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A unique aspect of what we do is that we use lasers as the basis of our communication signal. Specifically, our laser is a Gaussian beam, which will be discussed here.
Lasers
Laser beams have applications in many different fields of engineering from holography to additive manufacturing. The term laser originally stood for “Light Amplification by Stimulated Emission of Radiation”, but has since become synonymous with a type of light (usually visible, IR, or UV), that differs from something like a lightbulb in how the light is emitted. Both a laser and a lightbulb produce light in the same way; atoms transition from a higher quantum state to a lower, releasing energy in form of an electromagnetic wave. A laser differs from a lightbulb because these emissions occur at the same time and in the same direction, rather than at random and omnidirectional [1]. For a lightbulb, this process is called spontaneous emission; atoms in an excited state will randomly de-excite and emit photons of light. For a laser, the process is called stimulated emission, which creates the non-random nature of the emitted photons. This process occurs when a photon of a certain energy stimulates an atom to drop to its ground state, causing a second photon of the same energy to be emitted [1]. This gives laser light distinct properties, mainly that the light is monochromatic, coherent, and collimated. Lasers are monochromatic because the exact same “jump” is made by all the electrons in the atom, so practically all of the light emitted has the same wavelength. They are coherent, meaning the phase difference between the light emitted stays constant as the light propagates. Lasers are collimated, meaning the beam of light emitted spreads very little in relation to the distance the light propagates [1].
Gaussian Beams
A Gaussian beam is a type of laser beam that forms an intensity profile that takes the form of a Gaussian shape, shown in Fig. 1. This is because laser light is highly directional, and spreads very little away from the axis of propagation as it travels.
This makes it possible to make use of the paraxial wave equation to describe the propagation of the Gaussian beam, due to the limited transverse propagation of the Gaussian beam relative to its longitudinal propagation. As shown in Fig. 1, the intensity of a Gaussian beam is concentrated in the center of the beam. Therefore, the majority of the light stays close to the axis of propagation as it travels in the longitudinal direction. This distance is much smaller than the typical distance of propagation for UWOC, which ranges from 1-100 meters [3]. This allows one to make use of the paraxial approximation, which approximates the wave without accounting for the very small amount of transverse convergence and divergence that occurs due to diffraction. The paraxial wave equation comes from Maxwell’s equations that describe electromagnetic wave propagation, and the Gaussian beam is a solution to the paraxial wave equation. The derivation for electromagnetic wave propagation, derivation of the paraxial wave equation, and a demonstration of the Gaussian beam as a solution to the paraxial wave equation can all be found here.
The paraxial wave equation, shown in polar coordinates, is useful for gaining a fundamental understanding of the way a Gaussian beam of light propagates in a vacuum. In our research, the light will propagate through the underwater medium which will cause changes to the path of propagation, due to changes in the refractive index of the medium. As a result, the beam’s phase and amplitude will be affected both spatially and temporally, but a fundamental understanding of the propagation of the beam in vacuum is an essential part to using these beams to create practical communication links [2].
Figure 1: Gaussian beam intensity profile as a function of the radial position
Source: https://www.edmundoptics.com/knowledge-center/application-notes/lasers/gaussian-beam-propagation/
Paraxial Wave Equation:
Figure 2: Propagation of Gaussian beam in vacuum along z-axis with [2]
The majority of the light is focused at the center of the Gaussian beam, and the light gradually loses intensity as it gets radially further from the axis of propagation. The beam radius W0, is defined as the point where the intensity of the beam is of maximum intensity. The beam radius is dependent on the distance along the axis of propagation z, the wavelength of light λ, and the beam waist radius . The beam waist is the point where the Gaussian beam converges and diverges from, and the narrowest beam radius. Fig. 2 shows a visualization of the propagation of a Gaussian beam with radius of curvature F0 in a vacuum diverging from the beam waist [2].
References
[1] J. Walker. “Fundamentals of physics,” Halliday & Resnick, 10th ed. Vol. 2, p. 972-3, 978-9, 1241-2. (2014)
[2] L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005).
[3] H. Kaushal and G. Kaddoum, "Underwater Optical Wireless Communication," in IEEE Access, vol. 4, pp. 1518- 1547, 2016, doi: 10.1109/ACCESS.2016.2552538.
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