In laser optics propagation applications, the laser beam is typically modeled as a Gaussian beam with an irradiance profile that closely follows an ideal Gaussian distribution. However, real-world laser beams exhibit some deviations from the ideal Gaussian behavior. This article will discuss the key parameters that describe Gaussian beam propagation and their importance in optical systems.
Key Parameters in Laser Optics Propagation
When working with laser optics, beam size, divergence, and the Rayleigh range are commonly used to describe the characteristics of the beam as it propagates from surface to surface.
Gaussian Beam Waist: The beam waist is where the beam size reaches its minimum. This is the thinnest point of the laser beam. The waist is denoted as w0, which represents the half width or radius of the laser beam at its narrowest.
Beam Divergence: The half divergence angle (θ/2) describes how the beam spreads as it propagates away from the waist. The beam divergence increases as the distance from the waist increases.
Rayleigh Range: The Rayleigh range (zR) defines the distance over which the beam size increases by a factor of sqrt{2}. It is an important parameter in Gaussian beam propagation and is determined by:
Wavefront of Laser Optics
The wavefront of the laser beam is planar at the beam waist and becomes increasingly curved as the beam propagates. The phase radius of curvature is a function of the distance from the beam waist zz:
Manipulating Laser Optics Beams
In many laser optics systems, laser beams need to be manipulated, which requires optical components like lenses, mirrors, and prisms. Below, we describe some key phenomena associated with beam manipulation:
The behavior of an ideal thin lens can be described using the following equation:
Laser Optics Focal Shift
The phenomenon of Gaussian focal shift states that the intensity of a focused beam at a fixed distance from the lens is not maximized when the waist is placed at the target. Instead, the intensity is maximized when the waist occurs slightly before the target. This is a critical consideration when focusing laser beams for high-precision applications.
Collimating a Laser Optics Beam
Achieving a perfectly collimated beam (where the divergence is zero) is not feasible. However, a near-collimated beam can be achieved by either minimizing the divergence or maximizing the distance between the observation point and the nearest beam waist. The collimating lens should have a focal length equal to the distance from the beam waist to the lens.
Focusing a Laser Optics Beam to a Spot
Focusing a laser beam to the smallest possible size is essential in applications such as materials processing and surgery. To minimize the beam waist, a shorter focal length lens can be used. For example, with a magnification of 2, the output beam waist will be twice the input beam waist, and the output divergence will be half of the input divergence.
From the equation above, we can see that the focused beam waist can be minimized by reducing the focal length of the lens and |s|-f.
Reference
- https://www.zemax.com/
- https://www.edmundoptics.com/knowledge-center/application-notes/lasers/gaussian-beam-propagation/