Tuning and stability of a singly resonant continuous-wave optical parametric oscillator close to degeneracy

Wavelength tuning and stability characteristics of a singly resonant continuous-wave optical parametric oscillator (cw OPO) in the proximity of signal-idler degeneracy have been studied. The OPO is made singly resonant by using a Bragg grating as a spectral filter in the OPO cavity. The signal-idler frequency difference can be tuned from 0.5 to 7 THz, which makes the OPO suitable for cw THz generation by optical heterodyning. The operation of the OPO within this singly-resonant regime is characterized by a strong self-stabilization effect. A gradual transition to an unstable, doubly-resonant regime is observed for a signal-idler detuning smaller than ~ 0.5 THz.

Alfvén waves in inhomogeneous magnetic fields: An integrodifferential equation formulation

An integrodifferential formulation for the equation governing the Alfvén waves in inhomogeneous magnetic fields is shown to be similar to the polyvibrating equation of Mangeron. Exploiting this similarity, a time‐dependent solution for smooth initial conditions is constructed. The important feature of this solution is that it separates the parts giving the Alfvén wave oscillations of each layer of plasma and the interaction of these oscillations representing the phase mixing.

Q-Band beam wave-guide

Consideration is given to a 25-foot long Q-band (8 mm) confocal, zoned dielectric lens beam waveguide. Numerical expressions for the axial and radial fields are presented. The experimental set-up consisted of uniformly spaced zoned dielectric lenses, a transmitting horn and a receiving horn. It was found that: (1) the wave beam is reiterated when confocal, zoned dielectric lenses act as phase transformers in place of smooth surfaced transformers in beam waveguides; (2) the axial field is oscillatory near the source and the oscillation persists for about 25 cm from the source; (3) the oscillation disappears after one lens is used; (4) higher order modes with higher attenuation rates die out faster than fundamental modes; (5) phase transformers do not alter beam modes; (6) without any lens the beam cross-section broadens significantly in the Z-direction; (7) with one lens the beam exhibits the reiteration phenomenon; and (8) inserting a second lens on the axial and cross-sectional field distribution shows further the reiteration principle.

Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Radio wave heating of astrophysical plasmas

The coherent plasma process such as parametric decay instability (PDI) has been applied to a homogeneous and unmagnetized plasma. These instabilities cause anomalous absorption of strong electromagnetic radiation under specific conditions of energy and momentum conservation and thus cause anomalous heating of the plasma. The maximum plasma temperatures reached are functions of luminosity of the radio radiation and plasma parameters. We believe that these processes may be taking place in many astrophysical objects. Here, the conditions in the sources 3C 273, 3C 48 and Crab Nebula are shown to be conducive to the excitation of PDI. These processes also contribute towards the absorption of 21cm radiation

Analytical solution of the laminar mean flow wave equation in a lined or unlined two-dimensional rectangular duct

The prediction of the sound attenuation in lined ducts with sheared mean flow has been a topic of research for many years. This involves solving the sheared mean flow wave equation, satisfying the relevant boundary condition. As far as the authors' knowledge goes, this has always been done using numerical techniques. Here, an analytical solution is presented for the wave propagation in two-dimensional rectangular lined ducts with laminar mean flow. The effect of laminar mean flow is studied for both the downstream and the upstream wave propagation. The attenuation values predicted for the laminar mean flow case are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.

Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Component wave delineation of ECG by filtering in the Fourier domain

A complete solution to the fundamental problem of delineation of an ECG signal into its component waves by filtering the discrete Fourier transform of the signal is presented. The set of samples in a component wave is transformed into a complex sequence with a distinct frequency band. The filter characteristics are determined from the time signal itself. Multiplication of the transformed signal with a complex sinusoidal function allows the use of a bank of low-pass filters for the delineation of all component waves. Data from about 300 beats have been analysed and the results are highly satisfactory both qualitatively and quantitatively.

Exact nonlinear travelling hydromagnetic wave solutions

Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.

Four decades of research in solid state chemistry

Solid state chemistry was in its infancy when the author got interested in the subject. In this article, the author outlines the manner in which the subject has grown over the last four decades, citing representative examples from his own contributions to the different facets of the subject. The various aspects covered include synthesis, structure, defects, phase transitions, transition metal oxides, catalysts, superconductors, metal clusters and fullerenes. In an effort to demonstrate the breadth and vitality of the subject, the author shares his own experiences and aspirations and gives expression to the agony and ecstacy in carrying out experimental research in such a frontier area in India.

Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers: A finite element approach

Resonant sound absorbers are used widely as anechoic coatings in underwater applications. In this paper a finite element scheme based on the Galerkin technique is used to analyze the reflection characteristics of the resonant absorber when insonified by a normal incidence plane wave. A waveguide theory coupled with an impedance matching condition in the fluid is used to model the problem. It is shown in this paper that the fluid medium encompassing the absorber can be modeled as an elastic medium with equivalent Lamé constants. Quarter symmetry conditions within the periodic unit cell are exploited. The finite element results are compared with analytical results, and with results published elsewhere in the literature. It is shown in the process that meshing of the fluid domain can be obviated if the transmission coefficients or reflection coefficients only are desired as is often the case. Finally, some design curves for thin resonant absorbers with water closure are presented in this paper.

Mechanisms of variability and predictability of the tropical coupled ocean-atmosphere system

A conceptual model is proposed to explain the observed aperiodicity in the short term climate fluctuations of the tropical coupled ocean-atmosphere system. This is based on the evidence presented here that the tropical coupled ocean-atmosphere system sustains a low frequency inter-annual mode and a host of higher frequency intra-seasonal unstable modes. At long wavelengths, the low frequency mode is dominant while at short wavelengths, the high frequency modes are dominant resulting in the co-existence of a long wave low frequency mode with some short wave intra-seasonal modes in the tropical coupled system. It is argued that due to its long wavelength, the low frequency mode would behave like a linear oscillator while the higher frequency short wave modes would be nonlinear. The conceptual model envisages that an interaction between the low frequency linear oscillator and the high frequency nonlinear oscillations results in the observed aperiodicity of the tropical coupled system. This is illustrated by representing the higher frequency intra-seasonal oscillations by a nonlinear low order model which is then coupled to a linear oscillator with a periodicity of four years. The physical mechanism resulting in the aperiodicity in the low frequency oscillations and implications of these results on the predictability of the coupled system are discussed.

Spectral approach for the soliton and periodic solutions of the nonlinear wave equation

A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.

Schlieren visualization of shock wave phenomena over a missile-shaped body at hypersonic Mach numbers

The flow over a missile-shaped configuration is investigated by means of Schlieren visualization in short-duration facility producing free stream Mach numbers of 5.75 and 8. This visualization technique is demonstrated with a 41 degrees full apex angle blunt cone missile-shaped body mounted with and without cavity. Experiments are carried out with air as the test gas to visualize the flow field. The experimental results show a strong intensity variation in the deflection of light in a flow field, due to the flow compressibility. Shock stand-off distance measured with the Schlieren method is in good agreement with theory and computational fluid dynamic study for both the configurations. Magnitude of the shock oscillation for a cavity model may be greater than the case of a model without cavity. The picture of visualization shows that there is an outgoing and incoming flow closer to the cavity. Cavity flow oscillation was found to subside to steady flow with a decrease in the free stream Mach number.