Analog methods of nonlinear vibration analysis

This thesis presents methods by which electrical analogies can be obtained for nonlinear systems. The accuracy of these methods is investigated and several specific types of nonlinear equations are studied in detail.

In Part I a general method is given for obtaining electrical analogs of nonlinear systems with one degree of freedom. Loop and node methods are compared and the stability of the loop analogy is briefly considered.

Parts II and III give a description of the equipment and a discussion of its accuracy. Comparisons are made between experimental and analytic solutions of linear systems.

Part IV is concerned with systems having a nonlinear restoring force. In particular, solutions of Duffing's equation are obtained, both by using the electrical analogy and also by approximate analytical methods.

Systems with nonlinear damping are considered in Part V. Two specific examples are chosen: (1) forced oscillations and (2) self-excited oscillations (van der Pol’s equation). Comparisons are made with approximate analytic solutions.

Part VI gives experimental data for a system obeying Mathieu's equation. Regions of stability are obtained. Examples of subharmonic, ultraharmonic, and ultrasubharmonic oscillat1ons are shown.

Spatiotemporal instabilities in nonlinear Kerr media in the presence of arbitrary higher-order dispersions

Spatiotemporal instabilities in nonlinear Kerr media with arbitrary higher-order dispersions are studied by use of standard linear-stability analysis. A generic expression for instability growth rate that unifies and expands on previous results for temporal, spatial, and spatiotemporal instabilities is obtained. It is shown that all odd-order dispersions contribute nothing to instability, whereas all even-order dispersions not only affect the conventional instability regions but may also lead to the appearance of new instability regions. The role of fourth-order dispersion in spatiotemporal instabilities is studied exemplificatively to demonstrate the generic results. Numerical simulations confirm the obtained analytic results. (C) 2002 Optical Society of America.

Quadratic nonlinear technologies for femtosecond lasers

Quadratic optical nonlinearity chi((2)) can be exploited in femtosecond lasers and regarded as a significant new degree of freedom for the design of short-pulse sources. We will review our recent progress on developing nonlinear quadratic technologies for femtosecond lasers. Our nonlinear laser technology offers new properties for femtosecond lasers, including optical parametric amplifier with novel working regime, efficient second harmonic generation, and time telescope.

Nonlinear response and optical limiting in SrBi2Ta2O9 thin films

SrBi2Ta2O9 (SBT) thin films on quartz substrates were prepared by use of the pulsed-laser deposition technique. The nonlinear refractive indices, n(2), Of the SBT films were measured by use of z-scan techniques with picosecond pulses. Large negative nonlinear refractive indices of 3.84 and 3.58 cm(2)/GW were obtained for the wavelengths 532 nm and 1.064 mum, respectively. The two-photon absorption coefficient was determined to be 7.3 cm/GW for 532 nm. The limiting behavior of SBT thin film on a quartz substrate was investigated in an f/5 defocusing geometry by use of 38-ps-duration, 532-nm, 1.064-mum. laser excitation. (C) 2001 Optical Society of America.

Super-resolution with a nonlinear thin film: Beam reshaping via internal multi-interference

In laser applications, the size of the focus spot can be reduced beyond the diffraction limit with a thin film of strong nonlinear optical Kerr effect. We present a concise theoretical simulation of the device. The origin of the super-resolution is found to be mainly from the reshaping effect due to the strongly nonlinear refraction mediated multi-interference inside the thin film. In addition, both diffraction and self-focusing effects have been explored and found negligible for highly refractive and ultrathin films in comparison with the reshaping effect. Finally, the theoretic model has been verified in experiments with single Ge2Sb2Te5 film and SiN/Si/SiN/Ge2Sb2Te2 multilayer structures. (c) 2006 American Institute of Physics.

Super-resolution scanning laser microscopy with a third-order optical nonlinear thin film

In a configuration of optical far-field scanning microscopy, super-resolution achieved by inserting a third-order optical nonlinear thin film is demonstrated and analyzed in terms of the frequency response function. Without the thin film the microscopy is diffraction limited; thus, subwavelength features cannot be resolved. With the nonlinear thin film inserted, the resolution is dramatically improved and thus the microscopy resolves features significantly smaller than the smallest spacing allowed by the diffraction limit. A theoretical model is established and the device is analyzed for the frequency response function. The results show that the frequency response function exceeds the cutoff spatial frequency of the microscopy defined by the laser wavelength and the numerical aperture of the convergent lens. The main contribution to the improvement of the cutoff spatial frequency is from the phase change induced by the complex transmission of the nonlinear thin film. Experimental results are presented and are shown to be consistent with the results of theoretical simulations.

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r) similar to E-2(r). For ultrathin films of thickness d << lambda the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region. (C) 2007 Published by Elsevier B.V.