How to Build a Laser Death Ray
Self Focusing & Filamentation
If light gets intense enough, its electromagnetic field can affect the optical properties of the matter it is passing through. One such effect is when high light intensity will increase the index of refraction. If the laser beam is more intense in the middle, this means the index of refraction in the center of the beam is higher than at the edges. This makes even uniform matter act like a lens to focus the beam. When this happens, the beam is said to be self focused.
This effect only becomes apparent at very high power levels. In air, you only start to see self focusing at around 1×1010 watts. Note that the intensity does not matter; contrary to what intuition might tell you, it is the total power of the beam that matters, not how tight the beam is.
If nothing acted to stop self focusing, the light would collapse to a point, cause catastrophic ionization, and be entirely absorbed. However, before this happens, you generally tend to get small amounts of ionization. The low density plasma decreases the index of refraction of the air to act as a diverging lens. This expands the beam again, only to have it recontract due to self focusing. The net result is filamentation - a thin thread-like core of sparsely ionized air surrounded by a "sheath" of high intensity light. The plasma core of the filament is quite visible, forming a glowing streak through the air. In this form, the beam will maintain a tight focus, keeping a diameter of around 0.1 mm and intensities of around 5×1017 W/m2 until it loses too much energy to ionization and is absorbed. Each filament carries about 1×1010 W. If the beam has more power than this, it will split into multiple parallel filaments. When the filaments lose too much energy to ionization to continue propagating, two or more will merge together into one filament with enough power to continue propagation. A single filament can travel about 10 m to 10 km in air, depending on the pulse duration - Longer pulses have more energy, and the energy lost per distance to ionization is the same (about 2×10-6 J/m).
Filamentation only occurs for pulses with a duration of less than the time it takes for an electron to collide with another atom in the air. If the pulse is longer than this, at high enough intensities the electron would have enough energy after being accelerated by the light's electric field to knock off more electrons, which would in turn knock off even more electrons. This runaway process, called cascade ionization, would form a thick plasma that would absorb the beam. This limits filamentation to pulses shorter than about a picosecond. It takes about 10 nanoseconds for the electrons to recombine with the ions in the air, so for filamentation subsequent pulses should be delayed by more than about 10 nanoseconds from the previous pulse.
The extreme powers necessary for self focusing and filamentation mean that this will not come into play for any but the most extreme heat rays. However, it could be a useful trick to exploit for blasters. Because the ionization in the filaments saps power from the beam, it is desirable to delay the onset of filamentation until just in front of the target (this also helps to keep your position from being given away by a bright glowing beam pointing right back to you). Once at the target, however, the formation of the filaments means you no longer need to worry about depth of field effects since the filaments keep their focus as they blast through the target. Note that overcoming depth of field effects through chirping, self focusing, and filamentation only works in an atmosphere!
How do you keep the filaments from forming until just in front of the target? You use a technique known as chirping. Air is slightly dispersive. That means that some wavelengths propagate through air slightly faster than others. A chirped beam has a range of wavelengths, rather than just one. Some modern lasers can produce chirped beams (most notably Ti:Sapphire lasers). So make a pulse that is slightly too long in duration for its total energy to exceed the threshold for self focusing, with the slower moving wavelengths emitted at the beginning of the pulse and the faster moving wavelengths at the end. When the beam is chirped at just the right amount, the slowest moving wavelengths are slowed down just enough and the fastest moving wavelengths sped up just enough that all the light arrives at just in front of the target at the same time, bunching the pulse up to a shorter duration, increasing the power past the threshold of self focusing, and creating a filamented beam.
Self focusing to a filamented beam is a process that results from beam instabilities. While the filaments propagate straight in the original direction of the beam, you can't predict exactly where in the beam profile they will occur. If the filamentation occurs when the beam is wide, you will just get a random sprinkling of tiny craters in the surface of your target (although if you keep it up, you will eventually wear away a hole). Thus, you still are limited by diffraction effects to get a narrow beam where you start to filament if you want good target penetration.
An interesting characteristic of light filaments is that the initially monochromatic (single wavelength) laser beam gets turned into a beam of broadband white light when it begins to propagate as a filament. The light scattering is enhanced in the forward and reverse direction, making the beam appear brighter to the death ray user and to the target.