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  • mbenkerumass 6:00 am on February 22, 2020 Permalink | Reply
    Tags: , Lasers, ,   

    Gas Laser and Semiconductor Lasers 

    heliumconstruction

    The Gas Laser

    In laboratory settings, gas lasers (shown right) are often used to eveluate waveguides and other interated optical devices. Essentially, an electric charge is pumped through a gas in a tube as shown to produce a laser output. Gasses used will determine the wavelength and efficiency of the laser. Common choices include Helium, Neon, Argon ion, carbon dioxide, carbon monoxide, Excimer, Nitrogen and Hydrogen. The gas laser was first invented in 1960. Although gas lasers are still frequently used in lab setting sfor testing, they are not practical choices to encorperate into optical integrated circuits. The only practical light sources for optical integrated circuits are semiconductor lasers and light-emitting diodes.

     

    The Laser Diode

    ladio

    The p-n junction laser diode is a strong choice for optical integrated circuits and in fiber-optic communications due to it’s small size, high reliability nd ease of construction. The laser diode is made of a p-type epitaxial growth layer on an n-type substrate. Parallel end faces may functions as mirrors to provide the system with optical feedback.

     

    The Tunnel-Injection Laser

    The tunnel-injection laser enjoys many of the best features of the p-n junction laser in it’s size, simplicity and low voltage supply. The tunnel-injection laser however does not make use of a junction and is instead made in a single crystal of uniformly-doped semiconductor material. The hole-electron pairs instead are injected into the semiconductor by tunneling and diffusion. If a p-type semiconductor is used, electrons are injected through the insulator by tunneling and if the semiconductor is n-type, then holes are tunneled through the insulator.

     
  • mbenkerumass 6:00 am on February 15, 2020 Permalink | Reply
    Tags: Lasers,   

    Hermite-Gaussian, Laguerre-Gaussian and Bessel Beam 

    The Gaussian Beam [link] is not the only available solution to the Helmholtz equation [link]. The Hermite-Gaussian Beam also satisfies the Helmholtz equation and it shares the same wavefronts (shape) of the Gaussian Beam. Where it differs is in the distribution of intensity in the beam. The Hermite-Gaussian Beam distribution is a modulated Gaussian distribution in the x and y directions which can be seen as a number of functions in superposition. The below figures depict the cross-sections of ascending order intensity distributions for the Hermite-Gaussian Beam. Secondly, distribution orders zero through three are shown.

    hermitegau2hermitegau1

    The Complex amplitude of the Hermite-Gaussian beam labeled by indexes l,m (orders):

    hermitegaussian

     

    Laguerre-Gaussian Beams

    The Laguerre-Gaussian Beam is a solution to the Helmholtz equation in cylindrical coordinates.

    laguerregau1

    The shape of the Laguerre-Gaussian Beam intensity distribution is of a toroid which increases in radius for orders where m = 0 and for orders m > 0, it takes the form of multiple rings.

    laguerregau2

     

    The Bessel Beam

    The Bessel Beam, by comparison to the Gaussian Beam differs in that it has a ripple effect by oscillation in addition to a similar gaussian curve. The complex amplitude of the Bessel Beam is an exact solution to the Helmholtz equation, while the complex amplitude of the Gaussian beam is an approximate solution (paraxial solution).

    besselbeam

    B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Hoboken: Wiley, 2019.

     
  • mbenkerumass 6:00 am on February 13, 2020 Permalink | Reply
    Tags: Lasers,   

    Gaussian Beam Transmission Through Optical Components 

    The most important note about the transmission of a Gaussian Beam [link] through various optical components [link] is that the beam will remain Gaussian, given that the system is paraxial. The shape of the Gaussian beam will change according to the components, however.

    The complex amplitude of the Gaussian beam (width) is adjusted to the width of an optical component, for example.

    beam8

    The Gaussian beam that emerges from the above lens takes the following formulas:

    beam9

    Lenses may be used to focus the a Gaussian beam. This is achieved by positioning the lense appropriately according to the location of the beam waist. For applications such as laser scanning and compact-disk burning, it is desired to focus the beam to the smalles size possible.

    beam10

    The focused waist W0′ and the distance of the focused waist z’ are a function of the waist of the original beam and the focal length f of the lens.

    beam11

    Beams may also be relayed and expanded using lenses.

    relaylens

    beamexpansion

    A Gaussian beam, as do rays and waves behave differently for a plane mirror (i.e. spherical mirror with infinite radius) and spherical mirrors.

    beam12

    As is the case with geometrical ray optics, beam properties through a system can be modeled using the ABCD matrix method.

    beam13

    B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Hoboken: Wiley, 2019.

     
  • mbenkerumass 6:00 am on February 12, 2020 Permalink | Reply
    Tags: Lasers,   

    The Gaussian Beam 

    Wave optics as previously discussed operated under an ideal assumption that light can be confined to a uniform, rectangular shape that moves through space. A more realistic understanding of a wave that propagates through space is the goal of beam optics, which instead describes a light wave as a distribution of light.

    The Gaussian Beam

    The Gaussian beam is a common description of the distribution of a light beam which satisfies the Helmholtz equation. Light is concentrated towards the center of the beam in a Gaussian distribution.

    gaussianbeam

    The width of the beam is a minimum at what is termed the waist of the beam and the width increases at distances further from the waist. Eventually, the width of the beam would become very wide and the distribution of light would be wide enough, almost to approximate a spherical beam. In reference to the figure above, the leftmost distribution may for example be the distribution at the waist of the beam and the rightmost picture is the beam further from the waist. In a localized area, the beam exhibits similar characteristics to the ideal plane wave.

    beam1

    The width of the beam is determined by the following formula:

    beam2

    beam3

    The complex amplitude of the Gaussian beam is described by the following formula:

    beam4

    Further parameters of the beam used in the above formula are the following:

    • W(z): Beam width function (above)
    • R(z): wavefront radius of curvature
      beam5
    • ξ(z): Beam center point
      beam6
    • W0: Minimum Beam level, found at z = 0
      beam7

    B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Hoboken: Wiley, 2019.

     
  • mbenkerumass 6:00 am on January 23, 2020 Permalink | Reply
    Tags: Lasers, ,   

    The Oscillator 

    The oscillator is an important concept used in a variety of applications. One basic use of an oscillator is that of signal generation.

    An oscillator is a system with a gain and positive feedback. The gain must be greater than the loss in the feedback system, so that each time the signal goes through the aplifier in the system, a net gain is produced. The phase shift of a single round trip in the gain-feedback loop must also be a multiple of 2*pi so that a pure signal is repeatedly amplified.

    When these conditions are satisfied, the system is unstable and oscillation begins. Eventually, the amplifier gain becomes saturated and rather than a further increase of amplification, the added gain only compensates for system losses.oscillator

    Since the system is dependen upon a 2*pi phase shift (the period), an oscillator may be designed for a specific frequency. An oscillator generate a signal from noise by repeatedly amplifying the noise periodically.

    Although there are many applications for oscillators, a laser is fundamentally an optical oscillator, an optical signal generator. The maser, which stands for microwave amplification by stiumulated emission of radiation was used before the laser. The saser is an acoustic version of the laser, in which instead of emitting a beam of photons or electromagnetic radiation, an acoustic beam or signal is generated.

    The following outlines the operation of a laser; an optical amplifier placed inside of a resonator with a partially transmitting mirror as the output of the system.

    laser2

    B. E. A. Saleh and M. C. Teich, Fundamentals of photonics. Hoboken: Wiley, 2019.

     

     
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