Continuous single longitudinal mode lasers are useful for communication, data storage, display, and measurement applications. Intracavity doubling of continuous-wave (cw) yttrium aluminum garnet Y3Al5O12 (Nd:YAG) lasers is an efficient method of generating coherent visible light. When such lasers are end-pumped by laser diodes the overall efficiency is among the highest for lasers in this portion of the spectrum. Large amplitude fluctuations due to longitudinal mode coupling [1] have been a persistent problem, which has rendered these devices in appropriate for many applications. This amplitude noise can be eliminated by using intracavity elements such as an etalon or quarter-wave plates [2], or circumvented by placing the doubling crystal in an external resonator [3]. None of these solutions are ideal; however, since the end-pumped laser output power is highly sensitive to such losses as may be introduced by the insertion of intracavity elements, while the external cavity concept requires active stabilization to control its length so that resonance will be maintained even as the laser frequency drifts. On the other hand, a single frequency laser will naturally eliminate amplitude fluctuations in the second harmonic. To demonstrate this concept, we have developed an intracavity doubled Nd:YAG ring laser and result will be presented. This laser demonstrated exceptional performance as a single frequency unidirectional 1064 nm laser as well. The ring was operated both cw and repetitively Q-switched, providing efficient unidirectional, single transverse mode output in all case.
A typical linear laser resonator consists of two mirrors facing each other, as shown in Fig. 1.1.
Figure 1.1. Various types of linear laser resonators. (a) Confocal, (b) hemispherical, and (c) plane parallel.
Gain medium
(c) Gain medium
(b) Gain medium
(a)
These configurations create electric and magnetic field standing waves in the resonator with a period of one-half of an optical wavelength. These standing waves interact with only part of the volume of the laser material, thus creating spatial inhomogeneities in the gain medium. This effect is termed spatial hole burning [4], which causes multi-longitudinal mode oscillation as described below and illustrated in Fig. 1.2.
Suppose a linear or standing-wave laser is initially oscillating in the q-th axial mode. This leads to a standing-wave pattern for the field amplitude or optical intensity along the z axis, with peaks and nulls spaced by one-half optical wavelength. The inverted population in this laser will then be saturated in a similar spatially periodic fashion. One of the effects of this saturation will be to produce a spatial inverted-population grating or gain grating, which will introduce cross-coupling between the forward and backward-traveling wave components of the q-th axial mode.
Of more importance at this point, however, is the fact that, at least near the center of the cavity, the standing-wave pattern of the (q+1)-th mode which squeezes one more half optical wavelength into the cavity length will have its maximum intensity located just at the points that are left unsaturated by the q-th mode.
As a result of this, the gain competition between the two adjacent axial modes is much reduced, and both axial modes may well be able to oscillate simultaneously, even with strongly homogeneous laser medium, by using in essence different groups of atoms. Oscillation with any two adjacent axial modes at equal amplitudes will then saturate the population uniformly, at least in the center of the cavity, possibly discouraging the oscillation of any further axial modes. This behavior is sometimes seen, for example, in solid-state lasers, such as the Nd:YAG laser, which often seem to prefer to oscillate at steady state in just two axial modes.
Figure 1.2. A schematic diagram illustrating the spatial hole burning effect. (a) The standing wave that oscillating in the (q+1)-th axial mode in the cavity, (b) the standing wave that oscillating in the q-th axial mode, (c) The population inversion introduced by the q-th axial mode in the gain medium [4].
Single mode laser oscillation can be obtained by insertion of a frequency selective device, which suppresses oscillation of all other modes. Various designs to generate single frequency lasers were demonstrated [5-13]. One procedure is to couple the cavity that contains the laser medium to a shorter cavity that has widely spaced resonant frequencies [14]. For Nd:YAG, the homogeneous linewidth [15] is 180 GHz, and the required length of about 0.1cm is so short that prisms [16] or beam-splitter and double-mirror combinations are very difficult to fabricate [17] as shown in Fig. 1.3.
(a)
(b)
(c)
Figure 1.3. Single-frequency laser using stabilized tunable prism resonator to select wavelength and axial mode. M2: beam splitter, M1, M3, M4: laser mirrors [17].
The primary disadvantage of all the preceding mode selection devices is that the power in the suppressed mode is lost and does not contribute to the laser output.
Further, each of the techniques creates some additional loss for the desired mode. As a result, the efficiency of these longitudinal mode selection devices is limited to about 50 percent in the case of Nd:YAG lasers [18]. Placing a comparatively short section of active laser medium close to one of the end mirrors is another way to reduce the effectiveness of the spatial hole-burning process [19]. Higher efficiency can be obtained by eliminating the spatial hole burning. Replace the standing wave with the traveling wave propagating in the cavity; the spatial hole burning effect will be eliminated.
Ring laser cavity has been shown to be a robust method for producing single-frequency laser as operates at uni-direction propagation [20-24]. However, in
previous works, more than three or four mirrors for guiding of the laser light to form a closed loop formed the ring cavities. These complex configurations made the lasers bulky and expensive. In our work, a novel symmetrical two-mirror figure “8” ring cavity was demonstrated [25]. Different from the linear cavity, the propagation configuration looks like a figure “8”. With less optical components, this ring cavity is compact and free of astigmatism.
The study of polarization evolution in this nonplanar, reentrant ring cavity is also made. In the numerical simulation, the factors, which affect the polarization state within the cavity, were considered. By measuring the polarization of a linear-cavity laser, we also derived the thermally induced optical axis rotation in the gain medium, and determined the equivalent temperature-dependent dielectric tensor of the gain medium at various pump powers, which enable Jones matrix analysis of the polarization in the nonplanar ring laser cavity.
In addition to the figure “8” ring laser, we also demonstrate the multi-reentrant laser by the two mirror ring configuration. We not only prove that the multi-reentrant laser system is feasible experimentally, but also use fundamental laser theory to find the relation among cavity length, number of points, number of circulation, and the distance between center of gain medium and optical axis. The exact solution we obtained is experimentally verified with good agreement. A comparison between exact solution and paraxial approximation is also performed. The beam paths observing from the top, side, and end view are analyzed for various multi-reentrant laser cavities. The stability of the cavity is numerically analyzed and experimentally verified with good agreement, too. Finally, the differences in cavity configuration between TEM01 mode and the figure-8 mode are compared in this dissertation.
This ring laser system can be applied in picoseconds mode-locked laser because one of the advantages of the cavity is that it can reduce the cavity length while
maintaining a long round-trip length as shown in Fig.1.4. This is useful for a picoseconds mode-locked laser to reduce its cavity length. Typically, the cavity length around 1 m is required as the mode locked laser operated in the 100 MHz repetition rate. By using this multi-reentrant cavity configuration, it needs only 10 cm, which will be discussed in chapter 4.
Figure 1.4. Multi-reentrant laser configuration. The cavity round length can be an order of magnitude longer than the separation of the cavity mirrors.
The other application of the multi-reentrant ring laser is the compact laser gyroscope. Gyroscope is an instrument that helps maintain orientation in space. The application fields include civil and military aviation, submarine force, and cosmonautics, the sensor of an autonomous navigation system, a compass, to keep shaft sinking or drifting direction, to hold the direction of a gun barrel on a moving platform.
There are two kinds of optical gyroscopes, both based on the same principle.
Laser gyroscope is a laser with ring cavity. The laser cavity is made of three or four mirrors which form of a closed loop. Fiber gyroscope is a similar device, but the beams of the laser light are traveling along a fiber optic, which is in a form of a coil [26-28]. The laser gyroscope is shown in Fig. 1.5.
Figure 1.5. System setup of laser gyroscope with three mirrors [26].
Two laser beams are moving in opposite directions (clockwise and counterclockwise) in the same ring path. As the gyroscope is immovable, the two light beams have the same optical path and the same frequency, as the gyroscope rotates, the rotating interferometer effectively shortens the optical path traveled by one of the beams, while lengthening the other on the same value. Light propagates in the ring laser gyroscope; the change of optical path length causes a change of the ring resonator resonant frequency. Thus, counter-propagating beams in ring resonator have different frequencies, and produce a beat frequency ∆ν , which is directly proportional to the change of path length. Optical gyroscopes are based on the principle termed Sagniac effect [29]:
( )
1.1 4A λLν = Ω
∆
where λ is the laser wavelength, A is the area enclosed by that path, L is the total path of the ring, and Ω is the rotation angular velocity of the gyroscope.
From equation (1.1), by measuring the beat frequency of the two beams, we can get the angular rotation velocity of the flight vehicle. The key point of the laser
gyroscope technique is how to measure extremely small frequency difference. By using the multi-reentrant ring system, the optical path of laser beam propagation in the cavity is increased; this means that the effective cavity length is longer, so the measurement resolution is enhanced. Due to that, the possibility of creating an advanced rotation sensor with very high performance arises.
Another possibility to use the multi-reentrant laser is absorption spectroscopy.
Multi-pass cell has been widely used for the detection of weak atomic or molecular absorption lines due to its long optical path combined with compact cell volume [30-34] as shown in Fig. 1.6.
The length of the commercial multi-pass cell is around 36 m to 100 m. The principle is that introduce the tunable laser to the multi-cell, after multi reflected in the multi-pass cell, the out put laser beam intensity will be detected by the balance receiver, and the absorption value of the gas can be calculated form the formulaI = I0e−αl where α is the absorption coefficient, l is the total optical path of the multi-pass cell. The major advantage of our multi-reentrant ring laser is that the measurement would be more sensitive than the multi-pass cell in Fig. 1.6. The optical coating of the two mirrors for our experiment set up are all 99.8% reflectance for the 1064nm, the loss is 0.4% in one round trip. It is known that the laser out power is very sensitive for the stability of the resonator, once the laser intensity inside the cavity has a small variation, the output power response immediately. Although the gas absorption constant is usually very small, the power vibration which causes from the oscillation photons were absorbed by the gas atom would be observed obviously.
Figure 1.6. An absorption spectroscopy set-up using multipass cell [30].
Using the multi-reentrant laser cavity, the detection sensitivity can be further increased because the laser output power is much more sensitive to intracavity loss than a passive cell.
Designing a laser system involves integrating a number of different technologies. One of the critical technologies is the optical coating. For solid-state laser, there are three strict criterions to the multilayer dielectric films. They are the high-reflection coatings; reflectivity should be satisfied for different wavelengths, and high damage threshold. In our investigation, we have studied solid-state laser system for years and have many related patents. To develop high efficiency solid-state laser, we have also collaborated with the Industrial Technology Research Institute, Hsin Chu, for the high quality coating technology. In this dissertation, the basic theory and some simple optical thin film design models and rules are presented.