Spatial characteristics of the emitted laser beam

The cavity acts as a spatial filter by selecting only those light rays beams close to its central axis: the others are lost due to their distance from the axis and the size of the mirrors (Figure 8).

A laser operating in a steady state produces a light wave whose spatial structure does not change despite numerous round trips inside the cavity. In this case, the laser cavity must contain a light wave able to propagate in the cavity and remain constant after each round trip. This is known as a “Gaussian” wave whose light distribution is Gaussian in shape in the plane perpendicular to the axis of propagation. Physically, a Gaussian wave concentrates the light along the axis of the cavity. A Gaussian wave emitted through space is like a narrow beam of light and is called a Gaussian beam. By placing a small piece of cardboard or a detector perpendicular to the propagation axis of the wave (at the laser output) it is possible to measure the irradiance (the number of photons incident on a surface per unit area). Graphically, this irradiance will follow a Gaussian curve (Figure 9).

A certain spatial extension of the light wave can also be defined: the radius of the beam is equal to the distance between the optical axis and the spot where the irradiance is divided by 1/e2 in relation to the maximum irradiance of the wave.

A Gaussian wave propagates in a slightly different way from that described by classic geometrical optics. It has a minimum w0 at one place along the beam axis, known as the beam waist (Figure 10). Far from the waist, the beam diverges “in a straight line” at an angle of divergence θ. The divergence and the radius are correlated by the formula:

A helium-neon laser, for example, has a radius of approximately 1 mm at the beam waist, which corresponds to a very low divergence of 0.2 mrad (the beam must travel 5 m from the waist for its radius to double!). This is, of course, impossible for beams of light emitted by ordinary lamps.

The above formula also proves that if the divergence is high (for example if the beam is focused by a lens) then the radius of the beam at the waist is very small. Generally, it is possible to focus the laser beam at a radius of the same magnitude as the wavelength. This can also be done with an ordinary lamp but the difference is the number of photons that can be delivered per second onto a small area. This is very low for an ordinary lamp but huge for a laser. For example, a 633 nm beam with a power of 1 mW corresponds to a flux of 1015 photons per second and can easily be focused on a micrometre-wide spot (Figure 11). Thus, the power density of a simple helium-neon laser at a focal point is much greater than a sunbeam focused by a lens.

To summarise, an optical cavity selects a specific beam (a Gaussian beam) from the many photons spontaneously emitted by the “lamp-amplifying medium” and the number of photons carried by this beam is increased considerably, as it travels back and forth, by the process of stimulated emission. This beam can have a very low divergence and can be very precisely focused if the right optical tools are used.