Tunable four-wave mixing in low-mode-number optical fibers

Partially degenerate four-wave mixing for different pump wavelengths in step-index optical silica fibers with low mode numbers is considered. The frequency shifts that correspond to the phase match and the overlap integrals are calculated for a tunable pump. It is shown that when the interacting waves propagate in some combinations of the modes LP(01) and LP(11), four-wave mixing is possible for tunable pump wavelengths in the region from 0.4 to 0.9 μm, far from the minimum of the material dispersion.     

All-optical switch based on two-pump four-wave mixing in fibers without a frequency shift

We report an all-optical switch based on two-pump four-wave mixing in fibers. The switched signal is not shifted in frequency in this scheme. For different signal wavelengths, the pump wavelengths and powers can be optimized to achieve the best performance. The principle of how to design the switch is discussed in detail. A high extinction ratio of -60 dB is obtained when the pump parameters are optimized by a genetic algorithm that exhibits good convergence property and high computing efficiency. The effect of zero-dispersion wavelength fluctuations along the fiber on the switch is analyzed.     

Polarization mode coupling in circularly birefringent gratings

Polarization mode coupling in circularly birefringent gratings is analyzed. It is numerically found that efficient LP01x-LP02y mode coupling (where LP is linear polarization) is possible in a 50-cm-long circularly birefringent fiber grating formed in a terbium-doped borosilicate glass fiber and that complete LP01x-LP02y and LP01x-LP03y mode couplings result after a few-centimeter-long circularly birefringent grating that is formed in a bismuth-substitute iron garnet waveguide. Various parameters of polarization mode coupling in a number of circularly birefringent gratings are also computed.     

Degenerate four-wave mixing with a tunable excimer laser

We use a simple, forward-geometry degenerate four-wave mixing setup to monitor weak absorptions of various gas-phase molecules with a tunable excimer laser. With this technique, state-selective detection of H(2), CO, H(2)O, and O(2) is demonstrated. The dependence of the forward-geometry degenerate four-wave mixing signals on various experimental parameters (e.g., pressure, laser power) is determined. Several mechanisms for the generation of the observed signals are discussed, including diffraction from density gratings or thermal gratings and two-photon degenerate four-wave mixing.     

Dispersion effects in elliptical-core highly birefringent fibers

Modal birefringence and its sensitivity to temperature and hydrostatic pressure were measured versus wavelength in three elliptical-core fibers and one fiber with stress-induced birefringence. We carried out the measurements in the spectral range from 633 to 843 nm by using interferometric methods. In fibers with elliptical cores all the measured parameters showed high chromatic dependence, whereas in fibers with stress-induced birefringence this dependence was weak. We modeled the dispersion characteristics of two elliptical-core fibers by using the modified perturbation approach first proposed by Kumar. The modification consists of introducing into the expression for the normalized propagation constants an additional perturbation term that contains information about stress-induced birefringence. The results of modeling show that the temperature and pressure sensitivity of elliptical-core fiber are associated primarily with variations in stress induced by these parameters. The agreement between measured and calculated values of sensitivity in the worst case was equal to 20% for modal birefringence and temperature sensitivity and 50% for pressure sensitivity. Lower agreement between measured and calculated values of pressure sensitivity is most probably associated with uncertainties in the material constants used in modeling.     

Characteristics of four-wave mixing in a Bose-condensed atomic gas

An analysis is made of four-wave mixing of laser radiation interacting with an ultracold degenerate ensemble of boson atoms trapped in a magnetic trap. It is shown that the existence of long-range order in this type of atomic system leads to a new mechanism for the generation of the reversed wave whose experimental manifestation should differ from four-wave mixing in a nondegenerate gas. A similar nonlinear optical effect may be used for diagnostics of an ultracold gas at temperatures not much lower than the phase transition temperature. Pis’ma Zh. Tekh. Fiz. 25, 61–64 (November 26, 1999)     

Wide-field, surface-sensitive four-wave mixing microscopy of nanostructures

We describe a wide-field four-wave mixing (FWM) microscope with imaging characteristics optimized for examining nanostructures. The microscope employs surface-plasmon polariton (SPP) excitation in a gold film to achieve surface-sensitive imaging conditions. The SPP surface fields boost the FWM efficiency by 2 orders of magnitude relative to the excitation efficiency of the evanescent fields at a bare glass surface. We demonstrate two excitation geometries that completely suppress the electronic FWM response of the metal film while allowing the far-field detection of FWM radiation from nanostructures at the interface. We obtained wide-field FWM images from individual carbon nanotubes and nanoclusters of neocyanine molecules at image acquisition times of 1 s, demonstrating the potential for background free, surface-enhanced FWM imaging of nanomaterials.     

Enhanced method for the reconstruction of zero-dispersion wavelength maps of optical fibers by measurement of continuous-wave four-wave mixing efficiency

The zero-dispersion wavelength map of an optical fiber can be obtained from measurement of end-to-end four-wave mixing efficiency at various wavelengths. A fast and unambiguous algorithm for reconstruction of the zero-dispersion wavelength map of an optical fiber by measurement of four-wave mixing efficiency is proposed. This method can produce high-resolution results in a few seconds. We also study the limitations of this technique that are due to polarization-mode dispersion (PMD). Simple practical rules to avoid the effects of PMD in such measurements are established.     

Polarization of almost-plane waves

The general polarization behavior of almost-plane waves, in which the electric field varies slowly over a circular pupil, is considered, on the basis of an axial Hertz potential treatment and expansion in Zernike polynomials. The resultant modes of a circular aperture are compared with the well-known waveguide (or optical fiber) modes and Gaussian beam modes. The wave can be decomposed into partial waves of electric and magnetic types. The modes for a square pupil are also considered. The particular application of the effect on polarization of focusing the waves is discussed. Another application discussed is the Fresnel reflection from a dielectric interface, it being shown that the Fresnel reflection alters the relative strength of the electric and magnetic components.     

Optical manipulation of multiple stable states in photorefractive four-wave mixing

Abstract

We propose an approach to manipulate the convergence in multiple solutions of phase conjugate reflectivity in photorefractive four-wave mixing. Although a method forcibly adding a π-phase shift to an incident beam has been already proposed to control the reflectivity, some restrictions have been required in the boundary conditions for the successful operation. Here, we control the reflectivity with the boundary conditions in which the phase shift operation is ineffective by itself. In our method, the phase shift operation is combined with the procedure of turning an incident beam on and off. With a numerical analysis of four-wave mixing, we show that our new approach brings drastic change in the spatial distribution of the index grating and leads the phase conjugate reflectivity which was not manipulated previously.     

Degenerate four-wave mixing in the copolymer of phenylacetylene and norbornene

The results of optical phase conjugation experiments in a degenerate four-wave mixing geometry are reported at 532 nm in a new block copolymer of phenylacetylene and norbornene. The copolymer sample with an equal number of repeating units for the two homopolymers prepared by sequential addition of the monomers gives a third-order susceptibility value which is twice that of the homopolymer of phenylacetylene.     

Birefringence measurement under hydrostatic pressure in twistedhighly birefringent fibers

A new method of birefringence measurement in highly birefringent fibers influenced by hydrostatic pressure conditions up to 100 MPa is presented. The birefringence measurement method is based on twist-induced effects and has never been applied before in a high-pressure environment. The experiments were conducted using a specially designed pressure facility, which made it possible to simultaneously generate several mechanical perturbations, including twist and hydrostatic stress, and to investigate their effects on mode transmission in optical fibers. The results indicate that in the case of HB single-mode bow-tie fibers, hydrostatic pressure up to 100 MPa increased birefringence with a mean coefficient of (1/ΔB₀ )(Δβ)/dp=0.2%/MPa which is in very close agreement with our previous measurement based on Rayleigh scattering     

Analysis of power-dependent phase-matched four-wave mixing in dispersion-managed transmission systems

We investigate power-dependent phase-matched four-wave mixing (FWM) in wavelength division multiplexing transmission lines, in which positive and negative dispersion fibers are alternately arranged to manage the dispersion and the dispersion slope. The FWM effect shows power-independent phase matching when the channel power is low. However, it is power dependent at high power. The maximum FWM conversion efficiency is shifted away from the zero channel space in the case of power-dependent phase matching. Optimization of the dispersion system for suppression of the FWM effect is determined.     

Experimental and theoretical investigations of birefringent holey fibers with a triple defect

We have manufactured and characterized a birefringent holey fiber of a new construction. The birefringence in this fiber is induced by the highly elliptical shape of the core, which consists of a triple defect in a hexagonal structure. Using a hybrid edge-nodal finite-element method, we calculated the spectral dependence of phase and group modal birefringence for spatial modes E11 and E21 in idealized and in real fiber, whose geometry we determined by using a scanning-electron microscope. Results of our calculations show that technological imperfections significantly affect the fiber's birefringence. Normalized cutoff wavelengths for higher-order modes relative to the filling factor were also determined for the idealized structure. We observed a significant disagreement between theoretical and experimental values of cutoff wavelengths, which was attributed to high confinement losses near the cutoff condition. We also measured the spectral dependence of the phase and the group modal birefringence for spatial modes E11 and E21. The measured parameters showed good agreement with the results of modeling.     

Optical negative refraction by four-wave mixing in thin metallic nanostructures

The law of refraction first derived by Snellius and later introduced as the Huygens-Fermat principle, states that the incidence and refracted angles of a light wave at the interface of two different materials are related to the ratio of the refractive indices in each medium. Whereas all natural materials have a positive refractive index and therefore exhibit refraction in the positive direction, artificially engineered negative index metamaterials have been shown capable of bending light waves negatively. Such a negative refractive index is the key to achieving a perfect lens that is capable of imaging well below the diffraction limit. However, negative index metamaterials are typically lossy, narrow band, and require complicated fabrication processes. Recently, an alternative approach to obtain negative refraction from a very thin nonlinear film has been proposed and experimentally demonstrated in the microwave region. However, such approaches use phase conjugation, which makes optical implementations difficult. Here, we report a simple but different scheme to demonstrate experimentally nonlinear negative refraction at optical frequencies using four-wave mixing in nanostructured metal films. The refractive index can be designed at will by simply tuning the wavelengths of the interacting waves, which could have potential impact on many important applications, such as superlens imaging.     

Thermal properties of highly birefringent optical fibers and preforms

Temperature cycling of highly birefringent optical fibers and preforms has been used to investigate the thermal properties of bow-tie and elliptically clad structures. The thermal hysteresis of the birefringence is shown to be a direct consequence of the thermal history of the fiber or preform and has been related to volume changes in the stress-producing borosilicate sections. Annealing increases the axial stress as well as the stress anisotropy and hence the birefringence. Increases of up to a factor of 2 in the birefringence on suitable thermal treatment indicate a new method for further improvement of high birefringence fibers. The implications of the results in the design, fabrication, and use of such fibers are discussed.     

Temperature measurement by degenerate four-wave mixing with strong absorption of the excitation beams

We have made simultaneous temperature measurements by degenerate four-wave mixing (DFWM) and absorption spectroscopy of OH in a CH(4)-air, lifted-diffusion flame. After we corrected the DFWM data for laser beam absorption of as much as 60%, the DFWM-based temperatures were in good agreement with temperatures derived strictly from the absorption data, as well as a one-dimensional reacting flow simulation.     

Temperature-hydrostatic pressure cross-sensitivity effect in elliptical-core, highly birefringent fibers

We determine the cross-sensitivity coefficient that represents the interaction between temperature and hydrostatic pressure in Corning elliptical-core, highly birefringent (HB) fiber. The measurement method we propose is especially useful to determine the cross-sensitivity effects in weakly sensitive HB fibers. The method involves registration of the residual temperature drift of thermally compensated polarimetric sensors at specially chosen values of pressure applied to the sensing fibers.