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Showing papers on "Near and far field published in 1996"


Journal ArticleDOI
TL;DR: It is demonstrated that the novel geometric-optics method can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as ~6 and overall agreement has been obtained for the phase function.
Abstract: A new geometric-optics model has been developed for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. The model uses the ray-tracing technique to solve the near field on the ice crystal surface, which is then transformed to the far field on the basis of the electromagnetic equivalence theorem. From comparisons with the results computed by the finite-difference time domain method, we show that the novel geometric-optics method can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as ~6. Overall agreement has also been obtained for the phase function when size parameters along the minimum dimension are larger than ~20. We demonstrate that the present model converges to the conventional ray-tracing method for large size parameters and produces single-scattering results close to those computed by the finite-difference time domain method for size parameters along the minimum dimension smaller than ~20. The present geometric-optics method can therefore bridge the gap between the conventional ray-tracing and the exact numerical methods that are applicable to large and small size parameters, respectively.

457 citations


Journal ArticleDOI
TL;DR: In this article, a finite-difference time domain (FDTD) method for the solution of light scattering by nonspherical particles was developed for small ice crystals of hexagonal shapes including solid and hollow columns, plates, and bullet rosettes commonly occurring in cirrus clouds.
Abstract: The finite-difference time domain (FDTD) method for the solution of light scattering by nonspherical particles has been developed for small ice crystals of hexagonal shapes including solid and hollow columns, plates, and bullet rosettes commonly occurring in cirrus clouds. To account for absorption, we have introduced the effective permittivity and conductivity to circumvent the required complex calculations in the direct discretization of the basic Maxwell equations. In the construction of the finite-difference scheme for the time-marching iteration for the near field the mean values of dielectric constants are defined and evaluated by the Maxwell–Garnett rule. In computing the scattered field in the radiation zone (far field) and the absorption cross section, we have applied a new algorithm involving the integration of the electric field over the volume inside the scatterer on the basis of electromagnetic principles. This algorithm removes the high-angular-resolution requirement in integrating the scattered energy for the computation of the scattering cross section. The applicability and the accuracy of the FDTD technique in three-dimensional space are validated by comparison with Mie scattering results for a number of size parameters and wavelengths. We demonstrate that neither the conventional geometric optics method nor the Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20.

369 citations


PatentDOI
TL;DR: In this paper, a microwave near field microscope has a novel microwave probe structure wherein the probing field of evanescent radiation is emitted from a sharpened metal tip instead of an aperture or gap.
Abstract: A microwave near field microscope has a novel microwave probe structure wherein the probing field of evanescent radiation is emitted from a sharpened metal tip instead of an aperture or gap. This sharpened tip, which is electrically and mechanically connected to a central electrode, extends through and beyond an aperture in an endwall of a microwave resonating device such as a microwave cavity resonator or a microwave stripline resonator. Since the field intensity at the tip increases as the tip sharpens, the total energy which is radiated from the tip and absorbed by the sample increases as the tip sharpens. The result is improved spatial resolution without sacrificing sensitivity.

260 citations


Journal ArticleDOI
TL;DR: In this paper, a method for computing near-and far-field patterns of an antenna from its near-field measurements taken over an arbitrary geometry is presented, where an electric field integral equation is developed to relate the near fields to the equivalent magnetic current, and a moment method procedure is employed to solve the integral equation by transforming it into a matrix equation.
Abstract: A method is presented for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrary geometry. This method utilizes near-field data to determine an equivalent magnetic current source over a fictitious surface which encompasses the antenna. This magnetic current, once determined, can be used to ascertain the near and the far fields. This method demonstrates that once the values of the electromagnetic field are known over an arbitrary geometry, its values for any other region can be obtained. An electric field integral equation is developed to relate the near fields to the equivalent magnetic current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometric surfaces, illustrate the accuracy of this method.

134 citations


Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate a technique for contactless mapping of resistivity or dielectric constant of surfaces and films with a spatial resolution better than 100 μm using a specially designed resonant slit antenna and achieve subwavelength spatial resolution of λ/50.
Abstract: We demonstrate a technique for contactless mapping of resistivity or dielectric constant of surfaces and films with a spatial resolution better than 100 μm. This technique may be used for the nondestructive testing of semiconducting wafers, conducting polymers, oxide superconductors, and printed circuits. The principle of operation consists of the scanning of a tiny millimeter‐wave antenna at a very small height above an inhomogeneous conducting surface and measuring the intensity and phase of the reflected (transmitted) wave. We use a specially designed resonant slit antenna and achieve subwavelength spatial resolution of λ/50.

116 citations


Journal ArticleDOI
TL;DR: In this article, the axial dependence of the plasma density, electron temperature, plasma potentials, and the 488 nm argon ion emission intensity have been measured in argon helicon discharges excited by both right helical and Nagoya III antennas for various magnitudes and directions of the magnetic field B.
Abstract: The axial dependence of the plasma density, electron temperature, plasma potentials, and the 488 nm argon ion emission intensity have been measured in argon helicon discharges excited by both right helical and Nagoya III antennas for various magnitudes and directions of the magnetic field B. The plasma parameters were monitored with RF-compensated probes, while the emission line was detected with an optical emission spectrometer that incorporates an optical fibre and a miniature lens. The right helical antennas were designed to excite the m = +1 azimuthal mode when B is parallel () to the propagation vector k, and the m = -1 mode when B is antiparallel (#) to k. The plasma is found to be more dense in the former case (, m = +1), and the density peaks several antenna lengths downstream in the k direction. Nagoya III antennas are symmetric antennas that should excite the same azimuthal mode content in either magnetic field direction; indeed, the light profile was found to be independent of field direction. In the near field, under the antennas, the density is approximately the same for both antenna geometries and magnetic field directions. These results indicate that the m = +1 mode is preferentially excited regardless of the antenna helicity.

114 citations


Journal ArticleDOI
TL;DR: In this paper, a new method for the analysis of the diffraction of a plane wave impinging on a perfectly conducting circular cylinder in front of a generally reflecting surface is presented, characterized by its complex reflection coefficient, enabling us to treat a wide class of reflecting surfaces.
Abstract: A new method for the analysis of the diffraction of a plane wave impinging on a perfectly conducting circular cylinder in front of a generally reflecting surface is presented. The surface is characterized by its complex reflection coefficient, enabling us to treat a wide class of reflecting surfaces. The presence of the surface is taken into account by means of a suitable expansion of the reflected field in terms of cylindrical functions. The method gives the solution of the scattering problem in both the near and the far field regardless of the polarization state of the incident field. Numerical examples for dielectric interfaces are presented, and comparisons are made with results presented in the literature.

104 citations


Journal ArticleDOI
TL;DR: The experimental results indicate that tensile stress and cavitation are induced in front of the fiber tip at a distance far below the optical penetration depth of the laser radiation.
Abstract: Conversion of energy from a heat pulse to acoustic stress is theoretically and experimentally studied in detail. The heat pulse was generated by laser radiation delivered via an optical fiber into an absorbing liquid. The experimental results indicate that tensile stress and cavitation are induced in front of the fiber tip at a distance far below the optical penetration depth of the laser radiation. The occurrence of tensile stress in the acoustic near field of a submerged fiber is explained by acoustic diffraction of the thermoelastic expansion wave. Good agreement between experimental results and theoretical calculations based on a three-dimensional model was found.

97 citations


Journal ArticleDOI
TL;DR: Low temperature femtosecond-resolved near-field scanning optical microscopy is used to image excitonic spin behavior in locally disordered magnetic semiconductor heterostructures and space-time spectroscopies reveal a spin component to the exciton evolution in the presence of a magnetic field.
Abstract: Low temperature femtosecond-resolved near-field scanning optical microscopy is used to image excitonic spin behavior in locally disordered magnetic semiconductor heterostructures. A contrast between luminescence intensity and polarization profiles yields marked differences between carrier diffusion and spin transport over a spin-dependent energy landscape sharply defined by focused ion beam implantation. Space-time spectroscopies reveal a spin component to the exciton evolution in the presence of a magnetic field. Fundamental limitations on the measurement of circularly polarized luminescence in the near field are also demonstrated.

89 citations


Patent
15 May 1996
TL;DR: In this article, an illumination system for use in photolithography having an array optical element near the formation of a desired illumination field is described. But there is no condenser following the array or diffractive optical element.
Abstract: An illumination system for use in photolithography having an array optical element near the formation of a desired illumination field. Light or electromagnetic radiation from an illumination source is expanded and received by a multi-image optical element forming a plurality of secondary illumination sources in a plane. A condenser receives the light from the plurality of illumination sources. A array or diffractive optical element is placed on or near the focal point of the condenser. The illumination plane formed at the focal point of the condenser is within the near field diffraction pattern of the array or diffractive optical element. There is no condenser following the array or diffractive optical element. The use of the array or diffractive optical element permits the use of a condenser between the multi-image optical element and the array or diffractive optical element having a smaller numerical aperture than the emergent numerical aperture of the diffractive optical element, and generates a desired angular distribution with little dependance on the illumination source profile.

85 citations


Journal ArticleDOI
TL;DR: In this article, a method for probe characterization based on lithography on a photosensitive polymer without film development is proposed, where the light emitted by different kinds of probes in order to distinguish in situ the near field contribution from the far field contribution of the tip.
Abstract: We propose here a method for probe characterization based on lithography on a photosensitive polymer without film development. We record in near field conditions the light emitted by different kinds of probes in order to distinguish in situ the near field contribution from the far field contribution of the tip. This information, which cannot be deduced from far field diffraction, allows an estimation of the field confinement and of the expected resolution of the microscope.

Patent
31 Jul 1996
TL;DR: In this paper, a near field electromagnetic probe converts an incident energy beam into an interrogating beam which exhibits, in the near field vicinity of the probe, a transverse dimension that is small in relation to the wavelength of the energy beam.
Abstract: A near field electromagnetic probe converts an incident energy beam into an interrogating beam which exhibits, in the near field vicinity of the probe, a transverse dimension that is small in relation to the wavelength of the incident energy beam The probe comprises an energy source for providing the incident energy beam with a wavelength λ An antenna is positioned in the path of the incident energy beam and comprises at least a first conductive region and a second conductive region, both of which have output ends that are electrically separated by a gap whose lateral dimension is substantially less than λ The electromagnetic system which produces the incident energy should preferably have its numerical aperture matched to the far-field beam pattern of the antenna Further, the incident beam should have a direction of polarization which matches the preferred polarization of the antenna The near field probe system of the invention can also sense fields in the near field gap and reradiate these to a far-field optical detector Thus the probe can serve to both illuminate a sample in the near field gap, and to collect optical signals from an illuminated sample in the near field gap

Journal ArticleDOI
TL;DR: In this paper, an exact integration of the vector potential is performed without recourse to approximations, where only restrictions on the solution variables are that the observation point distance must be greater than the loop radius and that the polar angle must run between 0 and /spl pi.
Abstract: Assuming a known (constant) current distribution on the thin circular loop antenna of arbitrary radius in free space, an exact integration of the vector potential is performed without recourse to approximations. The only restrictions on the solution variables are that the observation point distance must be greater than the loop radius and that the polar angle must run between 0 and /spl pi/. The resulting vector potential infinite series solution possesses a real part composed of linear combinations of complete elliptic integrals of the first and second kind and an imaginary part composed of elementary functions. Thus, it is possible to obtain an exact solution which is valid everywhere that r>a and 0/spl les//spl theta//spl les//spl pi/. The electromagnetic field components of the constant current circular loop antenna are then determined by direct series differentiation. These solutions are valid in the near and induction fields, converging rapidly there, and are also valid in the far field, although many terms of the series are needed for convergence.

Patent
04 Jun 1996
TL;DR: In this article, a planar antenna with a coaxial ring-slot radiating elements formed through a conductive layer on a dielectric substrate is disclosed, and the antenna can be steered by adjustment of the relative phase difference or relative amplitude between the excited modes.
Abstract: A directional planar antenna is disclosed. The antenna has an array of coaxial ring-slot radiating elements formed through a conductive layer on a dielectric substrate. A number of probes, coupled to the ring-slot elements, selectively excite a separate resonant mode on each ring-slot element. The resonant mode supported by a ring-slot element depends upon the geometry of that ring-slot element. The resonant modes combine in the far field to form a radiation pattern directional in azimuth and elevation. By adjustment of the relative phase difference or relative amplitude between the excited modes, the radiation pattern can be steered.

Journal ArticleDOI
TL;DR: In this article, a near-field 3-antenna method for measuring the complex antenna factor (CAF) is proposed in order to reduce the effect of the measurement site and background noise.
Abstract: The near-field 3-antenna method for measuring the complex antenna factor (CAF) is proposed in order to reduce the effect of the measurement site and background noise. The transmission coefficients in the far-field region are calculated from those measured in the near-field and theoretically obtained near-field correction factors (NCF). The CAF of monopole antennas are measured using the proposed method in a frequency range up to 6 GHz. From the measurement results, the dependency of CAF values on the antenna distance is small. These results indicate that our theory including the NCF is applicable for the measurements of the CAF of simple-structure antennas.

Journal ArticleDOI
TL;DR: In this paper, a linear spiral sampling for bipolar planar near-field antenna measurements is proposed, which is, depending on range implementation, the most rapid polar near-filed data acquisition mode.
Abstract: This paper investigates linear spiral sampling for bipolar planar near-field antenna measurements. This sampling scheme is, depending on range implementation, the most rapid polar near-filed data acquisition mode. The near-field to far-field transformation is performed using a modified optimal sampling interpolation (OSI)/fast Fourier transform (FFT) approach. Measured far-field pattern results for a waveguide-fed slot array antenna are presented and are shown to have excellent agreement with results obtained from a conventional bipolar measurement.

Journal ArticleDOI
TL;DR: In this paper, a Newton method is presented for the approximate solution of the inverse problem to determine the shape of a two-dimensional crack from a knowledge of the far field pattern for the scattering of time-harmonic elastic plane waves.
Abstract: A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a two-dimensional crack from a knowledge of the far field pattern for the scattering of time-harmonic elastic plane waves. Frechet differentiability with respect to the boundary is shown for the far field operator, which for a fixed incident wave maps the crack onto the far field pattern of the scattered wave. Some numerical reconstructions illustrate the feasibility of the method.

Journal ArticleDOI
TL;DR: It is demonstrated that the use of a near-field probe to map the evanescent field of an optical standing wave in a fused-silica whispering-gallery mode microresonator results in only the lowest radial mode numbers' being strongly excited, as predicted.
Abstract: We demonstrated the use of a near-field probe to map the evanescent field of an optical standing wave in a fused-silica whispering-gallery mode microresonator. The periodicity of the observed standing wave allows us to estimate accurately the radial mode number of the whispering-gallery mode resonance that is being excited. We find that the use of a fiber half-coupler to excite these resonances in fused-silica microspheres results in only the lowest radial mode numbers’ being strongly excited, as predicted.

Journal ArticleDOI
TL;DR: In this article, the influence of the object index, size, and depth on the near field of a subwavelength object buried in a dielectric surface was investigated using a fully vectorial three-dimensional numerical approach.
Abstract: Using a fully vectorial three-dimensional numerical approach (generalized field propagator, based on Green’s tensor technique), we investigate the near-field images produced by subwavelength objects buried in a dielectric surface. We study the influence of the object index, size, and depth on the near field. We emphasize the similarity between the near field spawned by an object buried in the surface (dielectric contrast) and that spawned by a protrusion on the surface (topographic contrast). We show that a buried object with a negative dielectric contrast (i.e., with a smaller index than its surrounding medium) produces a near-field image that is reversed from that of an object with a positive contrast.

Journal ArticleDOI
TL;DR: In this paper, a comprehensive description of a modular optoelectronic measurement system for the characterization of high-frequency microelectronic devices and circuits is presented, where specific techniques to generate, synchronize to, and detect highfrequency electric signals are combined covering a frequency range of more than three orders of magnitudes from 2 to 4000 GHz.
Abstract: A comprehensive description of a modular optoelectronic measurement system for the characterization of high-frequency microelectronic devices and circuits is presented. Depending on application, specific techniques to generate, synchronize to, and detect high-frequency electric signals are combined covering a frequency range of more than three orders of magnitudes from 2 to 4000 GHz. We discuss on-chip electric-pulse generation by freely positionable photoconductive probes and by direct optical excitation of active devices. Alternatively, for measurements with external, electronically generated signals, the system is laid out to lock onto periodic signals of arbitrary frequency employed as clock signal for the circuit under test. With respect to detection, the following approaches are discussed: sampling with freely positionable electrooptic and photoconductive probe tips, and truly (probe-tip-free) all-optical testing based on the field-dependent optical nonlinearity of the circuit's substrate material. The probes are characterized concerning time resolution, linearity, sensitivity, and invasiveness. We demonstrate with a number of examples that the combination of the various modules allows one to optimize the approach to a specific testing problem. Measurements of the linear and nonlinear behavior of active and passive devices as well as circuits are presented. The electric field, respectively potential, is measured locally (point measurements) or in its spatial distribution (field mapping) both in the near and far field.

Journal ArticleDOI
TL;DR: Two-dimensional electromagnetic scattering from a perfectly conducting target embedded near the randomly rough surface of an isotropic lossy dielectric is investigated and far field scattering coefficient distributions suggest when the buried object should be discernible.
Abstract: Two-dimensional electromagnetic scattering from a perfectly conducting target embedded near the randomly rough surface of an isotropic lossy dielectric is investigated. The randomly rough surface is illuminated by a finite width beam from an antenna in the free space above the surface, with off-normal incidence. Standard integral equation methods are applied and include all subsurface interactions between the object and rough surface. For a chosen embedded target, Monte Carlo simulations are performed for a selection of ensembles of rough surface types intended to be suggestive of natural ground. Far field scattering coefficient distributions and corresponding synthetic images suggest when the buried object should be discernible. Sensitivities are explored in terms of surface type, polarization of the incident field, depth and orientation of target, soil characteristics, incidence angle, and beamwidth. Many of the scattering features identified should also apply in 3D.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a finite-difference time-domain (FDTD) technique for the analysis of radio wave scattering from geophysical surfaces, where the average surface is modelled as a flat, homogeneous half-space.
Abstract: A major difficulty in physical interpretation of radio wave scattering from geophysical surfaces is the lack of detailed information on the signatures of geologically plausible discrete objects. Although the aggregate response will never be dominated by any single object, differences in the population of discrete objects on or near the surface (their sizes and shapes, for example) can change the character of a radio echo markedly. When the average surface is modelled as a flat, homogeneous half-space, the field that "drives" the scattering process is a composite consisting of the incident plane wave and the reflected and transmitted plane waves, all of which are known quantities; the total field can then be defined as the sum of the driving field and the scattered field. When a discrete object is near the surface, the total field can be calculated using finite-difference time-domain (FDTD) techniques, and the scattered near field can be calculated accordingly. The Green's functions for electric and magnetic currents above and below the surface, obtained by Sommerfeld theory and employed in conjunction with Huygens' principle, transform the local scattered fields to the far field. The FDTD implementation accommodates discrete lossy dielectric and magnetic scatterers in the vicinity of a dielectric surface; extension to a lossy half-space is straightforward. Two-dimensional results for scattering from perfectly conducting circular cylinders above and below a dielectric surface agree with moment method solutions within a few percent. Results for scattering from a dielectric wedge exhibit expected forward diffraction and internal reflection phenomena.

Journal ArticleDOI
TL;DR: In this article, the interaction of tokamak plasma edge electrons with the electric near field generated by a lower hybrid slow wave antenna is studied, and an area-preserving map is derived to study the electron dynamics.
Abstract: The interaction of tokamak plasma edge electrons with the electric near field generated by a lower hybrid slow wave antenna is studied. Antenna field spectra of interest for current drive and/or plasma heating have lobes at high‐n∥ values (n∥≳30) intense enough for resonant acceleration of the relatively cold (∼25 eV) edge electrons. For waveguide electric fields, typically around 3 kV/cm, the higher‐order modes overlap in the phase‐space [B. V. Chirikov, Phys. Rep. 52, 263 (1979)], so that electron global stochasticity is induced. For Tokamak de Varennes (TdeV) [Decoste et al., Phys. Plasmas 1, 1497 (1994)] conditions and for 90° waveguide phasing, the stochastic limit in the current drive direction is about 2 keV, determined by the last overlapping mode. The progress of electrons through accessible phase space is very efficient: the TdeV 32 waveguide array can accelerate the electrons to the possible limit. An area‐preserving map is derived to study the electron dynamics. Surface‐of‐section plots fully ...

Journal ArticleDOI
TL;DR: The asymptotic waveform evaluation (AWE) method is one approach to construct a reduced order model of the input impedance or other useful electromagnetic parameters, such as S parameters and far field pattern as mentioned in this paper.
Abstract: Although full wave electromagnetic systems are large and cumbersome to solve, typically only a few parameters, such as input impedance, S parameters, and far field pattern, are needed by the designer or analyst. A reduced order modelling of these parameters is therefore an important consideration in minimising the CPU requirements. The asymptotic waveform evaluation (AWE) method is one approach to construct a reduced order model of the input impedance or other useful electromagnetic parameters. The authors demonstrate its application and validity when used in conjunction with the finite element method to simulate full wave electromagnetic problems.

Journal ArticleDOI
TL;DR: In this article, a near-field resistivity microscope is proposed to map normal-state resistivity of YBCO films at ambient temperature using millimeter-wave measurements, which is based on the idea that electromagnetic waves are transmitted through a narrow resonant slit with high efficiency.
Abstract: We demonstrate a new millimeter-wave technique for the resistivity mapping of large-area conducting films, namely, a near-field resistivity microscope. The microscope is based on the idea that electromagnetic waves are transmitted through a narrow resonant slit with high efficiency. By scanning this slit at fixed height above an inhomogeneous conducting surface and measuring the intensity and phase of the reflected wave, the resistivity of this surface may be determined with a 10-100 /spl mu/m spatial resolution using 80-GHz radiation. Using this technique, we map normal-state resistivity of 1 in /spl times/1 in YBCO films at ambient temperature. In some films we find inhomogeneities of the normal-state sheet resistance of the order of 10%-20%.

Journal ArticleDOI
TL;DR: In this paper, the authors considered a Kirchhoff-fractal electromagnetic model which is applicable to the problems of remote sensing, and systematically and parametrically analyzed the first-order fading characteristics.
Abstract: Whenever a coherent electromagnetic field illuminates a natural surface, it is affected by fading, and this is related to the surface roughness. A model of the electromagnetic interaction with the rough surface allows the determination of some of its parameters; accordingly, the characteristics of the radar echo return are of great relevance. In this paper we consider a Kirchhoff-fractal electromagnetic model which is applicable to the problems of remote sensing, and we systematically and parametrically analyze the first-order fading characteristics.

Journal ArticleDOI
TL;DR: A formalism is given in which the optical field generated by a near-field optical aperture is described as an analytic expansion over a complete set of optical modes that preserves the divergent behavior of the near field and the dipolar nature of the far field.
Abstract: A formalism is given in which the optical field generated by a near-field optical aperture is described as an analytic expansion over a complete set of optical modes. This vectoral solution preserves the divergent behavior of the near field and the dipolar nature of the far field. Numerical calculation of the fields requires only evaluation of a well behaved, one-dimensional integral. The formalism is directly applicable to experiments in near-field scanning optical microscopy when relatively flat samples are evaluated.

Journal ArticleDOI
TL;DR: In this article, the first images and the first spectrum obtained with a home-built near field optical microscope in the mid-infrared range were obtained with two intense infrared light sources: a cascade arc and the free electron laser CLIO for the time being, the spatial resolution is of the order of λ/4 (namely one micron).

Patent
25 Oct 1996
TL;DR: In this paper, a non-linear coupling between a low-frequency electric field and a laser beam in an electro-optic crystal was proposed for real-time two-dimensional far-infrared imaging applications.
Abstract: Apparatus and methods for characterizing free-space electromagnetic energy, and in particular, apparatus/method suitable for real-time two-dimensional far-infrared imaging applications are presented. The sensing technique is based on a non-linear coupling between a low-frequency electric field and a laser beam in an electro-optic crystal. In addition to a pratical counter-propagating sensing technique, a co-linear approach is described which provides longer radiated field--optical beam interaction length, thereby making imaging applications practical.

Journal ArticleDOI
TL;DR: In this paper, the physics behind the taper formation is examined in detail for the first time and equations describing the initial taper profile and the final aperture size are derived in terms of the experimental conditions.
Abstract: Consistently obtaining super‐resolution with scanning near‐field optical microscopy depends almost entirely on the ability to manufacture reproducibly probes with aperture sizes smaller than 100 nm. The probe fabrication process usually involves heating an optical fiber using a CO2 laser and melt‐drawing the glass to produce a taper. A number of variables ultimately define the taper shape but the actual effects these parameters have are still not clear. In this work, the physics behind the taper formation is examined in detail for the first time and equations describing the initial taper profile and the final aperture size are derived in terms of the experimental conditions. It is shown that the taper shape is primarily determined by the laser spot size. The pulling force, although important, has a lower significance. Continuum mechanics and Stefan’s law are used to show that the aperture size is closely related to the radius of the fiber at the start of the hard pull and the fiber temperature at that time. Further comparisons of experimental data with the expected taper profile exposes the heating effect of the CO2 laser. Further analysis is given using a form of Mie theory which describes the interaction of electromagnetic fields with cylindrical structures. These results give many significant insights into the fabrication process and the formation of the aperture.