What causes band gaps in acoustic systems?

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In summary, a bandgap is a gap in allowed frequency or energy levels in an acoustic material, caused by a regular array of wave scatterers.
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Beer-monster
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Not sure if this should have gone in help but here goes.

I'm doing some background reading into the subject covered by my final year project for my degree. In particular I'm trying to get a grip on the topic of band gaps (acoustic to be exact but I'm looking generally at the moment).

Although I understand what a band gap is in basic terms (a gap in allowed frequency or energy levels), I've found it very hard to find a simple explanation to help me understand the cause of this effect. I'm not as good as I should be at decyphering the mysterious physics language of Jargon :cry:.

I know the effect is caused by a regular array of wave scatterers but how this produces the effect still eludes me. Is it simple interference or something more complex and how would it produce such a pronounced gap?

I hope that was clear at that someone might be able to explain something complicated to a dunce like me I have a feeling my project hinges on it

Thanks
 
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  • #2
Think of the bands as being formed by the overlap of atomic orbitals.

In an isolated atom, you have electrons possesing specific discrete values of energy {given approximately by the Bohr relation E(n) = E(1)/n^2 }. It is, however more accurate to note that electron energies (according to better models) are functions of n,l,m (with no more than 2 electrons per energy level, according to Pauli). In any case, what I'm getting to is the density of states (DOS) for an isolated atom. If you plot the number of electrons (on the y-axis) vs. energy (on the x-axis) you get sharp (discrete spectrum) spikes at certain energies and nothing in between - so there are already forbidden energies for an isolated atom.

Now when you start combining several atoms, you cause these sharp spikes to spread out into a band, which is made up of many closely spaced levels. In some materials these bands (are close enough and wide enough that they) overlap and in some materials, they don't. Very simply, this is all there is to a bandgap.
 
  • #3
Thanks Goku, that clears the electric band gaps up. However how does this help overlap with wave phenomena such as light in photonic crystals.

As a stab in the dark (hope no one gets hurt)

Does the interference pattern caused when the wave scatters off an object mean that the light can only be in specific frequerncies (as the others cancel out) and then if you have many waves scattering of a regular arrangement these forbidden levels over lap like in a solid and you get a frequency band gap?

Or am I way off?

Thanks again
 
  • #4
Photonic band gaps are almost a direct analogy to electronic band gaps. Photonic band gaps can arise when there is a periodic variation in the refractive index of a material (Analogous to a periodic variation in electronic potential in the electronic case).

The simplest case of a photonic bandgap is in the case of a high reflecting dielectric stack, or a fibre Bragg grating. These structures have a periodic modulation in the dielectric constant (which, you should recall is the refractive index squared in optical media), which result in a particular wavelength (sometimes called the design wavelength) being strongly reflected due to the reflections from all the interfaces constructively interfering.

Note however that such a bandgap only applies to light traveling normal to the interface. Such bandgaps are referred to as 1 dimensional bandgaps. There are other, more complex structures that posess 2 and even 3 dimensional bandgaps (which are termed complete bandgaps).

An example of a structure posessing a 2D photonic bandgap would be a Photonic crystal fibre (PCF). PCF's guide light, not using total internal reflection, but by exploiting resonances as was done in the 1D case. Complete photonic bandgaps are difficult to acheive, but they have been demonstrated in artificial structures and in natural strucures such as Opal.

There is much promise in using Photonic bandgap materials for use in minaturised waveguide devices, and as such is a very active field of research (My group specialises in this type of research as a matter of fact). Googling any of the above topics should yield a more comprehensive overview of this fascinating subject.

Back to your original post, bandgaps arise as a direct result of resonances between two interfaces, resonances which are in turn a direct result of interference. A strong resonance enhances transmission between two interfaces, whereas a strong antiresonance prohibits transmission. By confining light within antiresonant structures, it can be trapped and guided in the same way total internal reflection can trap light within an optic fibre.

Claude.
 

1. What is a band gap?

A band gap refers to the energy difference between the top of the valence band and the bottom of the conduction band in a material. It is essentially a forbidden energy range where electrons cannot exist, and it plays a crucial role in determining a material's electronic and optical properties.

2. How does a band gap affect a material's conductivity?

Materials with a smaller band gap, or no band gap at all, are considered conductors because their valence and conduction bands overlap, allowing electrons to move freely. In contrast, materials with a larger band gap are insulators since there is a significant energy barrier that electrons must overcome to move from the valence to the conduction band.

3. What factors influence the size of a band gap?

The size of a band gap is primarily determined by the electronic structure of a material, which is influenced by its composition, crystal structure, and temperature. Generally, materials with more tightly bound electrons and larger atomic radii tend to have wider band gaps, while those with more delocalized electrons and smaller atomic radii have smaller band gaps.

4. How is the band gap related to a material's color?

Since the band gap determines which wavelengths of light a material can absorb and reflect, it is closely tied to a material's color. Materials with a smaller band gap absorb lower energy (longer wavelength) light, giving them a red or orange color, while those with a larger band gap absorb higher energy (shorter wavelength) light, appearing blue or violet in color.

5. Can the band gap of a material be altered?

Yes, the band gap of a material can be modified through various methods such as doping, alloying, and applying external stimuli like pressure or electric fields. These techniques can be used to tailor a material's properties for specific applications, such as creating semiconductors with desired band gaps for electronic devices.

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