What are Beam Expanders?
An optical beam expander also known as a collimator or up-collimator is a two, or more, element optical system which increases the diameter of a collimated input beam to a larger collimated output beam for applications such as laser scanning, interferometry, and remote sensing. In short, an optical beam expander takes a beam of light and expands its size. They are used to reduce the beam diameter which may be useful when using acousto- or electro-optic modulators. They are typically used in systems with a long beam path to keep the beam collimated, or to vary the focus spot size for a given lens. Modern laser beam expanders are afocal systems developed from well-established optical telescope fundamentals. In such systems, the object rays enter parallel to the optical axis of the internal optics and exit parallel to them. This means that the entire system does not have a focal length.
Working of Beam Expanders
A laser beam expander works in such a way that the input beam is expanded to a larger diameter. The concepts are derived from the fundamental principles of telescopic design. When a collimated laser beam is input to one side of the beam expander, a collimated beam is an output from the opposite end. The object space and image space rays converge at infinity. This characteristic defines a beam expander as an afocal system.
As shown in the above two figures there are two types of afocal beam expanders. Firstly, a Galilean beam expander consists of one diverging lens and one converging lens. The lenses are separated by the sum of their focal points, except that the diverging lens has a negative focal length. A beam input into the diverging lens propagates to the converging lens without reaching an intermediate focal point. Secondly, a Keplerian beam expander has two converging lenses, separated by the sum of their focal lengths. A collimated input beam converges to a focal point between the two lenses, then diverges to the output lens.
Beam Expander Theory
In a laser beam expander, the placement of the objective and image lenses is reversed. Keplerian beam expanders consist of two lenses with positive focal lengths separated by the sum of their focal lengths. They offer high expansion rations and allow for spatial filtering because the collimated input beam focuses to a spot between the objective and image lenses, producing a point within the system where the laser's energy is concentrated (Figure 3). However, this heats the air between the lenses, deflecting light rays from their optical path and potentially leading to wavefront errors especially in high-power laser applications.
Keplerian beam expanders have an internal focus which is detrimental to high power applications, but useful for spatial filtering in lower power applications
Galilean beam expanders, in which an objective lens with a negative focal length and an image lens with a positive focal length are separated by the sum of their focal lengths, are simple, lower-cost designs that also avoid the internal focus of Keplerian beam expanders (Figure 4). The lack of an internal focus makes Galilean beam expanders better suited for high-power laser applications than Keplerian designs.
Galilean beam expanders have no internal foci and are ideally suited for high power lasers applications
When using the Keplerian or Galilean designs in laser beam expander applications, it is important to be able to calculate the output beam divergence. This determines the deviation from a perfectly collimated source. The beam divergence is dependent on the diameters of the input and output laser beams.
The magnifying power (MP) can now be expressed in terms of the beam divergences or beam diameters.
When interpreting Equation 4 and Equation 5, one can see that while the output beam diameter (D0) increases, the output beam divergence (θO) decreases and vice versa. Therefore, when using a beam expander to minimize the beam, its diameter will decrease but the divergence of the laser will increase. The price to pay for a small beam is a large divergence angle.
In addition, it is important to be able to calculate the output beam diameter at a specific working distance (L). The output beam diameter is a function of the input beam diameter and the beam divergence after a specific working distance (L) (Figure 5).
A laser's input beam diameter and divergence can be used to calculate the output beam diameter at a specific working distance
Laser beam divergence is specified in terms of a half angle, which is why a factor of 2 is required in the second term in Equation 6.
A beam expander will increase the input beam and decrease the input divergence by the Magnifying Power. Substituting Equations 4 and 5 with Equation 6 results in the following:
Application 1: Reducing Power Density
Beam expanders increase the beam area quadratically with respect to their magnification without significantly affecting the total energy contained within the beam. This results in a reduction of the beam’s power density and irradiance, which increases the lifetime of laser components, reduces the chances of laser induced damage, and enables the use of more economical coatings and optics.
Although it may seem complicated, increasing the diameter of a laser using a beam expander may result in a smaller beam diameter far from the laser aperture. A beam expander will increase the input laser beam by a specific expansion power while decreasing the divergence by the same expansion power, resulting in a smaller collimated beam at a large distance. Laser beam expanders can also be used in reverse to reduce beam diameter rather than expanding it. This will invert the magnifying power, but divergence will be increased.
Application 2: Minimizing Focused Spot Size
Spot size is typically defined as the radial distance from the center point of maximum irradiance to the point where the intensity drops to 1/e2 of the initial value (Figure 6). The focused spot size of an ideal lens can be calculated by using wavelength (λ), the focal length of the lens (f), the input beam diameter (DI), the refractive index of the lens (n), and the beam’s M2 factor, which represents the degree of variation from an ideal Gaussian beam.
Spot size is usually measured at the point where the intensity I(r) drops to 1/e2 of the initial value I0
Spot size is fundamentally determined by the combination of diffraction and aberrations illustrated by red and blue, respectively, in Figure 7. Generally, when focusing laser beams, spherical aberration is assumed to be the only and dominant type of aberration, which is why Equation 11 only takes spherical aberration into account. In regards to diffraction, the shorter the focal length, the smaller the spot size. More importantly, the larger the input beam diameter the smaller the spot size.
By expanding the beam within the system, the input diameter is increased by a factor of MP, reducing the divergence by a factor of MP. When the beam is focused down to a small spot, the spot is a factor of MP smaller than that of an unexpanded beam for an ideal, diffraction-limited spot. However, there is a tradeoff with spherical aberration because it increases along with the input beam diameter.
Application 3: Compensating for Input Laser Beam Variability
Most commercial lasers specify an output beam diameter of the laser at the aperture with a tolerance that is often on the order of 10% or more. For many laser applications, a specific beam diameter is required at the end of the system. A variable beam expander can be inserted into the system to compensate for variability between individual laser units, ensuring that the final beam diameter is consistent for all systems.
Beam Expander Selection Criteria
When choosing a beam expander for an application, certain criteria must be determined in order to achieve the correct performance.
Sliding vs. Rotating Focusing Mechanisms:
The mechanics used to focus a beam expander or change the magnification of a variable beam expander are typically classified into two different types: sliding and rotating. Rotating focusing mechanisms, such as threaded focusing tubes, rotate the optical elements during translation. They have a lower cost than sliding focusing mechanisms due to their simplified mechanics, but they create the potential for beam wander due to the element rotation (Figure 8).
Exaggerated illustration of the beam wander that may be caused by rotating focus mechanisms
Sliding focusing mechanisms, such as helicoid barrels, translate the internal optics without rotating them, thus minimizing beam wander. However, this requires more complex mechanics than those of rotating focus mechanisms, increasing system cost. Poorly designed sliding optics may also have too much freedom of movement in the mechanics. While the pointing error in these poorly designed designs will not rotate when adjusted, it will be larger than for rotating optics or correctly designed sliding optics.
Internal Focus:
Keplerian beam expanders contain an internal focus that may be problematic in high power systems. The intense focused spot can ionize the air or lead to wavefront errors as a result of the heat deflecting light rays. Because of this, most beam expanders are Galilean to avoid complications caused by internal focusing. However, certain applications require spatial filtering which is only possible in Keplerian designs because of the internal focus capability.
Reflective vs. Transmissive:
Reflective beam expanders utilize curved mirrors instead of transmissive lenses to expand a beam (Figure 9). Reflective beam expanders are much less common than transmissive beam expanders, but have several advantages that make them the right choice for certain applications. Reflective beam expanders do not suffer from chromatic aberration, whereas the magnification and output beam collimation of transmissive beam expanders is wavelength dependent. While this is not relevant for many laser applications because lasers tend to lase at a single wavelength, it may be critical in broadband applications. The achromatic performance of reflective beam expanders is required for multi-laser systems, some tunable lasers, and ultrafast lasers. Ultrafast lasers inherently span a broader wavelength range than other lasers due to their extremely short pulse duration. Quantum cascade lasers also benefit from reflective beam expanders as transmissive options may not exist at their operating wavelengths.
Unlike transmissive beam expanders, the curved mirrors of this Canopus Reflective Beam Expander expand the incident laser beam. The holes on the side of the beam expander are integrated mounting features
Applications of Beam Expanders
Laser systems have become commonplace in applications across industries from medical treatment to materials processing. Beam expansion or reduction is a common application requirement in most labs using lasers or light sources and optics. A laser beam expander is often a crucial element in the success of individual systems. For high-powered sources, the addition of a beam expander can provide a controlled reduction of power density. Reducing divergence can assist in alignment and reduce the spot size at the final focus at the beam. Reducing divergence to control collimation also benefits demanding laser applications, particularly in long-path-length systems. Variable laser beam expanders may be necessary to compensate to variations in laser source beam size from unit to unit.
A multiple-prism beam expander is a unique beam magnification means which expands a light beam without focusing it and with the added option of achromaticity. A multiple-prism beam expander usually deploys two to five prisms to yield large, one-dimensional beam expansion factors. The use of this type of beam expander can be found in such applications as: Astronomy, Interferometry, Intracavity beam expansion, and Extracavity beam expansion, and Microscopy.
