Time Reversal Signal Processing has three main uses: creating an optimal carrier signal for communication, reconstructing a source event, and focusing high-energy waves to a point in space. A Time Reversal Mirror (TRM) is a device that can focus waves using the time reversal method. TRMs are also known as time reversal mirror arrays since they are usually arrays of transducers. TRM are well-known and have been used for decades in the optical domain. They are also used in the ultrasonic domain. Overview If the source is passive, i.e. some type of isolated reflector, an iterative technique can be used to focus energy on it. The TRM transmits a plane wave which travels toward the target and is reflected off it. The reflected wave returns to the TRM, where it looks as if the target has emitted a (weak) signal. The TRM reverses and retransmits the signal as usual, and a more focused wave travels toward the target. As the process is repeated, the waves become more and more focused on the target. Yet another variation is to use a single transducer and an ergodic cavity. Intuitively, an ergodic cavity is one that will allow a wave originating at any point to reach any other point. An example of an ergodic cavity is an irregularly shaped swimming pool: if someone dives in, eventually the entire surface will be rippling with no clear pattern. If the propagation medium is lossless and the boundaries are perfect reflectors, a wave starting at any point will reach all other points an infinite number of times. This property can be exploited by using a single transducer and recording for a long time to get as many reflections as possible. Theory The time reversal technique is based upon a feature of the wave equation known as reciprocity: given a solution to the wave equation, then the time reversal (using a negative time) of that solution is also a solution. This occurs because the standard wave equation only contains even order derivatives. Some media are not reciprocal (e.g. very lossy or noisy media), but many very useful ones are approximately so, including sound waves in water or air, ultrasonic waves in human bodies, and electromagnetic waves in free space. The medium must also be approximately linear. Time reversal techniques can be modeled as a matched filter. If a delta function is the original signal, then the received