Ring laser

Ring lasers are composed of two beams of light of the same polarization traveling in opposite directions ("counter-rotating") in a closed loop.

A ring can be constructed with other optically active materials that are able to conduct a beam with low losses.

This is the "monolithic crystal" design, and such devices are known as "non-planar ring oscillators" (NPROs) or MISERs.

Although some may consider Macek et al. has built the first large ring laser (1 m × 1 m),[6] the US patent office has decided the first ring laser was built under Sperry scientist, Chao Chen Wang, (see US Patent 3,382,758) based on the Sperry laboratory records.

Wang showed that simply rotating it could generate a difference in the frequencies of the two beams (Sagnac[7]).

Later it was found that any effect that affects the two beams in nonreciprocal fashion produces a frequency difference, as Rosenthal anticipated.

New phenomena unique to rings appeared, including lock-in, pulling, astigmatic beams, and special polarizations.

[10] The standard matrix methods for the beam characteristics — curvature and width — are given, as well as the Jones calculus for polarization.

As such, single Fourier components, or lines in frequency space are of major importance in ring outputs.

For low-Q rings, an empirical relation for 1/f noise has been ascertained, with the one-sided frequency power spectral density given by

Although it has been shown that ring lasers can be excited in all kinds of modes, including microwave-related modes, a typical ring laser mode has a Gaussian, closed shape, given proper adjustment of mirror position [14] The analysis of beam properties (curvature radius, width, position of waists, polarization) is done with matrix methods, where the elements of the closed beam circuit, mirrors and distances in between, are given 2 × 2 matrices.

The mirror sizes have to be chosen large enough to ensure that only very small portions of the gaussian tails are to be cut off, such that the calculated Q (below) is maintained.

for a mirror of focus length f. The relation between mirror radius RM and focus length f is for oblique incidence at angle θ, in plane: for oblique incidence at angle θ, perpendicular to the plane: resulting in astigmatic beams.

With a mass suspended on the rotatable mirror, a simple gravitational wave detector can be constructed.

This opens the way to classic precision side-band spectroscopy as is known in microwaves, except that the ring laser has side bands down to nHz.

When the dependence on perimeter L is taken into account for large rings, the relative difference between theoretical output frequency ft and actual output frequency f is inversely proportional to the fourth power of L: This is a huge advantage of large rings over small ones.

The quality factor Q of the cavity, as well as the time duration of the measurement, determines the achievable frequency resolution of a ring to a large extent.

At this time, the main limitation of mirrors is the extinction coefficient of the evaporated high-index material TiO2.

It is quite important for large rings to increase the quality factor Q, because it appears as 1/Q2 in the expression for noise.

The whole ring is filled with a HeNe mixture of suitable partial pressures (up to a few hundred Pascal), to achieve lasing and good suppression of multiple pairs of modes.

(Typically, the HeNe lasing gas at 633 nm is used; attempts for an argon ring laser failed.

[17]) Further, the lasing is excited with radio frequency to easily adjust the amplitude to just below the appearance of the second pair of modes.

The photon lifetime τ is measured on an oscilloscope, as the times are of the order of microseconds to milliseconds.

However, multilayer dielectric mirrors with 20–30 alternate (low L and high H index of refraction) SiO2 — TiO2 λ/4 layers achieve reflection losses (1 − r) of single parts per million, and an analysis [18] shows that losses of parts per billion can be achieved, if materials technology [19] is pushed as far as is done with fiber optics.

The losses are analyzed with a matrix method [20][21][22][23][24] that, given the success of surface treatment and reduction of absorption, shows how many layers have to be applied to reduce transmission accordingly.

Hereby, all calculations are strictly carried out up to the first power in the ks, assuming the materials are weakly absorbing.

The final result, after the stack is matched to the incoming medium (vacuum) and to the substrate [18] (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,[21] the second term the Koppelmann limit.

[25] However, if signal bandwidth is sacrificed, there is no known limit to ring laser size, either theoretically or experimentally.

This is the "monolithic crystal" design, and such devices are known as "non-planar ring oscillators" (NPROs) or MISERs.

They can maintain the propagation of light in exclusively the clockwise or counterclockwise direction as long as they remain powered.