Phase-matching Angle Research Articles

Terahertz wave parametric oscillations at polariton resonance using a MgO:LiNbO3 crystal.

Terahertz wave (THz-wave) parametric oscillations with a noncollinear phase-matching scheme at polariton resonance using a MgO:LiNbO3 crystal with a surface-emitted configuration are investigated. We investigate frequency tuning characteristics of a THz-wave via varying the wavelength of the pump wave and phase-matching angle. The effective parametric gain length under the noncollinear phase-matching condition is calculated. Parametric gain and absorption characteristics of a THz-wave in the vicinity of polariton resonances are analyzed.

Midinfrared Optical Parametric Amplifier With 6.4–11 $\mu \text{m}$ Range Based on BaGa4Se7

A widely tunable picosecond midinfrared (MIR) optical parametric amplifier (OPA) with wavelength ranging from 6.4 to 11 μm based on the BaGa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> Se <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sub> crystal was demonstrated. The MIR OPA was pumped by a 30 ps 1064-nm Nd:YAG laser and injected by a KTiOPO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> (KTP)-based narrow-bandwidth widely tunable near-infrared seed. The wide spectral generation using type-I (o → e + e) critically phase-matched parametric amplification in BaGa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> Se <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sub> was investigated. The output energies were measured to be ~38 μJ at 11 μm and up to ~100 μJ at 6.4 μm under pumping energy of ~4.1 mJ. Further, the type-I phase-matching angles of BaGa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> Se <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sub> crystal for idler light generation in the range of 6.4-11 μm were experimentally measured and the discrepancy between the experiment and theoretical calculation was discussed.

Investigation on frequency mixing effects in terahertz parametric oscillator with a noncollinear phase-matching scheme

The frequency mixing effects in terahertz parametric oscillator (TPO) with a noncollinear phase-matching scheme based on bulk lithium niobate (LiNbO3), including sum frequency generation (SFG), difference-frequency generation (DFG), optical parametric oscillation and cascaded optical processes are investigated. The analysis results indicate that the terahertz wave (THz-wave) with N-times frequency can be generated simultaneously from frequency mixing effects in TPO with noncollinear phase-matching scheme. To our best knowledge, this is the first study of the TPO generating THz-wave with N-times frequency in bulk LiNbO3. The frequency tuning characteristics of THz-waves via varying pump wavelength, phase-matching angle and working temperature are theoretically analyzed.

Concept of annular vector beam generation at terahertz wavelengths via a nonlinear parametric process.

In this paper, we describe our theoretical investigation and calculations for a terahertz (THz)-wave profile generated by difference frequency mixing (DFM) of focused, cylindrically symmetric, and polarized optical vector beams. Using vector diffraction theory, the second-order nonlinear polarization was estimated from the electric field components of the optical pump beams penetrating uniaxial, birefringent nonlinear optics (NLO) crystals, GaSe and CdSe. The approximate beam patterns of the THz waves were simulated using DFM formulation. The intensity patterns of the THz waves for GaSe and CdSe showed sixfold symmetry and cylindrical symmetry, respectively, based on the nonlinear susceptibility tensor of the crystals. As the phase-matching angle θ(PM) was constant with respect to the c axis of the NLO crystals, an annular vector beam with a narrow width was expected.

Partially deuterated potassium dihydrogen phosphate optimized for ultra-broadband optical parametric amplification

The refractive index of a potassium dihydrogen phosphate (KDP) crystal strongly depends on the deuteration fraction of the crystal. The wavelength dependence of the phase-matching angle in the near-infrared optical parametric process shows convex and concave characteristics for pure KDP and pure deuterated KDP (DKDP), respectively, when pumped by the second harmonic of Nd- or Yb-doped solid state lasers. Using these characteristics, ultra-broadband phase matching can be realized by optimization of the deuteration fraction. The refractive index of DKDP that was grown with a different deuteration fraction (known as partially deuterated KDP or pDKDP) was measured over a wide wavelength range of 0.4–1.5 μm by the minimum deviation method. The wavelength dispersions of the measured refractive indices were fitted using a modified Sellmeier equation, and the deuteration fraction dependence was analyzed using the Lorentz–Lorenz equation. The wavelength-dependent phase-matching angle for an arbitrary deuteration fraction was then calculated for optical parametric amplification with pumping at a wavelength of 526.5 nm. The results revealed that a refractive index database with precision of more than 2 × 10−5 was necessary for exact evaluation of the phase-matching condition. An ultra-broad gain bandwidth of up to 490 nm will be feasible when using the 68% pDKDP crystal.

Czochraski growth, defect analysis and refractive index of Ba2TiGe2O8 crystal with excellent optical nonlinearities

Ba2TiGe2O8 (BTG) shows excellent second-order nonlinearity and electro-optical effects. However, it is difficult to grow a perfect BTG single crystal, and the accurate refractive indexes of this crystal are unavailable at present. In this paper, a sizeable single BTG crystal with high quality was grown by Czochraski (CZ) method. SEM and EDS analyses of crystal defect indicate that the volatilization of GeO2 and the obvious supercooling feature of BTG melt were the main inducements of inclusion defects. The accurate refractive indexes were measured by the self-collimating method. The birefringence and SHG results show that the angle phase matching of SHG at 1064nm hardly be achieved in this crystal. Nevertheless, the effective frequency-doubled laser output may be achieved by using the technique of periodic polarization reversal for quasi phase matching. In view of the high optical transmittance and the huge nonlinear optical coefficients, BTG crystal may be a good candidate material for nonlinear optical devices and electro-optical devices.

Theoretical model of phase-matching angles for KDP crystals and its verification analysis

In final optics assembly of high-power solid-state laser, in order to improve the third harmonic generation efficiency, the accurate assembly and calibration of ultra-thin KH2PO4 (KDP) crystal with large-aperture is one of the key technologies to realize inertial confinement fusion. In order to meet the requirements for high efficiency and precision crystal of online installation, it is necessary to measure crystalline phase matching angle for achieving the highest third harmonic conversion efficiency of high power laser. In this paper, for the third harmonic conversion by ultra-thin type Ⅰ/Ⅱ KDP crystals with large-aperture, the relationship between phase matching angles at different locations on the crystal is obtained according to the nonlinear optical properties of the crystal. Based on the analysis of the propagation path of the laser beam in the crystal, the relationship among the crystal surface shape, the phase matching angle and the best deflection angle is given. On this basis, the theoretical model for phase-matching angle of type Ⅰ/Ⅱ KDP crystal is proposed, and verified by the experimental results. The results show that the difference in phase matching angle between the prediction values and the experimental results is within 10.0 rad, showing that the theoretical model for phase-matching angles of type Ⅰ/Ⅱ KDP crystals is valid. This model provides a simple and efficient prediction method to obtain the phase matching angle distribution in full aperture of KDP crystal.

Phase matching characteristics of deuterated ammonium dihydrogen phosphate crystals

Refractive indices for crystals ammonium dihydrogen phosphate (ADP), 30% deuterated ADP (DADP), 50% DADP, and 70% DADP are measured from 253 to 1529 nm with 5 × 10-6 accuracy. Numerical fits to modified double-pole Sellmeier equation are made. Second-harmonic generation, third-harmonic generation phase matching (PM) angles, and noncritical PM (NCPM) wavelengths are calculated using the Sellmeier parameters. The deuterated crystals show smaller PM angles than pure crystal. Fourth-harmonic generation process can be realized by DADP in smaller deuterium content than deuterated potassium dihydrogen phosphate (DKDP). The measured NCPM wavelengths are consistent with the calculated value. PM characteristics are compared between DADP and DKDP.

Tunable deep ultraviolet femtosecond sum frequency laser based on Ba1-xB2-y-zO4SixAlyGaz crystal

Tunable coherent deep ultraviolet (DUV) light sources, especially ultrashort pulse DUV lasers have great applications in the fields of time-resolved, material processing, spectroscopy, laser spectroscopy and laser fusion. In the UV region, the best choice of generating the laser pulses in the femtosecond or picosecond regime is the frequency up-conversation technique based on second order nonlinearities. Over the past three decades, quite a lot of nonlinear crystals, such as LiB3O5, βup-BaB2O4, KBe2BO3F2 and Ba1-xB2-y- zO4SixAlyGaz have been developed and employed for generating the femtosecond pulses in the blue, ultraviolet, and even the deep-ultraviolet region. A tunable deep ultraviolet femtosecond laser is experimentally studied based on the new nonlinear crystal Ba1-xB2-y-zO4SixAlyGaz It is a kind of low-temperature phase barium metaborate single crystal belonging to a trigonal system, doped with one or more elements selected from Si, Al and Ga. As an optimized β-BaB2O4 crystal, Ba1-xB2-y-zO4SixAlyGaz completely overcomes the shortcomings of deliquescence compared with β-BaB2O4, and its nonlinear efficiency and optical damage threshold have also been greatly improved. Using two crystals as second harmonic generation is to compensate for the spatial walk-off effect and the light path walk-off due to refraction effect The optical axis of the second Ba1-xB2-y-zO4SixAlyGaz is twice the phase matching angle with respect to the first one. In a femtosecond regime, short pulse provides high efficient frequency conversation due to their high peak powers, but the group velocity mismatch is a cognitive factor to limit conversion efficiency. It is obvious that after the frequency doubling, the second harmonic pulse and fundamental pulse separate from each other. The second harmonic pulse lags behind the fundamental pulse as they propagate through the crystal and the second harmonic pulse is broadened into a longer pulse duration than the fundamental pulse The method to compensate for the group velocity mismatch is to adjust the path length between the fundamental and second harmonic pulse by means of time delay line. It consists of beam splitters and mirrors. Tunable deep ultraviolet pulse within a wavelength range from 192.5 to 210 nm is produced, with a maximum average power of 5.8 mW, under a 2.78 W fundamental power. The average power of second harmonic, third harmonic and fourth harmonic are 1.28 W, 194 mW and 5.8 mW at the fundamental wavelength of 800 nm, corresponding to conversion efficiencies of 46.14%, 15.16% and 3% from the previous stage, respectively. The duration of the third harmonic pulse is 640.4 fs at 266.7 nm as measured by the cross-correlation technique.

Study on temperature adaptability extension of KTP frequency-doubling device

For the most commonly used KTP frequency-doubling crystal, its temperature adaptability range should be effectively extended. For this purpose, a compromise design is given by compreflensively considering both its effective nonlinear coefficient and the half-width of temperature range. The design method of KTP frequency-doubling device with a wide temperature range is analyzed in detail; furthermore, the curves of effective nonlinear coefficients, acceptance angles, and walk-off angles as a function of phase-matching angle are plotted via computer simulation. According to the results of theoretical study, a device used in the temperature range from -20 ℃ to 50 ℃ is designed and validated experimentally by the KTP external cavity frequency-doubling laser. Experimental results indicate that a peak conversion efficiency of 22.7% at 15 ℃ with a 70 ℃ temperature halfwidth is achieved by using the designed device. Compared with the commonly designed KTP frequency-doubling device, the temperature adaptability range increases notably although its frequency conversion efficiency decreases a little. Additionally, the effective nonlinear coefficient is still bigger than that of the commonly used crystals such as LBO and BBO when temperature halfwidth increases to 70 ℃. The above method would have the potential for extending the temperature adaptability range of other frequency-doubling devices.

Investigation on terahertz generation at polariton resonance of MgO:LiNbO3 by difference frequency generation

Abstract Terahertz (THz) wave generation at polariton resonance of MgO:LiNbO3 with a surface-emitted configuration is investigated. It is shown that by using crystal birefringence of bulk MgO:LiNbO3 crystal THz wave can be efficiently generated by difference frequency generation (DFG) in the vicinity of polariton resonances with Cherenkov phase matching scheme. The frequency tuning characteristics of THz wave via varying wavelength of difference frequency waves, phase matching angle and working temperature are numerically analyzed. Parametric gain coefficient in the low-loss limit and absorption coefficient of THz wave during DFG process in the vicinity of polariton resonances are analyzed.

Investigation on terahertz parametric oscillators using GaP crystal with a noncollinear phase-matching scheme

Terahertz parametric oscillator (TPO) using GaP as gain medium with a noncollinear phase-matching scheme is investigated. Frequency-tuning characteristics of the terahertz wave (THz-wave) by varying the phase-matching angle and pump wavelength are analyzed. Gain and absorption characteristics of the THz-wave are investigated. The characteristics of GaP and LiNbO3 (LN) are compared when the two crystals are used as gain medium for TPO. The analyses indicate that GaP is more suitable than LN to be used as gain medium for TPO.

Numerical evaluation of ultrabroadband parametric amplification in YCOB

The technique of optical parametric chirped pulse amplification has the potential to generate high-energy few-cycle pulses at high repetition rates, thanks to its high fidelity and ultrabroadband capability. The biaxial nonlinear crystal yttrium calcium oxyborate (YCOB) exhibits a favorable set of optical and thermal properties for these purposes. We evaluate numerically the performance of this crystal as the nonlinear medium in a parametric amplifier for a wide range of phase-matching parameters. We explore optimized ultrabroadband noncollinear optical parametric amplification by operating at phase-matching angles outside the principal planes.

Temperature-dependent Sellmeier equations of nonlinear optical crystal Na3La9O3(BO3)8

The principal refractive indices of Na3La9O3(BO3)8 (NLBO) crystal in the wavelength range of 0.363–2.325μm were accurately measured by using the minimum deviation method within the temperature range from 23.5°C to 160°C. We derived the expressions of thermal refractive index coefficient as a function of wavelength that could be used to calculate the principal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also derived and used to calculate the phase-matching (PM) angles for a frequency conversion device based on NLBO crystal at different temperatures. We found that the thermal refractive index coefficients of NLBO crystal changed from positive to negative values with the increase of wavelength. In addition, the phase matching conditions for third harmonic generation (THG) at different temperatures were also investigated.

Calculation of phase-matching conditions based on angle-dependent refractive index in biaxial crystals

We present a straightforward method for the calculation of phase-matching conditions based on the angle-dependent refractive index in biaxial crystals. Considering the refractive indices relying on angular orientation of wave vector and optical axis angle, we acquire the numerical curves of phase-matching angles. We then obtain the effective nonlinear coefficient for a spontaneous parametric down conversion (SPDC) process in BiB3O6 (BIBO) crystal, and ascertain the optimal phase-matching directions for types I and II. Moreover, we focus on the angular gradient of the pump and emission wave refractive indices near the exact phase-matching direction, and compare the SPDC with the double frequency process in the geometrical relations of the refractive index ellipsoids. This method is superior in ascertaining the space distribution of pump and emission waves, and it is convenient for deciding the parameters of phase matching without solving the quadratic Fresnel equations.

Bulk growth and nonlinear optical properties of thulium calcium oxyborate single crystals

New nonlinear optical (NLO) TmCa4O(BO3)3 (TmCOB) crystals were grown by the Czochralski method. X-ray powder diffraction results indicated that TmCOB crystals belong to the monoclinic system with space group Cm. The unit cell parameters were calculated to be a = 8.0679 A, b = 16.0140 A, c = 3.5224 A, with α = γ = 90° and β = 101.1115°. Disorder distribution of Ca2+ and Tm3+ in TmCOB crystals was observed, from which the molecular formula was found to be (Tm0.78Ca0.22)(Ca3.78Tm0.22)O(BO3)3. The relationships between the crystallographic axes and the optical principal axes were determined, and the refractive indices at different wavelengths were measured, from which the phase matching angle at 1064 nm in the ZX principal plane was measured and found to be (32.5°, 180°) and (32.5°, 0°). Furthermore, efficient second harmonic generation in the ZX principal plane was realized by a 1064 nm Nd:YAG picosecond laser, where more than 50% conversion efficiency was achieved for the (32.5°, 180°)-cut sample (4 × 4 × 11.8 mm3), with the effective nonlinear optical coefficient and the acceptance angle determined to be on the order of 1.1 pm V−1 and 3.1 mrad cm, respectively.

Set of Sellmeier equations for GaS and GaSe and its applications to the nonlinear optics in GaS(x)Se(1-x).

This paper reports a set of Sellmeier equations for GaS and GaSe that provide excellent reproduction of the phase-matching conditions for second- to sixth-harmonic generation of CO₂ laser radiation at 10.5910 μm in GaS(0.4)Se(0.6) at 20°C. In addition, this set of Sellmeier equations is found to reproduce well the phase-matching angles for second-harmonic generation of a Ti:Al₂O₃ laser-pumped BaB₂O₄ optical parametric generator at 2.14-2.9 μm and CO₂ laser radiation at 9.2(9.2007)-10.7(10.6746) μm measured by Kang et al. [Appl. Phys. B 108, 545 (2012)] in GaS(0.09)Se(0.91) and GaS(0.41)Se(0.59).

LD-side-pumped Nd:YAG/BaWO4 intracavity Raman laser for anti-Stokes generation

A diode-side-pumped actively Q-switched Nd:YAG/BaWO4 intracavity anti-Stokes Raman laser is demonstrated for the first time. The oscillation directions of the fundamental and the Stokes beams are separated at a phase-matching angle by introducing an additional coupled Raman cavity in the fundamental resonator. The highest 968nm anti-Stokes output power of 0.94mW is obtained with a 170W 808nm pumping power and a 7.5kHz pulse repetition frequency. Meanwhile, the Stokes power obtained is 4.2W.

Mismatch characteristics of optical parametric chirped pulse amplification

The stability of an optical parametric chirped pulse amplifier (OPCPA) is influenced by time and the angular matching of the input beams. We derived the Gaussian dependence of the monochromatic signal gain on the small mismatch between the signal and pump beams. Gain characteristics were also calculated for polychromatic amplification and the impact of different beam mismatches and interaction geometries was explained. The asymmetry of the energy gain, and the square root dependence of the phase matched wavelength on beam angles were found. The predicted dependences were verified in a noncollinear OPCPA system with LBO and KDP crystal amplifying pulses of a Ti:sapphire laser around a central wavelength of 800 nm, pumped by the third harmonic frequency of an iodine gas laser at a wavelength of 438 nm. The widths of the gain curves in the dependence on both the pump–signal or the phase matching angles varied from several tenths to a few milliradians. The gain curve widths dependent on the pump–signal pulse delay were about two thirds of the pump pulse width for moderate pumping and about a half of the pump pulse width for pumping on the order of GW cm−2. A stable gain output is achieved if angular and temporal fluctuations are fractions of the measured gain curve widths, and when the signal direction is between the pump and the crystal principal axis (i.e. in the psz geometry).

Refractive indices in the whole transmission range of partially deuterated KDP crystals

Refractive indices of partially deuterated potassium dihydrogen phosphate (DKDP) crystals with 55%, 70% and 80% deuterium contents were measured by auto-collimation method at 293 K between 0.254 to 1.529 μm. Dependence of refractive indices of DKDP on deuterium content show different trend in the infrared region as in uv-visible region. Dependence of n2 (the square of refractive index) on the mole fraction of deuterium shows a difference between pure KDP and partially deuterated KDP. The Sellmeier equations were obtained by the least square method. The non-critical phase matching angles calculated from the fitted formula were in good agreement with laser experiment results, by which the reliability of these Sellmeier equations was confirmed.