flat-top beams (original) (raw)
Author: the photonics expert (RP)
Definition: a light beam with a flat intensity profile
Alternative terms: top-hat beams, flattop beams
general opticsRelated: Gaussian beamsbeam shapersbeam homogenizersCreating a Top-hat Laser Beam Focus
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DOI: 10.61835/6ku Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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Contents
What is a Flat-top Light Beam?
A flat-top beam (or top-hat beam) is a light beam (often a transformed laser beam) having an intensity profile which is flat over most of the covered area. This is in contrast to Gaussian beams, for example, where the intensity smoothly decays from its maximum on the beam axis to zero. Such beam profiles are required for some laser applications. For example, one requires a constant intensity over some area in some techniques for the processing of semiconductor wafers and other materials. Also, nonlinear frequency conversion at very high power levels can be more efficient when performed with flat-top beams.
Figure 1: A flat-top beam profile (red) in comparison to a Gaussian (green) and super-Gaussian (blue) intensity profile. All three beams have the same optical power and the same effective mode area.
Typically, however, a flat-top beam profile still has some smooth edges, so that it can be approximated with a supergaussian profile, rather than a rectangular profile. A supergaussian intensity profile of order ($n$) is defined by the following equation: I(r) = {I_{\rm{p}}}\;\exp \left[ { - 2{{\left( {\frac{r}{w}} \right)}^{2n}}} \right]$$
The higher the order, the steeper are the edges of the profile.
Coherent and Incoherent Flat-top Beams
Flat-top beams can in principle be spatially coherent, having smooth phase profiles. However, flat-top beams made in practice (e.g. with certain beam homogenizers, or from multimode step-index fibers) are often spatially incoherent, having rather complicated phase profiles. In such cases, a flat intensity profile is achieved only with a superposition of many spectral components, each of which may have a quite structured intensity profile.
Figure 2: Beam quality factor ($M^2$) of supergaussian beams as a function of the supergaussian order. (1 corresponds to a Gaussian beam.)
Figure 2 shows the beam quality factor ($M^2$) of coherent supergaussian beams with flat phase front as a function of the supergaussian order. The more we approximate a rectangular profile with a high beam order, the worse is the beam quality; the ($M^2$) factor rises with no limit (and eventually we leave the regime where we can apply the paraxial approximation).
Propagation of Coherent Flat-top Beams
Note that in contrast to a Gaussian beam, a coherent flat-top beam is not a free-space mode. This means that during propagation in free space, the shape of the intensity profile will change. The steeper the edges of the intensity profile are, the more rapidly will such changes occur. Figure 3 shows a simulated example for an initially supergaussian beam profile with supergaussian order 8 and flat wavefronts.
Figure 3: Evolution of an initially supergaussian beam in free space.
The beam profile first contracts and then expands again, now getting smooth edges. Note that the color scale of each profile is adjusted such that the same color saturation is achieved on the beam axis; in reality, the intensity decreases for the expanding beam.
Of course, that change in beam profile may be negligible over the propagation distance required for the application. For beams with larger diameter and not too steep edges of the intensity profile, the beam size and shape may stay approximately constant.
Generation of Flat-top Beams
In many cases, a flat-top beam is obtained by first generating a Gaussian beam from a laser and then transforming its intensity profile with a suitable optical element. There are different kinds of beam homogenizers to do that transformation, using different operation principles; some are based on diffractive optics. Different types of beam shapers can differ a lot concerning spatially coherent or incoherent beam profiles, length of the usable top-hat region, sensitivity to input beam parameters etc.
Frequently Asked Questions
What is a flat-top beam?
A flat-top beam, or top-hat beam, is a light beam that has a nearly uniform intensity across a specific area. This contrasts with Gaussian beams, which have a peak intensity at the center that smoothly decays outwards.
What are flat-top beams used for?
They are used in laser applications where a constant intensity over an area is crucial. Examples include the processing of semiconductor wafers, other types of material processing, and efficient nonlinear frequency conversion at high power levels.
Why does the shape of a coherent flat-top beam change as it propagates?
Unlike a Gaussian beam, a coherent flat-top beam is not a natural free-space propagation mode. Its profile, particularly if it has steep edges, is altered by diffraction effects during propagation, causing the shape to change.
How can one generate a flat-top beam?
A common method is to start with a Gaussian beam from a laser and then modify its intensity profile using a suitable optical element. Various types of beam homogenizers, some based on diffractive optics, can perform this transformation.
How is a flat-top beam profile mathematically described?
A flat-top profile with smooth edges can often be approximated by a supergaussian function. The higher the order of the supergaussian profile, the steeper the edges of the beam become, more closely resembling a rectangular profile.
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