stack is matched to the incoming medium (vacuum) and to the substrate (the substrate index is ns), is: 1 - r = (4ns/nh)(nl/nh)2N + 2π(kh + kl)/(nh2 - nl2), where the first term is the Abélès limit, the second term the Koppelmann limit. The first term can be made as small as desirable by increasing the stack, . Thus it remains to decrease the extinction coefficients. N is then an adjustable parameter to minimize the overall losses (stacks with up to 50 pairs have been published). Large rings The perimeter dependence of the Signal/Noise ratio is This equation defines large rings with L >> Lcrit ≈ , where S/N becomes proportional to L2. Therefore, the sensitivity of large rings increases quadratically with size, hence the quest for ever larger Ring Lasers for Research. In the past it was thought that only small ring lasers avoid multimode excitation. However, if signal bandwidth is sacrificed, there is no known limit to ring laser size, either theoretically or experimentally. One of the major advantages of large rings is a quartic reduction of lock-in and pulling in large rings. Practical rings Ring lasers are sometimes modified to allow only one direction of propagation by placing a device into the ring which leads to different losses for different propagation directions. For instance, this could be a Faraday rotator combined with a polarizing element. One type of ring laser design is a single crystal design, where light reflects around inside the laser crystal so as to circulate in a ring. This is the "monolithic crystal" design, and such devices are known as "non-planar ring oscillators" (NPROs) or MISERs. There are also ring fiber lasers. Semiconductor ring lasers have potential applications in all-optical computing. One primary application is as an optical memory device where the direction of propagation represents either 0 or 1. They can maintain the propagation of light in exclusively the clockwise or counterclockwise direction as long as they remain powered. In 2017 a proposal was published to test general relativity by means of ring lasers. See also Optical ring resonators Ring laser gyroscope Semiconductor ring laser List of laser articles References Laser types