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# Laser Rayleigh Range: A Detailed Explanation

When working with lasers it is important to understand  the physical parameters that define system performance. Some of these specifications may be more familiar than others.  For example concepts like wavelength and divergence are commonly used  when describing the behavior of lasers.  On the other hand, parameters like, M-factor, beam caustic, and Rayleigh Range are less common, but equally important.

In this article I would like to talk a little bit more about the concept of laser Rayleigh Range.  In order to start the explanation please see, in figure 1,  an hypothetical Gaussian Beam after being focused by a lens. Figure 1. Gaussian beam traveling in free-space.  The beam waist (w0) is the smallest diameter of the beam.  Zr is the Rayleigh Range, b is the confocal distance, and ? is the divergence.

In order to explain the laser Rayleigh range we need to understand the concept of beam waist.  Even though we may imagine that light from a laser is collimated and doesn’t change dimensions, the truth is that it will have some divergence, meaning that the diameter of the beam will increase as it propagates in space.  There will be one point in which the beam diameter will be the smallest, that’s what we called the beam waist (w0) and we usually use it as an origin to start measuring the z-direction.  So by definition, the origin (z=0) is located at the beam waist.

From there we can define the Rayleigh Range as the distance from the beam waist where the area of the gaussian beam doubles, or in other words, where the diameter of the beam increases by sqrt(2) times the beam waist.  This can be expressed in a formula as: Where λ is the wavelength.

Twice the Rayleigh Range is called the confocal distance or more commonly known as the depth-of-focus.  Which can be understood as a tolerance of where the image plane can be placed without a lot of image degradation.  If any of you is familiar with photography, the depth-of-focus is where the image will appear to be in focus on the camera sensor.

Another reason why the Rayleigh range is important is that within this range the divergence of the beam is very small. So if you are in need to work with a highly collimated beam, your best chance is to work with a beam with a large Rayleigh Range.

In terms of field of curvature, within the Rayleigh Range we can consider that the Gaussian Beam has a plane wavefront (with a Gaussian Intensity distribution), while beyond the Rayleigh Range the wave front can be considered spherical.  That change in wavefront can help us to simplify or to better model our optical system specially if needing to work with diffractive elements or near the diffraction limits.