He–Ne LASER Beam Divergence

LASER stands for light amplification by stimulated emission of radiation. In an ordinary lamp, excited atoms emit light whenever they happen to, each photon going off in a random direction with a random phase. In a LASER, a photon passing an excited atom can trigger that atom to emit a second photon that matches the first in direction, phase and wavelength. The result is a beam built from one coordinated wave rather than a crowd of unrelated ones, and it behaves differently from ordinary light in several distinct ways.

Properties of LASER light

Five properties follow from that coordinated emission, and this experiment is built around one of them.

• Coherence. The photons stay in phase with each other over long distances, so the coherence length of a LASER runs to kilometres, against a few millimetres for a filament lamp.
• Directionality. An ordinary source radiates in every direction at once. A LASER emits along a single direction.
• Negligible divergence. Light from an ordinary source leaves as an expanding spherical wavefront and diverges quickly. A LASER's wavefront is close to flat, so it spreads by only about a milliradian, roughly a millimetre of growth for every metre travelled.
• High intensity. A spherical wavefront spreads its energy over an ever larger area, so an ordinary source dims quickly with distance. A LASER keeps its energy in a narrow beam, so the intensity stays close to constant over a long throw.
• Monochromaticity. A source usually called "monochromatic" still spreads its output over 100 to 1000 angstroms of wavelength. A LASER's spread is under 10 angstroms.

The He-Ne LASER

The tube in this experiment is a helium-neon LASER. It pumps atoms through a four-level scheme, which keeps the lower LASER level essentially empty and is what lets the LASER run continuously rather than in pulses. Neon is the active medium; helium only receives energy from the electrical discharge and passes it on to neon atoms in a collision. That discharge is the pumping agent, and because it runs continuously the output is continuous wave rather than pulsed. The beam is red, at λ = 6328 Å (632.8 nm), and it is neither efficient nor powerful: well under one per cent of the input power leaves as light, and the output itself is only a few milliwatts. For an experiment that only needs a steady, narrow beam, none of that matters.

Applications

The properties above are also why LASERs turn up well outside a physics lab, and the uses look different from field to field.

• Medicine. A CO₂ LASER cuts tissue in surgery. An argon-ion LASER reattaches a detached retina. In photo-radiation therapy, a dye called HpD is injected into a patient and collects in cancerous tissue; light at about 6300 Å then triggers photochemical reactions in the dye that destroy the tumour.
• Industry. LASER welding needs no physical contact with the parts, heats only a small local area, and can join dissimilar metals, down to micro-welds. The same beams cut, drill, mark, scribe and machine.
• Military. LASERs serve as weapons, and they guide rockets and satellites.
• Electronics. LASERs manufacture components and integrated circuits, and they drive CD players, printers, copiers and scanners.
• Science and engineering. LASERs carry signals through optical fibre, link submarines underwater, speed up certain chemical reactions, and record holograms.
• Research. LASERs observe distant objects and are a standard tool in spectroscopy.

Measuring the divergence

Negligible divergence is not zero divergence. A He-Ne LASER beam widens slowly as it travels, and that widening is what this experiment measures. Point the beam down a rail, place a screen in its path and note the diameter of the spot. Move the screen further along the same line and the spot is a little wider. The angular spread of the beam is worked out from those two spot sizes and the distance between them.

Call the two spot diameters W₁ and W₂, with W₂ the one measured further from the LASER, and D the distance between the two screen positions. The working formula is:

θ = √(W₂² − W₁²) / D

That square root is not arbitrary. A beam's radius grows with distance as W(z)² = W₀² + (θz)², so squaring the two spot diameters and subtracting cancels out the beam's starting waist W₀ and leaves only the growth caused by θ, which dividing by D then turns into an angle.

θ comes out in radians, since it is built from a ratio of lengths. Convert it to degrees and minutes with:

1 radian = 57.3° ; 1° = 60′