Ultrafast temporal pattern generation and recognition

Ultrafast temporal pattern generation and recognition with femtosecond laser technology is presented, analyzed, and experimentally implemented. Ultrafast temporal pattern generation and recognition are realized by taking advantage of two well-known techniques: the space-time conversion technique and the ultrafast pulse measurement technique. Here the temporal pattern for the designed multiple pulses, optimized with a preassumed Gaussian spectral distribution of an ultrashort pulse, is described. With the simulation of a Gaussian spectral distribution, we realize that the uniformity of the generated multiple ultrafast temporal pulses is relevant to the repeated number of modulation periods in the mask in the spectral plane. Moreover, the change of Gaussian spectral phases with the wavelengths in the modulated phase plate is considered. Experiments of ultrafast temporal pattern recognition by the frequency-resolved optical gating (FROG) characterization technique are also given. (C) 2004 Society of Photo-Optical Instrumentation Engineers.

Generation of near-field hexagonal array illumination with a phase grating

A hexagonal array not only is a nature-preferred pattern but also is widely used in optoelectronical materials and devices. We report a simple method of hexagonal array illumination based on the Talbot effect that has a theoretical efficiency of 100%. An experimental efficiency of 90.6% with a binary phase (0, pi) hexagonal grating is given. This method should be highly interesting for applications of hexagonal array illumination in optical devices as well as in other hexagonal cells. (C) 2002 Optical Society of America.

Generation of millimeter-wave in optical pulse carrier by using an apodized Moire fiber grating

A novel scheme is proposed to transform a Gaussian pulse to a millimeter-wave frequency modulation pulse by using an apodized Moire fiber Bragg grating in radio-over-fiber system. The relation between the input and output pulses is analyzed theoretically by Fourier transformation method and the requirements for the proposed fiber grating are presented. An apodized Moire fiber Bragg grating is designed and its characteristics are studied. It is shown that the proposed device is feasible, and the new scheme is believed to be an effective solution for the generation of millimeter-wave sub-carrier in future radio-over-fiber systems. (c) 2006 Elsevier B.V. All rights reserved.

I. Studies on bacteriophage DNA's and minicircular DNA's in M. lysodeikticus and E. coli 15. II. Flow dichroism of DNA solutions

Part I

Chapter 1.....A physicochemical study of the DNA molecules from the three bacteriophages, N1, N5, and N6, which infect the bacterium, M. lysodeikticus, has been made. The molecular weights, as measured by both electron microscopy and sedimentation velocity, are 23 x 10⁶ for N5 DNA and 31 x 10⁶ for N1 and N6 DNA's. All three DNA's are capable of thermally reversible cyclization. N1 and N6 DNA's have identical or very similar base sequences as judged by membrane filter hybridization and by electron microscope heteroduplex studies. They have identical or similar cohesive ends. These results are in accord with the close biological relation between N1 and N6 phages. N5 DNA is not closely related to N1 or N6 DNA. The denaturation T_m of all three DNA's is the same and corresponds to a (GC) content of 70%. However, the buoyant densities in CsCl of Nl and N6 DNA's are lower than expected, corresponding to predicted GC contents of 64 and 67%. The buoyant densities in Cs₂SO₄ are also somewhat anomalous. The buoyant density anomalies are probably due to the presence of odd bases. However, direct base composition analysis of N1 DNA by anion exchange chromatography confirms a GC content of 70%, and, in the elution system used, no peaks due to odd bases are present.

Chapter 2.....A covalently closed circular DNA form has been observed as an intracellular form during both productive and abortive infection processes in M. lysodeikticus. This species has been isolated by the method of CsC1-ethidium bromide centrifugation and examined with an electron microscope.

Chapter 3.....A minute circular DNA has been discovered as a homogeneous population in M. lysodeikticus. Its length and molecular weight as determined by electron microscopy are 0.445 μ and 0.88 x 10⁶ daltons respectively. There is about one minicircle per bacterium.

Chapter 4.....Several strains of E. coli 15 harbor a prophage. Viral growth can be induced by exposing the host to mitomycin C or to uv irradiation. The coliphage 15 particles from E. coli 15 and E, coli 15 T^- appear as normal phage with head and tail structure; the particles from E. coli 15 TAU are tailless. The complete particles exert a colicinogenic activity on E.coli 15 and 15 T^-, the tailless particles do not. No host for a productive viral infection has been found and the phage may be defective. The properties of the DNA of the virus have been studied, mainly by electron microscopy. After induction but before lysis, a closed circular DNA with a contour length of about 11.9 μ is found in the bacterium; the mature phage DNA is a linear duplex and 7.5% longer than the intracellular circular form. This suggests the hypothesis that the mature phage DNA is terminally repetitious and circularly permuted. The hypothesis was confirmed by observing that denaturation and renaturation of the mature phage DNA produce circular duplexes with two single-stranded branches corresponding to the terminal repetition. The contour length of the mature phage DNA was measured relative to φX RFII DNA and λ DNA; the calculated molecular weight is 27 x 10⁶. The length of the single-stranded terminal repetition was compared to the length of φX 174 DNA under conditions where single-stranded DNA is seen in an extended form in electron micrographs. The length of the terminal repetition is found to be 7.4% of the length of the nonrepetitious part of the coliphage 15 DNA. The number of base pairs in the terminal repetition is variable in different molecules, with a fractional standard deviation of 0.18 of the average number in the terminal repetition. A new phenomenon termed "branch migration" has been discovered in renatured circular molecules; it results in forked branches, with two emerging single strands, at the position of the terminal repetition. The distribution of branch separations between the two terminal repetitions in the population of renatured circular molecules was studied. The observed distribution suggests that there is an excluded volume effect in the renaturation of a population of circularly permuted molecules such that strands with close beginning points preferentially renature with each other. This selective renaturation and the phenomenon of branch migration both affect the distribution of branch separations; the observed distribution does not contradict the hypothesis of a random distribution of beginning points around the chromosome.

Chapter 5....Some physicochemical studies on the minicircular DNA species in E. coli 15 (0.670 μ, 1.47 x 10⁶ daltons) have been made. Electron microscopic observations showed multimeric forms of the minicircle which amount to 5% of total DNA species and also showed presumably replicating forms of the minicircle. A renaturation kinetic study showed that the minicircle is a unique DNA species in its size and base sequence. A study on the minicircle replication has been made under condition in which host DNA synthesis is synchronized. Despite experimental uncertainties involved, it seems that the minicircle replication is random and the number of the minicircles increases continuously throughout a generation of the host, regardless of host DNA synchronization.

Part II

The flow dichroism of dilute DNA solutions (A₂₆₀≈0.1) has been studied in a Couette-type apparatus with the outer cylinder rotating and with the light path parallel to the cylinder axis. Shear gradients in the range of 5-160 sec.^-1 were studied. The DNA samples were whole, "half," and "quarter" molecules of T4 bacteriophage DNA, and linear and circular λb₂b₅c DNA. For the linear molecules, the fractional flow dichroism is a linear function of molecular weight. The dichroism for linear A DNA is about 1.8 that of the circular molecule. For a given DNA, the dichroism is an approximately linear function of shear gradient, but with a slight upward curvature at low values of G, and some trend toward saturation at larger values of G. The fractional dichroism increases as the supporting electrolyte concentration decreases.

Stationary random response of multidegree-of-freedom systems

An approximate approach is presented for determining the stationary random response of a general multidegree-of-freedom nonlinear system under stationary Gaussian excitation. This approach relies on defining an equivalent linear system for the nonlinear system. Two particular systems which possess exact solutions have been solved by this approach, and it is concluded that this approach can generate reasonable solutions even for systems with fairly large nonlinearities. The approximate approach has also been applied to two examples for which no exact or approximate solutions were previously available.

Also presented is a matrix algebra approach for determining the stationary random response of a general multidegree-of-freedom linear system. Its derivation involves only matrix algebra and some properties of the instantaneous correlation matricies of a stationary process. It is therefore very direct and straightforward. The application of this matrix algebra approach is in general simpler than that of commonly used approaches.

Time domain synthesis of electro-optical birefringent system for optical waveform generation

In this paper is described a novel technique for producing an electro-optical intensity synthesizer which can generate different periodic time domain waveforms through only sine or cosine wave applied-voltages. The synthesizer presented here consists of a series of stages between two polarizers, with each stage consisting of an electro-optic element and a compensator. Every electro-optical element has the same applied-voltage function but different azimuth angles and ratios between the longitudinal and transverse lengths. The main principle is the synthesis of an electro-optic effect and a polarization interference effect in the time domain. This technique is based on an expanded Fourier positive-direction searching algorithm, which can not only simplify the calculation process but also produces many choices of structural parameters for different waveforms generation. A three-stage synthesis of an electro-optical birefringent system for continuous square waveform is undertaken to prove the principle.

Measuring ultrashort optical pulses using multi-shot second harmonic generation frequency resolved optical gating

Frequency resolved optical gating (FROG), is an effective technique for characterizing the ultrafast laser pulses. The multi-shot second harmonic generation (SHG) FROG is the most sensitive one in different FROGs. In this paper we use this technique to measure the femtosecond optical pulses generated by a conventional Ti:sapphire oscillator.

Double-line-density gratings structure for compression and generation of double femtosecond laser pulses

Grating pairs are widely used for pulse compression and stretching. Normally, the two gratings are identical. We propose a very simple structure with double-line-density reflective gratings for pulse compression and generation of double pulses, which has the advantages of no material dispersion, compact in volume, simple in structure, etc. The use of reflective Dammann gratings fully demonstrated the principle of this structure. The output pulses are well verified by a standard frequency-resolved optical gating apparatus. This structure will be highly interesting in ultrashort pulse compression and other more practical applications of femtosecond laser pulses. (c) 2007 Optical Society of America.

Measuring temporal fluctuation on femtosecond scale in a random medium

We report an observation of femtosecond optical fluctuations of transmitted light when a coherent femtosecond pulse propagates through a random medium. They are a result of random interference among scattered waves coming from different trajectories in the time domain. Temporal fluctuations are measured by using cross-correlated frequency optical gating. It is shown that a femtosecond pulse will be broadened and distorted in pulse shape while it is propagating in random medium. The real and imaginary components of transmitted electric field are also distorted severely. The average of the fluctuated transmission pulses yields a smooth profile, probability functions show good agreement with Gaussian distribution. (c) 2007 Elsevier B.V. All rights reserved.

Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets

Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.

Generation of double pulses in-line by using reflective Dammann gratings

Doubled femtosecond laser pulses in-line are needed in the collinear pump-probe technique, collinear second harmonic generation frequency-resolved optical gating (SHG FROG) and the spectral phase interferometry for direct electric-field reconstruction (SPIDER), etc. Normally, it is generated by using a Michelson's structure. In this paper, we proposed a novel structure with two-layered reflective Dammann gratings and the reflective mirrors to generate doubled femtosecond laser pulses in line without transmission optical elements. Angular dispersion and spectral spatial walk-off are both compensated. In addition, this structure can also compress the positive chirped pulse, which cannot be realized with a Michelson's structure. By adopting triangular grating and blazed gratings, the efficiency of the system would in principle be increased as the Michelson's scheme. Experiments demonstrated that this method should be an alternative approach for generation of the double compressed pulses of femtosecond laser for practical applications. (c) 2006 Elsevier GmbH. All rights reserved.

Tsunamis - a model of their generation and propagation

A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered.

An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model.

Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of non-linear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation.

A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation.

An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally.

The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.