# Diffraction of light in a tunnel

• Nikitin
In summary, when light passes through a narrow slit, it will diffract, but what happens when it passes through a waveguide with a radius similar to its wavelength? In this case, the light will bounce back and forth, creating patterns that resonate with the waveguide. If the width of the waveguide is too small, light will not propagate through it.

#### Nikitin

Hi. We all know that light will be diffracted when it goes through a slit that is around as narrow as its wavelength.

But what if a plane wave goes through a very long "tunnel" that has a radius around the same size as the its wavelength? What happens then? Do you still get diffraction?

Sure - at the end, when the light comes out again. And you might get strong attenuation inside if the tunnel is too narrow. A larger version of this is a glass fiber cable.

You are describing a waveguide. When the width of the waveguide is much larger than the wavelength of light, you can think of light bouncing back and forth as it travels down a tube (essentially geometric ray optics). But when the width of the waveguide is comparable to the wavelength of the light, then only one or a few modes can propagate through the waveguide, and you can't think of light traveling in this way, but rather the light forms various patterns which resonate with the waveguide. If the width is smaller than about 0.586*wavelength (for perfectly conducting walls), then light won't propagate down the guide -- it won't "fit", although some light will leak through if the guide is short enough.