CHRISTMAS LIGHTS ON the outside of your house might look awesome, but they really aren’t that much fun to hang up. This year, we are using something different—lasers. Yes, you can now add Christmas lights to the outside of your house with lasers. The basic idea is to stick a small device in your yard that shoots lasers at your house to make some spots. These spots then look like little bitty lights. When Christmas time is over, just pick up the laser out of the yard. It’s not quite as bright as your traditional lights, but it’s so simple to set up.

Diffraction

The first element of this device is the laser. I’m not going to talk about lasers today (but I will in the future) except to say the following:

• They mostly just produce one color of light (and thus one wavelength). So, a red laser creates light with a wavelength of something like 650 nm. We call this monochromatic.
• The light produced is coherent. This means that the all the light produced is in phase such that you could think of it as just one wave (with one wavelength).
• The laser light is collimated—such that it mostly just goes in one direction with very little beam spreading.

Yes, these are just approximately true—but let’s just work with this for now.

So, how do you take one laser and with it make many spots on your house? The answer is a diffraction grating—which is essentially a device with many super tiny lines on it. It turns out that when a wave (like light) passes through an opening, it sort of re-radiates. We call this diffraction. Suppose I have a plane wave coming to an opening, here’s what that would look like.

But if waves and bend through openings, wouldn’t that mean you could see around a corner of a doorway? In theory, yes. In practice—no. It turns out that the amount of bending for waves that travel through an opening depend on both the size of the opening and the wavelength of the wave. You only get noticeable effects when the size of the opening is around the same size as wavelength. Since red light has a wavelength of 650 nano meters, you need really small openings.

Interference

But what happens when two waves from different sources are at the same place and the same time? This is what we call interference. There are two extremes of what can happen. First, there is constructive interference. If both the waves are in phase such that their peaks are lined up, then the amplitudes of these waves will add together and produce a wave with twice the amplitude.

The other extreme happens when the two waves are out of phase such that the peak on one wave is the opposite the peak on the other wave. This is called destructive interference.

In these two examples I have the waves right on top of each other. However, it’s possible for two waves to come from different locations and interfere just at some point in space. That’s what we will have with a diffraction grating.

Diffraction Grating

There are all sorts of ways to get light to create an interference pattern when it shines through an opening. Let me just consider the method of using multiple openings. This is usually accomplished by using a series of super tiny lines on a glass plate—called a diffraction grating.

If we have light going through a bunch of openings, then this light will diffract in such a way that it will expand as it goes out of the slit. This light can be represented as different light rays. Here is a diagram showing light going through two adjacent slits with a separation distance d and diffracting at some angle θ.

Assuming the viewing location for this light (like the side of my house) is very far away, these two light paths are both essentially parallel and meet at the final location (I know that sounds tricky, but trust me—it’s OK). Here you can see that the light from the lower slit (path 2) will go a little bit farther than light from the upper slit (path 1). If this extra distance is the same as half the wavelength of the light then the light along path 2 will be completely out of phase. Light from path 1 and the two waves will completely cancel at the house (so no light). If the path difference is a whole wavelength, then the light along the two paths will be in phase and the two waves will constructively add together to make a brighter spot.

By changing the angle that light comes out of the slits, you would get different path length differences. Light will constructively interfere when this path length is an integer multiple of the wavelength of light. With a little bit of trig, we get the following expression.

So, you shine a single wavelength of light through multiple slits, and BOOM—you get a bunch of laser dots just like this.

Here you can see the laser, the diffraction grating (with reflections) and the dots on the screen. This is exactly what the Christmas laser lights do except that the diffraction grating isn’t just lines, it’s something else to produce bright spots in both the horizontal and vertical direction.

But once you have those bright spots, you have something that looks a lot like actual lights on your house.