Phase-matched Frequency Conversion Research Articles

Phase-matched frequency conversion in waveguides by means of transverse wavevector projections

We present a versatile technique for modal phase-matched second-harmonic generation in a waveguide, which relies on the incident electromagnetic field having transverse wavevector components on the input facet of the waveguide. Such a requirement is satisfied by using an angular-coupling arrangement, which allows for the excitation of modes having an odd spatial distribution that contribute to modal phase-matched second-harmonic generation. The strength of the second-harmonic signal is directly related to the angle at which the incident field is coupled into these modes. This is critical for on-chip nonlinear frequency conversion processes in the areas of optical communication, optical computing, and quantum computing.

Phase-Matched Coupling and Frequency Conversion of Terahertz Waves in a Nonlinear Graphene Waveguide

In this paper, we propose a novel technique for the phase-matched coupling and frequency conversion of terahertz (THz) waves. The principle of operation is based on nonlinear THz wave interaction in a graphene parallel plate waveguide filled with lithium niobate. The THz waves induce nonlinear polarization that modulates the effective permittivity of the waveguide by modifying the graphene conductivity. To model the evolution of the THz waves, small modulation amplitudes are presumed and a perturbation analysis is performed. First, two THz inputs (the pump and the signal) with distinct frequencies, that is, ${\boldsymbol{f}_1}$ and ${\boldsymbol{f}_2}$ , are considered. The two waves are coupled in a phase-matched fashion and show significant signal gain. Second, a third THz input with low intensity is considered at frequency ${\boldsymbol{f}_3}$ . Frequency conversion from ${\boldsymbol{f}_3}$ to a new frequency, that is, ${\boldsymbol{f}_4}$ , is attainable, assisted by the permittivity modulation induced by the co-propagating waves ${\boldsymbol{f}_1}$ and ${\boldsymbol{f}_2}$ . The generated frequency has a $\boldsymbol{\Omega } = {\boldsymbol{f}_1} - {\boldsymbol{f}_2}$ frequency detuning from the ${\boldsymbol{f}_3}$ frequency, that is, ${\boldsymbol{f}_4} = {\boldsymbol{f}_3} - ({{\boldsymbol{f}_1} - {\boldsymbol{f}_2}})$ . Thus, tunable frequency conversion can be achieved by controlling ${\boldsymbol{f}_1}$ , ${\boldsymbol{f}_2}$ , or ${\boldsymbol{f}_3}$ . Our numerical estimations show viable gain and conversion efficiency over the entire THz range considered, from $\text{0.1}$ to $\text{2}$ THz. The proposed technique is compact, tunable, and (in principle) spans the entire THz range.

Phase-matched frequency conversion below 150 nm in KBe2BO3F2.

Sum frequency mixing has been demonstrated below 150 nm in KBeBO3F2 by using the fundamental with its fourth harmonic of a 6 kHz Ti: sapphire laser system. The wavelength of 149.8 nm is the shortest ever obtained to our knowledge by phase matching in nonlinear crystals. The output powers were 3.6 μW at 149.8 nm and 110 μW at 154.0 nm, respectively. The phase matching angles measured from 149.8 to 158.1 nm are larger by 3-4 degrees than those expected from the existing Sellmeier equation. The measured transmission spectra of KBeBO3F2 crystals support the generation of coherent radiation below 150 nm.

Spectrally-isolated violet to blue wavelength generation by cascaded degenerate four-wave mixing in a photonic crystal fiber.

Generation of spectrally-isolated wavelengths in the violet to blue region based on cascaded degenerate four-wave mixing (FWM) is experimentally demonstrated for the first time in a tailor-made photonic crystal fiber, which has two adjacent zero dispersion wavelengths (ZDWs) at 696 and 852 nm in the fundamental mode. The influences of the wavelength λp and the input average power Pav of the femtosecond pump pulses on the phase-matched frequency conversion process are studied. When femtosecond pump pulses at λp of 880, 870, and 860 nm and Pav of 500 mW are coupled into the normal dispersion region close to the second ZDW, the first anti-Stokes waves generated near the first ZDW act as a secondary pump for the next FWM process. The conversion efficiency ηas2 of the second anti-Stokes waves, which are generated at the violet to blue wavelengths of 430, 456, and 472 nm, are 4.8, 6.48, and 9.66%, for λp equalling 880, 870, and 860 nm, respectively.

Silicon carbide--a high-transparency nonlinear material for THz applications.

Optical properties of 4H-SiC were measured using time-domain and Fourier transform spectroscopy in the range of 0.1-20 THz. A high-transparency region was found between <0.1-10 THz. Based on the obtained data and published results, the refractive indices for o-wave and e-wave were approximated in the form of Sellmeier equations for the entire transparency range. Phase matched frequency conversion was found to be possible at wavelengths from the visible through the mid-IR and further into the far-IR (THz) region beyond 17 μm. Extremely low absorption coefficient, high damage threshold, and the possibility of phase matching make this material highly suited for high power THz optics and generation.

Efficient and broadband Stokes wave generation by degenerate four-wave mixing at the mid-infrared wavelength in a silica photonic crystal fiber

Based on degenerate four-wave mixing (FWM), the broadband Stokes waves are efficiently generated at the mid-infrared wavelength above 2 μm, for the first time to our knowledge, by coupling the femtosecond pulses into the fundamental mode of a silica photonic crystal fiber designed and fabricated in our laboratory. Influences of the power and wavelength of pump pulses on the phase-matched frequency conversion process are discussed. When pump pulses with central wavelength of 815 nm and average power of 300 mW are used, the output power ratio of the Stokes wave generated at 2226 nm and the residual pump wave P(s)/P(res) is estimated to be 10.8:1, and the corresponding conversion efficiency η(s) and bandwidth B(s) of the Stokes wave can be up to 26% and 33 nm, respectively. The efficient and broadband Stokes waves can be used as the ultrashort pulse sources for mid-infrared photonics and spectroscopy.

High conversion efficiency fiber optical parametric oscillator

We present a χ(3) fiber parametric oscillator with high conversion efficiency from the input pump wave to the output parametric sidebands. By introducing an intracavity filter detuned from the oscillator's phase-matched frequency conversion efficiencies considerably higher than those possible when operating at the phase-matched frequency are demonstrated. Experimentally we are able to obtain a total internal conversion efficiency in excess of 93% from the pump to the Stokes and anti-Stokes sidebands.

Coherent quasi-cw 153 nm light source at 33 MHz repetition rate

We present a quasi-cw laser in a vacuum ultraviolet region at megahertz repetition rate. The narrowband pulses generated from an ytterbium-fiber laser system at 33 MHz repetition rate at the central wavelength of 1074 nm are frequency-converted by successive stages of LiB(3)O(5) crystals and KBe(2)BO(3)F(2) crystals. The generated radiation at 153 nm has the shortest wavelength achieved through phase-matched frequency conversion processes in nonlinear optical crystals to our knowledge.

Linear and nonlinear optical properties of MgO:LiTaO3

We derive new temperature dependent Sellmeier equations for the extra-ordinary and ordinary refractive indices of 0.5% MgO-doped stoichiometric LiTaO3 crystal. The equations are based on quasi phase-matched frequency conversion measurements, as well as on interferometric measurements of the thermal expansion and thermal dispersion. These equations fit experimental data over wide spectral ranges: 0.35–6 μm for the extra-ordinary wave and 0.375–3.75 μm for the ordinary wave, from room temperature up to 200°C. The nonlinear optical measurements set lower-limit values for the d 33, d 22, and d 24 elements of the second-order susceptibility tensor χ (2) of 12.9, 1.54, and 0.46 pm/V, respectively. The interferometric measurements enable one to determine the linear and quadratic expansion coefficients of 1.45762e−5 1/°C, and 2.68608e−8 (1/°C)2, respectively. The Sellmeier equations are in good agreement with previously published data.

LiGaTe2: A New Highly Nonlinear Chalcopyrite Optical Crystal for the Mid-IR

The chalcopyrite crystal LiGaTe2 was grown by the Bridgman-Stockbarger technique with sufficient size and optical quality that allowed the characterization of its linear (dispersion and birefringence) and nonlinear optical properties. X-ray structural analysis was performed on single crystals. The transmission was recorded in the 0.5−24 μm range, and Raman and IR-spectra were recorded in the 0−400 cm-1 and 180−400 cm-1 ranges, respectively. The clear transparency range of LiGaTe2 extends from 2.5 to 12 μm, the band-gap at room temperature is at 2.41 eV (515 nm), residual absorption limits the transmission near the band-edge, and the upper limit for the transmission is determined by the onset two-phonon absorption. LiGaTe2 is a positive uniaxial crystal that possesses sufficient birefringence for phase-matching. Its nonlinear coefficient d36 was estimated by phase-matched second harmonic generation to be 43 pm/V ± 10%. It is only the third crystal belonging to the AIBIII chalcopyrite family for which phase-matched nonlinear frequency conversion could be demonstrated, and of this group it exhibits the highest nonlinearity and figure of merit for nonlinear optical applications in the mid-infrared.

Coherent soft x-ray generation in the water window with quasi-phase matching.

We demonstrate enhanced generation of coherent light in the "water window" region of the soft x-ray spectrum at 4.4 nanometers, using quasi-phase-matched frequency conversion of ultrafast laser pulses. By periodically modulating the diameter of a gas-filled hollow waveguide, the phase mismatch normally present between the laser light and the generated soft x-ray light can be partially compensated. This makes it possible to use neon gas as the nonlinear medium to coherently convert light up to the water window, illustrating that techniques of nonlinear optics can be applied effectively in the soft x-ray region of the spectrum. These results advance the prospects for compact coherent soft x-ray sources for applications in biomicroscopy and in chemical spectroscopy.

Crystal growth and properties of AgGaTe 2

Large, crack-free single crystals of AgGaTe 2 were grown for the first time using the horizontal gradient freeze technique. As-grown samples were transparent from 1.2 μm to beyond 16 μm (the spectrometer limit): they exhibited near-theoretical transmission at long wavelengths, but in the near-infrared transmission was limited by scattering from second-phase precipitates (much like AgGaSe 2 and AgGaS 2). Dilatometer measurements on oriented single crystal revealed severely anisotropic thermal expansion similar in sign and magnitude to that of the sulfide and selenide analogs. Preliminary refractive index data suggests that the birefringence of AgGaTe 2 may be slightly too small for phase-matched frequency conversion, but additional measurements over a broader wavelength range are required to refine the Sellmeier fits.

Phase-matched frequency conversion in ionizing atomic gases.

We solve the one-dimensional wave equation for high-order mixing of the type ${\ensuremath{\omega}}_{h}=q{\ensuremath{\omega}}_{0}\ensuremath{-}l{\ensuremath{\omega}}_{c}(q\ensuremath{\gg}l&gt;=1)$ using a Keldysh-type model to describe the high-field atomic nonlinear susceptibility. When ${\ensuremath{\omega}}_{c}$ is selected to give static phase matching, we show that the conversion efficiency of the mixed field can be increased by about an order of magnitude compared to non-phase-matched high-order harmonic generation but that fundamental limitations are introduced by axial electron-density gradients.

Temperature sensitivity of KDP for phase-matched frequency conversion of 1 μm laser light

The magnitudes of the derivatives of the phase-matching angles with respect to temperature |/spl part//spl theta//sub pm///spl part/T| (milli-radians/degree celsius), for critically phase-matched frequency conversion using KDP (KH/sub 2/PO/sub 4/) have been directly measured for the five most interesting processes to inertial confinement fusion (ICF) laser-system designers: 2/spl omega/ I, 2/spl omega/ II, 3/spl omega/ I, 3/spl omega/ II, and 4/spl omega/ I. These measurements span an approximate temperature range of 25 to 90/spl deg/C, and were performed at a fundamental (1/spl omega/) wavelength of /spl lambda/=1.064 pm. The results are used to calculate the phase-matching thermal-sensitivity parameter |/spl beta//sub T/| (centimeter/sup -1//milliradian), for each conversion process.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Characterization of biaxial crystals for tangentially phase-matched frequency conversion

Ultraviolet radiation has been generated by tangentially phase-matched sum-frequency mixing in biaxial L-arginine phosphate (LAP) crystal for the first time using Nd:YAG output at 1064 nm and Rh 6G dye laser output at 560 nm as the two input sources. Characterization has also been made of such a cheap, biaxial crystal for its possible use in devices for tangentially phase-matched short wavelength generation. If the crystal is of proper cut, thickness and quality so that its maximum capability can be exploited it can replace the potassium dihydrogen phosphate (KDP) group of crystals for various applications.

Temperature-tuned noncritically phase-matched frequency conversion in LiB 3O 5 crystal

The new nonlinear crystal of lithium triborate, LiB 3O 5 (LBO), was investigated for frequency doubling and mixing of 1064 nm, 1135 nm and 1908 nm operated at the noncritically phase-matched (NCPM) temperatures of 149°C (for doubling 1064 nm), 77.4°C (for doubling 1135 nm), 112°C (mixing 1064 and 1135 nm) and 81°C (mixing 1064 and 1908 nm). The temperature tuning curves (from 0°C to 150°C), angular and temperature bandwidths are measured and compared with the calculated values.

Phase-matched frequency conversion in coupled waveguides

Equations are obtained for a three-frequency interaction of waves in coupled waveguides and it is shown that the efficiency of frequency conversion may be several orders of magnitude higher than the efficiency in single waveguides.

Coherent Emission from Rare Earth Ions in Electro-optic Crystals

We report the observation of coherent emission from three rare-earth ions in electro-optic crystals. Oscillation is observed from Nd3+ ions in Bi4Ge3O12, LiNbO3, and Ba0.75Ca0.25Nb26O at room temperature, and from Tm3+ and Ho3+ ions in LiNbO3 at 77°K. Second-harmonic radiation is obtained from LiNbO3:Tm3+ and electric-field modulation of threshold is observed for certain crystals of LiNbO3:Nd3+. The latter effect is believed to arise from crystal strain. The propagation angle for phase-matched second-harmonic generation is calculated to lie at 43° to the c axis for both LiNbO3:Tm3+ and LiNbO3:Ho3+ at 77°K. Phasematched second-harmonic generation from LiNbO3:Nd3+ is not possible, since the maser line is an extraordinary wave. However, the polarization of the maser line in LiNbO3:Nd3+ is appropriate for phasematched parametric frequency conversion in the near infrared. Attempts to observe such radiation were not successful due to the limited power available in the fundamental.