Phase-matching Angle Research Articles

Optimization of crystal phase-matching angle metrology instrument and error analysis

Finding the optimal phase matching angle of a potassium dihydrogen phosphate (KDP) crystal is vital for increasing the harmonic conversion efficiency, which plays a key role in Inertial Confinement Fusion (ICF). The aim of this study was to build and optimize an instrument, which can measure the optimal phase matching angle of a KDP crystal accurately. We designed and tested a new beam path, which made the alignment process much simple. We studied the temperature compensation method and applied it in the instrument. Several methods were used to investigate and reduce the errors of the instrument. The errors from laser energy, transmission unit, alignment system, energy meter, temperature, and environmental vibration were analyzed and optimized. The measurement accuracy of the instrument is 10 μradians in phase matching angle. The instrument had been manufactured and applied well in the laser fusion facility, which can save a lot of time and money.

Development of single-resonant optical parametric oscillator with tunable output from 410 nm to 630 nm

A single-resonant low-threshold type-I β-Ba2BO4 (BBO) optical parametric oscillator (OPO) with tunable output from 410 nm to 630 nm at 5 kHz repetition rate is reported. By taking the noncollinear phase matching method, low-threshold OPO operation could be obtained compared with the configuration of collinear phase matching, and the maximum optical–optical conversion efficiency of 11.8% was achieved at 500 nm wavelength when 0.4 mJ pump pulse energy was applied. When the noncollinearity angle was preset at 1.6°, 4.8°, and 6.3°, a continuously tuning output with a total spectral range of 220 nm was successfully obtained by adjusting the phase matching angle of the BBO crystal.

Angular birefringence phase matching behaviour of Lithium Triborate (LBO) crystal for second harmonic generation in broad wavelength range

Second Harmonic Generation (SHG) is a nonlinear optical process in which the frequency of the incident radiation gets doubled. There are various types of applications of SHG such as ultra-short pulse measurement, high resolution optical microscopy, characterization of the structure of 2D materials and its physical properties like the thickness of interlayer stacking, stacking angle between different layers, the grain boundary etc. It has also been used to determine the structure of Langmuir-Blodgett films of low symmetry. For SHG, various commercial nonlinear optical (NLO) crystals are generally used. Lithium Triborate (LBO) is one of the best NLO material among them due to its wide transparency range (160–2600 nm), high damage threshold (19 GW/cm2 @1064 nm, 1 ns) and high second order nonlinear coefficient. It has also the ability to establish birefringence phase matching condition for efficient SHG for different wavelengths. The crystal can be used for generation for SHG in broad wavelength range through angular phase matching method. For this, in this work detail investigation has been made to find out the optimum wavelength range that can be used for efficient SHG. This has been done by finding the variation of phase matching angle, second order nonlinearity etc. with respect to wavelength using the SNLO software. Both Type I and Type II phase matching has been considered for various planes of the crystal.

High power supercontinuum generation by dual-color femtosecond laser pulses in fused silica

High power supercontinuum (SC) is generated by focusing 800 nm and 400 nm femtosecond laser pulses in fused silica with a microlens array. It is found that the spectrum of the SC is getting broader compared with the case of a single laser pulse, and the spectral energy density between the two fundamental laser wavelengths is getting significantly higher by optimizing the phase matching angle of the BBO. It exceeds μJ/nm over 490 nm range which is from 380 nm to 870 nm, overcoming the disadvantage of relative lower power in the ranges far from the fundamental wavelength.

Second-harmonic and sum-frequency generation based on birefringence phase matching of BaMgF4 crystal.

BaMgF4 is a ferroelectric nonlinear crystal with a very wide transparency window ranging from 125 nm to 13µm of the wavelength. Therefore, it is a candidate material to generate ultraviolet or deep ultraviolet laser, which is very important in lithography, semiconductor manufacturing, and advanced instrument development. Here, the second-order birefringence phase-matching processes of the BaMgF4 crystal were studied, including second-harmonic generation (SHG) and sum-frequency generation (SFG). In the experiments, we measured the phase-matching angle, nonlinear frequency conversion efficiency, and angle bandwidth of SHG and SFG processes of BaMgF4 crystal, which are in well agreement with the theoretical calculations. This study may promote the research of nonlinear optical process of BaMgF4 crystal and also the further development of all-solid-state vacuum ultraviolet lasers.

Optical parametric generation in biaxial KTA crystal under pumping by YAG:Nd laser in arbitrary directions

Herein, on the basis of expressions for the refractive indices of isonormal waves, the possibility of performing collinear phase matching for optical parametric generation in arbitrary directions of a biaxial KTA crystal under pumping by radiation of a YAG:Nd laser is analyzed. The tuning curves that determine the tuning range of the signal and idler for type-I and II-type phase-matching and arbitrary angles θ and φ in cases where the tuning is carried out along the angle θ at a fixed angle φ and vice versa are calculated. The effective nonlinear coefficient is determined. It is shown that their maximum value is achieved аt a polar angle θ = 90° and type-II phase-matching. For the case of generation of eye-safe radiation the spectral and angular phase matching widths were estimated, as well as gain widths of KTA-OPO under monochromatic pumping.

Propagation of the angular spectrum of electromagnetic fields in uniaxial crystals of finite length in the regime of the paraxial approximation

In this paper we will analyze the propagation of the angular spectrum of the electromagnetic field through a finite length uniaxial crystal. We solve the boundary conditions of the fields at an interface of an isotropic medium and an uniaxial anisotropic medium with the optical axis in an arbitrary direction and soon after we choose the optical axis in a plane formed by the direction of propagation (z-axis) and the x-axis . We show how the couplings occur between the components of the field and in what situations we can give a vector or scalar treatment for the propagation. There is a considerable number of researchers working with the phenomenon of Spontaneous Parametric Down Conversion (SPDC). In most SPDC systems, the propagation of fields is neither orthogonal nor parallel to the optical axis. The calculations in this work are useful for this community. The results shown in the manuscript allow a precise evaluation of astigmatism as well as the walk-off for any phase match angle. So, I believe the results presented can be valuable for the SPDC community.

Linear and nonlinear optical properties of the piezoelectric crystal α-GeO2

We report the first measurements of phase-matching angles for second-harmonic generation, sum- and difference- frequency generations performed over the transparency range of the uniaxial α-GeO2 crystal. A simultaneous fit of these data provided dispersion equations. The optical damage threshold and the magnitude of the nonlinear coefficient d11 are also determined. We found | d 11 G e O 2 ( 0.67 μ m ) | = 0.76 ± 0.09 pm/V.

Calculating properties of non-collinear phase matching in two different polarization for KDP crystal

The properties of non-collinear phase-matching (PM) for potassium dihydrogen phosphate (KDP) crystal were calculated. The properties were calculated numerically for type I phase matching and type II-phase matching. The group delay dispersion (GDD) was determined for KDP at different slant angles and different types of phase matching. The slant angles were 0°, 40°, 60°, and 900°. The pumping, signal, and idler wavelengths were 354.7nm, 1064nm, and 532nm respectively. The time delay deepened on the phase-matching angle for three-wave that interact in KDP crystal founded. Ordinary refractive index and extraordinary refractive index discussed, by calculating these indices the birefringence at each wavelength determined. The group delay dispersion and time delay very important factors for optical communication, laser application, and nonlinear optics.

Bulk crystal growth, crystalline perfection and optical homogeneities of 2AP4N single crystals for second and third order frequency conversion and terahertz (THz) device applications

Bulk size organic 2AP4N single crystals were grown by a point seed rotation technique using methanol solvent. The lattice dimensions of the grown crystal and their various crystalline planes have been analyzed by XRD measurement and also the lattice strain was calculated. The lattice perfection was examined by HRXRD and found to be extremely good. The optical transparency and cut-off value of the grown crystal were analyzed by the UV–Vis NIR measurement. The crystalline homogeneity has been confirmed by the birefringence and Mach-Zehnder interferometry techniques. The SHG measurement has been carried out with different particles. The refractive indices of grown crystal have been measured in different wavelengths by prism coupling technique and the Sellmeier's co-efficient has been calculated. The Type-I and Type-II phase-matching angles were determined and the crystal was cut along the phase-matching angles. The third order nonlinear optical parameters were analyzed by Z-scan technique. In addition, the crystal shows potential to generate pulsed Terahertz (THz) radiation by optical rectification using 800 nm wavelength at 140 fs, obtained from Ti: Sapphire Laser. The generated THz spectrum is extended up to 3.0 THz. The maximum conversion efficiency of the generated signal is of the order of 0.64 × 10 −5 %. •Optically high quality with bulk size single crystal was grown by seed rotation technique •The grown crystal has high optical homogeneities and crystalline perfection •SHG efficiency is 4.5 times that of KDP material •Type-I and Type-II phase matching elements have been made •Third-order nonlinear susceptibility ‘ χ (3) ’ is 8.68 × 10 −8 esu. •The maximum conversion efficiency of the generated THz signal is 0.64 × 10 −5 %.

Refined Sellmeier equations for BaGa4S7.

This paper reports refined Sellmeier equations for the biaxial nonlinear crystal BaGa4S7 that provide a good reproduction of the phase-matching angles for second-harmonic generation (SHG) and sum-frequency generation (SFG) of the mid-IR outputs of Nd:YAG and Ho:YLF laser-pumped optical parametric oscillators (OPOs) and a frequency-doubled CO2 laser in the 0.7584-8.018 µm range. The theoretical results are found to agree with the recent experimental data for 1-µm-pumped optical parametric processes based on BaGa4S7 beyond 8 µm.

Characterization of partially deuterated KDP crystals using two-wavelength phase-matching angles

Partially deuterated potassium dihydrogen phosphate (DKDP) allows for the optical parametric chirped-pulse amplification of high-energy broadband optical pulses to generate ultrashort, high-peak-power pulses. Modeling and experimental optimization of the noncollinear interaction geometry require the combination of a model for the deuteration-dependent optical indices and knowledge of the deuteration level of the DKDP crystal being used. We study and demonstrate a novel experimental technique that determines the deuteration level of a DKDP crystal consistent with a specific index model, based on the phase-matching angles measured at two wavelengths. Simulations and experiments show that the simple two-wavelength technique allows for consistent results with three different index models, and in particular, for the characterization of four crystals with deuteration levels ranging from 70% to 98%.

Refined Sellmeier equations for AgGaSe2 up to 18 µm.

We present refined Sellmeier equations for AgGaSe2 that provide good reproduction of the phase-matching angles for frequency upconversion of CO2 laser radiation in the 1.7652-10.5910 µm range and for frequency downconversion in the 1.85-18 µm range thus far reported in the literature.

Analysis of the Spatial Properties of Correlated Photon in Collinear Phase-Matching

In this paper, the spatial properties of correlated photon in collinear phase-matching in the process of spontaneous parametric down conversion (SPDC) are researched. Based on the study of the phase-matching angle, non-collinear angle, and correlated photon wavelength, a theoretical model of non-collinear angular variation is derived, which can be used to estimate and predict the width of the correlated photon ring. The experimental measurement is carried out with CMOS camera, and the measurement results are consistent with the theoretical simulation results, which verifies the rationality of theoretical reasoning. Meanwhile, the change of the correlated photon divergence angle outside the crystal is studied, the closer the wavelength is to the degenerate, the smaller the measurement value of the divergence angle, which is agreement with the theoretical simulation. The results of the study play a reference role in the evaluation of the spatial properties of correlated photon and lay a foundation for the measurement of the correlated photon number rate and the calibration of a photodetector.

Frequency doubling of acousto-optic Q-switched Nd:YVO<sub>4</sub> cascaded Raman laser for narrow pulse-width 657 nm laser

Frequency doubling of second-Stokes in an acousto-optic Q-switched Nd:YVO<sub>4</sub> cascaded self-Raman cavity is demonstrated to achieve a narrow pulse-width red laser. A three-stage bonded YVO<sub>4</sub>/Nd:YVO<sub>4</sub>/YVO<sub>4</sub> crystal is designed by comprehensively considering the improvement of thermal effect, the performance of fundamental frequency laser and Raman conversion, to improve the Raman efficiency and output power. An LBO crystal cut for critical phase matching at room temperature is selected and used as a nonlinear optical crystal for realizing the frequency doubling of second- Stokes wave. Its phase matching angle (<i>θ</i> = 86.0°, <i>φ</i> = 0°) is very close to the non-critical phase matching angle and has a small walk-off angle, which is beneficial to the realizing of the high conversion efficiency of frequency doubling. In the experiment, the beam waist position of the pump light and the repetition frequency of the acousto-optic Q-switcher are optimized. Under an incident pump power of 14.2 W and a repetition frequency of 60 kHz, the highest average output power of 1.63 W and conversion efficiency of 11.5% are obtained for the 657 nm red laser emission. The pulse width of 657 nm red light is 11.5 ns at the maximum output power, which is much narrower than that generated by frequency doubling of ordinary neodymium-doped laser at a waveband of 1.3 μm. The result shows that the frequency doubling of the acousto-optic Q-switched Nd:YVO<sub>4</sub> cascaded self-Ramanlaser can take advantage of the pulse-width compression characteristics of Raman process to achieve a narrower pulse-width red light laser output.

Умножение частоты ТГЦ-излучения в нелинейных кристаллах боратов

We present the possibility of effective doubling of millimeter wave radiation in the range of 400-2500 μm in borate crystals. The phase matching angles are calculated. It is shown that for LN and β-BBO crystals the realization of o + o → e and e + o → e interactions is possible, and for LB4 only o + o → e. The walk-off angle, spectral and angular phase-matching bandwidth are calculated. An estimate is given of the maximum efficiency of SHG taking into account the measured optical damage threshold of 150 TW/cm2 for the LB4 crystal and 100 TW/cm2 for β-BBO.

Discretely Tunable Multiwavelength Visible Laser Based on Cascaded Frequency Conversion Processes

We demonstrate a discretely tunable multiwavelength visible laser through second harmonic generation (SHG) and sum frequency generation (SFG) of multiorder Stokes lasers generated from an external Raman laser oscillator. The Raman laser oscillator, driven by a 1064 nm laser with an energy of 120 mJ, is based on a cascade of Ba(NO3)2 and two axial orthogonal KGd(WO4)2 crystals. Through adjusting the angle of the SHG/SFG crystal, we obtain 16 visible wavelengths with a wide range from 579.5–658.4 nm. In addition, we investigate the output energy and conversion efficiency of the resulting laser with various phase-matching angles. We show that the maximum energy of the visible laser is 8.87 mJ with five wavelengths, and the corresponding total conversion efficiency is 7.4%. These experimental results demonstrate a practical and effective method of generating a discretely tunable multiwavelength visible laser.

Determination of nonlinear optical coefficients and efficient type-II second-harmonic-generation for TmCOB crystals

By Maker Fringe (MF) method, all of the nonlinear optical (NLO) coefficients including d11, d12, d13, d31, d32 and d33 of TmCa4O(BO3)3 (TmCOB) crystals were measured to be 0.19, 0.26, −0.61, −0.30, 1.66 and −1.25 pm/V, respectively. Based on which, the second-harmonic-generation (SHG) phase-matching (PM) characteristics of TmCOB crystals in two-dimensional principal planes and three-dimensional non-principal planes (space) were theoretically calculated, such as PM tuning curves, distribution of effective NLO coefficient (deff), beam walk-off angle, and angular acceptance bandwidth. At the fundamental waves of 1064 nm, the type-II optimal PM angles with largest deff for principal planes and space were decided to be (52.8°, 90.0°) (deff = 0.24 pm/V) and (118.0°, 77.2°) (deff = 0.35 pm/V), respectively. The type-II SHG of TmCOB crystals was found to present large acceptance angle bandwidth (~2–12 times of type-I values) and small beam walk-off angle (~0.2–0.4 times of type-I values). At a high input energy of 6.89 mJ (35 ps, 10 Hz, 1064 nm), the SHG transformation efficiency for an uncoated TmCOB crystal sample cut along type-II optimal angle (118.0°, 77.2°) with 12 mm in length was measured to be 55.9%, which achieved the same conversion efficiency grade as type-I optimal PM.

Efficient tunable terahertz generation via noncollinear phase matching in the ZnGeP2 crystal

A novel noncollinear phase-matching (PM) scheme was proposed by introducing a small tunable angle between two pump beams to maximize the effective nonlinear coefficient ( d e f f ) in tunable terahertz wave difference frequency generation in the Z n G e P 2 crystal. Compared with the collinear PM condition, the noncollinear geometry transfers the PM angle to be around θ = 90 ∘ for type-II ( o − e → o ) PM to fully use the maximum nonlinear coefficient d 36 , leading to a high conversion efficiency improved by tens of times in theory. Based on the theory of noncollinear PM, the angle-tuning characteristics were calculated and the crystal design was provided for efficient outcoupling. A rigorous theoretical model was built under small-signal approximation to show the affecting factors of noncollinear PM and reveal its superiority compared with collinear PM.

Tunable mid-IR optical parametric amplifier pumped at 1064 nm based on a wideband-gap BaGa4S7 crystal

A mid-infrared (IR) optical parametric amplifier (OPA) in a newly developed wide band-gap nonlinear crystal BaGa4S7 (BGS) was reported for the first time. The BGS-OPA was pumped by a 30 ps pulse 1064 nm laser operating at a repetition rate of 10 Hz. A maximum idler pulse energy of ~130 μJ at 7.25 μm was obtained at pump energy of ~6.9 mJ, corresponding to a pump to idler photon conversion efficiency of ~13%. Moreover, across 6.3–8.8 μm idler tuning range was demonstrated, with output energies of ~66 μJ at 6.3 μm and > 27 μJ over the entire tuning range under a fixed pump energy of ~4.1 mJ. Finally, the corresponding type-I (e → o + o) phase-matching (PM) angles of the generated mid-IR idler light in BGS were measured and compared with the theoretical calculation result based on the reported Sellmeier equations.