1. Introduction

Materials with strong nonlinear optical responses provide the basis for several important photonic functionalities [1]. In particular, CMOS-compatible materials with large second- and third-order nonlinearities could enable the realization of on-chip devices for high-speed optical switching, electro-optic modulation, data storage, wavelength conversion, and even lasing and amplification [2–9]. Silicon is the most traditional CMOS material, however, its bandgap of 1.1 eV is relatively narrow, making it opaque at visible and near-infrared (NIR) wavelengths. This prevents its use in the ultraviolet (UV) spectral regime, which is becoming more and more important for a number of applications, including environment monitoring, fluorescence spectroscopy, data storage, and lithography [10,11].

Silicon nitride (SiN) is another important CMOS-compatible material that has recently attracted more and more attention for on-chip nanophotonics applications [6–9]. A significant advantage of SiN lies on the tunability of its refractive index and bandgap which allows to finely adjust the optical properties by simply varying the relative percentage of silicon and nitride in the material composition [12,13]. In addition to the flexibility in the material design, the intrinsic large nonlinear refractive index of SiN [14,15] also allows for efficient third-order nonlinear processes which can be beneficial for many applications. Indeed, on-chip third-harmonic generation (THG), optical parametric oscillation, self-phase modulation, and supercontinuum generation in SiN structures have all been demonstrated [6–9]. All these studies, however, have been restricted to the visible and NIR wavelengths [6–9,14–17].

Resonant waveguide gratings (RWGs) consist of a surface grating that diffracts light both in and out of the waveguide mode. On resonance, the fields diffracted out interfere with the transmitted and reflected fields in such a way that it is theoretically possible to achieve 100% reflection whilst simultaneously enhancing significantly the optical field in the waveguide mode. Such high field localization can in turn increase the efficiency of harmonic generation and indeed various schemes have been demonstrated to this end [17–19].

In this paper, we demonstrate strong THG from 1064 nm fundamental wavelength to the UV wavelength of 355 nm both in SiN thin films and SiN resonant nanostructures. The third-order susceptibility of SiN films is found to exceed that of fused silica by as much as two orders of magnitude. We show that this response can be further enhanced by field confinement in a resonant waveguide grating (RWG) optimized for 1064 nm fundamental wavelength. The enhancement factor for THG is found to be about 2000 compared to the TH generated from a flat SiN film of similar thickness. Our results are particularly interesting for extending nonlinear light sources for on-chip devices.

2. Experimental details

The experimental setup for THG measurements (Fig. 1 ) is identical to that used for the SHG characterization described in Refs [16,17], except for different filters to allow for both the transmission of UV light and the elimination of any fundamental light or SHG after the samples. Specifically, a mode-locked Nd:YAG laser (1064 nm, 70 ps, 1 kHz) is used as the pump source, and any potential THG from the laser itself is removed with a NIR long-pass filter inserted before the SiN sample. The transmitted THG signal is detected by a photomultiplier tube (PMT), blocking the fundamental beam and SHG signal using a short-pass and an interference filter (central wavelength 355 nm). The polarization states of the fundamental and THG beams are controlled with calcite Glan polarizers. The sample is mounted on a high precision rotation stage to study THG as a function of the angle of incidence. In order to obtain sufficient signal from both reference (1 mm fused silica) and SiN films at the same fundamental laser power, a 25 cm focal-length lens is used to weakly focus the beam into a spot size of around 0.25 mm at the sample plane.

 

Fig. 1 Optical setup used for the THG measurement. M, mirror; L, Lens; GP, Glan prism; WP, wave-plate; LP, long-pass filter; SP, short-pass filter; IF, interference filter; RS, rotation stage, and PMT, photomultiplier tube. The Cartesian coordinate system (x, y, z) associated with the samples is also shown.

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The SiN films were deposited on 1-mm thick fused silica substrates using plasma enhanced chemical vapor deposition (PECVD) and a reactive gas mixture of 1000-sccm 2%SiH₄/N₂ and 30-sccm NH₃ at 300 °C [16,17]. The process temperature and pressure were 300°C and 1000 mTorr, respectively. Several films with different thicknesses in the range 100 nm-1.5 µm were prepared. The refractive indices of the films were determined by ellipsometry to be about 1.94 and 2.13 + 0.06i at 1064 nm and 355 nm, respectively. The SiN RWG was theoretically designed by the rigorous coupled-wave analysis (RCWA) [20,21] for efficient coupling of p-polarized fundamental light at 1064 nm into the waveguide mode. The RWG was then fabricated using nano-imprint techniques [17] on a 800 nm-SiN film with a grating period of 580 nm, a fill factor of 0.59 for SiN, a groove depth of 676 nm and a thickness of SiN waveguide layer of 124 nm.

3. Third-harmonic generation in SiN films

We first studied in detail THG from the SiN films. We first verified the cubic dependence of the signal intensity on the fundamental laser power. We emphasize that although all the measurements were conducted in atmospheric environment, no THG signal could be detected from air. In order to address the tensorial character of THG from the SiN films, we measured the Maker-fringes for different states (p and s) of the fundamental (in) and THG (out) polarization. For reference, similar measurements were performed from a 1-mm thick fused silica glass. Typical THG Maker-fringe patterns measured from a 200 nm thick SiN film as a function of the incidence angle are shown in Fig. 2 . For comparison, the Maker-fringes from the reference silica glass are also plotted and it is clear that the magnitude of the THG from the SiN film is significantly larger than that from the fused silica substrate. In addition, the Maker-fringes are observed for p_in-p_out and s_in-s_out polarization configurations but they vanish for p_in-s_out and s_in-p_out polarization states, respectively. This observation is consistent with the χ⁽³⁾ characteristics of isotropic materials where a given coordinate subscript of χ⁽³⁾_ijkl (-3ω,ω, ω,ω) (i,j,k,l = x,y,z) can only appear an even number of times and only one element of the χ⁽³⁾_iiii (-3ω,ω,ω,ω) is independent [1].

 

Fig. 2 Experimentally measured polarization-dependent THG Maker-fringe patterns, p_in-p_out (black circle) and s_in-s_out (blue square), from the reference fused silica and SiN samples under the same condition. The solid lines (black and blue) indicate theoretical fits. There is no detectable signal for the polarization configuration p_in-s_out and s_in-p_out.

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The total transmitted THG field corresponds to the superposition of the TH fields generated from the SiN film and fused silica substrate. This can be theoretically described by Green’s function formalism [22,23]. Measuring and performing a theoretical fit of the THG Maker-fringe patterns for SiN films of different thicknesses and the silica reference, we can estimate the third-order susceptibility χ⁽³⁾ (−3ω,ω,ω,ω) of SiN to be approximately 140 ± 30 times larger than that of fused silica. Using the standard value for fused silica of χ⁽³⁾ (−3ω,ω,ω,ω) = (2.0 ± 0.2) × 10⁻²² m²/V² [22] this means that the absolute value of the third-order susceptibility for our SiN films at the wavelength of 1064 nm is χ⁽³⁾ (−3ω,ω,ω,ω) = (2.8 ± 0.6) × 10⁻²⁰ m²/V². Such a large value of χ⁽³⁾ is comparable to that of traditional wide-bandgap semiconductor materials such as, ZnSe, TiO₂, CdS or composite materials that include CdSSe quantum dots embedded in glass [1].

4. Third-harmonic generation in SiN resonant gratings

It is well-known that nonlinear effects can be significantly enhanced by strong local fields in resonant structures [8,25,26]. For example, enhanced SHG from TiO₂ and SiN RWGs has been demonstrated where local field enhancement in the waveguide at the resonance condition leads to an increased nonlinear interaction [17,27,28].

In order to further enhance THG, we have fabricated a RWG from SiN with parameters as described in Section 2 and we now discuss the THG results obtained in this type of nanostructure. A scanning electron microscope (SEM) image of the fabricated grating is presented in Fig. 3(a) . From the parameters extracted from the SEM image [see Fig. 3(b)], theoretical analysis predicts a resonance angle of incidence around 16.74° for the fabricated structure for p polarization. The normalized simulated electric field |E/E₀|² around the grating structure based on RCWA at the resonance angle is also highlighted in Fig. 3(c), respectively, showing clear evidence of large field enhancement in the RWG.

 

Fig. 3 (a) Scanning electron microscope image of the fabricated RWG and (b) schematic image of cross-section of the SiN RWG sample. (c) shows the calculated square of the amplitude of the electric field |E/E₀|² normalized to the incident field E₀ in the vicinity of the RWG structure at resonant angle.

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We first measured the linear transmission of the SiN RWG for the p_in-p_out polarization configuration. The fundamental laser output was collimated into a 1 mm diameter beam so as to minimize the beam divergence and thus enable efficient coupling into the resonant waveguide mode. The resonance angle was found at 17.94° [Fig. 4(a) ], which differs by about 1.2° from that theoretically predicted. We attribute this small discrepancy to the small imperfections in the actual RWG structure, which are not accounted for in the theoretical prediction. Note that the imperfections in the manufacturing also lead to broadening and non-zero transmission of the linear resonance compared to a perfect design as can be seen from the measured transmission [17]. The Fabry-Pérot interference fringes from the substrate are also clearly visible in the RWG transmission.

 

Fig. 4 (a) Experimentally measured dependence of the linear transmission and of the THG intensity on the angle of incidence for different fundamental laser powers. The inset shows the cubic relation between the THG intensity and fundamental laser power for the SiN RWG and film. (b) p and s-polarized THG intensities as a function of the polarization of the fundamental beam (modulated by a half wave plate (HWP)). The states of polarization p and s are indicated.

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Using the same polarization configuration, the THG signal from the SiN RWG was then measured as a function of incidence angle of the fundamental beam. This dependence is also shown in Fig. 4(a) and it can be clearly seen how enhancement of the THG signal occurs around the resonance angle of the linear transmission curve. The THG measurements were repeated for increased input power, which confirms the cubic relationship between the THG intensity and the fundamental laser power [see inset in Fig. 4(a)].

In order to quantify the THG enhancement induced by the RWG, we subsequently conducted the THG measurements from a reference planar SiN film fabricated under the same conditions as the RWG. In particular, the reference SiN film and the film used to fabricate the RWG have the same thickness of 800 nm, and the THG signals were measured with the same setup interchanging the samples. The THG intensity from the reference SiN film was measured vs. the incidence angle and it is the maximum intensity at the optimum angle that is used as the reference value for the RWG. Significantly, comparing the maximum intensity of THG signal from the reference SiN film and the SiN RWG on resonance, we estimate that the THG enhancement factor in the RWG is around 2000. Although we are not able to evaluate directly the THG conversion efficiency due to the lack of a calibrated detector at 355 nm, we can still estimate theoretically the conversion efficiency from the SiN film using standard harmonic nonlinear optics formalism to be around 6 × 10⁻¹⁶ which would indicate approximately a 2 × 10⁻¹² conversion efficiency for the RWG at 10 mW fundamental power.

In order to attribute the observed strong THG enhancement to the field localization in the RWG, we have further studied the polarization dependence of the THG on resonance with a 1 mm collimated beam and 5 mW input power [Fig. 4(b)]. Maximum THG was obtained with the p_in-p_out configuration and we could not detect any TH signal for p_in-s_out, s_in-s_out, or s_in-p_out combinations. These observations clearly indicate that the enhanced THG from the RWG compared to the flat SiN film arises from the highly confined local fields in the grating on resonance. Of course, TH could in principle also be generated with the s_in-s_out combination (as with the SiN films), but, because the laser power is relatively low, the absence of linear resonance for the RWG for this particular polarization configuration prevents efficient THG [20].

In theory, the intensity of THG signal scales with the third power of the fundamental field intensity. Our experimental results on the other hand only show a 2000-fold enhancement. There are several reasons for this discrepancy. First, the area of enhanced local fields [Fig. 3(c)] covers only a relatively small fraction of the RWG unit cell. In addition, the fabricated structures have inherent imperfections, which further reduce the average strength of the local fields. It is then more reasonable to compare the THG enhancement factor to that obtained for SHG, i.e. 1000 as reported in [17]. Due to different scaling of the second- and third-order processes on the fundamental intensity, the enhancement factor for THG should be about 30000, which is still one order of magnitude larger than what we measured. This difference is most likely related to the tensorial properties of the second- and third-order effects. The second-order susceptibility of SiN films has a strong surface-normal character. The enhanced local fields in RWG thus also have favorable polarization properties for SHG. The third-order response, on the other hand, is isotropic making the direction of the enhanced local fields less important and we estimate that this difference can explain most of the discrepancy between the enhancement factors for SHG and THG.

5. Conclusion

In conclusion, we have investigated THG from SiN films and SiN resonant waveguide gratings. The third-harmonic susceptibility χ⁽³⁾ (-3ω, ω, ω, ω) of SiN film was determined to be (2.8 ± 0.6) × 10⁻²⁰ m²/V² at 1064 nm using the Maker-fringe technique, which is two orders of magnitude larger than that of fused silica. Using resonant enhancement in a RWG periodic structure we have also shown that the THG signal can be further increased by a factor of 2000 compared to the already large THG obtained from planar SiN films. The strong UV generation in this kind of CMOS-compatible material could have a wide range of applications for on-chip devices. We also believe that the quality of the RWG structures could still be improved and thus lead to an even larger increase in the enhancement factor. Finally, novel designs of RWG nanostructures which allow both the fundamental and SHG signal (which is also naturally generated) to be simultaneously resonant could enhance THG through a cascaded process.