# Distributed Bragg Reflectors for GaN-Based Vertical-Cavity Surface-Emitting Lasers
## 1 Introduction  
Propagation of electromagnetic waves in periodic media has produced a plethora of intriguing natural phenomena and useful applications. The natural world provides a rich collection of examples of bio-photonic structures including the wing of the _Morpho_ butterfly [1; 2], peacock feathers [3], the striking colors of flower petals [4], the iridescent laser from nacre shells [5], and light confinement in _C. Wailesii_ cell wall [6; 7], to name just a few [8]. Technological applications of periodic photonic structures include diffraction of X-rays in crystals, wavelength selection in fiber gratings, physical sensors and manipulation of light in photonic crystals. Distributed Bragg reflectors (DBRs), sometimes called Bragg mirrors or quarter wavelength stacks, represent one of the simplest periodic photonic structures. In a multi-layered structure with a periodic high-low contrast in the optical index of refraction, when the thicknesses of the individual layers equal to a quarter of the optical wavelength (\(\lambda\)/4) (or more broadly the odd multiples of a quarter wavelength such as 3/4, 5/4, etc. ), the successive reflections at each interface cause constructive interference for the reflective wave around the Bragg wavelength \(\lambda\), and the multiple layers act as a mirror with a tunable reflectivity and bandwidth. Multi-layered Bragg mirror structures were first demonstrated around 1940 with coatings of alternate dielectric layers [9; 10; 11]. These dielectric structures contributed to the formation of high-Qcavity in the early development of lasers. With advances in modern epitaxial techniques such as molecular beam epitaxy (MBE) and organometallic vapor phase epitaxy (OMVPE) in the 1970s, tremendous progress was made in the growth of AlGaAs heterostructures with atomic layer control. Single crystalline, epitaxial DBR mirrors were demonstrated in the 1980s [12], which was arguably the most important factor that led to the demonstrations of room-temperature of continuous-wave operation of vertical cavity surface-emitting lasers (VCSELs) in the infrared wavelengths [13; 14]. Currently III-V VCSELs play an important role in data communications, mobile sensing, and many emerging applications [15], with a projected global market of 3.89 billion USD by 2023 [16]. Since early 1990s, GaN-based blue light-emitting diodes (LEDs) and laser diodes (LDs) have revolutionized contemporary technologies in illumination and display. The technology of blue VCSELs, however, has not reached the same level of maturity. Beginning in the late 1990s there were reports of optically-pumped InGaN VCSELs [17; 18]. More than 10 years later, electrically-injected InGaN VCSELs were demonstrated in 2008 [19; 20]. At the preparation of this review article, after another 10 years of pursuit, GaN VCSELs have yet to be commercialized in spite of encouraging progress. It is accepted that a key component and bottleneck in the GaN VCSEL technologies is the preparation of DBR mirrors, in particular the DBR mirror on the substrate side. With the increasing interest in and reports of GaN VCSELs as a backdrop, this article aims to provide a review and assessment of this key element for VCSEL with an intention that, by outlining the experiences learned and remaining challenges, new breakthroughs and innovations will lead to the ubiquitous deployment of short-wavelength visible VCSELs in lighting, display, communication and other applications. This article is arranged in the following way, in Section 2 we will first review the different techniques in preparing DBR mirrors for VCSELs, followed by a discussion of the properties of and design constraints in fabricating DBR mirrors. Turning our focus to specific embodiments of DBR mirrors for GaN VCSELs, we will then review the development of both epitaxial (Section 3) and dielectric DBR mirrors (Section 4) and highlight the state of the art.