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Transparency

The optical responses are important properties to assess DUV NLO functionality. First, linear absorption should be measured; the material must be sufficiently transparent at both the fundamental and the doubled frequency. Diffuse reflectance and transmission measurements should be performed to assess whether the material is transparent down to at least 177.3 nm. Ideally, an electronic band gap of Eg > 7.08 eV (175 nm) is sought; however, as the gap increases typically the NLO coefficients decrease, a trade-off that needs to be circumvented. Diffuse reflectance measurements can determine the absorption edge above 200 nm, but vacuum-UV (VUV) transmission measurements on polished single crystals are required below.

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Owing to advances in electronic structure methods, various levels of materials theory can predict optical gaps of materials, with DFT the most popular8. Many local and semi-local exchange-correlation functionals for DFT will, however, underestimate the experimental DUV band gaps (Fig. 2)—by up to 40%! For this reason, DFT calculations that include non-local exchange, incorporated in hybrid-functionals9 or more advanced methods, must be performed on any predicted compound, as no reference experimental gap is available to assess the DUV viability. When the experimental gap is known, it can be enough to correct the underestimated gap, but this can impact other linear responses (e.g., the birefringence).

Phase-matching

SHG is most efficiently generated when the phase-matching conditions (PMC)10, n(2ω) = n(ω) are satisfied, where n is the refractive index. Therefore, at minimum, PMC requires that nmax(ω)−nmin(2ω) > 0. For crystals with normal dispersion, an indexed PMC can be achieved using the phase-matching (PM) angles over a specific range of wavelengths, i.e., a minimum PM wavelength < 177.3 nm is required.11 The wavelength range for the PMC is critically dependent on the birefringence: the larger the birefringence, the larger the phase-matching wavelength range. In most functional DUV NLO crystals, 0.07 ≲ Δn ≲ 0.10 at  nm. For small Δn, the PMC is difficult to achieve in the DUV, whereas Δn > 0.10 results in undesirable walk-off effects.

Experimental determination of the refractive indices, and birefringence, relies on high-quality single crystals. For an accurate measurement, either the minimum deviation technique, or the prism coupling method should be used on single crystals that have been indexed, cut, and polished10. The PM wavelength range (and angles) are then determined experimentally using measured n(λ) dispersion relations fit to analytical Sellmeier expressions11. Owing to the nature of the optimization problem and optical dispersion, the refractive indices should be measured at a minimum of five different wavelengths. After obtaining the Sellmeier equations, numerical solutions to the appropriate PM-angle equations may be performed to find the optimal directions and PM wavelength ranges12.

The refractive indices can also be obtained from electronic structure calculations. Because the refractive index is attributable to a first-order perturbation of the ground state wave functions, high-precision calculations utilizing a complete basis set and high numerical tolerances are required. Careful convergence tests should also be performed, otherwise erroneous results may be obtained (Fig. 2). Limitations imposed by the computational method on the band-gap accuracy also extend to predictions on calculated birefringence values. Best practice is to report computationally obtained refractive indices at the level of theory consistent with the most accurate band gap. However, in cases where the experimental gap is known, ad hoc corrections to the gap could be made followed by self-consistent calculation of the refractive indices at the experimental gap. Finally, the nonlinear SHG material response should be determined from single-crystal measurements. Individual dij coefficients—SHG coefficients—may be measured using the Maker-Fringe technique13. For DUV applications, a dij > 0.39 pm/V at  nm is required. Conversion efficiencies may also be reported provided authentic comparisons to known materials are performed.

The frequency-dependent and/or static dij values can also be calculated using perturbation theory, although in most cases it can be enough to report only the static response because most materials show negligible dispersion in the DUV. However, these optical responses are sensitive to the numerical approximations in the calculations. Important considerations are the number of empty conduction bands used in calculating the matrix elements for dij as variations up to 80% can occur if the number of empty states is insufficient14. The accuracy of the exchange-correlation functional in capturing the band gap and local chemical bonding environments should be assessed as the SHG response can vary on the order of 0.5 pm/V between local and nonlocal functionals. One should avoid choosing the functional based on which gives the highest value, but rather by understanding if the electronic and atomic structure descriptions of the material are well described.

It is best to provide as much experimental data about a new material as possible, as unsatisfactorily performed calculations can lead to erroneous conclusions about the capability of the DUV NLO material. If no experimental data are available for a predicted compound, the variations in the optical properties obtained from different levels of theory should be discussed to assess NLO performance.

Additional considerations

Laser crystals can be considered the “engines” of solid-state lasers. They are used for gain media, for frequency conversion, and to manage laser characteristics and performance. Like the engine of a car, if laser crystals are clean and working properly, they allow the larger system to operate at a higher level. In the case of a laser system, operating at a high level means creating a stable beam and reaching high optical powers. Some advantages of laser crystals over other solid-state gain media are that they typically offer less absorption, a narrower emission bandwidth, higher transition cross-sections, and higher thermal conductivity. Laser crystals are critical for enabling a wide variety of applications including laser materials processing, laser surgery, sensing, defense applications like rangefinding, and more.

Because laser crystals are sensitive optical components and are often used with high-power lasers, depositing the correct coatings onto them without introducing any defects is essential. While the complex geometries and high laser-damage threshold (LDT) requirements make the fabrication of laser crystals challenging, keeping several key considerations in mind helps ensure that the crystal and its coating behave as intended.

Fabricating Laser Crystals

Laser crystals are optical crystals typically doped with transition metals or rare earth ions. There are many different crystal types and shapes and each crystal has its own unique set of attributes that must be considered. Some common crystal shapes include rods, cubes, and zigzag slabs used to reduce thermal lensing and stress-induced birefringence.

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Raw boules, or synthetically grown ingots, of crystals are cut, ground, and polished to the tightly-toleranced specifications needed for the application. The parallelism and perpendicularity of the different faces of the crystal must be tightly controlled since the alignment of the crystal inside a laser cavity is crucial to proper functioning. Protecting previously polished surfaces while polishing the other surfaces is critical to maintaining surface quality. Polishing is carefully monitored to minimize subsurface damage, which could lead to light loss and even complete failure if high-power laser light scatters off of defects or is absorbed.

In-process metrology ensures that requirements for surface figure, parallelism, perpendicularity, dimensional specifications, and surface quality have been met. Careful cleaning of all polished surfaces prior to the deposition of the coatings is also important for preventing the introduction of any contamination such as slurry or blocking substances. Ultrasonic cleaning removes any leftover polishing compounds before coating. This is especially helpful for cleaning ground surfaces, as they are harder to clean by hand than polished surfaces. Finally, a manual inspection using a high-magnification microscope verifies cleanliness and quality, determining if an additional manual cleaning step is required.

Coating

Most laser crystals have two surfaces that need to be polished and coated, but depending on the crystal geometry, up to six different polished and coated surfaces may be needed. Coating multiple surfaces increases the complexity of the coating process. The specific order in which coatings are applied must be considered to preserve the surface quality of the remaining crystal faces and not damage any coatings that have already been applied. The tooling and blocking techniques used during coating are also critical to protecting already-coated surfaces and preventing unwanted overspray onto other surfaces. Tooling is designed to allow for the expansion of different materials during coating without getting damaged. In certain cases, polishing and coating steps are alternated. This is common when the surfaces adjacent to each other are both coated all the way to their edges.

Thin film coatings are deposited to improve transmissive and reflection properties. The specific coatings used are entirely dependent on the end application’s wavelength, power levels, environmental requirements (temperature, humidity, vacuum, radiation, salt spray, etc.), laser design, and other factors. The coatings are applied as single-band and multi-band wavelengths according to the customer’s specifications. Chamber geometry and evaporation techniques are important parameters that must be met in order to have perfect uniformity between all the parts. Multiband coatings are very carefully designed for repeatability with very discrete layer thickness control to get low-loss, non-absorbing films. Sometimes a whole crystal slab is coated, diced into smaller pieces, and then coated again to cover the newly-created surfaces.

Electron-beam (e-beam) coatings are slightly porous, and their behavior can slightly shift based on absorbing moisture or temperature increases, which drive out absorbed moisture. Figure 4 shows an example of how a change in temperature can impact spectral performance. Historical data and testing at the end-application’s operating conditions inform how the crystal will behave in the field. Other coating techniques such as ion-assisted deposition (IAD) and ion beam sputtering (IBS) can minimize shifting or eliminate it altogether by compressing the films to limit moisture intrusion. However, these techniques may introduce stress to the crystal and lower its laser damage threshold (LDT), so all requirements must be prioritized against each other.

For extremely difficult specifications such as narrow-band or multiband coatings, the placement of each individual crystal in the coating chamber is important to maintain repeatability (Figure 5). Parts are specifically arranged in the chamber to ensure uniformity among all parts. Any thickness errors are evaluated to determine if they will affect the crystal’s final performance.

Confirming Laser Crystal Quality

A wide range of in-process and post-process metrology including spectrophotometers, interferometers, high-power microscopy, dimensional gauging, photothermal absorption, and laser damage testing is used to verify key specifications. This is essential for optical suppliers to be confident that all customer requirements are actually met.

As many laser applications continue to move to higher powers, maintaining tight dimensional tolerances, high laser damage thresholds, and precise spectral performance becomes increasingly important for laser crystals. Speak to your optical component supplier when sourcing laser crystals to ensure that they have factored in the above considerations into their quotes and designs. Aligning on these requirements early on will reduce the likelihood of design iterations and make it more likely that your crystals will behave as needed in your final system.

This article was written by Karl George Jr., Laser Optics Business Development Manager, and James Karchner, Laser Optics Sales Manager, Edmund Optics. For more information, visit here  .