Lasers

A laser is a monochromatic coherent beam of light.

Glossary

• Monochromatic: a single wavelength
• Coherent: All the light waves move precisely together in the same phase, which gives the beam intense power.
• Beam Waist: The narrowest point of a laser beam. This isn't necessarily the emitter, the beam might be focused on a far away point.

Damage Types

• Dazzling: Temporarily blinding sensors
• Blinding: Permanently damaging optical sensors
• Heating: Damaging surface electronics (e.g. radar panel) and mechanics (e.g. gun mounts).
• Fracturing: Thermal stresses can cause cracks, or delamination of layers
• Weakening: Hot structural elements are not as strong and may buckle under load
• Melting: Melting away surface material
• Vaporising: Evaporating surface material
• Plasma Erosion: Plasma plume can physically erode material around it as it exits the hole

Physics

Irradiance

Measure of radiant power incident on a surface per unit area:

$I = \frac{P}{A}$

• I: $W/m^2$
• P: W, power
• A: m^2, spot size

Gaussian Beam Spot Size

The size of the laser beam, usually calculated at a given distance. The equation normally depends on the refractive index of the medium, in vacuum that's exactly 1 which slightly simplifies the equation.

$w(z) = w_0\cdot\sqrt{1+\left(\frac{z\lambda}{\pi w_0^2}\right)^2}$

Rayleigh Range is the distance to where the area of the spot size has doubled (i.e. irradiance has halved).

$z_R = \frac{\pi w_o^2}{\lambda}$

Beam divergence is a simplification of the gaussian spot size which assumes the laser is a cone with a constant divergence angle. This provides a simpler equation for spot size.

$w(z) = w_0 + z\theta$

• $w(z)$: $m$, spot size radius (w) at range (z)
• $w_0$: $m$, beam waist radius
• $z$: $m$, range (from beam waist to target, not emitter to target)
• $\lambda$: $m$, wavelength
• $\theta$: radians, beam divergence angle

Diffraction Limit

This sets the physical lower limit on beam divergence.

$\theta = 1.27\frac{\lambda}{D_{aperture}}$

• $\theta$: radians, beam divergence angle
• $\lambda$: $m$, wavelength
• D_{aperture}: m, aperture diameter

Beam Quality Factor

Diffraction limited is the best you can do, but beam quality measures how much worse it is in reality. This is a factor of the quality of your optics etc. This is measured as $M^2$, for a perfect system $M^2 = 1$.

$\theta_{actual} = M^2 \cdot \theta_{diffraction}$

Minimum Spot Size

The smallest spot size a laser can be focused to. Airy disc formula.

$R_{spot} = \frac{1.22 \cdot \lambda \cdot L}{D_{aperture}} \cdot M^2$

• $R_{spot}$ is the spot diameter
• $\lambda$ is the wavelength of the laser
• $L$ is the distance to the target
• $D_{aperture}$ is the diameter of the aperture
• $M^2$ is the beam quality factor

Jittered Spot Size

Assuming the emitter is vibrating, we can account for that by rolling it into spot size.

$R_{effective} = \sqrt{R_{spot}^2 + (L \cdot tan(\theta_{jitter}))^2}$

• $\theta_{jitter}$ RMS of jitter angle

Note that the small angle approximation says $tan(\theta) \approx \theta$, for laser pointing errors the jitter angle is always going to be tiny, so the tan function can be ignored.

References

• Gaussian beam Wikipedia
• Beam Quality Factor
• laserbeamsize
• xometry
  • Includes some example real world values for $M^2$