## How to Build a Laser Death Ray## Diffraction |

There is a fundamental physical limit on the ability of lasers to focus on their targets. It is called diffraction. To understand diffraction, you need to understand the behavior of waves.
When a freely propagating wave encounters a barrier, it can curve around the barrier. Think of ripples on the surface of a still pond passing a post sticking out of the water. Similarly, a wall with a single opening will let the wave through the opening, but the edges of the wave will curve out toward the sides, causing the transmitted wave to spread out. This phenomenon is known as diffraction. It happens with every kind of wave in nature. Light is a wave in the electromagnetic field, so light undergoes diffraction. It does not even require an object in the path of the wave, any beam of waves has a tendancy to spread out to the sides due to this effect. The smaller the wavelength of a wave in comparison to the size of the obstruction or opening, or the width of the beam, the less the wave diffracts. Since visible light has a very small wavelength, this is why light seems to travel in straight lines. It takes very narrow objects, such as hairs or thin scratches, to get noticable diffraction. This is easy to demonstrate with a laser pointer in a darkened room. Shine the beam at a wall. Now put a hair in the beam. You will see a streak appear on the wall through the laser dot perpendicular to the hair. The streak is the light diffracting around the hair.
When a laser beam is propagating freely, it will naturally tend to expand. This means that if you try to focus the beam down to a tiny point at a distant target, the beam might spread out to a much larger spot by the time it gets there. The amount the beam expands depends on the ratio of the initial width of the beam to the wavelength of the beam. In fact, we can determine the smallest possible spot size into which you can focus the beam: if we denote the diameter of the mirror, lens, or other opening in the laser or focusing element as D, the wavelength of the light as L, and the distance to the target as R, then the diameter of the smallest spot, S, is given by
S = 1.2 R L / D.
Make sure you use the same units for R, L and D (this will give S in that unit as well). The term 1.2 L / D is sometimes called the divergence angle A (even though the beam will be converging if S < D). With this terminology, S = R A.
For example, a laser that emits 5×10-7 meter wavelength light (or 0.5 microns, this puts it in the visible green) that is focused through a 0.1 meter lens at a target 1000 meters (1 km) away will have a minimum spot size of 6×10-3 meters (6 millimeters) and a divergence angle of 6×10-6 radians. The above formulas are only valid when R is much larger than D. The details of near field diffraction are too complex to cover here, although you will not be too far wrong using the formulas as long as R > D.
A note for the mathematically inclined: the beam profile at the focus is the 2D Fourier transform of the beam profile at the aperture. |