Third-order nonlinearity of Er(3+)-doped lead phosphate glass

The third-order optical susceptibility and dispersion of the linear refractive index of Er(3+)-doped lead phosphate glass were measured in the wavelength range between 400 and 1940 nm by using the spectrally resolved femtosecond Maker fringes technique. The nonlinear refractive index obtained from the third-order susceptibility was found to be five times higher than that of silica, indicating that Er(3+)-doped lead phosphate glass is a potential candidate to be used as the base component for the fabrication of photonic devices. For comparison purposes, the Z-scan technique was also employed to obtain the values of the nonlinear refractive index of Er(3+)-doped lead phosphate glass at several wavelengths, and the values obtained using the two techniques agree to within 15%.

Nonresonant third-order nonlinearity of antimony glasses at telecom wavelengths

We report measurements of the nonresonant nonlinear refractive index n(2) in antimony glasses at telecom wavelengths. The measurements were performed using the Z-scan technique with a 130 fs pulsed laser operating at five wavelengths in the range of 1400-1600 nm. Values of n(2)approximate to 10(-15) cm(2)/W were measured and a negligible two-photon absorption coefficient (< 0.003 cm/GW) was estimated for all glasses compositions. The samples present a good figure of merit for ultrafast all-optical switching. (c) 2006 American Institute of Physics.

Near-infrared third-order nonlinearity of PbO-GeO(2) films containing Cu and Cu(2)O nanoparticles

We report measurements of the nonlinear (NL) refractive index n(2) of lead-germanium films (LGFs) containing Cu and Cu(2)O nanoparticles (NPs). The thermally managed eclipse Z-scan technique with 150 fs pulses from a laser operating at 800 nm was used. The NL refractive index measured, n(2)=6.3x10(-12) cm(2)/W has electronic origin and the NL absorption coefficient alpha(2) is smaller than 660 cm/GW. The figure of merit n(2)/lambda alpha(2) is enhanced by more than two orders of magnitude in comparison with the result for the LGFs without the copper based NPs. (C) 2008 American Institute of Physics.

Tellurium enhanced non-resonant third-order optical nonlinearity in a germano-silicate optical fiber

碲掺杂的高非线性石英光纤

Third order intermodulation products generated on transmission through a nonlinear radio-on-fibre link

Two-tone intermodulation tests were simulated for an amplitude modulated radio-on-fibre link including fibre dispersion, nonlinearity and loss. The third-order intercept results are presented for varying fibre lengths and optical transmission powers.

Third-order intermodulation products generated on transmission through nonlinear radio-on-fibre link

Two-tone intermodulation tests were simulated for an amplitude modulated radio-on-fibre link including fibre dispersion, nonlinearity and loss. The third-order intercept results are presented for varying fibre lengths and optical transmission powers.

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Effect of third-order aberrations on dynamic accommodation

We investigate the potential for the third-order aberrations coma and trefoil to provide a signed cue to accommodation. It is first demonstrated theoretically (with some assumptions) that the point spread function is insensitive to the sign of spherical defocus in the presence of odd-order aberrations. In an experimental investigation, the accommodation response to a sinusoidal change in vergence (1–3 D, 0.2 Hz) of a monochromatic stimulus was obtained with a dynamic infrared optometer. Measurements were obtained in 10 young visually normal individuals with and without custom contact lenses that induced low and high values of r.m.s. trefoil (0.25, 1.03 μm) and coma (0.34, 0.94 μm). Despite variation between subjects, we did not find any statistically significant increase or decrease in the accommodative gain for low levels of trefoil and coma, although effects approached or reached significance for the high levels of trefoil and coma. Theoretical and experimental results indicate that the presence of Zernike third-order aberrations on the eye does not seem to play a crucial role in the dynamics of the accommodation response.

Third-order theory of spectacle lenses applied to correction of peripheral refractive errors

Purpose: To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Method: Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite ray-tracing. Results: The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes which are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, seems impossible in the majority of cases. Conclusion: The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.

Higher-Order Nonlinearity In Accretion Disks: Quasi-Periodic Oscillations Of Black Hole And Neutron Star Sources And Their Spin

We propose a unified model to explain Quasi-Periodic Oscillation (QPO), particularly of high frequency, observed from black hole and neutron star systems globally. We consider accreting systems to be damped harmonic oscillators exhibiting epicyclic oscillations with higher-order nonlinear resonance to explain QPO. The resonance is expected to be driven by the disturbance from the compact object at its spin frequency. The model explains various properties parallelly for both types of the compact object. It describes QPOs successfully for ten different compact sources. Based on this, we predict the spin frequency of the neutron star Sco X-1 and specific angular momentum of black holes GRO J1655–40, XTE J1550–564, H1743–322, and GRS 1915+105.

Ultrafast Switching Time and Third Order Nonlinear Coefficients of Microwave Treated Single Walled Carbon Nanotube Suspensions

Microwave treated water soluble and amide functionalized single walled carbon nanotubes have been investigated using femtosecond degenerate pump-probe and nonlinear transmission experiments. The time resolved differential transmission using 75 femtosecond pulse with the central wavelength of 790 nm shows a bi-exponential ultrafast photo-bleaching with time constants of 160 fs (130 fs) and 920 fs (300 fs) for water soluble (amide functionalized) nanotubes. Open and closed aperture z-scans show saturation absorption and positive (negative) nonlinear refraction for water soluble (amide functionalized) nanotubes. Two photon absorption coefficient, beta(0) similar to 250 cm/GW (650 cm/GW) and nonlinear index, gamma similar to 15 cm(2)/pW (-30 cm(2)/pW) are obtained from the theoretical fit in the saturation limit to the data for two types of nanotubes.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.