Showing papers on "Gaussian beam published in 1978"
TL;DR: In this article, a direct numerical integration of the wave equation is used to establish the validity of approximating the fundamental mode of graded-index fibers by a Gaussian function, and the fundamental modes of fibers, whose index profile can be expressed as a power law, are indeed very nearly Gaussian in shape.
Abstract: Direct numerical integration of the wave equation is used to establish the validity of approximating the fundamental mode of graded-index fibers by a Gaussian function. We show that the fundamental modes of fibers, whose index profile can be expressed as a power law, are indeed very nearly Gaussian in shape (that is probably also true for graded-index fibers with convex profiles other than a power law). Graphs and empirical analytical expressions are presented for the optimum Gaussian beam width parameter and for the propagation constant of the fundamental mode.
445 citations
TL;DR: The purpose of this paper is to show that when a lens-axicon combination is illuminated by a Gaussian beam, the transverse distribution of the focal ring is also aGaussian distribution.
Abstract: An axicon and a lens are combined to form an optical system producing a ring-shaped pattern. The purpose of this paper is to show that when a lens-axicon combination is illuminated by a Gaussian beam, the transverse distribution of the focal ring is also a Gaussian distribution. The typical width of this distribution was found to be, in the case of the lens-axicon combination, 1.65 times greater than the typical width of the Gaussian beam obtained by focusing the same beam using the lens alone. This focusing system is well suited for the drilling of good quality large diameter holes using a high power laser beam.
144 citations
TL;DR: In this paper, the light distribution produced by a lens with an annular aperture with approximately Gaussian cross-section is calculated by summing over Laguerre-Gaussian modes.
Abstract: The light distribution produced by a lens with an annular aperture with approximately Gaussian cross-section is calculated by summing over Laguerre-Gaussian modes. The advantage of this approach is that it gives the intensity at all points in space. This is of particular value when the cross-section of the annulus is narrow compared with its radius, because then the intensity varies slowly along the optic axis. Intensity is plotted for the region near the focus, far from the focus, along the optic axis, and on the geometrical cone of illumination. Contours of equal intensity in the focal region are also plotted. The possibility of constructing low-loss resonators with annular mirrors is also discussed.
75 citations
TL;DR: In this paper, the characteristics of a Gaussian beam that is reflected or transmitted by an interface separating a denser medium from a rarer medium are mainly described by means of numerical integration.
Abstract: The characteristics of a Gaussian beam that is reflected or transmitted by an interface separating a denser medium from a rarer medium are mainly described by means of numerical integration. An approximate result is shown to compare with the exact value obtained by numerical integration. The cases where the incident angle θ is arbitrary, that is, θ = θc (critical angle), θ → θc, θ ≷ θc are treated. Transmitted power in the rarer medium is obtained, from which properties of a lateral wave are found.
58 citations
01 Feb 1978
TL;DR: In this paper, the scattering of a Gaussian beam wave by a spherical object is treated exactly in terms of the vector wave functions without any restriction on the size or the position of the scatterer.
Abstract: The scattering of a Gaussian beam wave by a spherical object is treated exactly in terms of the vector wave functions without any restriction on the size or the position of the scatterer. Expressions obtained for the powers absorbed and scattered are given as linear combinations of the well-known Mie coefficients and can be readily applied to numerical computation. The corresponding problem for the scattering of a beam produced by a laser operating in the TEM01* mode is also solved.
48 citations
TL;DR: In this paper, the conical intensity pattern aragonite has been measured with an incident Gaussian beam (TEM00) of a helium neon laser and it is shown that the integrated intensities on either side of the Poggendorff dark circle are not equal, unless the far-field condition for Fraunhofer diffraction is satisfied.
Abstract: Detailed measurements of the conical intensity pattern aragonite have been carried out with an incident Gaussian beam (TEM00) of a helium neon laser. Quantitative agreement with theoretical calculations is found. It is shown that the integrated intensities on either side of the Poggendorff dark circle are not equal, unless the far-field condition for Fraunhofer diffraction is satisfied.
48 citations
TL;DR: In this article, the scattering of a Gaussian beam wave by a spherical object is treated exactly in terms of the vector wave functions without any restriction on the size or the position of the scatterer.
Abstract: The scattering of a Gaussian beam wave by a spherical object is treated exactly in terms of the vector wave functions without any restriction on the size or the position of the scatterer. Expressions obtained for the powers absorbed and scattered are given as linear combinations of the well-known Mie coefficients and can be readily applied to numerical computation. The corresponding problem for the scattering of a beam produced by a laser operating in the TEM01* mode is also solved.
48 citations
TL;DR: In this article, the prism system with a grating for an anastigmatic optical resonator for a dye laser of narrow linewidth and of short pulse duration is presented. But the design principle is not discussed.
Abstract: Basic properties are given of the prism anamorphic expander of a Gaussian beam composed of a couple of prisms in tandem. Its shorter overall length for a given expansion, relative ease of optical adjustment, a sharp selection of polarization component, and rather small inclusive dispersion make it an excellent beam expander in a specific laser cavity. The design principle is presented of the prism system with a grating for an anastigmatic optical resonator for a dye laser of narrow linewidth and of short pulse duration.
36 citations
TL;DR: In this paper, the nonlinear propagation problem of optical beams in media with an intensity dependent indices of refraction is solved in the case of a fundamental gaussian beam by assuming everywhere along the propagation path a quadratic index profile.
27 citations
TL;DR: In this article, a CW submillimeter waveguide laser operating on 190 and 195 μm DCN lines with high volumetric efficiency was described, where the laser cavity is a 3.2 cm inner diameter, 70 cm long, Pyrex tube with plane reflectors against its ends.
TL;DR: In this paper, the problem of tracking a well-collimated beam reflected repeatedly within a circular cross section undergoes periodic focusing and defocusing is analyzed by considering first the field excited by an isotropic line source inside a dielectric cylinder, and then converting this to Gaussian beam excitation by assigning a complex value to the source coordinate location.
Abstract: A well-collimated beam reflected repeatedly within a circular cross section undergoes periodic focusing and defocusing. This behavior is of interest for tracking of beams around a type of acoustic surface wave disk delay line, and it also relates to beam monitoring after oblique injection into the endface of a multimode optical fiber. The problem is analyzed by considering first the field excited by an isotropic line source inside a dielectric cylinder, and then converting this to Gaussian beam excitation by assigning a complex value to the source coordinate location. Because the wavelength is small compared to the cylinder radius, ray-optical methods are employed to construct the solution, with inclusion of such novel ingredients as the lateral ray shift on a curved boundary. Results are obtained for the amplitude and phase of the ray and beam field and for such beam parameters as the location of the focus the minimum beam width and the rate of beam divergence between successive reflections.
TL;DR: The modulation transfer function and the irradiance profile of a phase-compensated laser beam propagating through atmospheric turbulence are calculated for various values of the normalized transmitter diameter, D/r(0).
Abstract: The modulation transfer function and the irradiance profile of a phase-compensated laser beam propagating through atmospheric turbulence are calculated for various values of the normalized transmitter diameter, D/r0. Both focused Gaussian beam and collimated beam with modal phase corrections of arbitrary orders are considered using Zernike polynomials as basic correcting modes. Examples are given for low-order corrections such as tilt, focus, and astigmatism as well as for higher order corrections. The beam quality criteria, defined in terms of Strehl ratio, spot radius, and energy in a bucket, are used to measure the beam performance with different compensating modes. The effects on the beam propagation of central obscuration of the transmitter are also examined, and numerical results are given.
TL;DR: In this article, a numerical technique is described which is capable of providing useful data on the propagation characteristics of optical multimode guiding structures whose index of refraction variation may be quite arbitrary.
Abstract: The ability to predict the light propagation characteristics in various practical multimode guiding structures is very important in optical fiber communications and in optical image transfer. The usual mode-by-mode analysis is impractical when the guiding structure is capable of supporting hundreds or thousands of modes. In this study a numerical technique is described which is capable of providing useful data on the propagation characteristics of optical multimode guiding structures whose index of refraction variation may be quite arbitrary. As a specific example, the problem of infinite or truncated Gaussian beam propagation in a radially inhomogeneous fiber with parabolic index profile is solved. The numerical results for the infinite Gaussian beam case are compared with exact analytical data and they are in complete agreement.
TL;DR: In this paper, a new and simple technique for measuring the effective diameter of a laser beam used in material processing is described, and the time for the temperature of a spot heated by the laser beam to rise to 90% of equilibrium is compared with that predicted theoretically for a Gaussian TEM00 laser beam.
Abstract: A new and simple technique for measuring the effective diameter of a laser beam used in material processing is described. The time for the temperature of a spot heated by the laser beam to rise to 90% of equilibrium is compared with that predicted theoretically for a Gaussian TEM00 laser beam. A Gaussian beam diameter equivalent is thus deduced. This calculated diameter is of particular relevance to applications where the laser is used as a heat source.
TL;DR: In this article, a new type of compact Iight-weight Gaussian-beam launcher for producing a focused-microwave exposure field in biological experiments is described, which consists of a simple cylindrical waveguide excited with a balanced mixture of complementary modes and the diffracted field due to this waveguide aperture is made to illuminate a dielectric sphere (lens).
Abstract: A new type of compact Iight-weight Gaussian-beam launcher for producing a focused-microwave exposure field in biological experiments is described. This launcher is identical to the structure described by the authors elsewhere, except that a simple circular waveguide aperture, instead of a corrugated pipe is used to illuminate a dielectric sphere lens with the result that a considerable weight and size reduction of the launcher is achieved. The proposed structure consists of a simple cylindrical waveguide excited with a balanced mixture of complementary modes and the diffracted field due to this waveguide aperture is made to illuminate a dielectric sphere (lens). It is shown that a near-circular Gaussian beam is then pruduced in the image space of the sphere with a high focusing factor. Design details, theoretical calculation, and experimental results concerning a practical launcher are presented. Suitability of this compact structure for diathermy applications at a frequency of 2450 MHz is mentioned.
TL;DR: In this article, the propagation of optical beams in a circularly curved graded-index fiber has been studied and a closed-form expression for the kernel has been obtained, from which one can determine the field distribution at any point inside the fiber.
Abstract: In the present paper we have studied the propagation of optical beams in a circularly curved graded-index fibre. A closed-form expression for the kernel has been obtained, from which one can determine the field distribution at any point inside the fibre. For the special case of a Gaussian beam incident on the face of a fibre, an analytic expression for the intensity distribution has been obtained from which one can easily determine the path of the centre of the beam. Several incident conditions have been considered and it is shown that the beam, in general, follows a skew path, though there are specific cases when it stays in the meridional plane only. In practical cases the ellipticity introduced due to the bending of the fibre, is very small.
TL;DR: In this article, the problem of a reflected Gaussian beam after it has propagated through an inhomogeneous medium is studied and the characteristics of the displacement of the beam are described in detail.
Abstract: The problem of a reflected Gaussian beam after it has propagated through an inhomogeneous medium is studied. The characteristics of the displacement of the beam are described in detail. Three-layered media composed of two different homogeneous media and a finite stratified medium, whose permittivity decreases linearly with distance, are considered. The amount of the beam displacement obtained by this theory is much larger than that predicted by the conventional Goos–Hanchen shift.
TL;DR: The 3-D time-independent unpolarized radiative transfer equation is developed into a form amenable to numerical solution by expansion of the total intensity in orders of scattering by developing an eight-direction quadrature approximation to the source function and an optimized path-by-path intensity integration scheme.
Abstract: The 3-D time-independent unpolarized radiative transfer equation is developed into a form amenable to numerical solution by expansion of the total intensity in orders of scattering. A 2-D numerical algorithm is formulated using an eight-direction quadrature approximation to the source function and an optimized path-by-path intensity integration scheme. Computer code generated from the algorithm is used to examine the multiple scattering effects at 1.06 μm, 3.0 μm, and 10.6 μm in Deirmendjian C3 fog on a finite uniform intensity profile beam and an infinite Gaussian intensity profile beam. Transmission and backscatter for both beams are examined as well as contrast degradation of the uniform beam and spread of the Gaussian beam.
01 Oct 1978
TL;DR: In this paper, a simple and compact gaussian beam launcher to produce a focused microwave field for selective partial-body exposures in biological experiments is described, which consists of a Potter's dual mode horn with slight modifications and the aperture of this hom is loaded with a dielectric sphere.
Abstract: A simple and compact gaussian beam launcher to produce a focused microwave field for selective Partial-body exposures in biological experiments is described. The proposed structure consists of a Potter's dual mode horn with slight modifications and the aperture of this hom is loaded with a dielectric sphere (lens). It is shown that the resulting diffracted field in the image-space of the lens is a near-circular gaussian-beam with a high focusing factor. The details of an X-band test launcher with measured and theoretical results are presented. The simplicity of the proposed structure enables a compact and light-weight design of the launcher at the diathermy frequency of 2450 MHz.
TL;DR: In this paper, the self-focusing of a Gaussian electromagnetic beam in a collisional plasma, flowing transverse to the direction of propagation, was studied, and the collision term in the Boltzmann transfer equation was modified.
Abstract: Studies the self-focusing of a Gaussian electromagnetic beam in a collisional plasma, flowing transverse to the direction of propagation. On account of the finite flow velocity of the plasma, the collision term in the Boltzmann transfer equation gets modified. Hence the heating of the carriers and diffusion in the presence of the Gaussian beam becomes flow velocity dependent; the self-focusing of the beam thus gets considerably modified.
TL;DR: In this paper, the log-amplitude temporal frequency spectra of the fluctuations of a Gaussian beam propagating through weak turbulence are investigated using Rytov's method and the general formula for an arbitrary point of the beam cross-section, arbitrary beam parameters and arbitrary values of the inner scale of turbulence is obtained.
Abstract: The log-amplitude temporal frequency spectra of the fluctuations of a Gaussian beam propagating through weak turbulence are investigated using Rytov's method. The general formula for an arbitrary point of the beam cross-section, arbitrary beam parameters and arbitrary values of the inner scale of turbulence is obtained. Two particular cases of the log-amplitude scintillations, if the radius vector of the observation point is either parallel with, or perpendicular to the direction of the wind velocity, are analysed in detail. The low-frequency behaviour on the beam axis is characterized by two terms. The first is a constant depending on beam parameters and on the propagation region, and the second depends on the frequency and the focusing of the beam. The off-axis behaviour differs substantially from that on the beam axis. The deviation of the beam spectra shape in the high-frequency limit from that of the plane and spherical wave depends mainly on the beam radius in the receiving plane and is discussed fo...
TL;DR: Approximate solutions of the wave equation are investigated, which can be considered as Gaussian beams affected by third-order spherical aberration, which are good approximations to the beams emerging from media whose square refractive index is described by a fourth-degree polynomial of the transverse coordinate.
Abstract: Approximate solutions of the wave equation are investigated, which can be considered as Gaussian beams affected by third-order spherical aberration. In practical cases, such beams are good approximations to the beams emerging from media whose square refractive index is described by a fourth-degree polynomial of the transverse coordinate. The measure of their spherical aberration could be a means for the determination of the coefficient of the fourth-order term in the expression of the square refractive index of the graded-index medium.
TL;DR: In this paper, the effects of the Gaussian beam characteristics of the pump and laser beams on the behavior of a CW dye laser were examined, and it was found that the power out versus pump power curve exhibits a nonlinear shape.
Abstract: The effects of the Gaussian beam characteristics of the pump and laser beams on the behavior of a CW dye laser are examined. No assumption is made regarding the radial distribution of the excited state population. The results are compared to existing theory. It is found that the power out versus pump power curve exhibits a nonlinear shape.
TL;DR: In this paper, transfer matrices for an inclined plate and for the investigated medium bounded by two plates are derived for the beam parameters in the medium under study, including the position, dimensions, and radii of curvature of the beams in the meridional and sagittal planes.
Abstract: The transfer matrix mathod is used in a theoretical analysis of the transformation of a Gaussian beam passing through various optical elements of a laser anemometer such as lenses, inclined plane-parallel plates, and media with different refractive indices. The transfer matrices are found for an inclined plate and for the investigated medium bounded by two plates. Analytic expressions are derived for the beam parameters in the medium under study, including the position, dimensions, and radii of curvature of the beams in the meridional and sagittal planes. The misalignment of the laser anemometer optical system is calculated by scanning the element under study along the bisectrix of the intersection of two beams allowing for astigmatism. The main theoretical conclusions are compared with the experimental results.
TL;DR: It is shown that 1-D Gaussian beams propagate just as in an infinite medium with the refractive index neq of the particular excited TE or TM mode, from Maxwell's equations with a time dependence exp(-iωt).
Abstract: Very often for integrated optics applications Gaussian laser beams are coupled into thin film optical waveguides via, for example, a high index prism. To our knowledge the characteristics of a wave with a lateral Gaussian distribution propagating in a thin film have not as yet been reported. Of course, if the guide structure is such that 2-D confinement occurs transverse to the propagation direction, the Gaussian beam must couple into the 2-D waveguide modes; that situa tion will not concern us here. However, if the only guidance is along the x direction as in Fig. 1, aside from the waveguide patterns in this x direction, the Gaussian beam is otherwise unconfined. We show herein (perhaps not surprisingly) that such 1-D Gaussian beams propagate just as in an infinite medium with the refractive index neq of the particular excited TE or TM mode. From Maxwell's equations with a time dependence exp(-iωt), it is not difficult to show that Hx, the H-field component perpendicular to the layer boundaries, satisfies
TL;DR: In this paper, an analysis is made of the transmission of a Gaussian beam by an amplifier with a spatially inhomogeneous active medium and the results are used in estimating the precision of gain measurements by means of a probe beam.
Abstract: An analysis is made of the transmission of a Gaussian beam by an amplifier with a spatially inhomogeneous active medium. The results are used in estimating the precision of gain measurements by means of a probe beam. It is shown that even a slight inhomogeneity may distort the measured frequency dependences and spatial distributions of the gain.