Wave Optics
In optics, wave optics is a study of physical optics which focuses on the study of waves in optical systems and how they are affected by the device's geometrical structure and optical properties. Wave optics is a topic that is often taught in higher-level courses in optics. Wave optics is very important in the study of optical devices, including microscopes, telescopes, laser devices, and cameras. A simple wave optical system is a waveguide with a single input and a single output. Most waveguides are designed to contain a certain number of modes, which are linearly independent solutions of Maxwell's equations for the waveguide. These modes are usually degenerate, meaning that they have the same frequency, but different group velocities and different behavior in the time domain. For example, a waveguide with a single input and one output is a single-mode waveguide. The modes are all linearly independent solutions of the wave equation. A waveguide with two inputs and a single output is also typically a single-mode waveguide. A waveguide with two inputs and two outputs is usually a higher-order mode, meaning that it is not a linearly independent solution of the wave equation. Higher order modes can be split into their linearly independent components. The situation is analogous to the sum of a set of identical waves. The complete wave equation can be split into the equations for the individual waves, and a solution of the wave equation can be found for each of these separate waves. Each of these wave solutions is an individual mode, which in turn can be split into linearly independent solutions. When the number of modes in the waveguide is greater than one, the waveguide is referred to as a resonant waveguide. The vibrational behavior of a resonant waveguide can be described using the concept of a resonant frequency. The resonant frequency, or simply the resonant frequency, of a resonant waveguide is the frequency at which a single mode of the waveguide is tuned, or resonant. For example, a resonant waveguide with a ring-shaped cross-section is a waveguide with two modes, and the resonant frequency is the frequency at which the waveguide is tuned between the two modes.