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	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are described by Gaussian functions.
		R(z) is the radius of curvature of the wavefronts comprising the beam.
		The complex beam parameter plays a key role in the analysis of gaussian beam propagation, and especially in the analysis of optical resonator cavities using ray transfer matrices.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Gaussian_beam (817 words)

	Diffraction Limited Beams and Gaussian Optics
		Uniformly Illuminated Apertures: Generally, when discussing beam widths and beam shapes of microwave dishes and optical telescopes, it is usual to assume the simple case of uniform illumination, i.e., constant beam intensity across the aperture, with a sudden cut-off of the beam at the extremes of the aperture.
		It is a property of a Gaussian beam that the far-field radiation pattern is the same as the near-field.
		(4), and THETA3 = 0.0102", the corresponding FWHM diameter of the Gaussian beam at 10 L.Y. is:
	www.coseti.org /radobs14.htm (2170 words)

	1.2.2 Gaussian Beam Analysis (Site not responding. Last check: 2007-10-14)
		Gaussian beams are transformed to Gaussian beams by optical elements so that the beam profile is always known throughout the optical path.
		The disadvantage with Gaussian beams is that the beam is assumed to be of infinite extent.
		In Gaussian beam analysis the beam widths used are measured from the centre of the beam to the distance where the field amplitude has dropped to the 1/e level.
	www.drao-ofr.hia-iha.nrc-cnrc.gc.ca /science/ska/feed_options/node5.html (340 words)

	Gaussian beam (Site not responding. Last check: 2007-10-14)
		In optics, a Gaussian beam, named in honor of Carl Friedrich Gauss (rhymes with house), is a beam of light whose electric field intensity distribution is a Gaussian function.
		For a beam of wavelength λ at a distance z along the beam from the beam waist, the variation of the spot size is given by: :
		The divergence of a Gaussian beam, at a sufficient distance from the waist, tends to an angle: :
	www.serebella.com /encyclopedia/article-Gaussian_beam.html (571 words)

	Science Fair Projects - Gaussian beam
		When refracted by a lens, a Gaussian beam is transformed into another Gaussian beam (characterized by a different set of parameters), which explains why it is a conveninent, widespread model in laser optics.
		For a beam of wavelength λ at a distance z along the beam from the beam waist, the variation of the spot size is given by:
		The divergence of a Gaussian beam, at a sufficient distance from the waist, tends to an angle:
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Gaussian_beam (433 words)

	Melles Griot Optics Guide - Gaussian Beam Optics
		Unfortunately, the output from real-life lasers is not truly Gaussian (although helium neon lasers and argon-ion lasers are a very close approximation).
		In all cases, a circularly symmetric wavefront is assumed, as would be the case for a helium neon laser or an argon-ion laser.
		Diode laser beams are asymmetric and often astigmatic, which causes their transformation to be more complex.
	www.mellesgriot.com /products/optics/gb_1.htm (429 words)

	Michael Tidwell's Master Thesis
		As the sound wave traverses the light beam, the diffracted beam is intensity modulated according to the amplitude modulated envelope on the carrier signal.
		Gaussian beam theory states the smaller a Gaussian beam is focused, the greater the beam divergence (after the focused spot).
		The beam splitter is a 2 [mm] thick parallel plate beamsplitter which is anti-reflection coated on one side to reduce double reflections.
	www.hitl.washington.edu /publications/tidwell/ch7.html (2547 words)

	Gaussian Beam Propagation / Light Through Lenses / Beam Expansion Calculator
		In the equations above R is the radius of curvature, W is the beam radius, i is the squareroot of negitive 1 and &lambda is the wavelength.
		For a gaussian beam propagating through a lens A=1, B=0, C=-1/f (where f is the focal length) and D=1.
		For a gaussian beam propagating through air A=1, B=d (where d is the distance), C=0 and D=1.
	www.ee.byu.edu /photonics/Gaussian_Beam_Propagation.phtml (128 words)

	Olympus FluoView Resource Center: Laser Systems for Confocal Microscopy
		The coherence and polarization characteristics of a laser beam are measured by the distribution of light in the beam cross-section, or profile, which changes with increasing distance from the exit mirror of the laser.
		When the Gaussian beam diameter is equal to the diameter of the lens aperture, the output beam intensity profile is a mixture of the Gaussian function and that of an Airy disk.
		When a laser beam is focused by a lens onto an optical fiber, the coupling efficiency and characteristics of the beam that emerges from the fiber depend heavily on the fiber geometry.
	www.olympusfluoview.com /theory/confocallaserintro.html (5325 words)

	ALLEGRETTO WAVE Custom LASIK Excimer Laser System
		A small diameter laser beam or also known as spot size is very important for both accuracy and smoothness.
		If the size of the laser beam is larger the result is that the beam is too large to make fine adjustments throughout the cornea.
		The result is that with a small beam less than 1 mm with a gaussian profile allows for the proper and accurate treatment of the smallest curvatures of the cornea and also allowing for a smooth corneal surface.
	www.allegretto.ca /patient/beam.html (146 words)

	Olga Korotkova
		Gaussian beams) obtained by it were found to be in agreement with ones derived earlier by standard techniques.
		The effect of partial coherence (induced by a diffuser) on the scintillation index of the beam in the presence of weak atmospheric turbulence is investigated as a function of the correlation length of the diffuser and the propagation distance.
		The dependence of the fluctuating intensity of a class of stochastic electromagnetic beams on its polarization properties is studied as the beam propagates in a non-absorbing, homogeneous atmospheric turbulence described by the Kolmogorov’s model.
	www.pas.rochester.edu /~korotkov (5239 words)

	news
		The Gaussian decomposition method is most appropriate for workers who do diffraction calculations in systems that have no axis of symmetry, or systems that have three-dimensional apertures and obscuration, or for those who must propagate fields that are not Gaussian or flat-top.
		Gaussian beamlets are then synthesized from these rays at the focal plane, and superposed to calculate the total field, including all interference effects.
		Gaussian beam decomposition is an easier approach to performing physical optics calculations within a wide class of fully three-dimensional systems.
	www.ptbmagazine.com /ptb.feat_0399.html (1039 words)

	Melles Griot Optics Guide - Gaussian Beam Optics (Site not responding. Last check: 2007-10-14)
		In most laser applications it is necessary to focus, modify, or shape the laser beam by using lenses and other optical elements.
		Diode laser beams are asymmetric and often astigmatic, which causes their transformation to be more complex.
		Although in some respects component design and tolerancing for lasers are more critical than they are for conventional optical components, the designs often tend to be simpler since many of the constants associated with imaging systems are not present.
	optics.mellesgriot.com /opguide/gb_1.htm (429 words)

	FDTD Calculation of Focused Gaussian Beam Propagation
		To compare the effects of both a tissue phantom and cells on the propagation of a focused beam, the FDTD model was modified to include a focused Gaussian beam.
		Comparing this with the plot of the focused beam in a clear medium (Figure 6.4), it is evident that the beam is distorted, although it retains its basic shape.
		The radial beam profile through the focus (z=0 in Figure 6.5) is plotted in Figure 6.6 for a focused beam passing through a cell, a tissue phantom, and free space.
	www.nmr.mgh.harvard.edu /~adunn/papers/dissertation/node79.html (781 words)

	[No title]
		The parameter w0, usually called the Gaussian beam radius, is the radius at which the intensity has decreased to 1/e2 or 0.135 of its value on the axis.
		When a beam passes through a lens, mirror, or dielectric interface, the diameter is unchanged but the wavefront curvature is changed, resulting in new values of waist position and waist diameter (or Rayleigh range) on the output side of the interface.
		At large distances from a beam waist, the beam appears to diverge as a spherical wave from a point source located at the center of the waist.
	www.newport.com /servicesupport/Tutorials/default.aspx?id=112 (1682 words)

	The Changhuei Yang Research Group [Research]
		The focal beam profile of the Gaussian beam (a) measured by SHArP, (b) imaged by the CMOS imaging sensor.
		The focal beam profile of the Gaussian beam confined by an iris diaphragm in width (c) measured by SHArP, (d) imaged by the CMOS imaging sensor.
		The focal diffraction pattern of the Gaussian beam confined by an iris diaphragm in width (a) measured by SHArP (b) calculated.
	www.its.caltech.edu /~biophot/research/SHArP.html (287 words)

	Frequently Asked Questions about CO2 laser lenses for cutting
		The smallest theoretical diameter is, roughly, wavelength of the beam.
		inversely proportional to the diameter of the beam.
		laser beam - due to diffraction and beam divergence which in turn are related to dimensions being finite - will focus to a spot size that is directly proportional to the focal length of the lens and inversely proportional to the diameter of the laser beam at the point it meets the lens.
	www.parallax-tech.com /faq.htm (3037 words)

	Open Channel Foundation: Gaussian Beam Laser Resonator Program
		Laser resonators obey the laws of Gaussian beam propagation, not geometric optics.
		Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed.
		In addition to the internal beam elements the optical system may contain elements external to the resonator.
	www.openchannelfoundation.org /projects/Gaussian_Beam_Laser_Resonator_ (338 words)

	Arden Photonics \| Gaussian Beam
		The efficiency of coupling into a single-mode fibre may calculated from the overlap of the complex field functions of the incident Gaussian beam and the beam waist of the field in the fibre (known as the 'mode-field diameter').
		It was seen in equation (2) that the beam waist and the angle of divergence of a Gaussian beam are inter-related.
		This is in contrast to the geometric case of coupling into multimode fibre, where the angular extent of light, known as the fibre's numerical aperture, is determined by the refractive index difference between the core and cladding region of the fibre and is not related to its diameter.
	www.ardenphotonics.com /products/coupling.htm (758 words)

	Encyclopedia of Laser Physics and Technology - Gaussian beams, laser beam, fundamental transverse modes
		Gaussian beams are usually considered in situations where the beam divergence is relatively small, so that the so-called paraxial approximation can be applied.
		In terms of Gaussian beam parameters, the paraxial approximation requires that the beam radius at the focus is large compared with the wavelength.
		Gaussian beams are the lowest-order self-consistent field distribution in optical resonators (→ resonator modes) as long as there are no intracavity elements causing beam distortions.
	www.rp-photonics.com /gaussian_beams.html (1203 words)

	Experiment 5: Gaussian beams
		The diameter of the beam waist is approximately 0.48 mm.
		Position the translation stage on the optical bench so that the aperture is in the beam path, and visually center the aperture on the beam.
		Assuming that the beam waist is located right after the recollimating lens, calculate the beam radius at 100 m, 1 km, and 10 km.
	www.ee.bilkent.edu.tr /~ee428/manual/html/node9.html (589 words)

	Gabor-based narrow-waisted Gaussian beam algorithm for transmission of aperture-excited 3D vector fields through ...
		Gabor-based narrow-waisted Gaussian beam algorithm for transmission of aperture-excited 3D vector fields through arbitrarily shaped 3D dielectric layers
		We have previously developed computationally efficient Gabor-based, narrow-waisted (NW), discretized Gaussian beam (GB) algorithms for the determination of the 3D vector fields radiated by 2D arbitrary vector planar aperture distributions.
		Citation: Maciel, J., and L. Felsen (2002), Gabor-based narrow-waisted Gaussian beam algorithm for transmission of aperture-excited 3D vector fields through arbitrarily shaped 3D dielectric layers, Radio Sci.
	www.agu.org /pubs/crossref/2002/2001RS002556.shtml (221 words)

	Jose Mawyin / Stony Brook Laser Teaching Center
		A linearly polarize beam at 45 degrees from these axis will be separated because the components of the beam will propagate with different speed (propagation in a medium is related to the reffractive index).
		The efficiency of the beam addition and etalon flattening scheme was compared and appears that we can keep more of the initial light intensity with this multiple beam process.
		The transmission function of the etalon depends on the reflectivity of the etalon, the refractive index of the etalon material, the thickness of the etalon, and the angle of rays of the beam with respect to the normal of the etalon.
	laser.physics.sunysb.edu /~jose/flatbeam.html (2062 words)

	Photon Engineering FRED, Interferometry and Beam Propagation
		Each Gaussian beam is traced through the system and, at the desired plane in space, the individual Gaussian beams are summed together coherently to regenerate the optical field.
		The waist rays are initially propagated parallel to base ray and are displaced from the base ray by an amount that is proportional to the waist dimensions of the Gaussian beam.
		Gaussian beam decomposition algorithm has been further enhanced to model arbitrary polarized beams as well.
	www.photonengr.com /fred/interferometry.html (421 words)

	Model Gallery : Propagation of a 3D Gaussian Beam Laser Pulse (Site not responding. Last check: 2007-10-14)
		The first one is a 3D time domain simulation of Gaussian beam pulse propagation.
		The YAG (lambda=1.06 µm) laser beam pulse has its waist of the beam is inside the domain and the input and output boundaries are bent according to the spherical wave fronts of the Gaussian beam.
		The second one is a 2D simulation of the 2nd- harmonic generation from a wave propagating in a nonlinear material.
	www.femlab.com /showroom/gallery/955.php (197 words)

	Laser Focus World - Ray tracing alternatives model telecom systems
		And that gives the beam on the output surface directly, because the intensity of the beam on the output surface is proportional to the Fourier transform of the input beam squared.
		And those Gaussian beams would be distributed spatially across the front of the plane wave.
		But the Gaussian method also has limitations for situations in which aperture dimensions or object spatial frequencies are near to or below the wavelength of the light traveling through them.
	lfw.pennnet.com /Articles/Article_Display.cfm?Article_ID=97829&CFID=9994323&CFTOKEN=80567995 (921 words)

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