Internal reflection of one-dimensional bright spatial solitons

We study the reflection of one-dimensional spatial solitons at the non-linear interface between a Kerr-type medium and a linear medium. Our study places emphasis on determining the physical conditions under which the beam reflected by the non-linear interface is still a spatial soliton. We find that for small angles of incidence an elastic internal reflection takes place, in the sense that the reflected soliton is essentially the same as the incident one. For incidence angles near a critical angle, the reflected soliton becomes less intense and its reflection angle is smaller than the angle of incidence. Finally, for spatial solitons with input angles well above the critical angle, the main part of the energy is transmitted to the linear medium, and no soliton is internally reflected.     

Suppression of coherent inelastic Mössbauer scattering of synchrotron radiation at grazing angles of incidence

Coherent inelastic Mössbauer scattering (CIMS) of synchrotron radiation (SR) by an isotopic interface (a flat interface between two regions of matter differing in the concentration of the Mössbauer isotope) at grazing angles of incidence of the SR beam is investigated theoretically. The qualitative features of CIMS as compared with conventional optics at small grazing angles of the SR beam are determined. Specifically, it is shown that for CIMS by an isotopic interface, instead of the phenomenon of total external (internal) reflection well known in optics, total suppression of reflection of the CIMS beam occurs at grazing angles of the SR beam less than a critical angle, and a maximum of the transmission and reflection at distinguished CIMS frequencies appears near the critical angle.     

Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals

It is found that when a light beam is incident on a one-dimensional photonic crystal (1DPC) containing a defect layer, the lateral shifts of both the reflected and the transmitted beams are greatly enhanced near the defect mode of the 1DPC, whose location depends on the angles at a fixed frequency. The effect was studied by use of a Gaussian beam. The giant lateral displacement is due to the localization of the electromagnetic wave.     

Electrooptic reflection with surface plasmons

Electrooptic reflection with surface plasmons is studied both experimentally and theoretically. An attenuated total reflection (ATR) geometry is used in which a quartz electrooptic crystal onto which a thin Ag film has been evaporated is contacted to the hypotenuse face of a high-index prism. Modulation in the ATR of an He–Ne beam near the angle for surface plasmon excitation is observed when a low-frequency electric field is applied to the quartz crystal. Experiments have been done with both single and multiple boundary surface waves. The angular spectra show phase reversal structure due to the interference of the modulated reflected wave with the ATR wave. The modulated reflectance is calculated directly from a well-known solution to the boundary value problem in nonlinear optics. Good quantitative agreement with the observations is obtained.     

Reflection and refraction of the electromagnetic field in a semi-infinite plasma

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite (half-space) plasma, as well as the reflection coefficient, by using a general procedure based on equations of motion and electromagnetic potentials. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in plasma is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

Large Positive and Negative Lateral Displacements from Total Internal Reflection Configuration with a Weakly Absorbing Dielectric Film

It is theoretically shown that the simultaneously large positive and negative lateral displacements will appear when the resonant condition is satisfied for a TE-polarized light beam reflected from the total internal reflection configuration with a weakly absorbing dielectric film. Appearance of the enhanced negative lateral displacement is relative to the incidence angle, absorption of the thin film and its thickness. If we select an appropriate weakly absorbing dielectric film and its thickness, the simultaneously enhanced positive and negative lateral displacements will appear at different resonant angles. These phenomena may lead to convenient measurements and interesting applications in optical devices.     

Reflected and refracted electromagnetic fields in a semi-infinite body

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite body (either a plasma or a dielectric), as well as the reflection coefficient, by using a general approach based on the polarization equation of motion and electromagnetic potentials. The method consists of representing the charge disturbances by a displacement field in the positions of the moving charges. The propagation of an electromagnetic wave in matter is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived (the latter for the plasma). Bulk and surface plasmon–polariton modes are also identified for the plasma. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

Analysis of the axial transmission technique for the assessment of skeletal status

Ultrasonic wave propagation in human cortical bone has been investigated in vitro using the so-called axial transmission technique. This technique, which relies on velocity measurement of the first arriving signal, has been used in earlier investigations to study bone status during fracture healing or osteoporosis. Two quasi-point-source elements, one transmitter and one receiver (central frequency 0.5 MHz), were used to generate a wide ultrasonic beam, part of which strikes the sample surface at the longitudinal critical angle, and to receive the signals reflected from the sample surface. The analysis of the field reflected from a fluid-solid interface for an incident spherical wave predicts the existence of a lateral wave propagating along the sample surface at a velocity close to the longitudinal velocity, in addition to the ordinary reflected wave and vibration modes. The transducer-sample and the transmitter-receiver distances were chosen such that the lateral wave is the first arriving signal. Validation of the measuring technique was performed on test materials and was followed by experiments on human cortical bones. Experimental results (arrival time and velocity) strongly suggest that the first detected signal corresponds to the lateral wave predicted by theory.     

Tunneling of X-ray photons through a thin film under total internal reflection conditions

Tunneling of 0.154-and 0.139-nm x-ray photons through a thin film under total internal reflection conditions has been experimentally demonstrated. The NiSi₂ film 13 nm thick is deposited by magnetron sputtering on a polished Si substrate. A beam with an angular spread of 20″ is directed to the Si/NiSi₂ interface from the inside through the lateral surface of a sample. A peak associated with tunneling of photons from Si to air through the NiSi₂ film is observed at grazing angles of θ₁ > 0.4θ_c, where θ_c is the critical angle of total internal reflection at the Si/NiSi₂ interface. The integral intensity of tunneling peaks that is measured for various θ₁ angles agrees with the calculations.     

Net lateral shift of reflected beam due to surface plasmon resonance in Kretschmann configuration

When surface plasmon resonance is excited in Kretschmann configuration, the maximum Goos–Hänchen shift occurs at the resonant angle which is associated with the minimum value of reflectivity, but the maximum angular shift occurs at two incident angles beside the resonant angle. When the reflected beam is detected at Rayleigh range, the maximum net lateral shift of the reflected beam does not encounter the resonant angle and its magnitude is lager than that of Goos–Hänchen shift. Numerical simulation shows that theory agrees well with numerical results when the beam width is large enough.     

Optimizing textured structures possessing both optical gradient and diffraction properties to increase the extraction efficiency of light-emitting diodes

The external quantum efficiency of a light-emitting diode (LED) is strictly limited by total internal reflection and Fresnel reflection effects. In this study, we sought to optimize light extraction by monitoring the shape effects of four kinds of periodic textured structures (nanorod, inverted rod, pyramid, inverted pyramid) on the surface of gallium nitride (GaN)-based LEDs. We employed the three-dimensional rigorous coupled waves approach to calculate the direct emissions at different incident angles on the various textured structures, and then determined an optimized structure that would improve the extraction efficiency of LEDs. The optical gradient of the inverted pyramid structure could decrease not only the Fresnel reflection at incident angles less than the critical angle but also the total internal reflection at incident angles greater than the critical angle. Many inverted pyramid structures at the GaN–air interface, with various sizes and periods, provided enhancement factors of greater than 150%.     

Evaluation of Ni/Mn multilayer samples with glancing-incidence and take-off X-ray fluorescence analysis

A Glancing-Incidence and Take-off X-Ray Fluorescence (GIT-XRF) apparatus with which both incident angle of primary X-ray and take-off angle of fluorescent X-rays can be controlled has been newly developed for characterizing surfaces and interfaces. Using this apparatus, Ni/Mn multilayer samples were evaluated obtaining Take-off-Angle-Dependent X-Ray Fluorescence (TAD-XRF) curves at arbitrary incident angles of primary X-ray. In particular, we could obtain information on the near surface by measuring TAD-XRF curves at the incident angle less than the critical angle of total reflection for primary X-rays.     

Use of thermal imaging to characterize laser light reflection from thermoplastics as a function of thickness,laser incidence angle and surface roughness

Laser light reflection during the laser transmission welding (LTW) of thermoplastics has the potential to overheat and/or cause unintentional welding of adjacent features of the part being welded. For this reason, and in order to assess how much light is being absorbed by the transparent part (after measurement of the light transmitted through the transparent part), it is important to be able to quantify the magnitude and distribution of reflected light. The magnitude and distribution of the reflected light depends on the total laser input power as well as its distribution, the laser incidence angle (angle between the normal to the transparent part surface and the laser beam), the laser light polarization as well as the surface and optical properties of the transparent part. A novel technique based on thermal imaging of the reflected light was previously developed by the authors. It is used in this study to characterize the magnitude and distribution of reflected light from thermoplastics as a function of thickness (1–3.1 mm), laser incidence angle (20–40°) and surface roughness (0.04–1.04 μm). Results from reflection tests on nearly polished nylon 6 (surface roughness between 0.04 and 0.05 μm) have shown that, for the various thicknesses tested (1–3.1 mm), the total reflection was larger than the specular top surface reflection predicted via the Fresnel relation. From these observations, it is conjectured that, in addition to top surface reflection, the bulk and/or bottom surface also contribute to the total reflection. The results also showed that reflection decreased slightly with increasing thickness. As expected, for the p-polarized light used in this study, the reflection decreased with increasing angle of incidence for the range of angles studied. It was also found that when the surface roughness was close to zero and when it was close to the wavelength of the input laser beam (i.e. 940 nm), the reflectance values were close and reached a minimum between these two roughness values.     

Depth of formation of a reflected soft x-ray beam under conditions of specular reflection

Over a wide range of glancing-incidence angles, bremsstrahlung from an x-ray tube was used to measure the reflection spectra of an Si-SiO₂ system with different dioxide thickness near the Si L _2,3 ionization threshold. The angular dependence of the depth of formation of the reflected soft x-ray beam was determined experimentally and compared with that obtained from a theoretical analysis of the interaction between electromagnetic radiation and the surface of an isotropic solid. Fiz. Tverd. Tela (St. Petersburg) 40, 1360–1363 (July 1998)     

Positively and negatively large Goos–Hänchen lateral displacements from a symmetric gyrotropic slab

A detailed study on the lateral displacements of a transverse magnetic (TM) wave transmitted and reflected from a symmetric gyrotropic slab is presented. We give the analytic formulas for the transmission coefficient and the reflection coefficient, as well as the corresponding lateral displacements. It is found that due to the external magnetic field the displacement of a transmitted beam is different from that of reflected one, even for a lossless symmetric configuration. Furthermore, within the chosen frequency band, when the incident angle is near the Brewster angle, the shift of a reflected wave can be large with nonzero reflectance, and can be positive or negative depending on the direction of the applied magnetic field and the incident wave.     

Intensification of acoustic beams in crystals at mode conversion near total internal reflection

Geometrical conditions under which mode conversion occurs in a crystal near total internal reflection of an acoustic beam are found. In this case, the entire energy of an incident pump wave is spent on the excitation of a narrow intense reflected beam close in structure to an eigenmode. A consistent choice of orientations of the sagittal plane and surface that excludes the reflection of a parasitic wave of leakage is found.     

Lateral shift and tunneling of optical beam reflected from gradient-induced inhomogeneity

Two effects have been analytically and numerically studied: Goos-Hänchen shift, which is acquired by an optical beam reflected from a gradient inhomogeneity, and tunneling of radiation through a narrow induced inhomogeneity. A possibility of increasing the lateral beam shift in comparison with total internal reflection from a homogeneous medium is revealed. The dependence of the tunneling coefficient on the inhomogeneity parameters is determined and the critical inhomogeneity width at which the tunneling effect arises is found.     

Anomalous lateral beam shift and total absorption due to excitation of surface waves in materials with negative refraction

We studied electromagnetic beam reflection from layered structures that include materials with negative refraction. Excitation of leaky surface waves leads to the formation of anomalous lateral shifts in the reflected beams with single or double peak structures. The presence of reasonable losses within material with negative refraction, besides significant influence on manifestation of the giant lateral shifts, can lead to their total suppression and anomalously high absorption of the incident radiation. If, in addition to the resonant excitation of leaky surface waves, radiation inflow exactly compensates their irreversible damping, total absorption of the incoming radiation can be achieved for moderately wide beams.     

光波p分量在单轴晶体表面反射和折射的相位特性

根据单轴晶体的双折射和双反射性质,通过数值计算研究了光轴在入射面内并与晶体界面成任意角时光波p分量在单轴晶体表面反射和折射的相位特性.结果表明,光轴取向对相位变化有较大影响,光从光疏各向同性介质射入单轴晶体时,光轴方向改变反射光p分量的相位突变点,但对折射光p分量相位无影响.光从光密各向同性介质射入单轴晶体未发生全反射时,光轴方向同时影响p分量反射光和折射光的相位突变|发生全反射后,光轴方向影响反射光p分量的相位变化曲线.从单轴晶体出射到光疏各向同性介质未发生全反射时,光轴方向改变反射光p分量的相位跃变规律,折射光p分量在光轴方向和晶面成小角度时在布儒斯特角附近发生相位突变|发生全反射后,反射光p分量的相位变化曲线随光轴方向的改变发生较大变化.