What is Gaussian beam: Definition and 38 Discussions

In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or TEM00) transverse Gaussian mode describes the intended output of most (but not all) lasers, as such a beam can be focused into the most concentrated spot. When such a beam is refocused by a lens, the transverse phase dependence is altered; this results in a different Gaussian beam. The electric and magnetic field amplitude profiles along any such circular Gaussian beam (for a given wavelength and polarization) are determined by a single parameter: the so-called waist w0. At any position z relative to the waist (focus) along a beam having a specified w0, the field amplitudes and phases are thereby determined as detailed below.
The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears. Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w0 and of the z = 0 location for the two transverse dimensions x and y.
Arbitrary solutions of the paraxial Helmholtz equation can be expressed as combinations of Hermite–Gaussian modes (whose amplitude profiles are separable in x and y using Cartesian coordinates) or similarly as combinations of Laguerre–Gaussian modes (whose amplitude profiles are separable in r and θ using cylindrical coordinates). At any point along the beam z these modes include the same Gaussian factor as the fundamental Gaussian mode multiplying the additional geometrical factors for the specified mode. However different modes propagate with a different Gouy phase which is why the net transverse profile due to a superposition of modes evolves in z, whereas the propagation of any single Hermite–Gaussian (or Laguerre–Gaussian) mode retains the same form along a beam.
Although there are other possible modal decompositions, these families of solutions are the most useful for problems involving compact beams, that is, where the optical power is rather closely confined along an axis. Even when a laser is not operating in the fundamental Gaussian mode, its power will generally be found among the lowest-order modes using these decompositions, as the spatial extent of higher order modes will tend to exceed the bounds of a laser's resonator (cavity). "Gaussian beam" normally implies radiation confined to the fundamental (TEM00) Gaussian mode.

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  1. K

    A Mode matching to an optical cavity

    Hello! I need to mode match a laser light to an optical cavity and I am a bit unsure what is the most time efficient way of doing so. The cavity is a symmetrical bow-tie and I inject the light from one of the flat mirrors (the other 2 are concave). In this case, I want the shape of the gaussian...
  2. K

    A ABCD matrix formalism for real laser

    Hello! I have an optical setup and a laser producing a gaussian beam and I would like to get the waist of the beam at the end of the setup (i actually want to know what focal length to use for some lenses, such that I get a certain beam waist in the end). Getting the ABCD matrix for my setup is...
  3. M

    A Particle distribution in the longitudinal beam dynamics in accelerator

    In longitudinal beam dynamics, particles exhibits a synchrotron motion. The motion has an amplitude (action) dependant synchrotron frequency. The motion is defined in terms of rf phase devotion deviation ##\phi## as: ##H=\dot \phi^2/2 - \Omega_s^2 \cos(\phi)## I am trying to write the particle...
  4. Haorong Wu

    I Could a Gaussian beam be described as parallel at a large distance?

    Hello, there. Suppose a Gaussian beam is sent and is received at a great large distance, i.e., the propagation distance ##z \gg z_R## the Rayleigh distance. The Gaussian beam can be described by $$E_0 \frac {1}{w(z)} \exp \left ( \frac {-r^2}{w(z)^2}\right )\exp\left ( -i\left (kz+k\frac...
  5. S

    Polarization and intensity of a Gaussian beam

    The equation above (from Wikipedia), assumed that the Gaussain beam has polarization in x-direction, as I know that the polarization means that the oscillation direction of the electric field and so the intenisty... so how we get circular intensity in every direction which means in x and y...
  6. M

    I Gaussian beam in a Fabry-Perot interferometer

    Hello I am reading some introductory laser cavity stuff and I am a bit confused about the existence of gaussian beams in the Fabry-Perot interferometer. If you solve the stability condition for a cavity (i.e. asking for the q parameter to reproduce itself after one round trip) you get that in...
  7. P

    What exactly is the thermal lens effect?

    Hello, i just wanted to ask if you can explain to me what thermal lens effect is? I am supposed to answer why laser beam passing through ink or soy sauce creates this effect and i can't find any information on what actually this thermal lens is. I know of course that it is a lens, but why does...
  8. B

    Gaussian beam spherical mirror reflection question

    Homework Statement Gaussian beam of radius R_i and beam width w_i, The beam is reflected off a mirror with a radius of curvature R = R_i and the reflectivity of this mirror is given as rho(r) = rho_0*exp(-r^2/a^2), where r is the radial distance from the center of the mirror and a is a...
  9. Q

    Creating a two lens system of tunable focal length

    Hello, I would like to reduce the beam size of a laser by a factor of 10, with the purpose of replacing a long (750 mm) lens with a more compact design. Ideally I'd make a Galilean lens pair where the ratio of the focal lengths are 10:1 to produce a small collimated beam. However, I think I...
  10. S

    Ultraviolet Laser Beam Shaping With Constraints

    Homework Statement Homework Equations Lens equation 1/f = 1/d_o + 1/d_i Minimum Gaussian beam spot 2*w_0 = ((4 * lamda * F)/(pi * D)) Where: w_0 = beam waist (half beam diameter) lambda = wavelength F = focal length of lens D = diameter of incoming spot Don't forget to match units. Let...
  11. davidbenari

    The Mystery of the Missing Pi Phase Shift in Gaussian Beam Interference

    The superposition of a gaussian beam and a plane wave generates a pattern of rings whose phase shift before and after the focal plane (of the gaussian beam) is ##\pi##. This means that if you measure interference before and after you'll see the minimums and maximums of intensity invert. We can...
  12. ezgie

    Effect of Collimated lens on Gauss Beam

    Hello everyone, I am trying to find effect of collimated lens on gaussian beam propagation. Do you know how to solve that? I need any equations ,then going to use them via matlab. Thanks
  13. G

    Divergence and transversal extension integral definitions

    Hi. I am reading a paper about gaussian beams and the author says that gaussian beams have simultaneously minimal divergence and minimal transversal extension. In order to prove it, the author states that \mathrm{divergenece} \propto \int_{-\infty}^{+\infty} \frac{d\,k_{x}}{2\pi}...
  14. R

    Is starlight a TEM00 gaussian beam or plane wave?

    I am simulating a radio telescope and confused on what kind of source should I setup to simulate a star. Should it be a TEM00 gaussian beam or simply a plane wave?Cheers, Robin
  15. L

    Gaussian Beam Focusing: Find A(0) at Beam Waist

    A Gaussian beam has an intensity I(r,z), if the beam area at position Z is given by A(Z), then the beam gets focused by a lens of focal length f, what will the area of the beam be at the beam waist A(0) be? So I have been trying to figure this out for ages, I had to replicate an experiment in...
  16. A

    Determine the intensity profile and fwhm for gaussian beam.

    Homework Statement A beam of wavelength 600 nm has initially an intensity profile of Gaussian shape with a fwhm of 1 mm. Determine the intensity profile and fwhm 10 meter away.Homework Equations FWHM = λ/(2NA√(1 + I/Is)) The Attempt at a Solution [/B] FWHM1 = 1mm = 600 nm/(2NA√(1 + I/Is))...
  17. U

    Cubic phase modulation of a gaussian beam

    Hi all, I'm reading a paper on light sheet microscopy, i won't go into detail here but they are generating the light sheet by use of an Airy beam. They are using a term i don't understand when describing how the airy beam is generated. Quote "An Airy beam can be generated through the Fourier...
  18. D

    How Do You Calculate the Waist Radius and Location of a Gaussian Beam?

    https://www.physicsforums.com/attachments/73840 This is the problem I don´t understand, I know I hace to determine the distance z1 which correspond to the widht W1, but I try to solve equation of W1 and W2 for z1 and use the fact z2 = z1 + 0.1m, but I, my question is how to determine the waist...
  19. Greg Bernhardt

    Understanding Gaussian Beams: Definition, Equations, and Parameters

    Definition/Summary A Gaussian beam is an electromagnetic wave, usually a laser beam, with a Gaussian cross-sectional irradiance pattern. The Gaussian irradiance profile results in minimal spreading due to diffraction effects. The spot size w represents the radius or half-width at which the...
  20. A

    Simulation of a Gaussian beam in an optical waveguide

    I am trying to simulate a Gaussian beam through an optical waveguide having a circular cross-section in matlab. I am familiar with the theory of modes in an optical fiber and can analytically calculate the evolution of the beam by breaking down the beam into a sum of infinite modes. However, I...
  21. D

    Frequency doubling and gaussian beam problem.

    1. A Nd:YAG laser operates at a wavelength of 1064 nm and is used for frequency doubling in the non-linear material LiNbO3. The laser outputs 1 W of power in a TEM00 mode with a beam waist ω0 = 1.0 mm on the output mirror. A lens of focal length of 50 mm is placed immediately outside the...
  22. J

    Gaussian Beam Width and Refractive Index

    Homework Statement I know that in free space, the width of a Gaussian beam can be written as W=W_0\sqrt{1+(\frac{z}{z_0})^{2}}. However, I was wondering if it was possible to express this width as a function of refractive index instead (since I don't believe a Gaussian beam originating in say...
  23. M

    Gaussian Beam in a Symmetric Confocal Resonator.

    λHomework Statement A symmetric confocal resonator with mirror spacing d =16 cm, mirror reflectances 0.995, and n = 1 is used in a laser operating at λ[o] = 1 μm. (a) Find the radii of curvature of the mirrors. (b) Find the waist of the (0,0) (Gaussian) mode. (c) Sketch the intensity...
  24. Z

    Understanding Gaussian Beam Contraction and Divergence in Optics

    I am new to lasers. In the expression for q parameter, 1/q = 1/R - j(λ/πw^2) how did we come to know that w(z) is a measure of decrease in field amplitude E with distance? I can't feel it. Does the gaussian beam itself contract to the minimum diameter? Shouldn't a lens be required for this...
  25. F

    Gaussian beam and focusing versus geometrical optics

    Hello Forum, if we take a Gaussian beam whose waist occurs at the front focus of a positive lens, we will see that the Gaussian beam will have another waist at the back focus of the lens... That seems to be in contradiction with what happens in geometrical optics: if we place a point...
  26. F

    Gaussian Beam focusing with lens

    Homework Statement Find the condition needed for a gaussian beam with waist a distance d0 from a thin lens to be imaged (so its geometric image is at di from the lens as per 1/f=1/di + 1/d0) so that its new waist occurs at di, the geometric image position. Homework Equations...
  27. A

    A Gaussian beam is passing through a 2-lense system:

    Homework Statement The first lense has a shorter focal length than the second (f1/f2 The waist of the incoming beam is very far from the lense compared to the focal length & Rayleigh range. What distance between the two lenses would provide the best collimation (Rayleigh range) for the...
  28. R

    Intensity & Amplitude of Gaussian Beam

    Can tell me the exact relationship between the intensity and the amplitude for a gaussian beam ? I know that I is proportional to |A|2 .. but i want the value of this proportianality constant
  29. Y

    Gaussian beam passing through a circular aperture

    Hi all, when I have a Gaussian beam passing through a circular aperture: What should be the far field (Fraunhoffer's) distribution? Thanks in advance, Yoni
  30. K

    Is This a Standard Formulation of a Gaussian Beam?

    In the book "Fundamentals of Photonics", the form of the Gaussian beam is written as I(\rho,z) = I_0 \left(\frac{W_0}{W(z)}\right)^2\exp\left[-\frac{2\rho^2}{W^2(z)}\right] where \rho = \sqrt{x^2 + y^2} However, in some books (I forgot which one), the author use the following form I(R) =...
  31. E

    Diffraction: rectangular aperture and gaussian beam

    Is the Fresnel-Kirchhoff formula (FKF) valid also for gaussian beams? I a book starting from the gaussian intensity: U_0(x,y)=\sqrt{\frac{2}{\pi\omega_0^2}}\exp\left(-\frac{t^2+s^2}{\omega_0^2}\right) it said that using the FKF in free space the gaussian beam spreads (in far-field assumption)...
  32. J

    What should be the intensity of receiving fibers for proper reception?

    I have a transmitting fiber and a receiving fiber. Now the transmitting fiber core diameter is 50 micrometer and I want to know how many receiving fibers should be used so all light from transmitted fiber is received properly. As suggested by some friends beam follows the Gaussian...
  33. Y

    Focusing gaussian beam using a lens

    I am studying further about Gaussian optics. When Gaussian beam pass through a lens, the waist location is given by (z'-f) = (z-f)M^2 Where, z' is the waist location after lens, z is waist location before lens, f is the focal length of the lens M is the magnification. In Gaussian...
  34. F

    How Do You Calculate the Minimum Gaussian Beam Waist?

    Physics students out there...how do you find the Minimum Beam waist after being given the beam waist and the focal length of a lens? Please help!
  35. N

    Gaussian Beam focused using a lens

    Homework Statement Hello, I'm really confused about this one, =( Suppose I have a guassian beam that is colliminated (beam expanded) and then suppose i let it passed through a lens to focus it. Given an initial waist and focal length of the lens. How can i find the waist (or half width)...
  36. A

    Calculate Gaussian Beam Radius for FRAP Diffusion Coefficient

    I'm doing FRAP(fluorescence recovery after photobleaching) Diffusion coefficient is what I want to calculate. t=w^2*f/(4D) t:halftime of recovery fluorescence w:radius of the focused circular laser beam at the e^(-2) intensity f : correction factor for the amount of bleaching D:diffusion...
  37. N

    Gaussian Beam Optics Experiment: Measuring Beam Waist & Rayleigh Range

    I am doing a Gaussian Beam Optics Experiment - where I observe how lasers have a gaussian intensity profile. I've measured the beam radius at several points from the Laser in the far-field (ie. position 'z' >> Rayleigh Range). I want to know why is there a beam waist inside the laser. How...
  38. B

    Truncating a Gaussian Beam: Effects on Intensity and Other Parameters?

    Hi All, I am just wondering whether there is any kind soul to help me out with the following problem: If a gaussian beam is truncated by the circular aperture situated at the beam waist just before the entrance of a microscope objective lens, what should be the intensity distribution of...