# Second-Harmonic Generation of Blue Light in GaN Waveguides
## 1 Introduction  
The rapidly expanding field of photonics has a great need for efficient and compact coherent light sources in the blue and ultraviolet (UV) regions. Short wavelengths allow for precise focusing and generation of very fine patterns, while the high photon energy facilitates strong absorption in many materials, leading to efficient material processing [1; 2]. Laser diode technology used for the generation of UV light involves a number of challenges including low carrier injection and high threshold pump power, a lack of transparent and UV-resistant optical materials, and increased sensitivity to defects and surface roughness. Surface roughness and other anomalies inside the crystal can lead to strong wavefront distortions and scattering losses, an effect encountered especially with short wavelengths like UV [1; 2; 3; 4]. Studies have shown that AlGaN alloys offer unique properties and have great potential to overcome the disadvantages listed above. While there are some reports on the fabrication of AlGaN-based LEDs in deep UV [5; 6; 7; 8; 9], very limited information about direct-emitting AlGaN semiconductor lasers is available [10; 11]. Recent studies have been conducted on AlGaN-based optically-pumped UV laser structures, but electrically-pumped lasers with emissions below 320 nm have not yet been demonstrated [11; 12; 13]. Challenges related to the fabrication of electrically pumped GaN-, Al-GaN- and AlN-based UV laser diodes mainly stem from; (1) the deep Si-donor andMg-acceptor levels that hinder successful carrier injection; and (2) the high strain fields and dislocation densities that are due to large lattice mismatches between the substrate and active layers [14; 15; 16]. AlGaN alloys have unique linear and nonlinear optical characteristics that permit the utilization of this material for efficient nonlinear conversion into the blue and UV wavelength regions. The two most important properties are a wide transparency window and large nonlinear optical coefficients. Both GaN and AlN have a wide bandgap, corresponding to wavelengths shorter than the visible spectrum. The transparency window of GaN ranges from 13.6 \(\upmu\)m to 365 nm, while AlN remains transparent down to 200 nm [2; 17]. AlGaN belongs to the 6 mm point group, which lacks a center of inversion, and thus has five nonzero nonlinear optical coefficients from which only the two independent components, \(d_{31}\) and \(d_{33}\), need to be considered [2; 18]. The experimental value of the largest second-order coefficient, \(d_{33}\), ranges from 5.82 to 10.6 pmV\({}^{-1}\)[19]. Modal-dispersion phase matching or quasi-phase matching is required with AlGaN to exploit its nonlinearity since the birefringence is not sufficient to sustain an efficient second-harmonic generation (SHG), as was shown in our previous studies [20; 21]. While SHG in GaN and AlGaN has been reported occasionally, only limited data are available for wavelengths below 500 nm. The limitations in this wavelength range are often related to low-quality materials or challenges in waveguide fabrication, which leads to significant scattering and losses. However, with the recent developments in metalorganic chemical vapor deposition growth (MOCVD) and the processing of GaN and AlGaN, new opportunities to investigate SHG in these wide bandgap materials have arisen. For quasi-phase matching, a periodically modulated nonlinear structure is needed, which alternates the sign of the nonlinear coefficient in regular intervals and corrects for the relative phase mismatch between the fundamental and the frequency-doubled light without matching the phase velocities [22]. The polarity-controlled growth of \(+c\) and \(-c\) polarity regions of GaN can be achieved through adequate substrate preparation. The configuration in which the Ga-atoms bond, with three bonds toward the surface, is referred to as N-polar (or \(-c\) orientation), while the 180\({}^{\circ}\) rotated configuration is referred to as III-metal-polar (\(+c\)) [23].