Bragg and Brillouin diffraction

In summary: So basically with my setup you can't just use Bragg's law to calculate the angle for maxima?No, you need to use the equation to calculate the angle for maxima.And with that equation it is only valid when the incident and reflected angles are the same?Yes, because the angle for maxima is when the incident and reflected angles are equal.
  • #1
cooev769
114
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I'm supposed to give a seminar tomorrow for my 300 level experimental physics paper. The experiments we do our reports on are pre-determined and I pulled the short straw with the most bloody complicated on here, the acousto-optic modulator. I'm trying to get my head around it and I've spend the good part of the day and not gotten very far. I understand that you require constructive interference to produce the maxima and due to the varying refractive indices of the material we will get a weird equation. But the equation we are given is

sin (θ) = λ/2nd

Where θ the bragg angle, d is the wavelength of the sound wave in the acousto optic modulator. So it seems odd to me firstly how are the multiple maxima produced when the light in angle must equal the light out angle shouldn't that just produce on maxima. Secondly how can we just chuck n in for the quoted refractive index of the crystal when this varies at every point. How the hell is this equation derived specifically for brillouin scattering. There are no good sources of this on the internet.

Please help, thanks.
 
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  • #2
You are doing kind of a perturbation expansion here. The small changes of n lead to the Bragg scattering, but the condition for the maxima can be determined using the average value of n.
 
  • #3
Oh okay because the crystal came with a designated n and the Bragg equation seemed useless then because this would vary. Unlike normal Bragg diffraction though we change the frequency of the sound wave causes a change in the angle does this sound right?
 
  • #4
Sorry worded poorly. A Bragg angle is a defined angle for constructive interference of the incoming and outgoing wave. But in this case I'm guessing we can change the Bragg angle by varying the frequency of the sound wave is this correct?
 
  • #5
Yes, because changing the frequency of the sound wave you change also the wavelength of the sound which modulates the diffractive index and acts as a lattice for Bragg scattering.
 
  • #6
Sweet but for brag diffraction the theta in must equal the theta out. Seeing as you can keep the theta in constant and change the theta out I'm assuming it's fundamentally different?
 
  • #7
cooev769 said:
Sweet but for brag diffraction the theta in must equal the theta out.

Ok, it isn't a Bragg scattering, rather refraction at a grating.
 
  • #8
Well that's what I was taught. It's what my textbook introduction to optical electronics and this website says, so now I'm just doubley confused.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/bragg.html
 
  • #9
  • #10
Never mind had a chat to a solid state lecturer. Well Bragg's law tells you the angle at which theta is the incident and reflected angle producing constructive interference. Changing the lattice structure will require you to change the angle to get a new Bragg angle. This is different from my setup because with my set up we had a constant incident angle and altered the frequency of the waves to alter the outgoing angle. Which obviously wasn't equal to the incident angle like Bragg's law stare, yet when we used the equation we had to define theta as the outgoing angle only.
 

1. What is Bragg diffraction?

Bragg diffraction is a phenomenon in which X-rays or other types of electromagnetic radiation are scattered by a crystal lattice in a regular pattern. This pattern is caused by the interference between the incoming and outgoing waves, and can be used to determine the atomic structure of the crystal.

2. How does Bragg diffraction work?

In Bragg diffraction, a beam of X-rays or other electromagnetic radiation is directed at a crystal at a specific angle. The radiation is scattered by the atoms in the crystal, and the scattered waves interfere with each other. When the angle of incidence is just right, the scattered waves will constructively interfere, producing a diffraction pattern that can be observed.

3. What is the Bragg equation?

The Bragg equation, named after physicists William and Lawrence Bragg, relates the wavelength of the incident radiation, the spacing between atomic planes in the crystal, and the angle at which the diffraction occurs. It is written as nλ = 2dsinθ, where n is an integer representing the order of the diffraction, λ is the wavelength of the radiation, d is the spacing between atomic planes, and θ is the angle of diffraction.

4. What is Brillouin diffraction?

Brillouin diffraction is a phenomenon similar to Bragg diffraction, but instead of X-rays, it involves the diffraction of sound waves by a crystal. This phenomenon can be used to study the elastic properties of materials, as the frequency and direction of the diffracted sound waves can provide information about the crystal structure and its mechanical properties.

5. What are the applications of Bragg and Brillouin diffraction?

Bragg and Brillouin diffraction have numerous applications in materials science, physics, and engineering. They are commonly used to study the crystal structure and properties of materials, such as in X-ray crystallography and acoustic microscopy. They are also used in medical imaging techniques, such as X-ray diffraction imaging, and in the development of new materials for various applications.

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