Waveguide modes of hollow photonic-crystal fibers

Waveguide modes of microstructure fibers with a hollow core and a two-dimensionally periodic cladding are studied experimentally and theoretically. The spectrum of modes guided in the hollow core of these fibers displays isolated maxima, indicating that waveguiding is supported due to the high reflectivity of the fiber cladding within photonic band gaps. The main properties of the spectrum of modes guided in a hollow core of a photonic-crystal fiber and radiation intensity distribution in these modes are qualitatively explained in terms of the model of a periodic coaxial waveguide.     

Four-wave mixing of picosecond pulses in hollow fibers: expanding the possibilities of gas-phase analysis

Third-harmonic, difference-frequency, and sum-frequency generation processes in hollow fibers are experimentally studied with 30-ps pulses having an energy of several millijoules. The experimental dependence of the difference-frequency signal on the pressure of the gas filling the fiber agrees well with the results of calculations when the contribution of higher order waveguide modes is taken into consideration, thus indicating the importance of nonlinear-optical processes involving higher order waveguide modes of a hollow fiber. Hollow fibers are also shown to expand the possibilities of nonlinear-optical analysis of gases by allowing the generation of third-harmonic and sum-frequency signals, which vanish in the regime of tight focusing in a medium with normal dispersion. Received: 26 September 2000 / Revised version: 15 January 2001 / Published online: 30 March 2001     

Modes of capillary photonic-crystal fibers with hollow core

A rigorous method of integral equations has been used to calculate the dispersion characteristics, fields, and radiation patterns of the leaky modes of photonic-crystal fibers with a shell in the form of a bounded 2D photonic crystal composed of parallel quartz capillaries contacting each other and a core in the form of a defect of a photonic crystal with one capillary removed. It is shown that, when thick-walled capillaries (with an air content in the shell of about 28%) are used, these fibers can be single mode and have an overlap integral of the fundamental-mode field with the dielectric medium that is smaller by a factor of more than two (in comparison with similar fibers formed by air channels of circular cross section). The significant dispersion of the group velocity of the fundamental modes of fibers near the edge of the photonic crystal band gap has been found.     

Raman-resonance-enhanced composite nonlinearity of air-guided modes in hollow photonic-crystal fibers

Coherent anti-Stokes Raman scattering (CARS) is used to measure relations between the resonant (Raman) and nonresonant (Kerr-type) optical nonlinearities of air-guided modes in a hollow-core photonic-crystal fiber (PCF). We demonstrate that, due to its interference nature, CARS provides a convenient tool for measuring the contribution of the fiber cladding to the total nonlinearity sensed by air-guided modes in hollow PCFs. On a Raman resonance with molecular vibrations in the gas that fills the fiber core, a two-color laser field is shown to induce optical nonlinearities that are several orders of magnitude higher than the nonresonant Kerr-type nonlinearities typical of air-guided PCF modes.     

Four-wave mixing of picosecond pulses in hollow fibers: Phase matching and the influence of high-order waveguide modes

The processes of third-harmonic and difference-frequency generation through the four-wave mixing of picosecond pulses in gas-filled hollow fibers are experimentally studied. Due to the improvement of phase-matching conditions with an appropriate choice of the gas pressure and optimal parameters of the hollow fiber, we were able to use hollow fibers with a large length (up to 30 cm) for difference-frequency generation, which resulted in a considerable increase in the power of the difference-frequency signal at the output of the fiber. Our experimental data reveal a considerable influence of high-order waveguide modes on four-wave mixing processes in a hollow fiber. It is shown that the waveguide regime of nonlinear optical interactions implemented in hollow fibers removes the limitations on the efficiency of third-harmonic and sum-frequency generation, which are characteristic of the tight-focusing regime in media with normal dispersion and which are due to the geometric phase shift arising in tightly focused light beams.     

Four-wave mixing with large stokes shifts in heavily Ge-doped silica fibers

Four-wave mixing (FWM) in nonlinear germanosilicate fibers with GeO2 concentrations as high as 67 mol.% in the core is studied theoretically and experimentally. Large frequency shifts of 1875-3829 cm(-1) are observed in the mixed-mode pump parametric process. The dependence of FWM phase matching on the GeO2 concentration, core diameter, and index profile is demonstrated. The 2.5% conversion efficiency of an 887 nm signal to a 1.3 microm communication band is obtained at a 2 W cw pump power inside the fiber.     

Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion

We derive phase-matching conditions for four-wave mixing between solitons and linear waves in optical fibers with arbitrary dispersion and demonstrate resonant excitation of new spectral components via this process.     

Four-wave mixing in microstructure fiber

We report what we believe to be the first experimental demonstration of nondegenerate four-wave mixing in a microstructure fiber. The effect of the chi((3)) nonlinearity is enhanced in such a fiber because of the small core area, and we achieve phase matching by operating near the zero-dispersion wavelength (?750 nm) . We have observed parametric gains of more than 13 dB in 6.1-m-long fiber with a pump peak power of only 6 W. We compare our experimental gain results with those predicted by theory and explore the effects of Raman shift and (or) amplification and cascaded nonlinear mixing.     

砷化镓晶体中的四波混频

本文报道了以1.06μm调QNd:YAG激光脉冲,采用简并四波混频的方法,在未掺杂的GaAs单晶中产生红外位相共轭短脉冲。研究了该光脉冲的主要特性。用实验的方法探讨了影响共轭光强弱的主要因素。     

Four-wave mixing based 10-Gb/s tunable wavelength conversion in dispersion-flattened microstructure fibers

All-optical wavelength conversion of 10-Gb/s signal based on four-wave mixing is experimentally demonstrated in a 30-m-long dispersion-flattened microstructure fiber with small positive dispersion. For an average pump power of 26 dBm, the conversion efficiency was around -19.5 dB with the fluctuation less than ±1.4 dB, covering a conversion bandwidth of 20 nm. The eye diagram of the converted signal shows good eye opening.     

Phase-matched four-wave mixing of isolated waveguide modes of high-intensity femtosecond pulses in a hollow photonic-crystal fiber

Hollow-core photonic-crystal fibers with a special dispersion profile are shown to allow phase-matched nonlinear optical interactions of isolated air-guided modes of high-intensity femtosecond laser pulses confined in the hollow fiber core. We present theoretical and experimental studies of the four-wave mixing of fundamental and second-harmonic pulses of a Cr:forsterite laser with an initial pulse duration of about 50 fs and an intensity on the order of 10¹⁴ W/cm² in waveguide modes of a hollow photonic-crystal fiber with a core diameter of about 13μm.     

Four-wave mixing in non-step-index optical fibers: a sensitive technique for measurement of refractive-index profiles

Investigation of four-wave mixing 6.4-mum core-diameter fiber with 520-610-nm pump light is used to develop a new technique for characterizing the refractive-index profiles of non-step-index fibers. Deviation from the step-index profile is measured. Small variations in the refractive index between different segments of the same commercial fiber is measured with a sensitivity of 0.0001.     

Higher-order modes of photonic-crystal fibers

The propagation constants and the field distribution of the higher-order modes in photonic-crystal fibers have been studied. It is shown that the standard single-mode operation condition of a fiber, in which the first higher-order mode is cut-off, is not applicable to photonic-crystal fibers because the latter can guide higher-order eigenmodes, even when this condition is fulfilled.     

Four-wave mixing in long wavelength III-nitride QD-SOAs

Four wave mixing analysis is stated for quantum dot semiconductor optical amplifiers (QD SOAs) using the propagation equations (including nonlinear propagation contribution) coupled with the QD rate equations under the saturation assumption. Long wavelength III-nitride InN and AIInN QD SOAs are simulated. Asymmetric behavior due to linewidth enhancement factor is assigned. P-doping increases efficiency. Lossless efficiency for InAlN QDs for longer radii is obtained. Carrier heating is shown to have a considerable effect and a detuning dependence is expected at most cases. InN QD SOAs shown to have higher efficiency.     

Integral equations for photonic-crystal fibers

The integral and integro-differential equations for photonic-crystal waveguides (fibers) with both infinite and finite quasi-periodic dielectric coatings have been obtained, with previous consideration of the equations for 2D periodic photonic crystals with magnetodielectric and metallic inclusions. The corresponding numerical results are presented.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

Four-wave mixing in coupled semiconductor quantum dots

We present a theoretical analysis of four-wave mixing in coupled quantum dots subject to inhomogeneous broadening. For the biexciton transitions, a clear signature of interdot-coupling appears in the spectra. The possibility of experimental observation is discussed.     

Four-wave mixing and six-wave mixing in a four-level confined atomic system

We have investigated coexisting four-wave mixing and six-wave mixing (SWM) in ultra-thin, micrometre and long vapour cells. There exists competition between Dicke-narrowing features and polarization interference in the micrometre cell. The oscillation behaviour of SWM signal intensities and linewidths results from destructive interference. With a larger destructive interference, the SWM signal in ultra-thin cells shows a narrow spectrum, in contrast to the long cell case. Due to the Dicke-narrowing features, a narrow spectrum can be obtained, and such spectra can be used for high precision measurements and metrological standards.     

Enhanced four-wave mixing in a hollow-core photonic-crystal fiber

Hollow-core photonic-crystal fibers are shown to substantially enhance four-wave mixing (FWM) of laser pulses in a gas filling the fiber core. Picosecond pulses of Nd:YAG fundamental radiation and its second harmonic are used to generate a signal at the frequency of the third harmonic by the FWM process 3omega = 2omega + 2omega - omega. The efficiency achieved for this process in a 9-cm-long, 13-microm-hollow-core-diameter photonic-crystal fiber, designed to simultaneously transmit a two-color pump and the FWM signal, is shown to be approximately 800 times higher than the maximum FWM efficiency attainable with the same laser pulses in the tight-focusing regime.     

Four-wave mixing of optical and microwave fields

We demonstrate degenerate four-wave mixing involving both optical and microwave fields. This four-wave mixing process, with fields that differ in frequency by 5 orders of magnitude, results from stimulated Raman scattering of the optical field from an atomic ground-state Zeeman coherence in warm rubidium vapor, which is induced and maintained by the microwave field.