Third-harmonic Generation Process Research Articles

Short optical pulse refraction by a thin film of atoms at two-photon resonance

The refraction of a short pulse by a thin film of atoms at two-photon resonance is numerically considered with the process of third harmonic generation involved in the analysis. It is shown that a light pulse, being refracted by a thin film of resonance atoms, decays into subpulses, whose number is determined by the energy penetrating the film. The process depends on the angle of incidence. The variation on the resonance detuning allows compensation of the Stark effect and creation of preferable conditions for light pulse transmission. The effect of local field is similar in its action to the Stark effect, but its contribution to the frequency shift could be significant only in media with a greater concentration of the resonance atoms.

Characterization of third-harmonic generation in Fibonacci optical superlattices

A Fibonacci optical superlattice (FOS) made from a single crystal with a quasiperiodic laminar ferroelectric domain structure was proposed to realize a third-harmonic generation (THG) process. Due to its quasiperiodic structure, a FOS can provide more plentiful reciprocal-lattice vectors to compensate for the mismatch phase in optical parametric processes, which causes most of third-harmonic peaks labeled by the corresponding reciprocal-lattice vector indices. Numerical calculation shows that the THG spectrum exhibits a self-similarity property in real space. Effects of the phase mismatch of second-harmonic generation and THG, the bandwidth, and the relative intensity of the second harmonic peak on THG are discussed. We also found THG peaks for which the quasi-phase-matching condition in THG process is not completely satisfied. The physical origins of the phenomenon are presented and discussed.

Characterization of harmonic generation spectra in three-component Fibonacci optical superlattices

The second-harmonic generation (SHG) and third-harmonic generation (THG) processes in a three-component Fibonacci optical superlattice (TCFOS) are studied. The TCFOS is made from a single crystal with quasiperiodic laminar ferroelectric domain structure. It is found that the TCFOS can provide more reciprocal vectors to compensate phase mismatch in optical parametric processes, which results in more intense peaks in the SHG and THG spectra of the quasiperiodic superlattice. The intense SHG and THG peaks can be labeled with three indices. In real space, the SHG and THG spectra exhibit self-similarity which is inherent to the superlattice. In reciprocal space, the self-similarity is destroyed due to the dispersion effect of the optical material. Dependence of the THG peak intensity within the TCFOS on the second-harmonic phase mismatch and the third-harmonic phase mismatch is discussed and presented. Numerical calculations show that an efficient THG can be achieved when THG quasi-phase-matching condition is satisfied even though the SHG is quasi-phase-mismatched.

Characterization of harmonic generation in an intergrowth optical superlattice

In this paper we obtain an analytical solution to the harmonic generation processes in a quasiperiodic optical superlattice. The derived theory was applied to an intergrowth optical superlattice made from a single crystal with laminar domain reversal to realize third-harmonic generation processes. The quasiperiodic structure can provide more reciprocal vectors to compensate for the phase mismatches of the optical parametric processes, which make most of the intense harmonic peaks labelled by the corresponding reciprocal vector indices. The dependence of the harmonic intensity spectrum on structure parameters is presented. Conditions for efficient third-harmonic generation are also discussed in detail.

Continuous frequency tuning of a picosecond neodymium-glass laser in the UV and VUV

The results of an investigation of continuous frequency tuning of a neodymium laser in the UV and VUV ranges are reported. Generation of the sum frequency of second harmonic radiation and the radiation from a parametric light generator in the UV region (338–366 nm) is achieved. The optimal conditions for tuning UV radiation in the range 113.5–117.0 nm in third-harmonic generation processes in xenon and its mixtures with other gases are investigated. A third-harmonic generation efficiency of ∼5×10−4 and a tuning range >2600 cm−1 are obtained in the VUV range investigated.

A novel quasi-phase-matching frequency doubling technique

A new quasi-phase-matching technique for efficient second-harmonic generation is reported. It is based on the spatial periodic modulation of the light intensity along the propagation direction, rather than the conventional spatial periodic modulation of the nonlinear optical coefficients. It can be realized by using a novel dual-channel waveguide frequency doubler structure for the desired light intensity distribution. This dual-channel waveguide device has major advantages including very small beam size, high light intensity within long nonlinear-waveguide interaction length, highly efficient second-harmonic generation, ease in fabrication of the nonlinear channel waveguides without any spatially periodic poling, and low waveguide propagation losses. The new quasi-phase-matching technique can also be applied to third-harmonic generation and other nonlinear optics processes.

High-order nonlinear phase shift caused by cascaded third-order processes

We show, for the first time to our knowledge, that the fundamental beam that participates in the process of third-harmonic generation experiences an additional high-order nonlinear phase shift. The magnitude of the shift is proportional to the square of the pump intensity and the length of the sample and depends on the deviation from the exact phase-matched condition. This phase shift arises from cascaded third-order processes. Its value can exceed the value of the phase shift that originates from inherent fifth-order susceptibility of the nonlinear medium. Its sign is controllable by the sign of the phase mismatch of the third-harmonic generation process.

Laser control of third-harmonic generation by means of an additional EM field

Control of the third-harmonic generation process through an external electromagnetic field is observed in atomic Ca. The conversion efficiency can be modified when the third harmonic is produced in the vicinity of an autoionizing state. A second laser is used to produce strong radiative coupling between a low-lying bound state and the autoionizing state.

Optical third-harmonic generation at interfaces.

Optical third-harmonic generation (THG) is generally a weak process but is dipole allowed, therefore it occurs in all materials, including dielectric materials with inversion symmetry. We report that when using focused high-intensity ultrashort laser pulses, this normally weak THG process becomes highly operative at a simple air-dielectric interface and is much stronger than the bulk of most dielectric materials. We characterized this nonlinear optical response at interfaces as a phenomenological surface-enhanced THG in transmission and/or in reflection. This surface THG is further cascaded in transmission or reflection from layered composite dielectric materials of a high-low index of refraction, resulting in a marked increase in photon conversion efficiency than that of a single interface. Although the present THG efficiency is lower than that of a typical phase-matching harmonic crystal, it is important to note that the surface-enhanced optical THG is a fundamental physical process occurring at all interfaces and is relatively free from the constraint of a phase-matching condition and wavelength restriction. Using optical THG at an interface, it becomes possible to generate wavelengths at which harmonic crystals are unavailable. These findings may lead to a new development of surface-enhanced studies and prompt a reexamination of the processes of high-harmonic generation at interfaces using a focused beam.

Enhancement of third-harmonic blue-violet light at 440 nm by erbium ions in Er^3+–GeO_2-doped silica monomode optical fibers pumped at 1319 μm

The efficient generation of third-harmonic blue-violet light at 440 nm in short lengths of Er3+-doped germanosilicate single-mode optical fibers pumped at 1.319 μm is reported. Measurement indicates that the third-harmonic generation process that is due to a GeO2–SiO2 core is resonantly enhanced through the amplification of the signal light at 440 nm by population inversion of the erbium ions in the fiber core. An average signal power at 440 nm of ~5 μW was observed.

Two-band model description of electroabsorption and third-harmonic generation in 1-D MX linear chains

Within a two-band model, we investigate the electroabsorption (EA) and third-harmonic generation (THG) processes in halogen-bridged mixed-valence Pt complexes: PtCl, PtBr and Ptl. For PtCl, the theoretical THG spectrum shows three peaks, corresponding to (i) a three-photon resonance at 0.83 eV originating in a M(etal)-M(etal) transition; (ii) a two-photon resonance at 1.5 eV from an M-M band-edge transition; and (iii) a three-photon resonance at 1.6 eV from an M-X transition. The latter two peaks account well for the twin-peak structure seen experimentally. We show that the twin-peak intensity strongly decreases from PtCl to PtBr and disappears for Ptl. We also discuss the theoretical EA spectra due to localized defects (polarons, bipolarons, kinks, and excitons).

Third-order sum-frequency generation in droplets: experimental results

New experimental third-order sum-frequency generation (TSFG) spectra are presented for CCl4 droplets. The droplet radii are discretely tuned over a size range in increments of 1 part in 6000. For each droplet radius only one or a few of the many possible TSFG peaks are dominant. Both low- and high-resolution TSFG spectra of D2O droplets are measured. The possible generating waves are the stimulated Raman radiation [known to occur at the morphology-dependent resonance (MDR) frequencies] and the internal fields at the incident laser frequency, which is usually not on a MDR. The experimental findings suggest that the resultant TSFG frequency must be near an output MDR. A physical description of the third-harmonic generation (THG) process in droplets is presented. MDR’s are treated as traveling waves that rotate in the azimuthal direction. Their azimuthal phase velocities are derived, and the concept of phase matching among the MDR’s is presented. The relation between phase matching and spatial overlap of MDR’s is discussed. Reasons are presented for the low probability of having the THG or TSFG frequency on or near a MDR.

Two-photon resonant third-harmonic generation in polysilanes.

Third-order nonlinear-optical susceptibility spectra \ensuremath{\Vert}${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})\ensuremath{\Vert} have been obtained for poly(dihexylsilane) (PDHS) and poly(dibutylsilane) (PDBS) films by third-harmonic generation (THG) measurements for a fundamental photon energy region from 1.90 to 2.15 eV, which covers the two-photon absorption (TPA) for PDHS but not for PDBS. The \ensuremath{\Vert}${\mathrm{\ensuremath{\chi}}}^{(3)}$\ensuremath{\Vert} spectrum for PDHS shows a prominent peak at about 2.08 eV with a maximum value of about 2.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ esu, while there is no enhancement effect in PDBS in the same fundamental photon energy region. These results provide direct evidence for the two-photon-resonant THG process in polysilanes due to the one-photon-forbidden $^{1}$${\mathit{A}}_{\mathit{g}}$ exciton detected by TPA and electroabsorption measurements.

Mechanisms for the production of harmonics in free electron lasers

Harmonics in the radiation of a free electron laser are useful for extending the range of tuning, may originate in spontaneous or parametric processes, and can take part in stimulated emission or amplification. These mechanisms exhibit interesting analogies with those of nonlinear optics. Apart from the well known nonparametric gain analogous to stimulated Brillouin scattering, they include third-harmonic generation and other four-wave mixing parametric processes, with spatial harmonics of the electron density taking the place of the higher-order terms in the nonlinear dielectric susceptibility. We investigate these mechanisms using a one-dimensional model.

Detection of atomic nitrogen by third harmonic generation

The four-wave mixing technique of third harmonic generation (THG) was used to detect gas-phase atomic nitrogen atoms. Ground state N(4S03/2) atoms were produced in a microwave discharge and monitored via 120 nm radiation which was generated by a 360 nm pulsed dye laser beam focused into the post-discharge region. The THG excitation features were blue-shifted from the 3s 4PJ→2p3 4S03/2 atomic resonance lines. Both the frequency shift and VUV intensity were sensitive to the N(4S03/2) concentration as expected for the THG process. Absolute concentration was determined using standard flow reaction calibration and yielded a minimum sensitivity of 3×1013 cm−3. Similar THG detection schemes for atomic nitrogen metastable states (2p3 2D0j and 2p3 2P0J) are discussed. The third harmonic generation technique possesses a number of potential advantages for in situ optical diagnostics.

Harmonic generations in an optical Fibonacci superlattice.

An optical Fibonacci superlattice has been proposed to produce the second-harmonic generation and the third-harmonic generation, which is the sum frequency of the second-harmonic and the fundamental frequency in the same material. Because of the quasiperiodicity of the optical Fibonacci superlattice, the phase mismatches of the optical parametric processes caused by the frequency dispersion of the refractive index can be compensated with the reciprocal vectors which the optical Fibonacci superlattice provides. A theory which analyzes the second-harmonic generation and the third-harmonic generation processes in the material and the calculations applied to the optical Fibonacci superlattice made from a single ${\mathrm{LiNbO}}_{3}$ crystal is presented in detail. The calculations show that the efficiencies of the second-harmonic generation and the third-harmonic generation are comparable to, or even larger than, those obtained with commonly used phase-matching methods.

Theory of millimeter wave nonlinearities in semiconductor superlattices

A study of the impact of semiconductor superlattices on millimeter wave nonlinearities is reported. χ(3) as large as 10−2 esu can be achieved by using 250 GHz radiation. Self-induced transparency is also predicted, and its competition with the third-harmonic generation process is quantified.

Third-harmonic generation and ionisation processes in Kr

Third-harmonic generation and multiphoton ionisation were simultaneously monitored at several pressures in Kr gas following excitation by a strongly focused dye laser, tunable over the range 338 to 350 nm. The results indicate that the multiphoton ionisation signals due to the nf' [ 1 2 ] autoionising series of Kr and the III ★ band of Kr 2 are strongly enhanced by the third-harmonic radiation in the vacuum ultraviolet.

Non-adiabatic effects in third-harmonic generation: A coupled-equations study for Cl 2

A coupled-equations approach is used to calculate four-photon transition amplitudes in a third-harmonic generation process for the Cl 2 molecule. It is shown that non-adiabatic interactions between Rydberg and valence states interfere with radiative interactions at high intensities ( I ⩾ 10 8 W cm 2 ), thus producing unusual intensity dependences in third-harmonic efficiencies.

Orientational and electronic contributions to the third-order susceptibilities of cryogenic liquids

Alternating current Kerr effect and third-harmonic generation (THG) are reported for the cryogenic liquids CO, O2, N2, and Ar pumped by CO2 TEA laser radiation. The THG experiments measure the hyperpolarizability, while the Kerr effect measurements probe the total nonresonant third-order susceptibility χ(3), arising from both molecular orientation and electronic hyperpolarizability. The THG process in liquid CO is dominated by a vibrational two-photon resonant contribution for the CO2 R(6) pump line at 9.35 μm. By studying the interference between the resonant and nonresonant contributions in liquid CO–O2 mixtures the hyperpolarizability of liquid O2 has been determined relative to the two-photon resonant χ(3) of liquid CO. These measurements give the first experimental confirmation for liquid media that the two-photon resonance contribution to polarized scattering consists of both narrow and broad linewidth components associated with, respectively, the isotropic and anisotropic Raman polarizabilities.