# Evaluation of Optimal Visible Wavelengths for Free-Space Optical Communications
## 1 Introduction  
Free-space optical (FSO) communication transmits data through the atmosphere using laser beams, eliminating the need for physical transmission media such as fibers or cables. With global demand for higher data throughput and improved spectral efficiency rising, FSO systems have become increasingly attractive as both supplements to and replacements for conventional radio-frequency (RF) links, particularly in environments where the RF spectrum is congested or infrastructure deployment is challenging [1, 2, 3, 4, 5]. A closely related and rapidly evolving field is visible-light communication (VLC), which operates in the visible portion of the electromagnetic spectrum. VLC has demonstrated considerable promise for short-range applications, including indoor wireless networking (e.g., Li-Fi), building-to-building line-of-sight communication, vehicle-to-vehicle links, and rapidly deployable emergency systems. Its key advantages include the use of anunlicensed spectrum, strong immunity to RF interference, and compatibility with low-cost, readily available visible-light laser diodes capable of supporting high data rates [1; 2; 3; 4; 5]. Despite these benefits, the performance of FSO systems is highly susceptible to atmospheric conditions--most notably fog, rain, dust, and turbulence--which degrade signal quality through scattering and absorption [6; 7]. Among these impairments, fog poses the most severe challenge, introducing significant optical attenuation that reduces the link margin and transmission distance. Since attenuation effects are wavelength-dependent, the choice of operating wavelength is a critical determinant of system reliability in limited-visibility scenarios. While infrared (IR) wavelengths have traditionally dominated FSO research due to their favorable long-distance propagation characteristics, visible wavelengths, particularly 650 nm (red), 532 nm (green), and 405 nm (violet), present promising alternatives for short-range, low-cost systems [8; 9]. These wavelengths offer high modulation bandwidth and potentially higher quantum efficiency, and they are compatible with widely available silicon-based photodetectors, which can also function as energy-harvesting devices in integrated VLC/FSO designs [10]. Numerous analytical and empirical models have been developed to estimate wavelength-dependent attenuation in foggy environments. However, many of these rely on detailed atmospheric parameters--such as particle size distribution and refractive indices--derived from Mie scattering theory, which are often difficult to obtain or model in practice [1; 2; 3]. Empirical formulations by [PERSON], [PERSON], and [PERSON] [5; 11; 12] attempt to correlate attenuation with visibility, while [PERSON] et al. [13] introduced refinements by distinguishing between advection fog and radiation fog, each with distinct scattering profiles. Recent studies [6; 7; 8; 9] have also questioned the assumption that longer wavelengths are always superior under all weather conditions. Although these models provide valuable theoretical insight, their applicability to compact, real-world systems is often limited by their complexity and data availability. In contrast, experimental research [14; 15] suggests that visible wavelengths may offer favorable trade-offs in terms of energy efficiency and data throughput, particularly in short-range systems. Various modulation techniques--including amplitude, phase, and pulse schemes--have also been evaluated for FSO applications, with performance dependent on target range and system architecture [16; 17]. Additional work on laser diode efficiency [18; 19; 20] further supports the potential of visible wavelengths for compact, power-conscious optical communication systems. However, direct experimental comparisons of visible wavelengths under identical conditions remain limited.