# Second-Harmonic Generation of Blue Light in GaN Waveguides
## 2 Materials and Methods  
In this study, III-metal-polar GaN waveguides were used. A 1200 nm thick Ga polar GaN was grown on a low-temperature AlN buffer layer on sapphire using an MOCVD reactor. The growth temperature was 1040 \({}^{\circ}\)C with Ga (C\({}_{2}\)H\({}_{5}\))\({}_{3}\) (triethylgallium) and NH\({}_{3}\) as the source gases. Details on the growth can be found elsewhere [31, 32, 33, 34, 35]. To transform planar waveguides into rectangular waveguides of selected widths, a standard photolithography process was used with the resulting waveguide widths ranging from 3-50 \(\upmu\)m [35, 36]. The final measurements were performed on samples with parallel waveguides of 10 \(\upmu\)m width and 10 \(\upmu\)m spacing. Figure 1a presents a cross-sectional scanning electron microscopy (SEM) image of a waveguide facet that was used to couple-in the light into the waveguides. A cross-sectional trench was prepared using the following procedure: First, a 1 \(\upmu\)m thick platinum protective layer was deposited using an ion-beam induced deposition with a 0.43 nA beam current; next, a cross-section using a 6.5 nA ion beam was milled. This was followed by a 80 pA milling of the exposed cross-section to obtain a polished surface. The thickness of the GaN waveguides was determined by the SEM analysis of the cross-sectional samples to be around 1150 nm. Although the waveguides exhibited very smooth surfaces, the analysis of the image taken by a CCD camera mounted above the sample revealed that most of the light scattering took place at the side surfaces of the waveguides. To confirm this, SEM images from the side facets were also recorded. It was found that the roughness of the sides was especially high for the waveguides with a stripe width below 5 \(\upmu\)m. This is highlighted by a direct comparison of waveguides with a side roughness of 3 \(\upmu\)m and 20 \(\upmu\)m wide, as presented in Figure 1b. In addition, sidewall roughness is relatively more important in narrower waveguides, therefore, most SHG measurements were performed on GaN waveguides of 10 \(\upmu\)m width and 1 mm length. In order to produce waveguides of an appropriate length, straight lines perpendicular to the waveguide direction were scribed by a UV laser on the back of the sapphire wafer. The wafer was then cleaved along the scribed lines. The fabricated waveguides were used to probe SHG in GaN waveguides at room temperature. Figure 2 presents schematics of the experimental setup used to investigate the nonlinear response in GaN waveguides. A Ti:sapphire laser was used as the excitation source. Typical excitation wavelengths were in the range of 850-950 nm, which led to a second-harmonic response in the blue. Femtosecond pulses were injected into the waveguide by the end-fire coupling technique. The SHG signal generated in the waveguide was separated from the pump wave and analyzed with a spectrograph and a photon counting camera. The output of the femtosecond laser system was nearly identical to that of a transform-limited fundamental pulse with a tunable central wavelength. The pulse duration was 40 fs (full-width at half-maximum, FWHM), the repetition rate was 1 kHz, and the spectral width was 30 nm (FWHM). The pulse energy was wavelength dependent from 1 to 100 \(\upmu\)J and could be controlled by a tunable neutral density (ND) filter, which was used before the end-fire coupling system. The beam diameter was adapted with a beam expander to the size of the in-coupling lens for efficient focusing. The coupling lenses and sample holder were mounted on _xyz_ translation stages enabling precise positioning of the focal point of the laser beam onto the front facet of the waveguide. The output beam was focused onto the front face of the waveguide using a lens with a 10 mm focal length. The size of the beam at the waveguide facet was approximately 10 \(\upmu\)m. This is equal to the waveguide width in order to dominantly excite the fundamental mode in the y-direction.