Arming Sharks with Lasers

by Scott Mattison (@FoolsPizza)

In the immortal words of Dr. Evil: “Every creature deserves a warm meal.” To meet this call to action, we have devised a method for efficiently providing sharks with laser beams. To accomplish this, we are going to have to design a high energy laser source that is capable of being submerged in water.

SharkwithLaser
Rendering of proposed design (not to scale)

I will preface this blog post with the knowledge that someone has in fact put a laser onto a shark. As the laser used could not even blind a fish, much less cook one, I do not think it meets our demands.

Building a working laser isn’t that hard; however, designing a laser to attach to a shark has some special challenges. I am going to break down some of the design process over a few posts. Ignoring the ethics of the matter (it’s bad) or if we this is even a good thing for the sharks (it’s not), the first thing we need to do is decide what wavelength of light we want the laser to be.

For this decision, and many future ones, the most important variable that we face is that we will be working in the ocean. You may have noticed that the ocean is blue, at least in the deeper parts. Despite a somewhat odd popular opinion, the ocean is not blue because it is reflecting the sky. In fact the ocean and the sky are actually blue for completely different reasons. To understand this we will have to talk a bit about physics of how light interacts with the environment.

There are many ways light can interact with the world, but the two methods that primarily define how we observe the world are scattering and absorption. Scattering of light in the atmosphere due to small particles, known as Rayleigh scattering, preferentially scatters shorter wavelengths of light than longer wavelengths. Rayleigh scattering is what gives the sky its blue coloring. Readers who are familiar with wavelengths of visible light may be thinking that blue isn’t the shortest wavelength, and asking why isn’t the sky violet. This question is an answer for another time, but the short answer is: colors are crazy.

Unlike the sky, the ocean is blue because of absorption. Absorption occurs as an interaction between light and the electrons of molecules. If the energy level of photon of light is equivalent to the energy difference between two electron energy levels then the electrons may absorb that photon. Without delving too much into the quantum mechanics here, the electron configurations of water make it absorb light of longer wavelengths (more red) better than it absorbs light of shorter wavelengths (more blue).

Water does not absorb light so strongly that we see these effects on a small scale, hence a glass of clean water will appear clear instead of blue. However, over a distance of several meters this absorption starts to become very pronounced. When scuba diving, the deeper a diver goes into the water the less color they will be able to see. In fact, during deep water scuba certification you actually take a color chart down with you as you dive and get to observe the loss of color first hand.

Since absorption takes place over such a long distance, in smaller bodies of water and in bodies of water with a lot of sediment and debris, scattering begins to play a larger role in the appearance of the water. Scattering is why a lot of lakes and beaches will appear brown or green in color instead of blue as light is being scattered back from within the water before the absorption process can play a significant enough role to make water appear blue.

So, what does this all mean for our shark and its warm and tasty meal? Well for starters, this means that we will want to select our wavelength of light based on our desired operating distance. I am not a marine biologist; however, it may be reasonable to assume that we want our shark to be able to cook a warm meal from at least 100 feet away. Based on this distance and the absorption levels of light by water, we are going to want to match the wavelength of our light source to the absorption of the ocean and go for a light source that is shorter.

774px-Water_absorption_coefficient_large
Absorbance of visible light by water. Horizontal axis is wavelength in nanometers and the vertical axis is absorbance in inverse meters. This figure is reproduced from Wikipedia all rights belong to the original authors.

Looking at the graph above, there is a minimum absorbance around 420 nm, but for reasons we will discuss in more detail in my next post, we want to select a wavelength of light that will penetrate more deeply into biological tissues. Despite biological tissues being mostly water, as a general rule, longer wavelengths penetrate more deeply than shorter wavelengths. This is why two-photon microscopy has taken on such a large role in biological imaging as it uses two photons of a longer wavelength to excite a fluorescent molecule in the same way as a single photon of half the wavelength would. This phenomenon allows researchers to probe fluorescent molecules much deeper in biological tissues. For our shark, this means we are going to need to strike a balance between long wavelengths of imaging depth and short wavelengths for effective range.

Assuming we want half of our light from our laser to hit our shark’s target at a range of 100 feet, we can use what is referred to as the Beer-Lambert law to calculate the maximum acceptable absorbance of water.

Beer Lambert 2

The equation above gives the simplified form of the Beer-Lambert law where we assume half of the initial photons hit their target. α in this case is the absorbance and Δx is the distance the light traveled through some absorbing medium (water).

HELP

Next, we can determine our Δx in meters from feet with a simple unit conversion. Also we can use two neat properties of the natural logarithm to simplify our equation and make it easily solvable. 

Finally we can solve our equation to determine the maximum value we can have for absorbance.
soLVE

Our answer (0.0227 inverse meters) comes out to be very close to a wavelength of 500 nm (found using the graph above), meaning we will be arming our shark with a laser that would appear very teal-blue upon observation. Tune in to my next blog post for a rousing discussion of building an actual laser that will operate well underwater.