Brillouin Science And Information Theory Pdf Merge
Brillouin Science And Information Theory Pdf Merge Pdf
A young information theory scholar willing to spend years on a deeply. Brillouin, Jaynes. Download elementary information theory or read online here in PDF or EPUB. Please click button to get elementary information theory. Information science. A classic source for understanding the connections between information theory and physics. Zyxwvutsrq zyxwvutsrqpo IEEE JOURNAL O F QUANTUM ELECTRONICS, VOL. 9, SEPTEMBER 1966 649 zyxwvu On the Theory of Stimulated Brillouin Scattering with Stokes Feedback zyxwvutsrqp P. LAMBROPOULOS, S. KERN, Abstract-The interaction of hypersound and light inside a laser cavity with Stokesfeedbackisstudied.Quantum equations of AND R.
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Stimulated Brillouin Review: Invented 50 Years Ago and Applied Today
Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA
Correspondence should be addressed to ; ude.htuomtrad@erimrag
Received 1 July 2018; Accepted 3 October 2018; Published 2 December 2018
Academic Editor: Gang-Ding Peng
Copyright © 2018 Elsa Garmire. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Stimulated Brillouin scattering (SBS) is embedded today in a variety of optical systems, such as advanced high-power lasers, sensors, microwave signal processors, scientific instrumentation, and optomechanical systems. Reduction in SBS power requirements involves use of optical fibers, integrated optics, micro-optic devices, and now nano-optics, often in high Q cavities. It has taken fifty years from its earliest invention by conceptual discovery until today for SBS to become a practical and useful technology in a variety of applications. Some of these applications are explained and it is shown how they are tied to particular attributes of SBS: phase conjugation, frequency shifts, low noise, narrow linewidth, frequency combs, optical and microwave signal processing, etc.
1. Conceptual Invention
As a graduate student at MIT, I was fortunate to have Charles Townes, originator of the maser and laser, as my Ph.D. advisor. In 1963 we published a paper that first introduced the concept that the newly discovered stimulated Raman scattering (SRS) process creates coherent molecular oscillations. Because the incident light in this laser-stimulated process is coherent, the resulting emission can occur by a parametric process due to interaction between the coherent molecular oscillations and the coherent light [1].
When Professor Townes learned that solid state physicists called these oscillations optical phonons, he realized that similar parametric interactions could occur between laser light and the acoustic branch of the phonon spectrum, that is, between laser light and acoustic oscillations, or sound waves. Weak spontaneous Brillouin scattering from acoustic waves had been predicted by Brillouin and already observed using narrow-line spectra. We called this new process stimulated Brillouin scattering (SBS) and set about experiments to demonstrate it.
Our first paper statement of the idea said: “The generation of molecular oscillations or phonons by the interaction between intense maser beams and matter… should also lead to generation of intense high-frequency sound waves” [2].
Comparing spectra, the Brillouin shift is much smaller than the Raman shift because the velocity of acoustic waves is much less than the velocity of light. This was already known from the spectrum of spontaneous scattering, where the Raman process gives a much larger shift than Brillouin scattering.
Parametric processes require conservation of both energy and momentum. The pump light suffers an inelastic collision and some of its photon energy is transferred to the acoustic wave; energy conservation requires , where is the pump laser frequency, the frequency of the down-shifted scattered light, and the frequency of the acoustic wave. The inelastic scattering process robs the incident photons of energy equal to the acoustic vibrational energy, so the scattered photons will be decreased in energy by this amount. This scattered wave, at frequency , is traditionally called the Stokes wave.
Conservation of momentum determines the frequency shift in the acoustic wave through a vector equation requiring the momentum before the collision to equal the total momentum after the collision: , where the bold print represents vectors. Since the acoustic wave velocity is typically 10−5 of the velocity of light, the acoustic wave vector will typically be much larger than light’s wave vector. The largest can and still conserves momentum when the Stokes wave is exactly in the backward direction. Then the magnitudes obey . Inserting the equality of the wave vector to frequency divided by wave velocity and then simplifying the equation gives . Since << 1, a simple form for the Brillouin shift is Stimulated Brillouin scattering occurs when a beam of laser light generates a parametric process that simultaneously produces an exactly retroreflected Stokes beam and an acoustic wave traveling in the forward direction. Energy conservation requires that the Stokes beam frequency is reduced from the laser frequency by the frequency of the acoustic wave. Momentum conservation determines that the acoustic wave frequency shift is proportional to the ratio of the acoustic wave velocity to the velocity of the laser beam.
The Brillouin-induced acoustic frequencies are usually very much larger than typical acoustic waves, often called hypersonic. Typical materials are quite lossy at hypersonic frequencies, so hypersonic wave signals decay rapidly in time, causing a broadening to the scattered lines which is proportional to the loss. High resolution spectroscopy of the Brillouin signals can provide considerable information about the high-frequency mechanical elasticity of these materials.
Any narrow-line light source sees spontaneous Brillouin as weak inelastic scattering from thermal acoustic waves. When the waves are moving away from the light beam, the largest signal is observed in retroreflection and the Stokes shift moves to longer wavelengths, as in stimulated Raman scattering. When the acoustic waves are moving toward the light beam, their frequency will add to the frequency of the laser beam and the scattered light will have a frequency increased by the acoustic wave frequency. This is called the anti-Stokes wave.
Historically the term “Stokes” was named for Sir George Gabriel Stokes, who in 1852 described the change in wavelength of fluorescence, which is always at lower photon energy than the incident light. When Raman scattering was discovered, similar shift to lower photon energy was called Stokes light. When Raman scattering was discovered to have weak signals at shorter wavelength than the incident light, this was called “anti-Stokes” light. The terminology has stuck and is used in SBS as well.
2. Initial Experimental Demonstrations and Theory
The first experimental demonstration of SBS was in solids, by Chiao, Townes, and Stoicheff [3]. Chiao was a graduate student in our group who joined after I did and Stoicheff was a visitor from Canada who was an expert in Fabry-Perot interferometers. He taught us how to use this etalon to separate very small frequency shifts. The Brillouin Stokes line showed up in interferograms with smaller frequencies (at smaller radii of curvature) than the laser line, as shown in Figure 1. The results validated our theory.