In most cases, a laser emits light in the form of a laser beam. This means that the light dominantly propagates in a certain direction, typically with most of the optical power concentrated to a small area of the order of a square millimeter.
Laser beams are often close to Gaussian beams, where the transverse profile of the optical intensity of the beam can be described with a Gaussian function, the width of which varies along the propagation direction. This variation of beam size can be very small for beams with large width or very fast for tightly focused beams.
Generally, laser beams exhibit a high degree of spatial coherence, which is related to a high beam quality. As a result, such beams exhibit good focusability and the potential to form collimated beams with very low beam divergence.
The propagation of Gaussian beams can be calculated with a set of relatively simple equations. For beams with non-ideal beam quality, one can use a generalized set of equations which also involves the so-called beam quality factor M2. In this case, the questions cannot predict the detailed evolution of beam profile, but only of the beam radius based on the second moment of the intensity profile (D4σ method).
The optical power of a laser beam may hardly change during propagation in a transparent medium, or quickly decay in an absorbing or scattering medium. Inhomogeneous media (i.e., media with a locally varying refractive index) can also distort the shapes of laser beams. This can happen due to e.g. thermal effects such as thermal lensing in a gain medium.
Most laser beams are linearly polarized, i.e., the electric field oscillates in a certain direction perpendicular to the propagation direction. Some lasers, however, emit light with an undefined, fluctuating polarization state.
A laser beam of visible light with sufficiently high power may be visible when propagating in air. This is because a tiny portion of the optical power is scattered by dust particles and/or density fluctuations in the air and can therefore reach the observing eye. When the laser beam hits some diffusely scattering object, such as a white screen, a much brighter spot is seen on that screen, since most of the optical power is scattered at this point.
Near Field and Far Field of Laser Beams
The near field of a laser beam is understood to be the region around the beam waist (focus). The far field concerns the beam profile far from the beam waist, i.e., in a distance from the focus which is large compared with the effective Rayleigh length. The far field intensity profile reveals details of the beam divergence, which in the near field can be obtained only with wavefront measurements. As it is often not practical to access the far field directly, one may use a focusing lens (or mirror) to obtain an intensity profile in its focal plane which reveals a scaled-down version of the far field pattern.
Limitations for the Focusing of Laser Beams
Laser beams can be used for transmitting optical energy to rather small spots or with low beam divergence over large distances. However, there are limitations to this, which involve the optical wavelength, the beam quality and the transverse size of the used focusing or collimation optics. Some of these limitations are discussed in the following, always assuming propagation of the beam through a homogeneous medium (i.e., with no added beam distortions on the way).
If a laser beam is focused to a spot (beam waist) with beam radius w0, it exhibits a certain beam divergence angle which is inversely proportional to the waist beam radius and proportional to the optical wavelength in the M2 factor:
The used focusing optics must be able to handle that amount of beam divergence; a limitation for that results from the limited numerical aperture of the optics. Also, if the focus has to have a large distance from the focusing optics and/or the waist beam radius is small or the beam quality is low, the beam radius in the focusing optics will necessarily be quite large. A correspondingly large open aperture of the optics is required. Such factors can in practice set a lower limit to the achievable beam radius in the focus, or an upper limit to the tolerable M2 factor of the beam.
In some cases, one optimizes the beam radius in the beam focus such that the beam radius at a certain distance from the focus is as small as possible. For that purpose, one has to choose the waist beam radius such that the effective Rayleigh length of the beam equals the mentioned transmission distance. The resulting beam radius at the distant position will then be ≈1.41 times the waist beam radius.
If the sent-out beam does not have to have its focus at the focusing optics, one should place the focus in the middle between the optics and the distant point. Ideally, the effective Rayleigh length will then be half the transmission distance. The beam radius at the distance spot will be identical to that at the focusing optics, and ≈1.41 times larger than in the beam focus.
For example, if a Gaussian laser beam at 1064 nm should be sent to the moon (distance 380 000 km) in order to illuminate a small spot there, the ideal beam radius in the focus will be 8 m, such that the Rayleigh length is 190 000 km. The beam radius in the focusing optics and on the moon will then be 11.3 m. If the used sending telescope cannot be that large, the illuminated spot on the moon will be larger.
When creating a beam focus in some distance from some focusing optics with a limited open aperture, the possible waist beam radius will increase if that distance is increased. Furthermore, there is a maximum to that distance; in the extreme case, the distance equals the effective Rayleigh length of the beam, and the resulting waist beam radius will be smaller than the beam radius at the focusing optics by the square root of 2 (≈1.41). One can thus easily calculate the Rayleigh length based on the initial beam radius and thus the maximum focusing distance.
Experimental Characterization of Laser Beams
There are various devices and techniques for characterizing a laser beam in various respects:
- The total optical power carried by a laser beam can be measured with a powermeter. There are also energy meters for measuring pulse energies of pulsed lasers.
- The intensity profile (irradiance profile) can be measured with some kind of beam profiler, which may be based on a camera. Some laser beams exhibit “hot spots”, i.e., regions with higher intensity, which may play role in damage phenomena. There can also be satellite structures, halos and other deviations from beam uniformity. Note that the shape of the beam intensity profile may change during propagation, and is also not always stable over time.
- Some devices do not measure the whole beam profile, but only a beam radius or diameter. Note that the beam radius is usually not defined as a half width at half maximum (HWHM) value, but as the radial position where the intensity falls to 1/e2 times the peak intensity. This comes from the context of Gaussian beams.
- Wavefront sensors, for example of the Shack–Hartmann type, can be used to measure the shape of the optical wavefronts.
- The beam quality (M2 factor) can be calculated from multiple intensity profiles or from intensity and wavefront measurements at one location only.
- A laser beam may exhibit beam pointing fluctuations, which can be measured by monitoring the position (center of gravity of the intensity distribution) at a suitable location.
- The polarization state maybe roughly characterized based on the power transmission of a polarizer for different orientations, or more completely with various techniques for polarimetry.
For many laser applications, it is essential to have proper means for beam diagnostics, as many possible problems can be identified with such instruments.
|||H. Kogelnik and T. Li, “Laser beams and resonators”, Appl. Opt. 5 (10), 1550 (1966)|
|||A. E. Siegman, “Defining, measuring, and optimizing laser beam quality”, Proc. SPIE 1868, 2 (1993)|
|||A. E. Siegman, Lasers, University Science Books, Mill Valley, CA (1986)|
See also: laser light, collimated beams, coherence, beam quality, Gaussian beams, beam divergence, beam pointing fluctuations, polarization of laser emission, speckle, beam profilers, powermeters, Spotlight article 2010-04-08
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