As this method reduces the conversion efficiency as well, a trade-off has to be made between nonlinear conversion efficiency, spatial beam quality, and longevity of the nonlinear crystal. In the case of critical phase matching, elliptical focusing generally yields an increased conversion efficiency and improved beam quality at a given power density.

If the focus on the fundamental beam is located in the center of the nonlinear crystal, then the focus size of the fundamental beam must be increased to increase the beam size in the nonlinear crystal. Thus, the fundamental focusing and harmonic beam shaping optics would need to be redesigned. If the form factor of the device is to remain unchanged, then the beam size on focusing and beam-shaping optics elements decreases.

This increases the power density on the optics and, consequently, decreases lifetime of the optics. Increasing the incident laser power on a nonlinear crystal can have undesirable side effects. For example, permanent damage may occur in the crystal over time.

With accumulated exposure, this damage can result in generally decreasing power intensity as well as generally increasing astigmatism. Therefore, correcting the astigmatism with optics may require frequent compensating adjustments, which would be impractical in commercial applications.

Moreover, the astigmatism also may rapidly increase to the level where accurate compensation is not possible even with adjustment.

Generating a shorter output wavelength also can accelerate the degradation of the crystal because the output photons are more energetic and, therefore, can change characteristics of or even permanently damage the crystal. Thus, at shorter output wavelengths, astigmatism and other adverse beam quality and intensity effects also may increasingly occur.

When scaling the harmonic power e. The focus size in the nonlinear crystal may need to be changed to re-optimize. This can require a major optical and optomechanical redesign of the nonlinear wavelength converter module. The wavelength converter includes a nonlinear crystal and beam shaping optics The beam shaping optics can include one or more lenses, mirrors, or other optical components. An additional beam shaping optics not illustrated , which also can include one or more lenses, mirrors, or other optical components, may be positioned on the opposite side of the nonlinear crystal from the beam shaping optics A laser beam is projected at the nonlinear crystal The laser beam has a focus that is outside the nonlinear crystal in at least one plane perpendicular to a beam propagation direction of the laser beam For example, this plane may be parallel to the dashed lines representing the beam size The distance between the center of the nonlinear crystal and the focus can be set or adjusted.

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For any given Gaussian or near-Gaussian beam, the beam diameters, measured along two mutually perpendicular axes x and y, both also being perpendicular to the beam propagation direction , are functions of the distance z-z0 to the focus locations, as seen in Equation 1 and Equation 2. The time-averaged fundamental power density D F at the spatial peak of the beam profile can be calculated as a function of the beam radii, as seen in Equation 3. If, for example, the nonlinear optical process is second harmonic generation, the beam sizes and the power density of the harmonic beam and the conversion efficiency for a given crystal position can be calculated based on the fundamental beam sizes described in Equations 1 and 2.

In the presence of walk-off this can be achieved by using a numeric simulation of the harmonic generation for focused Gaussian beams. Similar numerical models are available for other nonlinear optical wavelength conversion processes. The crystal position z and thus the beam size can be chosen so that the fundamental power density remains high enough to achieve the desired conversion efficiency and harmonic output power, while, within the limits of this boundary condition, both fundamental and harmonic power densities are minimized, so that the spot lifetime of the nonlinear crystal is maximized.

Typical distances between a position of the focus and a location of the nonlinear crystal range from millimeters to tens of centimeters. However, other distances are possible. In an example, the power of the harmonic radiation with a wavelength of nm, generated in a nonlinear crystal , such as BBO, is doubled while fundamental and harmonic power density in the nonlinear crystal remain unchanged.

Under these conditions the crystal spot lifetime remains unchanged as well. This can be achieved by doubling power of the fundamental laser s , as well as the beam area inside the nonlinear crystal In this example the major axis of the ellipse is parallel to the walk-off. The beam size in the nonlinear crystal can be increased by increasing the size of a focus located inside the nonlinear crystal As a result the beam area on a downstream optics at a distance of, for example, 0.

When using the embodiments disclosed herein, the same DUV power and DUV power density in the nonlinear crystal can be achieved by maintaining the original focus size and position and moving the nonlinear crystal downstream of the focus by 0. This is a significant improvement over previous systems. The distance the nonlinear crystal is moved upstream or downstream of the focus can vary, and moving the nonlinear crystal downstream of the focus by 0. The nonlinear crystal can be configured to provide phase matching to achieve efficient nonlinear interactions in a medium.

The nonlinear crystal may utilize critical phase matching, noncritical phase matching, quasi-noncritical phase matching, or quasi-phase matching.

## Nonlinear wavefront shaping with optically induced three-dimensional nonlinear photonic crystals

Nonlinear crystals, such as the nonlinear crystal , are typically grown in boules, and then cut into individual crystal elements. The input and output surface are polished after cutting. The dimensions of the available crystal elements depend on the properties, such as boule size and boule quality, of the chosen nonlinear optical material.

Nonlinear optical crystals may have length dimensions from 1 mm to 50 mm, width dimensions from 3 mm to 20 mm, and height dimensions from 0. A nonlinear crystal of any size suitable for a desired application can be used in the embodiments disclosed herein. As seen in FIG. The power density at the beam size is less than the density at the beam size Thus, the nonlinear crystal is affected by part of the laser beam with a lower power density.

The beam size inside the nonlinear crystal can be optimized by adjusting the position of the nonlinear crystal outside the focus When using techniques disclosed herein, changes to the size and location of the focus of the laser beam can be avoided. As the waist size and location of the focus can remain unchanged, the beam size on the beam shaping optics downstream of the nonlinear crystal may remain unchanged. More particularly, the beam size on the beam shaping optics downstream of the nonlinear crystal may not decrease. Downstream of the nonlinear crystal , the laser beam includes a fundamental beam and a harmonic beam While the harmonic beam is illustrated in a particular manner in FIG.

## Spatiotemporal phenomena in nonlinear optics contributions

The wavelength converter can use a divergent or convergent beam inside the nonlinear crystal In one plane parallel or perpendicular to the walk-off or in both planes, the fundamental beam is focused outside the crystal as shown in FIG. The size of the focus can be chosen so that it provides a short enough Rayleigh range, and, thus, a large enough beam divergence to reduce the power density on the beam shaping optics to a level that provides the desired optics lifetime.

If power scalability is intended for the wavelength converter , the beam size on the beam shaping optics is chosen to be large enough so that the required maximum power density on the beam shaping optics is not exceeded for the highest intended fundamental and harmonic powers that will be present in a power-scaled version of the wavelength converter.

The margin depends on the specific beam quality requirement for an application.

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The divergence or convergence of a laser beam can be described by Gaussian beam propagation. The beam divergence parallel to a given lateral axis at a given position z along the beam propagation direction is the arctangent of the first derivative of Equations 1 and 2. Therefore, the divergence angle at a given location can be decreased by increasing the waist size. Typical values of the angular acceptance, which is defined as a half angle herein, for harmonic generation into the DUV are on the order of 0. The acceptance angle can depend on the nonlinear process, the nonlinear crystal material being used, and the length of the nonlinear crystal.

The acceptance angle can be calculated based on the Sellmeier equations for the nonlinear crystal material. Alternatively a software package can be used to calculate the angular acceptance. The nonlinear crystal position along the axis of the beam propagation direction can be chosen so that the power density in the nonlinear crystal meets the requirements needed to achieve the desired trade-off between one or more of or between two or more of conversion efficiency, spatial beam quality, crystal lifetime, or crystal spot lifetime.

For nonlinear wavelength conversion, the conversion efficiency increases with increasing power density, so that an as small as possible beam size in the nonlinear crystal may be desirable to maximize the conversion efficiency. On the other hand, the nonlinear crystal may experience damage induced by the generated harmonic or even by the fundamental radiation, so that crystal spot used for wavelength conversion has a limited lifetime.

The exact scaling laws can depend on the specific damage mechanism experienced by the crystal. However, the crystal lifetime decreases with increasing power density, so that an as large as possible beam size in the crystal may be desirable to maximize the spot lifetime. A nonlinear crystal spot shift may trigger a service-event for the wavelength converter, so maintaining a large enough spot lifetime e. The crystal lifetime, as a whole, is the sum of the spot lifetimes for all crystal spots.

If the spot lifetime decreases linearly with decreasing spot size i. For damage mechanisms that follow a scaling law, which is faster than linear e. The nonlinear crystal provides wavelength conversion of the laser beam The wavelength converter enables scaling of the second harmonic power by increasing the fundamental power from the primary laser source used to generate the laser beam The optimum power density can be maintained by moving the nonlinear crystal farther away from the focus Changes to the fundamental focusing optics design may not be needed.

Minor changes in the harmonic beam shaping optics may still be performed to compensate for possible effects induced by the different positions of the nonlinear crystal and beam size in the nonlinear crystal For example, the changed location and power of a possible thermal lens inside the crystal may be compensated for. However, these changes are minor compared to a complete redesign of the wavelength converter optics train. Such changes can be accommodated by taking advantage of adjustable beam shaping components for the harmonic beam, such as an adjustable beam expanding telescope or a Cooke triplet, in the downstream beam shaping optics In an instance, a focus for a particular nonlinear crystal that places the nonlinear crystal outside the focus and provide a laser beam with desired parameters can be determined in a two-step process.

First, the fundamental beam size in the nonlinear crystal , as a function of the nonlinear crystal location, can be determined by using the techniques disclosed herein. Second, the harmonic beam size can be calculated based on the fundamental beam size. Using these calculations the distance between the focus and the nonlinear crystal can be chosen so that the fundamental and harmonic power densities meet specifications for a particular application.

A laser source containing a laser active medium generates fundamental radiation, such as the laser beam , in the beam propagation direction The laser source may be, for example, a solid state laser, semiconductor laser, gas laser, fiber laser, CW laser, mode-locked laser, Q-switched laser, gain-switched laser, laser with a built-in nonlinear wavelength converter, or another type of laser.

The laser beam emitted by the laser source may be a diffraction-limited or near diffraction-limited Gaussian beam. Other types of laser beams are possible. In an instance, the laser source is an exchangeable laser source. An exchangeable laser source that is part of the nonlinear optical system can be exchanged with a laser source of identical design as a field replaceable unit upon its failure or once it reaches the end of its service lifetime.

An exchangeable laser source that is part of the nonlinear optical system also can be exchanged with a laser source of a different design, such as a higher power laser source, to improve the performance e. In this case, the out-of-focus position of the nonlinear crystal can be adjusted, as described herein, to achieve an optimal trade-off between harmonic power and lifetime of the nonlinear crystal The laser beam projects through beam shaping optics upstream of the nonlinear crystal The beam shaping optics may comprise a single lens or multiple lenses and may generate a circular or elliptical focus with or without astigmatism.

The beam shaping optics may or may not be adjustable. The beam shaping optics may be located between the laser source and the nonlinear crystal or may be integrated into the laser source A focus of the laser beam is outside the nonlinear crystal in at least one plane perpendicular to a beam propagation direction of the laser beam The location and size of the focus can vary. Typical distances between the focus position and the nonlinear crystal range from millimeters to tens of centimeters.

However, focus sizes and distances to the nonlinear crystal outside of this range are possible. The nonlinear crystal is disposed in a crystal mount assembly Thus, the nonlinear crystal may be on or in the crystal mount assembly The crystal mount assembly may be fabricated of metal such as, but not limited to, aluminum, stainless steel, copper, copper-tungsten, or nickel.

## Speaker summary | ColOpt

The crystal mount assembly also may be fabricated of ceramics or other materials. The crystal mount assembly may be a spring-loaded assembly, wherein the nonlinear crystal is positioned in an L-bracket and held in place by springs along one or multiple axes perpendicular to the beam propagation direction The springs press the nonlinear crystal onto or against the L-bracket.

Due to the limited angular acceptance of the nonlinear optical interaction, the angle tolerance may be in the range from 0. Therefore, the crystal mount assembly may contain features to adjust the phase matching angle of the nonlinear interaction. Such features include, but are not limited to rotation stages actuated by a manual fine thread screws, manual micrometer actuators, manual differential micrometer actuators, or motorized actuators.