Rayleighlengden

Rayleighlengden is a term used in optics and acoustics to describe a characteristic length scale associated with wave scattering. It is named after the British physicist Lord Rayleigh. The Rayleigh length, often denoted as $z_R$, is a measure of how far a beam of light or sound can travel before its beam width increases significantly due to diffraction.

For a Gaussian beam, which is a common model for laser beams, the Rayleigh length is defined as $z_R = \frac{\pi w_0^2}{\lambda}$, where $w_0$ is the beam waist (the minimum radius of the beam) and $\lambda$ is the wavelength of the light or sound. At a distance equal to the Rayleigh length from the beam waist, the beam radius has increased by a factor of $\sqrt{2}$.

In essence, the Rayleigh length indicates the region where the beam can be considered approximately collimated. Beyond this distance, diffraction effects become more pronounced, causing the beam to diverge more rapidly. This concept is important in various applications, including laser focusing, optical trapping, and the design of optical systems. It helps engineers and scientists understand how tightly a beam can be focused and how far that focus can be maintained.