Lithium triborate (LiB3O5) or LBO is a non-linear opticalcrystal. It has a wide transparency range, moderately high nonlinear coupling, high damage threshold and desirable chemical and mechanical properties. This crystal is often used for second harmonic generation (SHG, also known as frequency doubling), for example of Nd:YAG lasers (1064nm → 532nm). LBO can be both critically and non-critically phase-matched. In the latter case the crystal has to be heated or cooled depending on the wavelength.
Lithium triborate was discovered and developed by Chen Chuangtian and others of the Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences. It has been patented.[1]
LBO exhibits a unique combination of desirable physical and optical characteristics that make it highly effective for nonlinear frequency conversion:
Wide Transparency Range: LBO is transparent from the ultraviolet (UV) to the mid-infrared (MIR) spectrum, typically ranging from 160 nm to 2600 nm. This broad transparency allows for versatile applications across different laser wavelengths.
High Damage Threshold: It possesses a remarkably high laser-induced damage threshold (LIDT), often cited as one of the highest among common NLO crystals (e.g., 25 J/cm$^2$ for 1064 nm, 10 ns pulses; some sources report >90 J/cm$^2$ at 355 nm with femtosecond pulses). This property makes it particularly suitable for high-power and high-energy laser systems.
Moderate Nonlinear Coupling: While its effective nonlinear coefficient is not as high as some other crystals like BBO, it is still sufficiently large (about three times that of KDP) to achieve efficient frequency conversion.
Low Walk-off Angle: LBO exhibits a small walk-off angle, especially under non-critical phase-matching (NCPM) conditions. Walk-off refers to the spatial separation of interacting beams due to birefringence, and a small walk-off angle ensures better beam overlap and higher conversion efficiency over longer crystal lengths.
Wide Acceptance Angle: LBO has a wide angular acceptance, meaning that the efficiency of frequency conversion is less sensitive to variations in the input beam's angle. This eases alignment requirements and makes the crystal more robust in practical systems.
Good Chemical and Mechanical Stability: LBO is non-hygroscopic, meaning it does not readily absorb moisture from the air, which simplifies handling and storage compared to hygroscopic crystals like BBO. It also has good mechanical properties, with a Mohs hardness of approximately 6, making it durable and easier to process.
High Optical Homogeneity: High optical homogeneity (∂n ≈ 10$^{-6}$/cm) ensures minimal wavefront distortion and high output beam quality.
Crystal Structure and Chemical Properties
LBO crystallizes in the orthorhombic system with point group mm2 and space group Pna21. Its lattice parameters are approximately a=8.4473 Å, b=7.3788 Å, and c=5.1395 Å. The crystal structure is composed of interconnected borate groups (BO$_{3}$ triangles and BO$_{4}$ tetrahedra) forming a three-dimensional network, with lithium atoms occupying interstitial sites within this network. This rigid and dense structure contributes to its excellent mechanical stability and high damage threshold.
Specific heat: 1060 J/kg·K (or 1.91 J/cm$^3 \cdot$K)
Crystal Growth
Due to its incongruent melting behavior, LBO crystals cannot be grown from a pure melt using conventional Czochralski or Bridgman methods. Instead, they are typically grown by the flux method (also known as melt-solution crystallization), often using the Kiropoulos method. Molybdenum oxide (MoO$_{3}$) is a common solvent used in the flux, sometimes in combination with other fluxes like LiF, Li$_{2}$O, or B$_{2}$O$_{3}$ to improve solution stability and crystal quality.
The flux growth process involves:
Precisely mixing lithium, boron, and oxygen compounds in a crucible.
Heating the mixture to a high temperature to form a melt-solution.
Carefully controlling the temperature cycle and maintaining a stable temperature gradient to induce slow crystal growth.
Introducing a seed crystal (often grown along the crystallographic "c" direction or [001]) onto the surface of the melt-solution.
Gradually lowering the temperature or pulling the crystal to allow for controlled growth.
Cooling the furnace slowly once the crystal reaches the desired size.
Challenges in LBO crystal growth include the potential for flux inclusions within the crystal, which can affect optical quality. Continuous improvements in heat field configuration and flux composition aim to produce larger, higher-quality, and more homogeneous crystals with reduced defects.
Nonlinear Optical Characteristics and Phase Matching
LBO is a biaxial crystal, which means it has three distinct principal refractive indices (nx, ny, nz). This property allows for various phase-matching configurations. Phase matching is crucial for efficient nonlinear optical frequency conversion, ensuring that the interacting light waves remain in phase as they propagate through the crystal.
LBO can be phase-matched using both critical phase matching (CPM) and non-critical phase matching (NCPM):
Critical Phase Matching (CPM): In CPM, phase matching is achieved by carefully orienting the crystal at a specific angle relative to the propagating laser beam. LBO supports both Type I and Type II phase matching.
Type I Phase Matching: Involves two fundamental photons with the same polarization (e.g., both ordinary or both extraordinary) interacting to produce a second-harmonic photon with orthogonal polarization. For LBO, Type I SHG is commonly achieved in the XY and XZ planes, with a broad phase-matching range from approximately 554 nm to 2600 nm.
Type II Phase Matching: Involves two fundamental photons with orthogonal polarizations generating a second-harmonic photon. LBO supports Type II SHG in the YZ and XZ planes, with a phase-matching range from about 790 nm to 2150 nm. CPM, while flexible in wavelength tuning by angular adjustment, can suffer from "walk-off" effects, where the ordinary and extraordinary beams travel at slightly different angles, leading to reduced interaction length and conversion efficiency for long crystals.
Non-Critical Phase Matching (NCPM): LBO is particularly renowned for its broad NCPM capabilities. In NCPM, the crystal is cut such that the phase-matching condition is satisfied when the light propagates along one of the principal axes (e.g., x-axis or z-axis), where the walk-off angle is effectively zero.
Temperature Tuning: NCPM in LBO is primarily achieved by precise temperature tuning. By heating or cooling the crystal to a specific temperature, the refractive indices change, satisfying the phase-matching condition for a given wavelength. For instance, Type I SHG of 1064 nm light (from Nd:YAG lasers) can be NCPM at around 149 °C. Type II NCPM for 1319 nm is possible around 43 °C.
Advantages of NCPM: The key advantages of NCPM include zero walk-off, very wide angular and spectral acceptance bandwidths, and maximum effective nonlinear coefficient. These properties enable the use of longer crystals for higher conversion efficiency and produce a higher quality output beam, making LBO ideal for continuous-wave (CW) and quasi-CW laser applications where beam quality and high average power are critical.
Spectral NCPM (SNCPM): LBO also exhibits spectral non-critical phase matching at certain retracing points (e.g., near 1.3 μm). At these points, the phase-matching condition is less sensitive to changes in wavelength, offering very broad spectral acceptance.
Sellmeier Equations: The refractive indices of LBO can be precisely described by Sellmeier equations, which relate the refractive index to the wavelength (λ) and temperature. For example, at T=20 °C (with λ in μm):
Nonlinear Optical Coefficients: The nonlinear optical susceptibility tensor elements for LBO (e.g., d31, d32, d33) determine its efficiency in converting light. Typical values at 1064 nm are d31=(1.05±0.09) pm/V, d32=−(0.98±0.09) pm/V, and d33=(0.05±0.006) pm/V. The effective nonlinear coefficient (deff) depends on the specific phase-matching geometry.
Applications
LBO crystals are extensively used in various nonlinear optical applications due to their exceptional properties, particularly in high-power and high-repetition-rate laser systems:
Second Harmonic Generation (SHG):
Efficiently doubles the frequency of high peak power pulsed Nd-doped lasers (e.g., Nd:YAG at 1064 nm to 532 nm green light, or Nd:YLF at 1053 nm to 527 nm).
Also used for SHG of Ti:sapphire, Cr:LiSAF, and dye lasers, generating visible and UV wavelengths.
Achieves high conversion efficiencies, often over 70% for pulsed and 30% for CW Nd:YAG lasers, with excellent output stability and beam quality.
Third Harmonic Generation (THG):
Converts fundamental laser light (e.g., 1064 nm from Nd:YAG) to its third harmonic (355 nm UV light). LBO's high transparency in the UV and low absorption make it an excellent choice for this application, especially for high-power UV lasers.
Conversion efficiencies over 60% for pulsed Nd:YAG lasers have been reported.
Fourth Harmonic Generation (FHG):
Can be used to generate the fourth harmonic (e.g., 266 nm from 1064 nm) by doubling the 532 nm output from an SHG stage. While absorption below 300 nm is higher, LBO can still be useful for DUV generation.
Optical Parametric Oscillators (OPOs) and Amplifiers (OPAs):
LBO is an excellent material for OPOs and OPAs, which produce widely tunable infrared radiation. Both Type I and Type II phase-matching configurations are used.
OPOs pumped by SHG and THG of Nd:YAG lasers and excimer lasers (e.g., XeCl at 308 nm) have been demonstrated, enabling tunable output from the visible to the mid-infrared.
Type I OPA pumped at 355 nm with 30% conversion efficiency and Type II NCPM OPO pumped by XeCl excimer laser with 16.5% conversion efficiency have been reported.
Sum Frequency Generation (SFG) and Difference Frequency Generation (DFG):
LBO can be used for SFG to generate tunable UV and VUV radiations by mixing different wavelengths.
It also finds applications in DFG for generating mid-infrared wavelengths.
High-Power Industrial Lasers: Its high damage threshold and excellent thermal properties make LBO crucial in industrial applications such as laser marking, micromachining (e.g., internal medical devices, semiconductors, fuel injector nozzles), and 3D additive manufacturing.
Medical Aesthetics: The growing demand for laser-based cosmetic procedures (e.g., hair removal, skin rejuvenation, tattoo removal) utilizes LBO crystals in high-power and stable laser systems.
Ultrafast Lasers: Thin LBO crystals are used for frequency conversion in femtosecond (fs) pulse width lasers due to their broad bandwidth capabilities.
Comparison with Other NLO Crystals
LBO is often compared to other widely used NLO crystals, particularly Beta-Barium Borate (BBO) and Potassium Titanyl Phosphate (KTP):
LBO vs. BBO:
Transparency: BBO has a broader transparency range, extending deeper into the UV (down to ~190 nm) than LBO (160 nm).
Damage Threshold: Both have high damage thresholds, but LBO generally exhibits higher bulk damage resistance, especially for long pulses and high average power.
Hygroscopicity: LBO is non-hygroscopic, offering better chemical stability and easier handling/storage compared to BBO, which is hygroscopic and requires protective encapsulation.
Walk-off & Acceptance Angle: LBO has a smaller walk-off angle and wider acceptance angle, particularly beneficial for high-power CW and quasi-CW applications. BBO has larger walk-off but also larger effective nonlinear coefficient.
NCPM: LBO offers robust NCPM, while BBO generally relies on CPM, which can introduce walk-off.
Cost: LBO can sometimes be more cost-effective for specific high-power applications than hydrothermal KTP.
LBO vs. KTP:
Transparency: KTP has good transparency in the visible and near-infrared, but LBO generally offers a wider range, extending further into the UV.
Damage Threshold: LBO typically has a significantly higher damage threshold than KTP, especially for high peak power applications. This makes LBO more suitable for high-power frequency doubling where KTP might suffer from "gray tracking" (photodarkening).
Thermal Lensing: LBO exhibits minimal thermal lensing compared to KTP, leading to better beam quality in high-power applications.
Applications: While KTP is excellent for SHG of Nd:YAG to green light in moderate power systems, LBO is preferred for higher power and more demanding applications requiring higher stability and longer lifetime.
Recent Advancements
Recent advancements in LBO crystal technology focus on:
Improved Crystal Growth Techniques: Efforts are continuously made to grow larger, higher-quality crystals with enhanced optical homogeneity and fewer defects (e.g., inclusions, striations). This includes optimizing thermal fields and flux compositions.
Advanced Coatings: Development of anti-reflection (AR) coatings, including anti-reflection structured surfaces (ARSS), to further reduce surface reflection losses and increase the laser-induced damage threshold, especially in the UV range.
Customization: Growing demand for custom-designed LBO crystals tailored for specific applications, including various sizes, shapes, and orientations, with specialized coatings.
Integration: Better integration of LBO crystals into compact, high-efficiency laser systems for various industrial, medical, and scientific uses.
Research: Continued research into novel crystal growth and processing techniques to push the boundaries of LBO's performance for next-generation laser systems.
These ongoing developments underscore LBO's enduring importance as a versatile and high-performance material in the field of nonlinear optics.
Kokh, A. E., et al. "LBO grown crystals habitus modification by the heat field configuration." Nonlinear Frequency Generation and Conversion: Materials and Devices XIX. Vol. 11264. SPIE, 2020.
Lei, Ting, et al. "Anti-reflection structured surfaces (ARSS) on Lithium triborate (LBO): need, challenges, and recent successes." Laser-Induced Damage in Optical Materials 2024. Vol. 13358. SPIE, 2024.
"Comparing the Advantages and Disadvantages of BBO Crystals and LBO Crystals." Laser Crylink. [Online]. Available: https://www.laser-crylink.com/bbo-crystals-and-lbo-crystals/
"Comparing Different Nonlinear Optical Crystals For Frequency Conversion: BBO, LBO, And KTP." Meta-Laser. [Online]. Available: https://www.meta-laser.com/news/comparing-different-nonlinear-optical-crystals-70339590.html
Thorlabs. "LBO Crystals for Second and Third Harmonic Generation." [Online]. Available: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=16709
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