# Matter Wave Analogies

1. Sep 15, 2011

### jbox23

I understand the concept of matter waves. Light has wave-particle duality; it has both wave-like (electromagnetic wave) and particle-like (photons) properties. Similarly, according to de Broglie, all particles (electrons, protons, etc.) have a wave-like property, with their momentum (where momentum = mass x velocity) related to their de Broglie wavelength through the equation:

$\lambda = \frac{h}{p}$

Photonic crystals affect the motion of electrons. Electromagnetic waves can be propagated through a photonic crystal lattice structure, and through considering the frequencies of these electomagnetic waves at points within the Brillouin zone, it is possible to compose graphs showing the respective electronic band gaps.

What I don't get is how photonic crystals are analogous for matter waves?

2. Sep 15, 2011

### ZapperZ

Staff Emeritus
This post is very confusing.

Where do you get the idea that photonic crystals are analogous for matter waves?

Photonic crystals affect the "motion" of photons! That's why they are call photonic crystals, rather than electronic crystals. Photonic crystals have photonic band gaps, as opposed to electronic band gaps.

I do not see the connection with "matter waves".

Zz.

3. Sep 15, 2011

### jbox23

It is possible to consider two-dimensional photonic crystals in the microwave regime as analogies for matter waves.

I am aware that photonic crystals affect the motion of photons in a similar way that semiconductor crystals affect the motion of electrons. Photons (behaving as waves) either do or do not propagate through the photonic crystal structure depending on their wavelength. Wavelengths of light that are allowed to travel are known as modes, and groups of allowed modes form bands, and disallowed bands of wavelengths are photonic band gaps. Similarly the periodic potential in a semiconductor crystal affects electron motion by defining allowed and forbidden electronic energy bands.

So I guess the two things are analogous through the comparisons that can be made between photonic band gaps and electronic band gaps, but I'm not sure.

4. Sep 15, 2011

### ZapperZ

Staff Emeritus
I'm sorry, but why are you going through all this convoluted example just to simply find an analogous scenario to demonstrate matter waves? What about simply use an electron diffraction experiment as a much more transparent example of matter waves?

Zz.

5. Sep 15, 2011

### jbox23

I'd just like to know and understand how to relate these two things (photonic crystals & matter waves)