# Octave Spanning Supercontinuum in Titanium Dioxide Waveguides

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) as an alternative platform that remained until now relatively unexplored. TiO

_{2}is a promising material thanks to a transparency window spanning from the visible to the mid-infrared wavelengths [23], high linear and nonlinear refractive indices (of >2.3 and 30 times, respectively, larger than silica [24,25]) and a wide bandgap (3.4 eV) allowing a negligible TPA beyond 800 nm. Its thermo-optic properties can also be of great interest for thermal stability [26,27,28]. Moreover, thin films can be prepared by several techniques such as e-beam evaporation, atomic layer deposition (ALD), plasma-enhanced chemical vapour deposition (PE-CVD) or sol-gel process [29]. Therefore, it has become increasingly desirable to consider this cost-efficient material in different scenarios such as subwavelength optical waveguides [30], integrated optical resonators [25,27,31,32], infrared high speed transmissions [33] or sensing applications [34,35]. Quite recently, several studies aimed at taking advantage of the Kerr nonlinearity of TiO

_{2}and have reported the observation of self-phase modulation induced spectral broadening of a femtosecond pulse [24], the parametric wavelength conversion of a continuous wave [25] as well as the efficient generation of photon triplet [36].

_{2}-based on-chip waveguide. The manuscript is organized as follows. We first describe the properties of the cm-long on-chip waveguides in which SC generation is demonstrated. Next, we detail the experimental set-up based on a femtosecond fibre laser at 1.64 µm and finally we analyse the main features of the generated supercontinua.

## 2. TiO_{2} Waveguide Design and Fabrication

_{2}onto a 2′ thermally oxidized Si wafer (SiO

_{2}thickness = 2.0 µm). TiO

_{2}deposition is performed by DC magnetron sputtering of a 99.9% pure titanium under an argon oxygen controlled atmosphere. It is well known that different TiO

_{2}phases can be obtained: rutile [37,38], anatase [39,40] or amorphous [25,40]. In this case, Raman spectroscopy experiments (not shown) reveal that the layers are dominantly in the anatase phase. The 2.2 cm-long waveguides considered in the following are obtained by I-line patterning of the UV sensitive resist AZ MiR 701. The patterned resist is then used as a protective mask during the subsequent reactive ion etching of the TiO

_{2}layer. After stripping of the residual mask, strip waveguides featuring a typical width of 1.5 µm are obtained as shown by scanning electron microscope (SEM) image displayed in Figure 1a. This image shows that the fabrication process leads to asymmetric sidewalls such that the top width (w

_{1}= 1.345 µm) is shorter than the base width (w

_{2}= 1.487 µm), so that the waveguide section is close to a right trapezoid.

_{2}(the estimated refractive index for the anatase TiO

_{2}layer at 1.64 µm is 2.35) and the silica layer (refractive index = 1.44) or the surrounding air is highly beneficial for a strong light confinement. The refractive index for anatase phase TiO

_{2}layer reported in Ref. [40] appears as a good starting point for the numerical investigation of the optical properties of the waveguides. By operating a commercial mode-solver relying on finite element method (COMSOL Multiphysics

^{®}), we found that the structure may sustain 4 modes. The modal intensity distributions of the two lowest orders modes are displayed for the transverse electric (TE) and transverse magnetic (TM) in Figure 1b1,b2, respectively. The TE polarized fundamental mode of interest features an effective area [41] of 0.54 µm

^{2}with 85% of the energy carried out by the mode confined within the TiO

_{2}core at a wavelength of 1.64 µm. In addition, as detailed in the following (Figure 4a), in the spectral region around 1.6 µm, the fundamental mode features an anomalous regime of chromatic dispersion which is a prerequisite for ultra-broad SC generation [25]. Compared to previous works [24,33,42], such an anomalous dispersion is obtained thanks to a thicker layer.

_{0,0}mode exhibits a lower confinement and thus an effective area increased by about 30% as compared to the fundamental mode.

## 3. Experimental Setup

_{2}waveguides is ensured by a butt coupling technique through lensed fibres (Figure 2b1) characterized by a working-distance of 14 µm. To reduce the insertion losses through such butt-coupling of light, the component design includes 1 mm-long tapers (Figure 2b2) at both ends of the waveguide. Note that the nonlinear propagation of the initial pulse, equivalent to a near fundamental soliton pulse (N~1) [43], within the segment of standard anomalous dispersion SMF 28 fibre between the fs-laser output and the TiO

_{2}waveguide leads to the tuning of the central wavelength of the initial pulse from 1.56 µm towards 1.64 µm through Raman soliton self-frequency shift (see Figure 2c).

## 4. Supercontinuum Generation

#### 4.1. Experimental Results

_{2}waveguide. The input peak power of the fs-pulses injected into the waveguide was estimated to almost 1.3 kW (corresponding to a soliton number N = 15 [2,43]) but given the experimental difficulty to evaluate precisely the energy coupled into the fundamental mode, this value remains a rough estimate. By means of a careful adjustment of the input polarization aligned to the fundamental TE mode which is expected to be in anomalous dispersion regime at the pump wavelength, an octave-spanning supercontinuum spectrum is then generated, with a central part ranging from 1050 nm up to 1910 nm (−20 dB spectral width in Figure 3a). Compared to the pioneer experiments of spectral broadening leading to tens of nanometres around 1550 nm reported by Evans et al. [24], the present results represent a significant improvement by much more than one order of magnitude. A third harmonic signal is also generated into the waveguide [45] so that visible light is also clearly observed by the naked eye in the early stage of propagation as can be seen from the photography taken from the top of the waveguide (Figure 3b,c). From these pictures, we can also notice that green light is generated first, followed by yellow, orange and then red, which is consistent with the progressive frequency shift of the femtosecond pulse during its propagation within the nonlinear waveguide. The visible light emitted along the waveguide represents therefore an indirect but practical way to track the longitudinal evolution of the central wavelength of the Raman-shifted soliton. However, the level of losses of TiO

_{2}in the visible region remains slightly too high and, given the sensitivity of our spectral analysis devices, has prevented the detection of the visible part of the generated light at the output of the 2-cm-long waveguide.

_{2}material. The TE fundamental mode is expected to be anomalous around the pumping wavelength, therefore enabling a soliton-driven SC dynamics [3,46]. Moreover, we confirm here that the waveguide presents two zero dispersion wavelengths that ultimately limit the spectral expansion of our supercontinuum [47]. Note also that the TM mode lies in the normal dispersion regime at the pump wavelength and its considerable dispersion value makes that only a negligible broadening can be expected (not presented here because similar to the input pulse). This point therefore further explains the high polarization sensitivity of the input conditions.

#### 4.2. Numerical Simulations

_{k}’s are the dispersion coefficients associated with the Taylor series expansion of the propagation constant β around the central frequency. Note that we do not include terms based on the two-photon absorption (α

_{2}) and three photon absorption (α

_{3}) since titanium dioxide presents negligible nonlinear absorption in the spectral region of interest. The main limitations of the above GNLSE is related to the fact that visible light obtained through frequency tripling of the input pulse cannot be modelled [49,50] and that it assumes a pure single-mode propagation. However, note that the aim of these numerical simulations is to qualitatively reproduce the observed SC generation. Indeed, several parameters of the TiO

_{2}waveguide such as its dispersive properties or the exact value of the nonlinear coefficient have not been experimentally assessed yet and would deserve a devoted study that is well beyond the scope of the present letter. The exact physical features of the optical pulse entering into the waveguide are not accurately known but it can be considered as an initial 90-fs transformed-limited hyperbolic-secant pulse centred at 1.64 µm (as shown in Figure 2c). For the qualitative discussion, our numerical simulations used a nonlinear index value (n

_{2}= 0.16 × 10

^{−18}m²/W) and a Raman coefficient inferred from the literature [24], which leads to a nonlinear parameter about 1.2 W

^{−1}·m

^{−1}.

_{sol}is the angular frequency of the soliton and P

_{sol}its peak power. The calculated phase matching curves are shown in Figure 5a. These curves help to understand the results of the simulations summarized in Figure 5b which have to be compared with spectra recorded and depicted in Figure 4. In particular, the resulting supercontinuum is bounded by two dispersive waves located around 1.2 and 2.3 µm. Note that the SC bandwidth can be controlled by a suitable engineering of the waveguide dispersion. Here the main experimental SC features and evolution as a function of input energy are well predicted from the GNLSE simulations. In particular, the soliton frequency-shift towards 1.9 µm wavelength as well as the position and the blue-shift of the dispersive waves are indeed well reproduced. The optical signal to noise ratio being much higher in our simulations compared to our experiments, we find spectral features in Figure 5 that can be only hardly observed in the experimental results. Nevertheless, we conclude that our approach based on the GNLSE captures most of the dominant spectral properties of the SC generated in our TiO

_{2}waveguides.

#### 4.3. Discussion

_{0,0}mode for different widths of the waveguide. Figure 6b displays the experimental spectrum obtained in two other TiO

_{2}waveguides with distinct widths as well as the corresponding numerical simulations. Once again, a good agreement is obtained. The broader waveguide (width = 1.8 µm) exhibits an all-normal dispersion regime. Therefore, the self-phase modulation and wave-breaking dynamics are dominant effects governing the spectrum expansion [2,51,52].

## 5. Conclusions

_{2}optical waveguide. Following soliton-based nonlinear dynamics, the spectral broadening of femtosecond pulses at 1.64 µm leads to the generation of new wavelengths from the visible up to 1.92 µm, that is, this involves spectral components covering more than an octave. Both experiments and simulations also stress the crucial importance of the geometrical parameters of the waveguide structure that governs the dispersion properties and ultimately the supercontinuum extent. This study therefore confirms the strong potential of TiO

_{2}for nonlinear applications. With further reduction of the propagation losses combined with more advanced dispersion engineering of the waveguide and optimization of the device length, noticeable enhancements of the resulting SC source are expected and decade spanning SC could potentially be reached. Using TiO

_{2}in amorphous phase can also be a source of improvement. The use of wideband coupling grating structures such as reported in [42] that are able to handle femtosecond pulses could also improve the stability of the source and increase the power coupled within the waveguide.

_{2}appealing for pumping with cost-efficient fibre laser sources operating around ytterbium typical wavelength (1.06 µm) as well as the versatile titanium-sapphire ultrashort lasers. Other intrinsic advantages of TiO

_{2}such as the absence of TPA and its thermal stability are also critical to enable the efficient generation of continuum from sources delivering longer picosecond or nanosecond pulses, which paves the way for future theoretical and experimental investigations.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) Scanning Electron Microscope image of the cleaved strip TiO

_{2}waveguide (

**b1**,

**b2**) Corresponding mode profiles at 1640 nm and associated effective index for the first transverse electric (TE) and transverse magnetic (TM) respectively.

**Figure 2.**(

**a**) Experimental setup involved for generation of supercontinuum in TiO

_{2}waveguides. (

**b1**) Sketch of the waveguide and butt-coupling thanks to lensed fibres and (

**b2**) the corresponding optical microscope image of the taper used for the coupling. (

**c**) Spectrum of the injected soliton pulse centred at 1640 nm compared with the spectrum of a 90 fs sech

^{2}pulse (

**c**).

**Figure 3.**(

**a**) Optical supercontinuum recorded at the output of the 2.2-cm-long 1.5-µm-wide TiO

_{2}waveguide (blue solid line) compared to the input pulse spectrum (red solid line). The overall spectrum is reconstructed from the overlap of the spectra obtained from both optical spectrum analysers of our setup. (

**b**) Photography of the visible light emitted from the waveguide. (

**c**) Zoom of the emitted visible light.

**Figure 4.**(

**a**) Dispersion profiles of the fundamental TE

_{0,0}and TM

_{0,0}modes of the 1.5 µm wide waveguide. The material dispersion is plotted with solid black line. (

**b**) Optical supercontinua measured at the output of the TiO

_{2}waveguide for various coupled energy conditions. For the better reading of the figure, the various spectra were vertically offset. The part of the spectrum ranging from 2200 nm to 2400 nm has been shaded because residual contribution of spurious double-order mode may contribute to the spectrum.

**Figure 5.**(

**a**) Phase matching curve for a pump wavelength at 1.64 µm (initial pump) and at 1.82 µm (shifted soliton). (

**b**) Numerical simulations of supercontinuum generation obtained in a 2.2-cm-long 1.5-µm-wide TiO

_{2}waveguides for different input energies of the femtosecond pulses. For the clarity of the figure, the various spectra were vertically offset. The areas corresponding to the phase matched dispersive waves are coloured.

**Figure 6.**(

**a**) Dispersion profiles of the fundamental TE

_{0,0}mode of the waveguide for different widths (1.4, 1.5 and 1.8 µm). (

**b**) Experimental spectra (blue lines) and corresponding numerical simulations (red lines) for (

**b1**) 1.4 µm and (

**b2**) 1.8 µm. For the clarity of the figure, the various spectra were vertically offset.

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## Share and Cite

**MDPI and ACS Style**

Hammani, K.; Markey, L.; Lamy, M.; Kibler, B.; Arocas, J.; Fatome, J.; Dereux, A.; Weeber, J.-C.; Finot, C.
Octave Spanning Supercontinuum in Titanium Dioxide Waveguides. *Appl. Sci.* **2018**, *8*, 543.
https://doi.org/10.3390/app8040543

**AMA Style**

Hammani K, Markey L, Lamy M, Kibler B, Arocas J, Fatome J, Dereux A, Weeber J-C, Finot C.
Octave Spanning Supercontinuum in Titanium Dioxide Waveguides. *Applied Sciences*. 2018; 8(4):543.
https://doi.org/10.3390/app8040543

**Chicago/Turabian Style**

Hammani, Kamal, Laurent Markey, Manon Lamy, Bertrand Kibler, Juan Arocas, Julien Fatome, Alain Dereux, Jean-Claude Weeber, and Christophe Finot.
2018. "Octave Spanning Supercontinuum in Titanium Dioxide Waveguides" *Applied Sciences* 8, no. 4: 543.
https://doi.org/10.3390/app8040543