Second-order Diffraction Research Articles

Long-period fiber gratings spontaneously written by a mechanism markedly different from Hill grating formation

Pumping a nonlinear germanosilicate fiber with intense near-infrared femtosecond laser pulses for supercontinuum generation may invoke multiphoton-assisted photosensitivity of glasses to write a long-period fiber grating. In sharp contrast to the spontaneous formation of a Hill grating that resonates with the writing wavelength through first-order diffraction, the long-period fiber grating resonates with the writing wavelength through second-order diffraction. This finding highlights the surprising light-matter interaction in a waveguide.

First- and second-order analysis of resonant waves between adjacent barges

Water wave diffraction by two parallel closely spaced rectangular barges is investigated, to characterise the general problem of LNG offloading from a floating plant into a shuttle tanker. It is well known that large free-surface motions, in the gap between the hulls, are predicted by diffraction theory; in model tests amplitudes of at least five times that of the incident wave amplitude have been observed. A second-order diffraction calculation is used, based on a quadratic boundary element method, to examine the behaviour of this characteristic configuration and to examine the influence of spacing between the hulls. The free-surface near-resonant behaviour at first and second order is interpreted in the context of simple linear analytical solutions for three-dimensional flow in an open-ended gap.

Second-order wave diffraction by a circular cylinder using scaled boundary finite element method

The scaled boundary finite element method (SBFEM) has achieved remarkable success in structural mechanics and fluid mechanics, combing the advantage of both FEM and BEM. Most of the previous works focus on linear problems, in which superposition principle is applicable. However, many physical problems in the real world are nonlinear and are described by nonlinear equations, challenging the application of the existing SBFEM model. A popular idea to solve a nonlinear problem is decomposing the nonlinear equation to a number of linear equations, and then solves them individually. In this paper, second-order wave diffraction by a circular cylinder is solved by SBFEM. By splitting the forcing term into two parts, the physical problem is described as two second-order boundary-value problems with different asymptotic behaviour at infinity. Expressing the velocity potentials as a series of depth-eigenfunctions, both of the 3D boundary-value problems are decomposed to a number of 2D boundary-value sub-problems, which are solved semi-analytically by SBFEM. Only the cylinder boundary is discretised with 1D curved finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The method can be extended to solve more complex wave-structure interaction problems resulting in direct engineering applications.

Silica hydrogel formation and aging monitored by pyrene-based fluorescence probes

Fluorescent probes pyrene (Py), di(1-pyrenylmethyl)ether (DiPyM) and newly synthesized 2,3-bis-[4-(1-pyrenemethoxy)methylphenyl]butane (DiPyS) were used to monitor the formation and aging of silica hydrogel prepared from poly(glyceryl silicate) (PGS) sol. The fluorescence emission spectra of these probes are sensitive to their environment and this feature is utilized for monitoring the evolution of silica hydrogels prepared in this work. The polarity of hydrogel matrix during sol–gel transition assessed by all three pyrene probes decreases in the first stage of hydrogel formation, for about 2 h, followed by a gradual increase in polarity and reaching the constant level after 24 h for at least 2 weeks. The process of crosslinking was assessed by DiPyM and DiPyS. These fluorescent probes possess two pyrene structures, which ability to form a dynamic intramolecular excimer can be used to monitor the degree of hydrogel crosslinking with time. These data support the polarity measurements that the hydrogel network is predominatly formed within the first 2 h, stabilized within the 24 h, and that there is a minor increase in the network density for about 10 days until reaching the constant level. In addition, utilizing the second-order diffraction of scattered excitation light may also be used to obtain an adequate information about the silica hydrogel evolution. In summary, this paper demonstrates that pyrene-type fluorescent probes represent simple and precise tool for characterization of formation and aging of the silica hydrogels.

Lasing by Second-Order Bragg Diffraction in Dye-Doped POLIPHEM Gratings

A composite LC/polymer structure, patented as POLIPHEM, when properly doped with a dye is a promising material for compact tunable laser sources. We analyze the properties of distributed feedback system in a form of volume periodic grating in a medium with gain. The conditions required for lasing threshold achievement are considered for second-order Bragg diffraction regimes. First experimental results on the lasing in POLIPHEM DFB oscillator are reported.

Use of body-fixed coordinate system in analysis of weakly nonlinear wave–body problems

When a weakly nonlinear wave–body problem is considered in an inertial coordinate system, high-order derivatives appear in the higher-order body boundary conditions and make it difficult to get convergent and accurate results, especially for bodies with sharp corners or high surface curvatures. In this paper, a new method taking the advantage of the accelerated body-fixed coordinate system is proposed to avoid derivatives of the velocity potential on the right-hand side of the body boundary conditions. A domain decomposition method is applied with the use of the body-fixed coordinate system in the inner domain and the Earth-fixed coordinate system in the outer domain. The second-order radiation and diffraction of bodies with and without sharp corner are studied in the time domain and verified. A numerical beach is applied. Unlike the other methods which transfer the high-order derivatives to lower-order ones by using Stokes-like theorems, it is straightforward to generalize the present method to higher than second-order radiation problems and to the nonlinear wave–body analysis when the forward speed or current is included.

Coupled-wave analysis of second-order Bragg diffraction II Threshold conditions for distributed-feedback laser oscillations

The coupled-wave approach was used for the analysis of volume gratings in a medium with light gain for the sake of oscillation threshold determination in the second-order Bragg diffraction regime. The conditions for self-starting oscillations were analytically determined and found to be optimal for mixed phase-amplitude gratings. The properties of a distributed-feedback laser scheme are derived on the basis of the obtained results.

First- and second-order Poisson spots

Although Thomas Young is generally given credit for being the first to provide evidence against Newton’s corpuscular theory of light, it was Augustin Fresnel who first stated the modern theory of diffraction. We review the history surrounding Fresnel’s 1818 paper and the role of the Poisson spot in the associated controversy. We next discuss the boundary-diffraction-wave approach to calculating diffraction effects and show how it can reduce the complexity of calculating diffraction patterns. We briefly discuss a generalization of this approach that reduces the dimensionality of integrals needed to calculate the complete diffraction pattern of any order diffraction effect. We repeat earlier demonstrations of the conventional Poisson spot and discuss an experimental setup for demonstrating an analogous phenomenon that we call a “second-order Poisson spot.” Several features of the diffraction pattern can be explained simply by considering the path lengths of singly and doubly bent paths and distinguishing between first- and second-order diffraction effects related to such paths, respectively.

Focus Monitor Using Asymmetric Diffraction Rays by Off-Axis Monopole Illumination

Some methods of focus monitoring for lithography tools use nontelecentric imaging delivered from phase shift masks and require double exposure. A newly proposed focus monitoring method requires neither a special mask nor double exposure. A mask pattern of 1:1 duty ratio is illuminated by an off-axis monopole source. The positive first-order diffraction ray from the pattern is designed to advance in the direction of the optical axis. Then, the second-order diffraction ray is not generated. Only zeroth-order and the first-order diffraction rays contribute to imaging. At defocus, the pattern shifts sideways. On the other hand, a double-pitch pattern does not shift at defocus because rays are generated at symmetrical positions against the optical axis. The focal value is obtained by measuring their relative position. For an ArF immersion exposure tool of 1.3 numerical aperture (NA), pattern sizes of 86 nm half pitch and 43 nm half pitch were used. The focus position was measured from the relative position between the two patterns.

Generation of cavity field cluster and GHZ states using Bragg-regime atom interferometry

We propose two schemes for engineering cavity field cluster and GHZ states. The schemes are based on multiport atom interferometry in the Bragg-regime cavity QED. The second-order off-resonant Bragg diffraction of two-level atoms is utilized for generating the desired state. The derived schematics are shown to be experimentally feasible under the prevailing cavity QED research scenario.

Coupled-wave analysis of second-order Bragg diffraction I Reflection-type phase gratings

Coupled-wave analysis was applied to the problem of optical wave diffraction in a thick reflection-type phase grating in a condition of second-order Bragg regime. Within the approximation of two resonant waves in a medium with phase (refractive index) modulation, an analytical formula was derived for the diffraction efficiency. A shift of the maximum of a diffraction efficiency contour from the position determined by vector synchronism (second-order Bragg resonance) was detected.

Second-order hydrodynamic effects on an arrangement of two concentric truncated vertical cylinders

The second-order diffraction problem by a piston-like arrangement that consists of two concentric surface piercing cylinders is considered. The developed matched axisymmetric eigenfunction expansion solution methodology in cylindrical co-ordinates is based on the semi-analytical formulation of the velocity potentials in the various fluid regions which are defined by the geometry of the two-body arrangement. The main difficulty associated with the specific configuration originates from the fact that the geometry defines two fluid regions that extend up to the free surface in which the inhomogeneous second-order free surface boundary condition has to be fulfilled. To this end the associated velocity potentials in these regions are decomposed into a number of components defining the so-called ‘free’ and ‘locked’ waves. The latter are calculated by solving the resulting Sturm–Liouville problems. The seek second-order velocity potential in the whole fluid domain is then derived by enforcing matching conditions for the radial velocities and the fluid pressures at the cylindrical boundaries of adjacent fluid domains. Numerical results concerning the second-order hydrodynamic loading and the wave run-up on the cylinders are given, whereas special attention is given at incident wave frequency regions where the first-order exciting wave forces attain maximum values due to the resonant fluid motions in the moonpool.

Demultiplexer with blazed waveguide sidewall grating and sub-wavelength grating structure

We propose an original diffraction grating demultiplexer device with a very small footprint, designed for the silicon-on-insulator waveguide platform. The wavelength dispersive properties are provided by a second-order diffraction grating designed to be lithographically defined and etched in the sidewall of a curved Si waveguide. The grating is blazed to maximize the -1st order diffraction efficiency. The diffracted light is coupled into the silicon slab waveguide via an impedance matching subwavelength grating gradient index antireflective interface. The waveguide is curved in order to focus the light onto the Rowland circle, where different wavelengths are intercepted by different receiver waveguides. The phase errors were substantially reduced using an apodized design with a chirped grating, which assures a constant effective index along the grating length. The simulated crosstalk is -30 dB. The device has 15 channels with a spacing of 25 nm, thus a broadband operational bandwidth of 375 nm. Its performance approaches the diffraction limit. The layout size is 90 microm x 140 microm, which is the smallest footprint yet reported for a mux/dmux device of a similar performance.

First Approach to the Analysis of the Lasing Conditions in POLIPHEM© Structures

We report a study devoted to the creation of a distributed feedback device on a basis of waveguide with periodical composition polymer – liquid crystal. Due to the refractive indices difference between the components the Bragg diffraction grating is formed, which provides coupling of the forward and backward propagating waves. The influence of the gain and conditions of laser oscillation threshold are analyzed for gain-type reflection grating. The conclusion is done on the advantage of second-order Bragg diffraction exploitation. Numerical simulations demonstrated the stability of the waveguide mode.

GENETIC MODERATION OF THE CANNABIS INDUCED PSYCHOSIS

Column-supported structures are commonly used in offshore industries. The prediction of the free surface elevation in the vicinity of the supporting columns is important for structural safety and air gap design. Because the tension leg platform is normally supported by four vertical columns, model experiments are carried out to study the diffraction of regular waves by a four-cylinder structure. The experiments are designed to measure the free surface elevation at multiple locations close to the cylinder surfaces. By analysing the measured data, the amplitudes of the first-order and second-order harmonic wave elevations are obtained. To validate the diffraction theory with regard to predicting the free surface elevation, the experimental and numerical results are compared and show that the second-order diffraction theory is effective in predicting the free surface elevation, even for steep waves. The important phenomenon of near-trapping is also investigated in the experiment. For a specific incident wave frequency, near-standing wave motion can be observed inside the structure. Different wave headings are also investigated to describe the dependence of first-order and second-order near-trapping phenomena on the incident wave direction.

Molecular packing and phase transitions of side-chain liquid crystalline polymethacrylates based on p-methoxyazobenzene

The phase structures and transition behaviors of a series of side-chain liquid crystalline (LC) polymethacrylates based on p-methoxyazobenzene (PMnAzs, n=6, 8, 10, 12) were studied using differential scanning calorimetry, one- and two-dimensional (1D and 2D) wide-angle X-ray diffraction, and Fourier transform infrared spectroscopic experiments. The LC phase transition of PMnAz follows the sequence of smectic A (SmA)↔nematic (N)↔isotropic (I). For PM10Az and PM12Az, the transition of SmA-to-N is not complete upon heating. In the low-temperature SmA phase, the polymers adopt a fully interdigitated side-chain packing with the smectic layer period almost identical to the side-chain length. For all the four samples, the first-order diffraction of the SmA structure only renders when the temperature approaches the transition of SmA ↔ N, with the intensity much lower than that of the second-order diffraction. The absence of the first-order diffraction at low temperatures is ascribed to the possible matching of the electron densities between the center portion of the side-chain sublayer and the main-chain sublayer of the SmA structure. Since only the mesogens from the same main-chain sublayer can stack parallel together, the distribution of the azobenzene domains may cause some sort of density undulation within the smectic layer. Among the samples, PM6Az presents the strongest undulation with some additional orders. We also examined the annealing effect on the H-aggregation of PMnAzs. It is found that isothermal annealing at a temperature slightly higher than the Tg of PM8Az and PM10Az can significantly enhance the UV absorption at 326nm, indicating a further development of H-aggregation. However, for PM6Az and PM12Az, the UV–vis spectrum of the annealed sample is nearly identical to that without annealing.

$H_{2}$ and $H_{\infty}$ Designs for Diving and Course Control of an Autonomous Underwater Vehicle in Presence of Waves

H 2 and H infin designs applied to the diving and course control of an autonomous underwater vehicle (AUV) considering the presence of wave disturbances are described. The six-degrees-of-freedom equations of motion of the vehicle are described as a linear model and divided into three noninteracting (or lightly interacting) subsystems for speed control, steering, and diving. This work is based on the slender form of the Naval Postgraduate School (NPS, Monterey, CA) AUV, considering that the subsystems can be controlled by means of two single-screw propellers, a rudder, port and starboard bow planes, and a stern plane. A model of the AUV dynamics is presented with the first- and the second-order wave force disturbances, i.e., the Froude-Kriloff and diffraction forces. An algorithm of nonlinear regression for the rationalization of the subsurface sea spectrum is provided in this case study. The obtained results are analyzed and evaluated in the frequency domain comparing the controllers performance considering or not the inclusion of the model of waves.

High-energy angle resolved reflection spectroscopy on three-dimensional photonic crystals of self-organized polymeric nanospheres

We report on the optical characterization of three-dimensional opal-like photonic crystals made by self-organized nanospheres of poly[styrene-(co-2-hydroxyethyl methacrylate)] having a face centred cubic (fcc) structure oriented along the [111] direction. A detailed optical characterization of the samples is presented using angle resolved reflection spectroscopy in specular geometry. The investigated energies are between a/lambda=0.5 and a/lambda=1.5 (where a is the lattice parameter and lambda is the light wavelength), a region in which both first and second-order Bragg diffraction are expected. Some interesting features as branching of the Bragg peak dispersion and high energy reflection peaks are revealed. We compare the experimental data with theoretical calculations using both Bragg diffraction and band structure approach. A comparison with recent results reported in the literature is also presented.

Higher-order acoustic diffraction by edges of finite thickness

A cw solution of acoustic diffraction by a three-sided semi-infinite barrier or a double edge, where the width of the midplanar segment is finite and cannot be ignored, involving all orders of diffraction is presented. The solution is an extension of the asymptotic formulas for the double-edge second-order diffraction via amplitude and phase matching given by Pierce [A. D. Pierce, J. Acoust. Soc. Am. 55, 943-955 (1974)]. The model accounts for all orders of diffraction and is valid for all kw, where k is the acoustic wave number and w is the width of the midplanar segment and reduces to the solution of diffraction by a single knife edge as w-->0. The theory is incorporated into the deformed edge solution [Stanton et al., J. Acoust. Soc. Am. 122, 3167 (2007)] to model the diffraction by a disk of finite thickness, and is compared with laboratory experiments of backscattering by elastic disks of various thicknesses and by a hard strip. It is shown that the model describes the edge diffraction reasonably well in predicting the diffraction as a function of scattering angle, edge thickness, and frequency.

Second-order sum-frequency wave diffraction by a truncated surface-piercing cylinder in bichromatic waves

This work considers the second-order sum-frequency diffraction problem for a stationary truncated surface-piercing circular cylinder in bichromatic waves. The solution method was based on a semianalytical formulation of the second-order sum-frequency diffraction potential. The boundary conditions were properly satisfied by introducing the “locked” and the “free” wave components of the nonlinear velocity potential. The method was validated by comparing the calculated results with numerical data previously reported by other authors. Particular attention was paid to the second-order sum-frequency heave forces and the change in the wave run-up configuration due to the existence of the lower fluid domain underneath the truncated cylinder.