm to 0.80 µm) increases the wavelength range that experiences anomalous dispersion by 170 nm. This means that a broader bandwidth is expected from wider waveguides. Another result of the increased waveguide dimensions is that the waveguide supports three modes at the pump wavelength in the TM polarization, namely the fundamental TM00 and two higher order modes TM10 and TM20.
3. Experimental results
The experimental setup for SCG is depicted in Fig. 2. Ultrashort pulses with a center wavelength of 1064 nm are provided with a mode-locked Yb-doped fiber laser (Ekspla, LightWire FF200). The laser provides pulses with about 115 fs duration, a repetition rate of 41 MHz, and a maximum average output power of 200 mW (maximum pulse energy 5 nJ). The pulses are coupled into the Si3N4 waveguides with a coupling loss of about 9 dB using an aspheric lens. The two particular chips selected here, out of 40 chips, contain 20 waveguides of various widths each with a height of 1.0 µm, and a length of 5.5 mm. To control the pump power, a half-wave plate and a polarizing beam splitter are used. A second half-wave plate is used to set the input polarization for excitation of quasi-TM modes. The supercontinuum is collected using a lensed fiber and recorded using an optical spectrum analyzer (Ando AQ6315A) and a near-infrared spectrometer (Avantes NIRline). To minimize the collection of undesired scattered light during the measurements, the waveguides have two bends that provide an offset, d in Fig. 2, of 0.6 mm between the input and output waveguide facets.
The supercontinuum spectrum generated in a waveguide with w = 0.8 µm, at the maximum available incoupled pulse energy, Ep, of 590 pJ is shown in Fig. 3(a). This pulse energy is limited by the coupling losses. The generated spectrum extends from the blue, at 470 nm at a -30 dB level, and ends in the infrared at 2130 nm. This is, to our knowledge, the widest super-continuum ever generated on a chip, measured in relative bandwidth (more than 2.1 octaves) as well as absolute bandwidth (more than 495 THz).
To more systematically characterize the supercontinuum, we measured the output spectra versus incoupled pulse energy of the pump laser. The results for a waveguide with w = 0.775 µm are summarized in Fig. 4. One can see that the spectrum continuously broadens with increasing Ep. A dispersive wave becomes noticeable at Ep = 355 pJ with its peak at 648 nm. The peak shifts to shorter wavelengths as the power increases, until it reaches 635 nm at Ep = 462 pJ. In these experiments, no damaging of the waveguides occurred. However, we found a damage threshold of 1 nJ (incoupled) in other experiments with 10-ps pulses. At low pump energies a small signal can be seen at 532 nm, which we identified to be scattering of infrared pump laser radiation in the OSA. However, this background peak becomes clearly exceeded by visible supercontinuum radiation as the pump energy increases. The blue radiation centered around 480 nm occurs above Ep = 248 pJ and is clearly visible in the photograph shown in Fig. 3(b). A small spectral feature centered at 1200 nm can be seen at low pulse energies as well. We found that this background feature consists of weak radiation from the pump laser, but is surpassed by supercontinuum radiation at pump energies beyond 350 pJ.
To characterize the supercontinuum as a function of the waveguide dispersion, we injected the pump laser into waveguides of various widths. The results are shown in Fig. 5 for w = 0.675 to 0.775 µm. The incoupled Ep differs only slightly from waveguide to waveguide (610±25 pJ) due to some variation in coupling losses. It can be seen that the SCG broadens with increasing w at both the short wavelength side as well as the long wavelength side. This observation is in agreement with what is expected from the broadening of the anomalous dispersion range in Fig. 1(b).
4. Numerical calculations
For a theoretical modeling of the observed SCG, we used the multi-mode nonlinear Schrödinger equation (MM-NLSE, see Appendix) . The equation describes the interaction of multiple transverse modes such as through self and cross-phase modulation, four-wave mixing, and self-steepening. We calculate that for the combination of our spatial pump beam parameters and our waveguide parameters only the fundamental mode (TM00) and one higher order mode (TM20) are excited and that the incoupled pulse energy is estimated to be evenly distributed among the two modes at a wavelength of 1064 nm. The nonlinear coupling coefficient between the fundamental and higher order mode is calculated by evaluating their overlap integral.
In the calculations, we restrict ourselves to the waveguide dimensions that provided the widest SCG as shown in Fig. 3(a) (h = 1.0 µm, w = 0.8 µm, 5.5 mm propagation length). The effective area of the fundamental mode is calculated to be 0.55 µm2 for this cross section and the resulting nonlinear coefficient, γ, is 2.6 W−1m−1 at a wavelength of 1064 nm. The corresponding nonlinear length is calculated to be 0.15 mm. In the model the dispersion of the waveguide is included up to the 18th order. The dispersion parameter, D, is calculated as 60 ps/(nm km) at the pump wavelength and the resulting dispersion length is 0.37 m. To include a realistic decay of the field amplitudes during propagation we take a propagation loss of 1.3 dB/cm into account, which was measured at the pump wavelength and results in an effective length of 5.1 mm for the waveguide length used. Due to the huge bandwidth of the generated spectrum, it is important to consider the wavelength dependence of the effective mode area and, hence, a wavelength dependence of the nonlinear coefficient. This dependence is introduced by means of a so-called shock term . We neglected the Raman effect, which appears justified in view of previous experiments with SCG in silicon nitride waveguides [19, 21], where Raman scattering did not significantly affect the obtained supercontinuum. As the input light field we take a Fourier-limited pulse with 115 fs duration and a center wavelength of 1064 nm. Calculations show that the chirp introduced by the coupling optics can be neglected.
Figure 6(a) shows the spectrum of the total output (blue) calculated with a total pulse energy of 590 pJ that is equally divided over the fundamental and the higher order mode as in the experiments. In calculations where the pulse energy in the higher order mode was varied we found that the bandwidth of the output spectrum is not sensitive to the amount of pulse energy in the higher order mode, because the mode undergoes normal dispersion in the waveguide. For comparison the measured spectrum from Fig. 3(a) is shown in red. It can be seen that, besides a slight red-shift of the generated spectrum, the overall agreement between the calculated and measured supercontinuum is good. For example, both clearly show the presence of two dispersive waves. A possible reason for the red-shift might be a remaining uncertainty in the refractive index data. Furthermore, we calculated the position of the dispersive waves by their phase-matching condition  and found them to lie at 710 nm and 2080 nm, which is in good agreement with the obtained data. Similarly, the generation of blue light at 480 nm, which is observed in the experiments, is not explained with our current model, and a closer investigation is subject of ongoing research. In Fig. 6(b) the spectral broadening during the propagation is shown, calculated such as in Fig. 6(a), and it can be seen that already after a propagation of 2 mm most of the bandwidth is obtained.
In conclusion, we have shown ultra-broadband on-chip supercontinuum generation in CMOS-compatible Si3N4 waveguides. When pumped at a center wavelength of 1064 nm with pulses of 115 fs duration, the generated spectrum ranges from the visible blue range (470 nm) to the infrared (2130 nm) and comprises a spectral bandwidth of more than 495 THz. This is, to our knowledge, the widest supercontinuum ever generated on a chip. The measurements show that the bandwidth of the supercontinuum spectrum increases with the incoupled pulse energy and with the waveguide width. A physical model based on the multi-mode nonlinear Schrödinger equation shows that only the fundamental mode contributes to the SCG into which only half of the available pump energy was coupled (≈ 300 pJ). This suggests that a more efficient SCG might be obtained, possibly also with further increased spectral bandwidth. This might be achieved with an improved spatial control of the input coupling, e.g., by means of tapered waveguides, such that all of the available pulse energy is coupled into the fundamental mode.
The wide bandwidths of the spectra demonstrate the huge potential of integrated nonlinear optics using Si3N4/SiO2 waveguides, provided here using the TriPleX platform . The visible to infrared coverage, extending throughout most of the transparency range of Si3N4 and SiO2, appears to be highly attractive for applications such as for self-referencing optical frequency combs  on a chip or widely tunable light sources for label-free microscopy and imaging  in life sciences.
The supercontinuum generation in the waveguides presented here was modeled by numerically solving the multimode generalized nonlinear Schrödinger equation (MM-NLSE) which was derived first in reference . We neglect the Raman scattering contribution as it has been reported to not significantly affect SCG in silicon nitride waveguides [19, 21] which yields the following set of equations:
The evolution of the temporal envelope of the mode p, Ap(z,t), is described in a reference frame that travels with the group velocity β(1) of the fundamental mode. The electrical field is assumed to have a frequency centered at ω0 and to travel with a phase velocity of measured relative to the one of the fundamental mode β(0). The higher order dispersion coefficients are the respective n-th expansion coefficients of the Taylor series of the propagation constant centered around ω0, which accounts for the dispersion of the waveguide. The nonlinear interaction of the p-th mode with modes l,m,n is described by the overlap integrals which can be interpreted as an effective area of the respective nonlinear interaction, . The frequency dependence of the nonlinearity is included by the shock-time constants
This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs. We thank W. Hoving (Anteryon BV, The Netherlands) and W. J. Mulder (Avantes BV, The Netherlands) for arranging a short-term loan of the NIR spectrometer.
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