An understanding of the generation of higher harmonics in Lamb waves is of critical importance for applications such as remaining life prediction of plate-like structural components. The objective of this work is to use nonlinear Lamb waves to experimentally investigate inherent material nonlinearities in aluminum plates. These nonlinearities, e.g. lattice anharmonicities, precipitates or vacancies, cause higher harmonics to form in propagating Lamb waves. The amplitudes of the higher harmonics increase with increasing propagation distance due to the accumulation of nonlinearity while the Lamb wave travels along its path. Special focus is laid on the second harmonic, and a relative nonlinearity parameter is defined as a function of the fundamental and second harmonic amplitude. The experimental setup uses an ultrasonic transducer and a wedge for the Lamb wave generation and laser interferometry for detection. The experimentally measured Lamb wave signals are processed with a short-time Fourier transformation (STFT) and a chirplet transformation-based algorithm, which yield the amplitudes of the frequency spectrum as functions of time, allowing the observation of the nonlinear behavior of the material. The increase of the relative nonlinearity parameter with propagation distance as an indicator of cumulative second harmonic generation is shown in the results for two different aluminum alloys. The difference in inherent nonlinearity between both alloys as determined from longitudinal wave measurements can be observed for the Lamb wave measurements, too.

An FM transmitter becomes the new feature in recent portable electronic development. A low power, integrable FM transmitter filter IC is required to meet the demand of FM transmitting feature. A low pass filter using harmonic rejection technique along with a low power class-AB output buffer is designed to meet the current market requirements on the FM transmitter chip. A harmonic rejection filter is designed to filter FM square wave signal from 70MHz to 110MHz into FM sine wave signal. Based on Fourier series, the harmonic rejection technique adds the phase shifted square waves to achieve better THD and less high frequency harmonics. The phase shifting is realized through a frequency divider, and the summation is implemented through a current summation circuit. A RC low pass filter with automatic tuning is designed to further attenuate unwanted harmonics. In this work, the filter's post layout simulation shows -53dB THD and harmonics above 800MHz attenuation of -99dB. The power consumption of the filter is less than 0.7mW. Output buffer stage is implemented through a resistor degenerated transconductor and a class-AB amplifier. Feedforward frequency compensation is applied to compensate the output class-AB stage, which extends the amplifier's operating bandwidth. A fully balanced class-AB driver is proposed to unleash the driving capability of common source output transistors. The output buffer reaches -43dB THD at 110MHz with 0.63Vpp output swing and drives 1mW into 50 load. The power consumption of the output buffer is 7.25mW. By using harmonic rejection technique, this work realizes the 70MHz-110MHz FM carrier filtering using TSMC 0.18um nominal process. Above 800MHz harmonics are attenuated to below -95dB. With 1.2V supply, the total power consumption including output buffer is 7.95mW. The total die area is 0.946mm2.

In many mathematical problems, we are expected to compare the interesting quantities. Thus, the use of well-known inequalities will be required. Techniques of using these inequalities to solve inequality problems vary from problem to problem. In this paper, we will introduce commonly used well-known inequalities in high school mathematical contests and discuss the solving strategies for inequality problems.

Lithium niobate (LiNbO3) and Lithium tantalate (LiTaO3) are high-performance nonlinear optical materials that have been popularly used in electro-optical modulation and nonlinear optics. Second-harmonic generation (SHG) microscope is applied to get SH images, as compared to etching method. SH image method has the advantage of faster and non-invasive inspection. Our system can rapid and non-destructive mapping of the detailed features of the crystal fibers in three dimensions. By simulation, we can explain that in the interface of +Z and ¡VZ domain, because the Li ions can stay in positive and negative two stable energy valleys. It may induce stronger SH intensity by QPM than +Z and -Z domain.

Optical second harmonic generation (SHG) is a nonlinear process that converts two photons of frequency w to a single photon of frequency 2w. In the electricdipole approximation, this process requires a noncentrosymmetric medium. For thin films present at the interface between two centrosymmetric media¡Ðsuch as the interface between two liquids, the interface between a liquid and air, or for the surface of a variety of insulators and semiconductors¡Ðonly the molecules which participate in the asymmetry of the interface contribute to the SHG. Surface SGH from molecules which exhibit a large nonlinear optical response at a specific wavelength can be used to measure the relative surface coverage of molecules at the interface as a function of the external electrochemical parameters. The polarization dependence of the surface SHG can be used to estimate the average molecular orientation of chromophores at the liquid/liquid electrochemical interface. The potential dependence of the SHG from the interface provides important information on the position of the adsorbed chromophores with respect to the interface.

Modern satellite, wireless communications, and radar systems often demand wideband performance for multi-channel and multi-function operations. Among these applications, phased array antennas play an important role. This dissertation covers two wideband phased array antennas, one produces linear polarization and one produces circular polarization. The main difference between these two phased array antennas is the antenna array. For the linearly polarized array, a wideband microstrip line to slotline transition is used to feed a Vivaldi antenna. For the circularly polarized array, a wideband microstrip line to parallel stripline transition is used to feed a spiral antenna. From 3 to 12 GHz, the linearly polarized beam is steered over ± 15º. Since the electromagnetic spectrum is limited and has to be shared, interference is getting serious as more and more wireless applications emerge. Filters are key components to prevent harmonic interference. The harmonic signals can be suppressed by cascading additional lowpass filters or bandstop filters. A bandstop filter combining shunt open stubs and a spurline is proposed for a compact size and a deeper rejection. Two lowpass filters with interdigital capacitors and slotted ground structures are also studied. Harmonic suppression can also be achieved with the modification of bandpass filters. Three conventional bandpass filters with spurious passbands are investigated. The first one is a dual-mode patch bandpass filter. The second passband of the proposed filter is at 2.88fo, where fo is the fundametal frequency. The second filter is an open-loop bandpass filter. Two open stubs are added to achieve high suppression in the second harmonic signal. The suppression of 35 dB at the second harmonic is obtained. For the third filter using half-wavelength open stubs, a T-shaped line is used to replace the quarter-wavelength connecting line. The T-shaped line has the same response with the connecting line in the passband. Furthermore, the T-shaped line works as a bandstop filter at the second harmonic. Finally, a new compact slow-wave resonator and bandpass filters are presented. A simple transmission-line model is used to predict the resonant frequency. Compared with the conventional uniform half-wavelength resonator, the slow-wave resonator shows a 25% size reduction.

Silicon nanocrystals (NCs), especially Si NCs embedded in SiO₂, have been studied intensely for decades for their potential application in silicon photonics, especially as efficient room temperature light emitters. Despite progress in fabricating photonic devices from Si NCs, the origin of the efficient photoluminescence (PL), the electronic and microscopic structure of the nanocrystals, and the structure of the elusive NC/SiO₂ interfaces for the oxide-embedded nanocrystals, remain controversial. Optical spectroscopy provides a powerful noninvasive tool for probing the structure of the Si NCs, including the active buried NC/SiO₂ interfaces of embedded particles. In this thesis work, oxide-embedded and free-standing alkyl-passivated silicon nanocrystals, prepared by different techniques, have been studied by linear and nonlinear optical spectroscopies. Cross-polarized 2-beam second-harmonic and sum-frequency generation (XP2-SHG/SFG) has been applied spectroscopically to study oxide embedded Si NCs of different sizes (3 to 5 nm diameter) and interface chemistries. The SHG/SFG spectra of silicon nanocrystals (Si NCs) prepared by implanting Si ions uniformly into silica substrates, then annealing, are compared and contrasted to their spectroscopic ellipsometric (SE) and photoluminescence excitation (PLE) spectra. Three resonances--two close in energy to E₁ (3.4 eV) and E2 (4.27 eV) critical-point resonances of crystalline silicon (c-Si), and a broad resonance intermediate in energy between E₁ and E₂--are observed in all three types of spectra. These features are observed in conjunction with a sharp 520 cm⁻¹ Raman peak characteristic of c-Si and an a-Si tail in the Raman spectra. The appearance of bulk-like CP resonances in the parallel PLE, SE and SHG/SFG spectra from Si NCs suggests the basic electronic structure of the bulk c-Si is preserved in nano-particles as small as 3 nm in diameter, albeit with significant size-dependent modification. At the same time, the prominence of a non-bulk-like resonance intermediate in energy between E₁ and E₂ CPs in all three types of spectra demonstrates the important contribution of nano-interfaces to the electronic structure.We also applied Raman spectroscopy to study oxide-embedded and oxide-free alkyl-passivated Si NCs with diameters ranging from 3 nm to greater than 10 nm synthesized by thermal decomposition of hydrogen silsesquioxane (HSQ). While oxide matrix complicates the size-dependence of the Raman peak shift for oxide-embedded nanocrystals, the Raman peak of the free-standing alkyl-passivated Si NCs shifts monotonically with NC size. / text

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