Group Velocity Mismatch Research Articles

Type-I frequency-doubling characteristics of high-power, ultrafast fiber laser in thick BIBO crystal

We report on experimental realization of optimum focusing condition for type-I second-harmonic generation (SHG) of high-power, ultrafast laser in "thick" nonlinear crystal. Using single-pass, frequency doubling of a 5 W Yb-fiber laser of pulse width ~260 fs at repetition rate of 78 MHz in a 5-mm-long bismuth triborate (BIBO) crystal we observed that the optimum focusing condition is more dependent on the birefringence of the crystal than its group-velocity mismatch (GVM). A theoretical fit to our experimental results reveals that even in the presence of GVM, the optimum focusing condition matches the theoretical model of Boyd and Kleinman, predicted for continuous-wave and long-pulse SHG. Using a focusing factor of ξ=1.16 close to the estimated optimum value of ξ=1.72 for our experimental conditions, we generated 2.25 W of green radiation of pulse width 176 fs with single-pass conversion efficiency as high as 46.5%. Our study also verifies the effect of pulse narrowing and broadening of angular phase-matching bandwidth of SHG at tighter focusing. This study signifies the advantage of SHG in "thick" crystal in controlling SH-pulse width by changing the focusing lens while accessing high conversion efficiency and broad angular phase-matching bandwidth.

Pump phase transfer and its control in hybrid seeded optical parametric amplifiers

Abstract Due to the existence of spatial walk-off and/or group-velocity mismatch effects, pump-to-signal phase transfer becomes inevitable during parametric amplification. We experimentally demonstrate that in hybrid seeded optical parametric amplifiers (OPAs) that include two OPA stages seeded by the signal and idler waves, respectively, the phase of the output signal can be restored to its initial value, although there are spatial and temporal phase fluctuations on the pump source. This method significantly relaxes the requirement for high pump beam quality, which is always very stringent in parametric amplification systems. With the introduction of this scheme into birefringent phase-matching OPAs or chirped-pulse OPAs, it should be promising to achieve intense femtosecond laser pulses that are close to the diffraction limit in space and ultra-high contrast in time, simultaneously.

Cross-modulation instability in inhomogeneous normal-dispersion fiber amplifiers

The conditions of the onset of a modulation instability of the signal wave in a doped fiber due to nonlinear cross-modulation interaction with the pump wave are investigated. The analysis takes into consideration the pump depletion and the group-velocity mismatch of the interacting waves. A dispersion relation coupling perturbation parameters with those of pump, analytic expressions governing the integral growth rate of a harmonic perturbation, and other important characteristics determining the dynamics of the signal-wave cross-modulation instability are obtained. Based on computer simulation, the behavior of the above characteristics as a function of the initial signal-wave power, fiber length, and group-velocity mismatch of the pump and signal waves is investigated.

Nonlinear Raman-Nath diffraction of femtosecond laser pulses.

We study the nonlinear Raman-Nath diffraction (NRND) of femtosecond laser pulses in a 1D periodic nonlinear photonic structure. The calculated second-harmonic spectra represent frequency combs for different orders of transverse phase matching. These frequency combs are in close analogy with the well-known spectral Maker fringes observed in single crystals. The spectral intensity of the second harmonic experiences a redshift with a propagation angle, which is opposite the case of Čerenkov nonlinear diffraction. We analyze how NRND is affected by the group-velocity mismatch between fundamental and second-harmonic pulses and by the parameters of the structure. Our experimental results prove the theoretical predictions.

Space-time coupling in upconversion of broadband downconverted light

We investigate the up-conversion process of broadband light from parametric down-conversion (PDC), focusing on the spatio-temporal spectral properties of the sum-frequency generated (SFG) radiation. We demonstrate that the incoherent component of the SFG spectrum is characterized by a skewed geometry in space-time, which originates from a compensation between the group-velocity mismatch and the spatial walk-off of the fundamental and the SFG fields. The results are illustrated both by a theoretical modeling of the optical system and by experimental measurements.

A Silicon Waveguide for Tailoring Dispersion of Transverse Electric and Magnetic Modes

A novel silicon waveguide structure is proposed that provides simultaneous dispersion engineering for both transverseelectric (TE) and transverse-magnetic (TM) modes. There is a dispersion of approximately ± 250 ps/(nm·km) over a 1404-nm and a 904-nm bandwidth for the fundamental quasi-TM and quasi-TE modes, respectively. The nonlinear parameters of the modes and the group velocity mismatch are also studied for an optimum structure. It is explained that mode coupling is feasible before the temporal separation of the modes occurs and that it can be enhanced due to the reduced dispersion of the modes. Enhanced mode coupling and the different dispersion properties of the modes can be utilized for enriching and controlling nonlinear effects. Therefore, this waveguide can ensure efficient implementation of photonic functions based on polarization effects.

Second harmonic generation of ultrashort pulses in refractive-index-linear-modulating nonlinear crystals

We present a theoretical model to deal with second harmonic generation (SHG) of ultrashort pulses in refractive-index-linear-modulating (RILM) nonlinear crystals. New coupled-wave equations were derived based on plane wave propagation. Under the undepleted-pump approximation, the analytic solutions for SHG of ultrashort pulses were obtained. The second harmonic (SH) pulse width and the efficiency were optimized in terms of the RILM parameter and the chirp coefficient of fundamental pulses. The results show that modulation of the refractive index (RI) in nonlinear crystals leads to a spectral localization of SHG that compensates the group velocity mismatch (GVM) and therefore compresses SH pulses. The modulation complicates the SHG process, which determines the pulse width, and the conversion efficiency varies with length and bandwidth. Especially, an overshooting compression phenomenon was found, which arose mainly from internal interference of the carrier frequency component in a SH pulse.

Simple method of optimizing second-harmonic generation under imperfect phase-mismatching conditions caused by group-velocity mismatch and group-velocity dispersion

A simple method of thickness optimization of a nonlinear optical crystal used for second-harmonic generation involving group-velocity mismatching and group-velocity dispersion is discussed on the basis of the feature parameter ΔS. An approximate analysis formula for thickness with respect to the maximum second-harmonic intensity is obtained, which is applicable to the optimization of second-harmonic generation.

Linear electro-optic effect for femtosecond laser pulses in linear chirped MgO:LiNbO3 and its compensation for phase mismatch and group-velocity mismatch

For linear electrooptic (EO) effect of femtosecond laser pulses that propagates along the direction of non-optical axis in linear-chirped and periodically poled MgO:LiNbO3 (LCPPLMN), we explore the compensation scheme for the phase mismatch and the group-velocity mismatch between the o- and e-light, and discuss the effect of the linear chirp parameter of the LCPPLMN on the waveform of the output o- and e-light. It is found that, for any input pulse duration, the phase mismatch and the group-velocity mismatch can be simultaneously compensated by the optimization of the linear chirp parameter. As a result, high conversion efficiency of linear EO effect can be performed. In addition, we discuss the influence of the linear chirp parameter on the temporal evolutions of the output o- and e-light pulse.

Ultrabroadband supercontinuum and third-harmonic generation in bulk solids with two optical-cycle carrier-envelope phase-stable pulses at 2 μm

We report on the generation of ultrabroadband supercontinuum (SC) by filamentation of two optical-cycle, carrier-envelope phase-stable pulses at 2 μm in fused silica, sapphire, CaF₂ and YAG. The SC spectra extend from 450 nm to more than 2500 nm, and their particular shapes depend on dispersive properties of the materials. Prior to spectral super-broadening, we observe third-harmonic generation, which occurs in the condition of large phase and group velocity mismatch and consists of free and driven components. A double-peaked third-harmonic structure coexists with the SC pulse as demonstrated by the numerical simulations and verified experimentally. The SC pulses have stable carrier envelope phase with short-term rms fluctuations of ∼ 300 mrad, as simultaneously measured in YAG crystal by f-2f and f-3f interferometry, where the latter makes use of intrinsic third-harmonic generation.

English

The generation of the slow modes in a planar photonic crystal waveguide has been highlighted theoretically and experimentally in the two last decade. However, the exploitation of this phenomenon to control the light propagation in the optical integrated circuits faces several obstacles and technological locks. On the one hand, it is almost impossible to excite this type of modes in the slowing light devices because of the group velocity mismatch and even if we are able to overcome this problem, the frequencies of the slow modes are very close to the band edge which causes the optical signal distortion by high value of group velocity dispersion. On the other hand, the slow modes are characterized by a special spatial distribution of the electromagnetic field which extends beyond the defect which serves as a wave guide, this lead to an intense interaction of a part of the guided light with the holes of photonic crystal and cause the appearance of the different type of losses. Several solutions have been proposed to address these various issues and our contribution is in this perspective, and more specifically, it is trying to find the parameters that enable an optimal coupling of the fast modes of our planar photonic crystal waveguide into his slower one. To achieve this goal, we chose to work in two stages. First, we have sought the structural parameters that will help us to generate a slowly mode with zero-dispersion effect. After, we have worked and demonstrated the efficient static coupling of light into the slow modes photonic crystal waveguide.   Key words: Slab waveguide, photonic crystal, slow modes, efficient coupling.

Effect of pulse slippage on beat wave THz generation in a rippled density magnetized plasma

Beat wave excitation of terahertz radiation by nonlinear mixing of two laser pulses in a ripple density magnetized plasma is investigated allowing for the effect of pulse slippage. The lasers' ponderomotive-force-induced electron drift couples with the density ripple to produce a nonlinear current that resonantly drives the terahertz at the beat frequency. Density ripple provides the phase matching while the magnetic field, transverse to the direction of laser propagation, provides a transverse component to current density. However, the group velocity mismatch between the lasers and the terahertz radiation leads to slippage of the latter behind the laser pulses leading to saturation of the terahertz amplitude.

Surface-reflection-initiated pulse-contrast degradation in an optical parametric chirped-pulse amplifier

We study a novel mechanism of pre-pulse generation in an optical parametric chirped-pulse amplification (OPCPA) system through an analytical approach together with numerical simulations. The acquired pre-pulses are initiated from the surface-reflection-induced modulation of the seed spectrum and occur as a consequence of high-order distortion of such modulated spectrum due to the instantaneous gain saturation effect. We demonstrate that the intensities of pre-pulses increase quadratically with the initial temporal modulation-depth of the stretched signal pulse as well as the conversion efficiency prior to substantial pump-depletion. Explicit formulas for estimating the contrast limit due to surface reflections are present. We also discuss the impact of group-velocity mismatch on the pre-pulse generation. The results of this work may deepen our cognition on the complexity of the pulse-contrast problem in OPCPA systems.

Compact dual-crystal optical parametric amplification for broadband IR pulse generation using a collinear geometry

A novel compact dual-crystal optical parametric amplification (DOPA) scheme, collinearly pumped by a Ti:sapphire laser (0.8 μm), is theoretically investigated for efficiently generating broadband IR pulses at non-degenerate wavelengths (1.2 μm~1.4 μm and 1.8 μm~2.1 μm). By inserting a pair of barium fluoride (BaF(2)) wedges between two thin β-barium borate (BBO) crystals, the group velocity mismatch (GVM) between the three interacting pulses can be compensated simultaneously. In this case, the obtained signal spectrum centered at 1.3 μm is nearly 20% broader and the conversion efficiency is increased, but also the pulse contrast and beam quality are improved due to the better temporal overlap. Furthermore, sub-two-cycle idler pulses with carrier-envelope phase (CEP) fluctuation of sub-100-mrad root mean square (RMS) can be generated. Because a tunable few-cycle IR pulse with millijoule energy is attainable in this scheme, it will contribute to ultrafast community and be particularly useful as a driving or controlling field for the generation of ultrafast coherent x-ray supercontinuum.

Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

We interpret the purely spectral forward Maxwell equation with up to 3${^{\rm rd}}$ order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named nonlinear wave equation in frequency domain, includes both quadratic and cubic nonlinearities, delayed Raman effects and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due to competition between self-steepening, Raman effects and self-steepening-like effects from cascading originating in the group-velocity mismatch between the pump and second harmonic. We analyze the first-order contributions, and show that this balance can be broken to create fast or slow pulses. Through further simulations we demonstrate few-cycle compressed solitons in extremely short crystals, where spectral phenomena such as blue/red shifting, non-stationary radiation in accordance with the non-local phase matching condition and dispersive-wave generation are observed and marked, which help improving the experimental knowledge of cascading nonlinear soliton pulse compression.

Optical Cherenkov radiation in an As_2S_3 slot waveguide with four zero-dispersion wavelengths

We propose an approach for an efficient generation of optical Cherenkov radiation (OCR) in the near-infrared by tailoring the waveguide dispersion for a zero group-velocity mismatching between the radiation and the pump soliton. Based on an As(2)S(3) slot waveguide with subwavelength dimensions, dispersion profiles with four zero dispersion wavelengths are found to produce a phase-matching nonlinear process leading to a broadband resonant radiation. The broadband OCR investigated in the chalcogenide waveguide may find applications in on-chip wavelength conversion and near-infrared pulse generation.

Optical, spectral and phase-matching properties of BIBO, BBO and LBO crystals for optical parametric oscillation in the visible and near-infrared wavelength ranges

The phase-matching properties of BIBO, BBO and LBO crystals for optical parametric oscillators (OPO) with wavelength tuning in the visible and near infrared spectral ranges were numerically investigated. The phase-matching configurations with a pump wavelength of 520 nm that provide the largest effective nonlinearity in each crystal were considered and compared. In addition, dispersive characteristics, including the group velocity mismatch and group velocity dispersion, which are of significant importance in femtosecond OPOs, were calculated. Finally, the attainable gain bandwidths for each crystal were estimated.

Ultra-short laser pulse compression by using the group-velocity-matched cascaded quadratic nonlinearity

A new method for compressing ultra-short laser pulse has been proposed in which cascaded quadratic nonlinearity with tilt pulse is used. The pulse compression scheme with group velocity matching between fundamental harmonic (FH) and second harmonic (SH) pulses in a single BBO crystal has been analyzed theoretically. The compressed results have been investigated and compared between the cases of group velocity matching and mismatching. Furthermore, the influences of the phase mismatching between the FH and SH pulses, the length of the nonlinear crystal, the initial peak intensity and pulse-duration of the FH pulse on the pulse-duration compression have been analyzed and simulated. The results show that the matched group velocity between FH and SH pulses can improve significantly both the temporal profile and the spectrum distribution of the compressed pulse. High quality compression can be achieved by optimizing and selecting the parameters such as phase mismatch, length of the nonlinear crystal, initial intensity and so on. For the fundamental pulse with 800 nm central wavelength, 100 fs duration and 50 GW/cm2 peak intensity, the 20fs output FH pulse has been achieved, and at the same time the 14 fs SH pulse has also been generated in 25 mm-long BBO crystal with Δk=60 mm-1 (1.98° detuning angle) and external tilt angle γ0=74°.

Nonlinear Cascaded Femtosecond Third Harmonic Generation by Multi-grating Periodically Poled MgO-doped Lithium Niobate

Nonlinear cascaded femtosecond third harmonic generation was experimentally investigated pumped by 100 fs pulses at optical communication band 1550 nm using a multi-grating 5 mol. % MgO-doped periodically poled lithium niobate crystal. The optimized efficiency of 10.8% was achieved with the simultaneous phase-matching of the second harmonic and sum frequency process. And the third harmonic spectrum reached as broad as 8.7 nm because of the choosing of a small group velocity mismatching between the fundamental and second harmonic pulses. Nonlinear cascaded method will provide a reference for the efficient frequency conversion in the high intensity range.

Raman effect on parametric amplification gain spectra of different frequency propagation regimes in polarization maintaining fibers

The expression of gain is derived from nonlinear Schrödinger equation with consideration of raman effect when two laser pulses with different wavelengths are emitted into birefringence fiber along two polarization axes. The gain characteristic input laser pulses of different frequencies are revealed by comparing the laser pulses of identical frequency. The result show that the gain spectra will apparently differ when input laser pulses have different frequencies in normal dispersion regime and anomalous dispersion regime. The intensities of outboard gain peak about stokes part and anti-stokes part increase and frequency deviates from central frequency as group velocity mismatch increases. Therefore, the THz pulse can be extracted. The gain spectrum will be apparently different from that with no Raman effect taken into account, when the two polarization modes, are in different dispersion regimes. The symmetry of gain spectrum will be damaged. The intensity of gain peak of stokes is apparently stronger than the peak of anti-stoke.