Types Of Phase Matching Research Articles

Analytical description of photonic waveguides with multilayer claddings: Towards on-chip generation of entangled photons and Bell states

We present a theoretical description of slab and ridge waveguides with multilayer claddings, such as Bragg reflection waveguides (BRWs), using analytical expressions based on Fresnel and Airy formulas. This approach simplifies the waveguide calculations in comparison with more traditional techniques such as the transfer matrix method or direct stitching of plane-wave solutions at layer interfaces. Approximate but simple and straightforward analytic relations describing the effective indices and group velocities of guided modes in arbitrary 1D BRWs are derived. The formalism is then extended to 2D ridge waveguides using the effective index method. The approach is employed to engineer BRWs where several types of phase matching are present simultaneously at the same wavelength, as well as BRWs where photons generated by spontaneous parametric downconversion have the maximal degree of polarization entanglement. These results promote the use of BRWs as on-chip entangled photon sources, and facilitate on-chip generation of multiple optical Bell states. The designs are based on the AlGaAs fabrication platform and are within reach of experimental realization.

A high-power narrow-linewidth optical parametric oscillator based on PPMgLN

A high-power and narrow-linewidth tunable optical parametric oscillator based on PPMgLN is presented. The phase matching type e → e + e is used to avoid the walk-off effect and utilize the maximum nonlinear coefficient d33 (27.4 pm V−1) of the PPMgLN crystal (5 mol% MgO doped). When the pump power of the 1064 nm laser is 50 W and the temperature of the PPMgLN crystal is 100 °C, average output power of 15.8 W is obtained with a slope efficiency of 40.6%. The 1.655 μm signal and 2.98 μm idler output powers are 9.5 W and 6.3 W, respectively. The linewidth of the 1.655 μm signal laser is 1.00 nm before compression and 0.05 nm after compression. The compression ratio is 20. The linewidth of the 2.98 μm idler laser is within 0.30–0.63 nm based on theoretical analysis of the linewidth of the 1064 nm pump laser and 1.655 μm signal laser. The output wavelength can be tuned from 1.6 to 1.8 μm and from 3.1 to 2.7 μm by changing the temperature of the 31.2 μm PPMgLN crystal from 30 to 200 °C.

Transversal magneto-optical Kerr effect in two-dimensional nickel magnetoplasmonic crystals

Resonant transversal magneto-optical Kerr effect (TKE) is experimentally studied in 2D nickel magnetoplasmonic crystal. Gradual transition between collinear and bi-directional types of surface plasmon-polariton phase matching and its influence on TKE resonances are observed by measuring and analyzing dependence of reflectance and TKE spectra on the azimuthal angle.

Upconversion of Broadband Infrared Radiation into Visible Light for Different Pumping Parameters

The influence of pump radiation parameters such as the polarization and the spectral width of infrared radiation on the conversion of broadband radiation in lithium niobate crystals was investigated. The spectra of converted radiation were calculated for two types of phase matching in the negative uniaxial crystal by taking into account the convergence of the light beam in the crystal. Experimental spectra were obtained and compared with the calculated spectra.

Realisation of four-wave mixing phase matching for frequency components at intracavity stimulated Raman scattering in a calcite crystal

The possibilities of implementing four-wave mixing (FWM) phase matching at stimulated Raman scattering (SRS) in a birefringent SRS-active crystal placed in a cavity with highly reflecting mirrors have been theoretically and experimentally investigated. Phase-matching angles providing conditions for five types of phase matching are determined for a calcite crystal. These types are characterised by different combinations of polarisation directions for the interacting waves and ensure FWM generation of either an anti-Stokes wave or the second Stokes SRS component. In agreement with the calculation results, low-threshold generation of the second Stokes SRS component with a wavelength was observed at angles of incidence on a calcite crystal of and , under SRS pumping at a wavelength of . This generation is due to the FWM coupling of the first and second Stokes SRS components with the SRS-pump wave.

An Azo-Bridged Ferroelectric Liquid Crystal with Highly Enhanced Second and Third Harmonic Generation

A laterally azo-bridged trimer ferroelectric liquid crystal (FLC) incorporating a strong chromophore along its polar axis was synthesized and characterized by polarized-light optical microscopy, differential scanning calorimetry, two-dimensional X-ray diffraction analysis, electro-optical measurements, and nonlinear optical (NLO) investigations. This mesogen exhibits a thermodynamically stable enantiotropic SmC* phase and a bistable ferroelectric switching in a surface stabilized cell with bookshelf geometry. It gives the resonance-enhanced d(22) coefficient of 28 pm V(-1) (λ = 1.369 μm) for second harmonic generation (SHG), the largest NLO susceptibility reported to date for all FLCs. At the same wavelength, a new type of helicoidal phase matching assisted by the helical SmC* structure was identified. When the second harmonic wavelength of 780 nm is far away from the resonance wavelength (λ(max) = 572 nm), the d(22) coefficient is reduced to 6.8 pm V(-1) (λ = 1.56 μm). In addition to a strong SHG activity, the trimer also shows a strong third harmonic generation (THG) with an estimated third-order nonlinear susceptibility of χ((3)) = ~3 × 10(-11) esu (λ = 1.56 μm), among the largest χ((3)) value reported from THG measurements for liquid crystals. This work enables viable applications of FLCs in nonlinear optics and offers an innovative approach to develop new FLCs with larger NLO strength.

Blue 473-nm solid state diode pumped Nd:YAG/BiBO microchip laser

AbstractIn this paper we present a design of a compact, low power diode-pumped CW Nd:YAG laser operating at 946 nm with intracavity blue light generation at 473 nm for battery operated applications. The nonlinear crystal used in the experiment is a BiBO crystal cut for phase-matching type I. Using 0.8 W of pumping power, 20-mW stabile output power of blue light was achieved. The second harmonic generation conversion efficiency was 2.5%.

Nonlinear optical properties of strontium tartrato‐antimonate(III) dihydrate, Sr[Sb2{(+)‐C4H2O6}2]·2H2O

AbstractThe tensor of nonlinear optical susceptibility for second harmonic generation [dSHG ijk ] of hexagonal (point group 6) strontium tartrato‐antimonate(III) dihydrate, Sr[Sb2{(+)‐C4H2O6}2]·2H2O, was determined using the Maker fringes method and a Nd:YAG laser with a wavelength of 1064 nm. The largest component of the tensor dSHG 333 amounts two times dSHG 111 of α‐quartz. Effective nonlinear optical susceptibility dSHG eff is given for phase matching type I for several wavelengths (for type II dSHG eff is nearly zero). The thermal stability of crystals of Sr[Sb2{(+)‐C4H2O6}2]·2H2O was determined in the temperature range from 153 K to 573 K by means of thermal expansion measurements and thermogravimetry. The temperature dependence of thermal expansion coefficients is given in the range from 153 K to 293 K. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonlinear optical coefficients and phase-matching conditions in Sn<sub>2</sub>P<sub>2</sub>S<sub>6</sub>

Phase matching conditions and second and third order nonlinear optical coefficients of Sn2P2S6 crystals are reported. The coefficients for second harmonic generation (SHG) are given at lambda = 1542 nm and 1907 nm at room temperature. The largest coefficients at these wavelengths are d111 = 17+/-1.5pm/V and d111 = 12+/-1.5pm/V, respectively. The third-order subsceptibilities chi(3) 1111 = (17 +/- 6) . 10-20m2/V2 and chi(3) 2222 = (9 +/- 3) . 10-20m2/V2 were determined at lambda = 1907 nm. All measurements were performed by the Maker-Fringe technique. Based on the recently determined refractive indices, we analyze the phase-matching conditions for second harmonic generation, sum- and difference-frequency generation and parametric oscillation at room temperature. Phase-matching curves as a function of wavelength and propagation direction are given. Experimental phase-matched type I SHG at 1907 nm has been demonstrated. The results agree very well with the calculations. It is shown that phase-matched optical parametrical oscillation is possible in the whole transparency range up to 8 microm with an effective nonlinear coefficient deff approximately 4pm/V.

Compact [formula omitted] blue laser with a composite Nd:YAG

A compact and simple design for an LDA-end-pumped intracavity doubling high-power blue laser with a composite Nd:YAG laser on the 4 F 3/2 to 4 I 9/2 laser transition in a flat-curved cavity is demonstrated. The nonlinear crystal used in the experiment is an LBO crystal cut for phase-matching type I. Through the thermo-lensing effect of the laser crystal at high-pumped power, the optimum mode-matched and efficient intracavity doubling are realized at the same time. The maximum output power at 473 nm was 600 mW when the absorbed, pumped power of 15 W , and the optical-to-optical conversion efficiency is 4%. The stability of blue output power is 3.2% within 2 h .

Experimental and theoretical investigation of generation of a cross-polarized wave by cascading of two different second-order processes

A nonlinear optical effect in which a linearly polarized wave propagating in a single quadratic medium is converted into a wave that is cross polarized to the input wave is investigated theoretically and observed experimentally in β-barium borate crystal. It is proved that this effect is a result of cascading of two different second-order processes. It starts with the generation of an extraordinary second-harmonic wave by type I interaction and is followed by type II difference-frequency mixing between the second-harmonic wave and the ordinary fundamental wave. The experiment was performed (a) for phase-matched type I interaction and non-phase-matched type II interaction and (b) for non-phase-matched type I interaction and phase-matched type II interaction. The observed generation of a cross-polarized wave is to our knowledge the only cubic effect whose first manifestation has been observed in quadratic crystal.

Attosecond time-scale intra-atomic phase matching of high harmonic generation.

Using a model of high-harmonic generation that couples a fully quantum calculation with a semiclassical electron trajectory picture, we show that a new type of phase matching is possible when an atom is driven by an optimal optical waveform. For an optimized laser pulse shape, strong constructive interference is obtained in the frequency domain between emissions from different electron trajectories, thereby selectively enhancing a particular harmonic order. This work demonstrates that coherent control in the strong-field regime is possible by adjusting the peaks of a laser field on an attosecond time scale.

Theoretical and experimental studies of noise suppression for intracavity frequency doubled lasers with phase matching type I or II

A general physical model consisting of two arbitrary birefringent elements is presented and studied based on Jones matrix calculation. The resonant frequencies and polarization directions of the two kinds of fundamental wave eigenmodes are given in general case. The stability of the intracavity frequency doubled cw laser emission is analyzed under multi-longitudinal modes operation. The conditions for noise suppression of the second harmonic output are derived for both types of phase matching. Experiment results are in good agreement with the theoretical analyses.

All-solid-state high-repetition-rate optical source tunable in wavelength and in pulse duration

A synchronously pumped optical parametric oscillator (OPO) employing periodically poled lithium niobate (PPLN) efficiently generates diffraction-limited short pulses that are tunable in the 1.45–1.56-µm spectral range, with their duration adjustable from ≈1 ps–15 ps and output power as high as 630 mW. The pump laser that produces these unique OPO characteristics is a 200-MHz, 2.5-W average power, diode-pumped Nd:YVO4 laser emitting at 1064 nm and passively mode locked by a nonlinear mirror (NLM) technique. One can select the output pulse width from the vanadate laser to be either 16 or 6 ps simply by choosing the appropriate NLM configuration. Significantly enhanced performance of the mode-locked Nd:YVO4 laser was obtained with a critically phase-matched type I LiB3O5 crystal. A comparison of this crystal with type II KTiOPO4 is reported.

Nonlinear polarization evolution in type I and type II second-harmonic-generation crystals applied to the mode locking of a pulsed Nd:YAG laser

We report experimental results on the mode-locked operation of a flash-lamp-pumped Nd:YAG laser using the recently developed technique based on nonlinear polarization evolution in a second-harmonic-generation crystal. It is the first time such a technique has been applied to a pulsed laser. A pulse train with duration close to 25 ps has been produced using two different configurations. One was based on a phase-matched type II crystal (KTP); the other one used, for the first time, a mismatched type I crystal (KNbO3). Mode-locking threshold and performances are compared between the two types of crystal.

CARS microscopy with folded BoxCARS phasematching

Three-dimensional microscopy based on coherent anti-Stokes Raman scattering (CARS) is a powerful new imaging technique, in which the contrast arises from molecular vibrations. Based on a simple numerical model, it is shown how the CARS interaction volume depends on the focusing parameters and the type of phasematching used. Collinear phasematching yields an ellipsoidal interaction volume, with lateral dimensions that readily cause vignetting of the CARS signal emission at the collection microscope objective. A folded BoxCARS phasematching geometry, on the other hand, results in an almost cylindrical interaction volume - at the cost of a reduced resolution, for which the possible vignetting of the CARS emission is much reduced. In addition, this type of phasematching provides spatial separation of the signal from the input laser beams, permitting simple signal detection of low frequency vibrational modes. Calculations show that when CARS is performed in a microscopic volume, the phasematching restraint on tuning over the vibrational band is strongly relaxed. A first example of CARS imaging using a folded BoxCARS imaging geometry is shown.

Enhancement of Second-Harmonic Generation in Helicoidal Distributed Feedback Structure of a Ferroelectric Liquid Crystal Using Two Counter-Propagating Fundamental Waves

Second-harmonic generation (SHG) was observed in an unwound ferroelectric smectic C* liquid crystal using two counter-propagating fundamental waves. A remarkable enhancement occurred when SH light wavelength approached to the optical pitch of the helicoid. This enhanced signal based on a helicoidal distributed feedback action is proportional to the fourth power of the sample thickness in thick cells, and becomes larger compared with the conventional phase-matched SHG signal in relatively thick samples. The crossover points of the SH intensities in the two phase matching types shift toward thinner cell thickness in materials with a larger dielectric anisotropy.

SHG and internal conical refraction experiments in CsTiOAsO/sub 4/, comparison with KTiOPO/sub 4/ and KTiOAsO/sub 4/, for 1.32-μm type II SHG

The internal conical refraction angles between 0.5321.32 /spl mu/m, the phase-matching directions of 1.064 /spl mu/m type I second harmonic generation (SHG) and of 1.32-/spl mu/m type II SHG are measured in a sphere of CsTiOAsO/sub 4/ (CTA). The relative sign and absolute magnitude of two independent quadratic nonlinear coefficients are determined by 1.32-/spl mu/m phase-matched type II SHG conversion efficiency measurements in a sphere and strips: d/sub 15/=1.09/spl plusmn/0.09 pm/V and d/sub 24/=1.7/spl plusmn/0.6 pm/V at 0.65 /spl mu/m. AH the results are compared with previous work. The comparison of CTA with KTiOPO/sub 4/ and KTiOAsO/sub 4/ is made in order to evaluate the crystal which provides the highest conversion efficiency for 1.32-/spl mu/m type II SHG depending on the crystal length and on the beam waist radius.

Phase-matching considerations of four-wave interaction processes in biaxial crystals

In light of the principle of phase matching (PM) in biaxial crystals, PM types for four-wave interaction processes are discussed. The relationships among the refractive indices of the four interacting waves are analyzed to classify PM topologies. A computer program is developed to characterize and obtain PM directions and their loci. As examples, PM loci for direct third-harmonic generation in four biaxial crystals are presented.

Noncritical vectorial phase matchings in nonlinear optics of crystals and infrared up-conversion

The exact analytic expressions for the vectorial group phase matching (PM) conditions have been obtained for sum and difference frequency generation processes ω 3 = ω 1 ± ω 2 ( ω 3= ω 2 − ω 1) in nonlinear anisotropy crystals, which ensure a wide-band conversion of signals ( ω 2) and images. The tangential PM conditions for all possible interaction types in the negative and positive uniaxial crystals have been studied. Scanning of the frequency of vectorial group PM has been studied by examples of LiNbO 3, LiIO, and HgGa 2S 4 crystals when changing the pump direction or pump frequency ω 1. The possibility of tuning the wide-band operation all over the transparency region of the LiIO 3, crystal has been shown. The double noncriticality conditions of PM in frequency cd; and acceptance angle have been studied and the possibility of their realization in a near and middle infrared region (IR) has been shown. A generalization of consideration to the other types of noncritical PMs (including multiples ones), has been made, including at an angle 90° between the propagation directions of waves with frequencies ω 1 (1) and ω 2 (2). The method of definition of the spectral bandwidths and acceptance angles of critical and noncritical PM taking into account the concordant change in the propagation angles of waves 1 and 2 has been proposed.