Modification of solitary waves by third-harmonic generation

The effect of phase-matched third-harmonic generation on the structure and stability of spatial solitary waves is investigated. A power threshold for the existence of two-frequency spatial solitons is found, and the multistability of solitary waves in a Kerr medium owing to a higher-order nonlinear phase shift caused by cascaded third-order processes is revealed.     

Chirp control in third-harmonic generation due to cross-phase modulation

Received: 16 October 1997/Revised version: 16 January 1998     

Quantum dynamics of formation of an unstable field state in the process of intracavity third-harmonic generation

The dynamics of the Wigner functions and quantum entropy of the fundamental and third-harmonic modes is studied for the process of intracavity third-harmonic generation. It is shown that quantum dynamics of the system strongly depends on the coupling coefficient of the interacting modes. The dynamics of the transition of the system from a stable to an unstable state is investigated.     

Depth-resolved multiphoton polarization microscopy by third-harmonic generation

We achieve depth-resolved polarization microscopy by measuring third-harmonic generation induced by a tightly focused circularly polarized beam. In crystals exhibiting strong birefringence this signal is dominated by positively phase-matched third-harmonic generation. This process occurs in only optically anisotropic media, in which the birefringence compensates for the phase mismatch between the fundamental and the third harmonic induced by dispersion. Both the intensity and the polarization of the emitted signal provide information on the local optical anisotropy. We demonstrate the technique by imaging biogenic crystals in sea urchin larval spicules.     

Imaging Caenorhabditis elegans embryogenesis by third-harmonic generation microscopy

In this study, third-harmonic generation (THG) imaging measurements were performed to characterize different developmental stages of the nematode Caenorhabditis elegans (C. elegans) embryos. Femtosecond laser pulses (1028 nm) were utilized for excitation. THG image contrast modality proved as a powerful diagnostic tool, providing valuable information and offering new insights into the complex developmental process of C. elegans embryogenesis.     

Far-field distribution of third-harmonic generation by two crossed beams

The far-field intensity distribution of the third harmonic generated in a thin silica plate by two laser beams crossed at a small angle comprises four peaks approximately symmetric with respect to the bisector. The measurement of the intensity ratio of the inner to the outer peaks yielded values scattered from 10 to 20, surprisingly larger than the combinatorial value 9. The phase-matching factor, as determined by the full three-dimensional calculations required by the absence of axial symmetry, accounts for the observed ratio and its fluctuations. Received: 14 November 2002 / Published online: 22 May 2003 RID="*" ID="*"Corresponding author. Fax: +7-95/1941-994, E-mail: fomichev@imp.kiae.ru     

Inverse problem of cascaded third-harmonic generation

Based on some numerical techniques such as split-step Fourier transformation, fourth-order Runge-Kutta and successive iteration method, the fundamental field was calculated from the known third-harmonic (TH) field in the process of TH generation (THG) using one doubling and one mixing KDP crystals. The effects of the monochromatic initial fields on the iteration numbers and the calculation precision were discussed. The inverse solution of the broadband laser pulse with linear frequency chirp was also carried out. The results show that the method proposed in this paper is available and efficient, which gives a new way to design and optimize the process of THG.     

Temporal characterization of short-pulse third-harmonic generation in an atomic gas by a transmission-grating Michelson interferometer

By use of a transmission-grating-based Michelson interferometer, second-order interferometric as well as intensity autocorrelation traces of the third harmonic of a Ti:sapphire 50-fs laser beam produced in Ar have been measured. The duration of the harmonic is found to be that expected from lowest-order perturbation theory. At this wavelength, the performance of the interferometer with respect to pulse-front distortion and dispersion is found to be satisfactory. This result is a first step toward the use of the interferometer for the temporal characterization of higher harmonics or harmonic superposition forming attosecond pulse trains.     

Measurement of third-order nonlinear susceptibilities by non-phase matched third-harmonic generation

The third-order susceptibilities χ _xxxx ⁽³⁾ (?ω₃;ω₁,ω₁,ω₁) of some liquids, solids and air are determined by third-harmonic generation. The samples are placed behind the focal region of a laser beam in an evacuated environment to avoid third-harmonic generation of the surroundings. For fluid media the sample cell is made out of two thin fused quartz plates and oriented to an angle of zero net third-harmonic production in each window (minimum Maker fringe position).     

Laser frequency stabilization by means of optical self-heterodyne beat-frequency control

We propose and demonstrate a novel frequency-stabilization scheme that provides linewidth narrowing and at the same time is compatible with high-speed frequency agility. The method relies on sensing and control of a heterodyne beat signal derived from a fiber interferometer and functions in the absence of a fixed reference frequency. Our demonstration utilizes a short-external-cavity diode laser equipped with an intracavity electro-optic crystal for frequency correction. The stabilization method is shown to suppress impressed laser frequency modulation by nearly 2 orders of magnitude. Without further modification of our scheme we also demonstrate laser frequency tuning control.     

Third-order nonlinear susceptibilities of dye solutions determined by third-harmonic generation

The third-order nonlinear susceptibilities _xxx ⁽³⁾ (–₃; ₁, ₁, ₁) versus concentration are determined for rhodamine 6G, fuchsin, and methylene blue in methanol. Third-harmonic generation of a modelocked Nd-glass laser is applied. The real and imaginary part of the nonlinear susceptibility are measured. A resonance enhancement due to absorption bands is observed.     

Continuum generation of the third-harmonic pulse generated by an intense femtosecond IR laser pulse in air

The continuum generation by intense femtosecond IR laser pulses focused in air including the effect of third-harmonic generation is investigated. We have used a theoretical model that includes the full spatio-temporal dynamics of both the fundamental and the third-harmonic pulses. Results of our numerical calculations show that a two-color filamentation effect occurs, in which the third-harmonic conversion efficiency remains almost constant over the whole filament length. It is found that this effect is rather independent of the wavelength of the input beam and the focal geometry. During the filamentation process the third-harmonic pulse itself generates a broad continuum, which can even overlap with the continuum of the fundamental pulse for the longer pump wavelengths. In consequence, the continuum generation generated by intense IR laser pulses is further extended into the UV. PACS 42.65.Jx; 42.65.Ky; 52.35.Mw     

Semi-classical theory of two-photon resonant third-harmonic generation

A semi-classical density matrix theory based on the Method of Averages is used to derive an expression for the third-harmonic generation intensity I^3ω as a function of the fundamental intensity I^ω in the neighbourhood of a two-photon resonance. The result takes account of optical Stark shifts, two-photon saturation and both homogeneous and inhomogeneous broadening. At high intensities, I^3ω∝I^ω, in contrast to the case where optical Stark shifts are ignored for which I^3ω∝(I^ω)^-1.     

Spectral modulation of third-harmonic generation by molecular alignment and preformed plasma

We demonstrate spectral modulation of third-harmonic generation from molecular alignment effects. The third harmonic spectrum is broadened or narrowed under different influences of cross-phase modulations originating from various molecular alignment revivals. Furthermore, the spectrum and spatial distribution of the generated third harmonic pulse change dramatically in the presence of a preformed plasma. Under the influence of a preformed plasma, a narrower third harmonic spectrum is observed, and the conical third-harmonic pulse increases while the axial part decreases. The investigation provides an effective method to modulate the spectral characteristic and spatial distribution of third-harmonic generation from intense femtosecond filament.     

Second-and third-harmonic generation by carbon nanotubes irradiated with femtosecond laser pulses

Femtosecond pulses of a Cr:forsterite laser are used to study second-and third-harmonic generation in a layer of single-wall carbon nanotubes produced by low-velocity spraying. The harmonic amplitude in our experiments scales as (I _p)ⁿ as a function of the pump intensity I _p, with n=2 and 3 for the second and third harmonics, respectively. This scaling law holds up to pump intensities on the order of 10¹²W/cm². The ratio of the maximum signal to the averaged background in the spectra of the second and third harmonics is estimated as 50 and 30, respectively. The second and third harmonics produced by a linearly polarized pump field are also linearly polarized, with their polarization vectors oriented along the polarization direction of the pump field. The capabilities of nonlinear-optical methods for structural and morphological analysis of carbon nanotubes are discussed, as well as ways to create solid-state carbon-nanotube generators of optical harmonic.     

Characterization of third-harmonic generation from femtosecond laser-excited silicon

Third-harmonic generation (THG) from silicon crystals excited by femtosecond pulses has been studied. THG as a function of probe pulse delay from linear and circularly polarized probe pulses was examined. Both polarizations exhibit a fast, 300 fs drop in THG when the Si is pumped by pulses with fluence above the melting threshold. This drop for both polarizations indicates that electronic effects dominate THG in laser-melted Si since structural effects should principally influence THG from linearly polarized probes, suggesting that care needs to be exercised in interpreting THG signal as an ultrafast probe of crystalline structure in semiconductors.     

Atom-density distribution in a metal vapor cell studied by third-harmonic generation

The density distribution of Cs atoms in a metal-vapor cell designed for nonlinear optical and spectroscopic measurements has been investigated by the THG technique. For high heater powers the desnity-distribution function was found to display a dip in the central part of the cell. Explanation of the phenomenon and criteria to eliminate it are proposed.     

Enhancement of third-harmonic generation in nonlocal spatial solitons

We report on the observation of Type I third-harmonic generation induced by a train of femtosecond laser pulses in nematic liquid crystals. We find that as the average power of the train is increased, the frequency conversion process is enhanced as a consequence of the tight confinement of the pulses into a nonlocal spatial soliton.     

Efficient generation of Bessel beam arrays by means of an SLM

We use a Spatial Light Modulator (SLM) to produce arrays of Bessel beams by using multiple axicon phase-masks on the SLM. This approach utilises the whole of the SLM, rather than just a thin annular region (which is the case if the SLM is in the far-field of the generated Bessel beams). Using the whole SLM rather than just an annular region means that the required intensity on the SLM is an order of magnitude lower for a given power in the Bessel beams. Spreading the power over the whole SLM is important for high-power applications such as laser micromachining. We allow the axicons to overlap and interfere in the hologram, so the axial length of the Bessel beam core is maintained as we add more beams to the array.     

Dramatic enhancement of third-harmonic generation in three-dimensional photonic crystals

We have observed a dramatic enhancement of third-harmonic generation in 3D polystyrene-air photonic crystals pumped by a near infrared laser beam. As the pump wavelength is tuned, the peak of the enhancement occurs when the third-harmonic wavelength approaches the short-wavelength edge of the band gap. We show that the origin of the enhancement is phase matching provided by the periodic structure of the photonic crystals.