1. Introduction

All optical signal processing is a critical requirement for future ultra-high speed telecommunication networks in order to meet the growing demand for greater bandwidth, network flexibility, low energy consumption and costs. Achieving this in the form of photonic integrated circuits (PICs) is expected to yield important benefits [1]. The efforts spent on this subject have naturally targeted highly nonlinear materials such as chalcogenide glasses (ChG) [2,3] and semiconductors, such as silicon and AlGaAs [4–13]. Combined with their large refractive index (typically > 3), which can in turn lead to waveguides with extremely tightly confined (even sub-μm) optical modes, this has produced nonlinearities (γ) exceeding 300,000 W^-1km^-1 for semiconductor nanowires [6,8,13], and approaching 100,000 W^-1 km^-1 for chalcogenide glass nanotapers [3], allowing nonlinear optics at sub-watt power levels on millimeter length scales, with the added benefit of yielding very tight bend radii with negligible losses [14]. However, in spite of these advantages, both semiconductors and chalcogenide glasses still pose several challenges. For integrated nanowires [6–9,13], linear propagation losses [14–16] are difficult to reduce below a few dB/cm (due to surface roughness scattering and surface state absorption) and achieving low coupling loss requires a significant effort [17,18]. In addition, for silicon in particular, nonlinear losses due to two-photon absorption (TPA) as well as TPA generated free-carriers are well known to pose a serious limitation to device performances at higher powers [19–23]. While these detrimental effects can be in principle reduced, for example by way of p-i-n junctions [20] to sweep carriers away, the intrinsic material nonlinear figure of merit of Si (FOM = n₂/βλ =1.8 [3], where β is the TPA coefficient, n₂ the Kerr nonlinearity and λ the pulse central wavelength) in the telecommunications window (1530–1620nm) is low [23]. While chalcogenide glasses are promising materials for photonics [3,24–26] due to their nonlinear parameters (comparable to silicon) [21], and due to their high nonlinear figure of merit, the associated fabrication technology as well as the intrinsic material stability are clearly not yet on the same level as silicon or silica glass.

Silica glass, on the other hand, has arguably become the “silicon” of the fiber-optic transmission world due to its extremely low loss, high manufacturability, stability, low cost as well as low nonlinearity. However, some of these properties (such as the latter) pose significant drawbacks for nonlinear all-optical signal processing. Typical values of γ in standard glass fibers are several hundred thousand times smaller than in SOI or chalcogenide glass nanowires [3,21,27]. Notwithstanding this, however, we recently presented the first demonstration of continuous-wave (CW) nonlinear optics in high index doped silica-glass (Hydex^® [28]) based waveguides [29], achieving four wave mixing (FWM) in ring resonators with only a few mW of CW optical pump power.

Hydex^® glass has achieved significant success since its introduction in 2003 as a platform for advanced linear optical photonic integrated circuits [28], with applications ranging from high-order filters for telecommunications applications (with > 80dB rejection ratios [30]) to micro ring resonators [31] for optical sensing of biomolecules. This novel material has an optical refractive index range of 1.45 to 1.8 at 1550nm, and when surrounded by low index glass (such as silica for example), can form high index contrast, low loss waveguides with very tight modal field confinement (< 1.5 × 1.5 μm² ) and small bend radii of < 50 μm. The excellent sidewall verticality (<1 degree) and low roughness that can be achieved in these waveguides results in propagation losses well under 0.1dB/cm. Further, achieving this low loss does not require high temperature annealing, as it does for other high index glasses such as SiON, for example. This results in a fabrication process for Hydex^® waveguides that is CMOS compatible [28].

In this paper, we demonstrate significant nonlinear phase shifts (1.5π via self-phase modulation) in a 45cm long high index doped silica-glass (Hydex^® [28]) based waveguide at peak optical pump powers below 60W. Moreover, we observe negligible nonlinear (multiphoton) absorption or saturation effects even up to the extremely high peak intensities of 25GW/cm². This is in stark contrast with silicon and even chalcogenide glasses that display nonlinear saturation at intensities well below this level (0.05 GW/cm² for silicon in [21] and 2GW/cm² in chalcogenide glass [25]). Our results imply that the efficiency of nonlinear processes in this material system, particularly in resonant structures such as ring resonators, is not expected to saturate, as it has been instead observed in silicon devices [32]. By fitting our experimental results, we obtain a nonlinear Kerr coefficient (n₂) for the waveguide 5 times higher than in silica glass, in agreement with previous experiments on ring resonator [29]. The results presented here, along with those of [29], show that the nonlinear performance of this material system, together with its high reliability, design flexibility, and manufacturability raise the possibility of a new platform for future low-cost nonlinear all-optical PICs.

2. Device

Our device consisted of a chip with a 45cm long spiral waveguide together with a range of shorter waveguide with lengths ranging from <1mm to 2cm. The films were deposited using Chemical Vapor Deposition (CVD) and the waveguides patterned via high resolution photolithography followed by reactive ion etching [28]. The entire chip is ~ 6.5 mm × 6.5 mm and coupling between single mode fibers and the waveguides is accomplished via integrated spot size transformers that expand the mode of our tightly confined waveguides out to those dimensions matching a single mode fiber (SMF). The 45cm long spiral waveguide is contained within a square area of 2.25mm × 2.25 mm, with a separation between adjacent waveguides of ~ 7 μm. With bend radii kept to × 50 μm, the losses were negligible. The waveguide core (see SEM picture in Fig. 1, which shows the core prior to the SiO₂ upper cladding deposition) consisted of n = 1.7 (at 1550nm) Hydex^® glass with a cross section of 1.45 μm × 1.50 μm, surrounded on all sides by fused silica with an index of n = 1.44. Finite element simulations (Fig. 1) show a tightly confined mode with most of the energy lying inside the waveguide core. As the vertical and horizontal dimensions of the core are comparable, there is little difference between the quasi-TE (n_eff = 1.6084) and quasi-TM (n_eff = 1.6079) modes, with the effective indices differing by 4.7×10^-4 (due to form birefringence). The modal effective area, defined as:

where E(x,y) is the major component of the (modal) electric field, was calculated to be 2.0 μm² for both TE and TM modes. Because of the various waveguide lengths available on the chip, we were effectively able to perform “cutback” measurements. From these measures, we could estimate propagation loss of < 0.06dB/cm and pigtail coupling losses (fiber to waveguide) of 1.5dB/facet, for a total insertion loss of ~ 6dB for the 45cm waveguide and ~3dB for the short waveguide segments.

 

Fig. 1. (left) SEM image of a Hydex^® waveguide cross section prior to deposition of the SiO₂ upper cladding layer. (right) Modal electric field distribution of the major component for the quasi-TM mode.

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3. Experiment

In order to investigate the nonlinear response of our waveguides at high optical peak powers, we used a mode-locked fiber laser emitting near transform limited pulses at a repetition rate of 16.9MHz. The pulse duration (FWHM) could be tuned from 1.7ps down to ~350fs by using various bandpass filters, with corresponding peak powers ranging from 60W up to 200W. To obtain higher peak powers these could be amplified by an erbium doped fiber amplifier (EDFA) to more than 1kW, although this also introduced a significant spectral deformation due to nonlinearity within the amplifier. The pulses, either amplified or directly drawn from the modelocked laser, were sent through a fiber variable attenuator and polarization controller and then coupled into the 45cm waveguide via the fiber pigtails. The shortest waveguide on the chip allowed us to account for any nonlinear effects occurring in the pigtails, which were determined to be negligible. We first measured the nonlinear absorption of our device by monitoring the optical transmission as a function of the input peak power (pulse duration ~450fs), using the EDFA at peak powers up to ~ 500W (coupled into the waveguide).

For the self-phase modulation (SPM) experiments, we used the output of the modelocked laser (5nm bandpass filter) without amplification in order to minimize extraneous SPM induced by the amplifier. By experimentally measuring the pulse spectra directly from the laser, we performed a reverse Fourier transform of the spectral amplitude (assuming no spectral phase) to obtain the input temporal pulse. The autocorrelation was calculated for the simulated input pulse and compared to its experimental counterpart. Accordingly, a dispersion induced chirp (equivalent to ~25m of propagation in a +22ps²/km waveguide) was introduced in the model in order to obtain a good comparison between theory and experiments. We estimated that the pulses immediately prior to the device had a maximum peak power of ~60W and a time duration of 1.7ps. Given the 45 cm length of the waveguide, this power was large enough to observe significant spectral self-broadening. Evolution of this pulse was simulated using the nonlinear Schrodinger equation:

where A is the pulse envelope, z the propagation distance, α the linear loss coefficient, β₂ the group velocity dispersion coefficient, T the propagation time and γ the nonlinear parameter. Eq. (2) was solved numerically using a split-step algorithm, and the output spectrum after the 45 cm waveguide (with the input and output fibers taken into account) was compared with the experiment. The unknowns in Eq. (2) are the nonlinear parameter γ and the group velocity dispersion β₂. We numerically varied these 2 parameters until the best fit between simulation and experiment was obtained for every input power level.

 

Fig. 2. Linear transmission out of the 45cm waveguide for coupled peak powers up to 500W.

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4. Results and discussion

Figure 2 shows the nonlinear transmission versus optical peak power inside the waveguides for input pulses of ~450fs (FWHM) duration. These results clearly indicate that our waveguides display negligible nonlinear (or multi-photon) absorption, even up to peak powers of ~ 500W corresponding to an intensity >25GW/cm². This is truly extraordinary, and corresponds to a value which is much higher than the typical threshold in which either silicon or even chalcogenide glasses begin to display saturation effects [19–21,25].

The output spectra, broadened by SPM, are presented in Fig. 3 for different input peak powers, showing a good agreement between simulation and experiment. In this experiment the input pulse duration was increased to 1.7ps by decreasing the band-pass filter width. A slight asymmetry in the output SPM broadened spectra can be observed when the input power is increased as a result of both input temporal pulse asymmetry (not accounted for in the simulations) and the temporal chirp. We found that waveguide dispersion did not have a significant impact on the SPM results; hence, we were unable to determine its value from the SPM measurements. However, by measuring the free spectral range of ring resonator devices across the C-band [29], we established an upper limit of the total dispersion of our 45cm waveguide of +/- 200 ps²/km, implying that the dispersion length (~12m) is significantly longer than the waveguide length. Moreover, theoretical calculations of the waveguide (form) dispersion indicate a range of -15 to -25 ps²/km from 1550nm to 1560nm, implying that any significant dispersion would arise primarily from material dispersion. The expected low dispersion raises the possibility of exploiting the nonlinear effects in long structures, such as in the 45cm spiral waveguide, thereby increasing the effective total induced nonlinear interactions.

 

Fig. 3. Experimentally measured output power spectrum (solid blue lines), and theory (dashed red lines) for different input (coupled) power levels.

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By fitting the experimental SPM broadened spectra to theory we obtain a nonlinear parameter, $\gamma =\frac{2\mathrm{\pi ·}{n}_2}{A_{\mathrm{eff}}\lambda },$ - more than 200 times larger than that of standard single mode fiber (SMF). This increase is a result of both a larger nonlinear coefficient n₂, and a tightly confined mode leading to a reduced effective area. Furthermore, we obtain a Kerr nonlinearity (n₂) for the Hydex^® waveguides of 1.1 × 10^-19 m²/W, or ~ 5x silica glass [27]. This is within the experimental error associated to the value reported by our recent four-wave mixing experiments in ring resonators with the same material and cross section [29]. It is also in good agreement with Miller’s rule that relates the nonlinear coefficient with the linear index [33]. Whereas this value of n₂ is much smaller than that of semiconductors and chalcogenide glasses, the combination of very low linear and negligible nonlinear losses allow the possibility of employing very long waveguides as well as high quality resonant structures (e.g. ring resonators) to greatly enhance the nonlinear optical device efficiency to achieve nonlinear performance at <10mW power levels [29].

5. Summary

We have demonstrated efficient nonlinear self-phase modulation at peak optical powers <60W near 1550nm in high index doped silica glass based waveguides. We have also shown that these waveguides display negligible nonlinear (multiphoton) absorption up to peak intensities of >25GW/cm². By fitting our experiments to theory, we obtain a nonlinearity (γ) of 220 W^-1 km^-1 and a value of n₂ of 5x silica glass. The nonlinear performance of these devices, together with their very low linear loss and CMOS compatible fabrication technology, shows that they have a strong potential as a platform for future all-optical photonic integrated circuits.