Axicons form a quasi-Bessel beam with nearly zero diffraction over a
given region, known as their depth-of-field (DOF). After this region, the
beam continues propagating in a ring-like pattern (Figure 5.5). Traditional,
refractive axicons are considered either conical lenses or prisms.
Light transmits through them and then refracts at the conical surface.
Reflective axicons with a reflective conical surface are also employed in
certain situations such as ultrafast laser systems. The broad wavelength
bandwidth inherent to ultrafast lasers would experience significant chromatic
dispersion transmitting through a refractive axicon, while this dispersion
is avoided in reflective axicons (Figure 5.6). Quasi-Bessel beams
can also be generated using holographic methods with high diffraction
efficiencies but suffer from a diffraction-modulated axial profile.
Bessel beams experience little to no diffraction within their propagation
distance and provide an excellent DOF, which makes them ideal for applications
such as laser material processing and corneal surgery. Clean
cuts with sharp edges can be generated in the DOF because of the uniform
beam diameter.
Section 5.5: Circularizing Beams
with Cylinder Lenses
Cylinder lenses are similar to spherical lenses in the sense that they use
curved surfaces to converge or diverge light, but they have optical power
in only one dimension and will not affect light in the perpendicular dimension.
This is impossible to accomplish using spherical lenses as light
will focus or diverge uniformly in a rotationally symmetric manner. Cylinder
lenses play an important role in the manipulation and shaping of
laser light and are used for forming laser light sheets and circularizing
elliptical beams.
Two orthogonal directions define the reference system of cylinder lenses:
the power direction and the non-power direction. The first direction
is called the “power direction” because it runs along the curved length
of the lens, and is the only axis with optical power (Figure 5.8). The second
direction is called the “non-power direction” because it runs along
the length of the lens without any optical power. The length of the cylinder
lens along the non-power direction can extend without affecting
the optical power of the lens. Cylinder lenses can have a variety of form
factors including rectangular, square, circular, and elliptical shapes.
Because laser diodes diverge in an asymmetrical pattern, a spherical optic
cannot be used to produce a circular collimated beam from a diode.
The lens acts on both axes at the same time, maintaining the original
asymmetry. An orthogonal pair of cylinder lenses allows each axis to be
treated separately.
To achieve a symmetrical output beam, the ratio of the focal lengths of
the two cylinder lenses should match the ratio of the x and y beam divergences.
Just as with standard collimation, the diode is placed at the focal
point of both lenses and the separation between the lenses is therefore
equal to the difference of their focal lengths (Figure 5.9).
Laser diodes may have a very large divergence due to their small output
apertures, which can be a challenge when trying to collimate because
divergence has a direct effect on the allowable length of the
system, as well as the required sizes of the lenses. The relationship
between divergence and beam size is described in Section 2: Gaussian
Beam Propagation on pages 8-11. As the relative positions of each component
are fairly fixed due to their focal length, it is possible to calculate
the maximum beam width (d) at each lens using the focal length of
the lens (f) and the divergence angle (θ) of the axis it is collimating. The
clear aperture of each lens must then be larger than the corresponding
maximum beam width.
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DOF
Figure 5.5: Schematic of a traditional refractive axicon showing the
Bessel beam region in the DOF and the ring-shaped beam that propagates
after the overlap region
Incident Laser Beam
Reflective
Axicon
Bessel Beam
Region
Figure 5.6: Schematic of a reflective axicon which, like the traditional
axicon, creates a Bessel beam region in the DOF and a ring-shaped
beam after the overlap region but, unlike traditional axicons, is independent
of wavelength
Cladding Layer
Active Layer
Cladding Layer
Emitting Area
Fast axis
Slow axis
Figure 5.7: The geometry of laser diodes causes them to produce
elliptical beams with two different divergence angles
5.3