Introduction to Optical Metrology

2	Laser Beams

2.1    GAUSSIAN BEAMS

Use of a laser beam is an obvious choice in many metrological applications. When the laser is oscillating in TEM₀₀ mode, the beam has a Gaussian profile, and its spatial extent is very small. It is important to understand its propagation and manipulation by the lens or any other image-forming component. Since light is characterized by wave motion as well, we begin with the three-dimensional wave equation and search for a solution, which would resemble a laser beam. The wave equation is given by

${\nabla }^2\mathit{u}-\frac{1}{c^2}\frac{{\partial }^2\mathit{u}}{\partial t^2}=0$

(2.1)

where:

u is the wave amplitude

∇² = (∂²/∂x²) + (∂²/∂y²) + (∂²/∂z²) is the Laplacian

We will consider a monochromatic wave traveling along the +z-direction and express the solution as ...