Laser Generation

In this section, we will discuss pumping mechanisms to excite active ions to higher levels for population inversion, laser resonators for control of amplification and creation of special beam profiles, Q-switching techniques to increase the power of the laser output to very high levels, thermal and birefringence effects produced by the heating of the laser medium affecting the beam quality etc. related to laser generation in solid state, gas, semiconductor, dye, free electron and X-Ray lasers. Although these technologies vary very much for each of the above-mentioned lasers, there are lots of common factors as can be seen from the following paragraphs.

Pumping or excitation mechanisms

First requirement in the generation of laser is the creation of population inversion. Input energy in various forms have to be supplied to the gain media for excitation and transition of ground level atoms, molecules, ions or electrons as the case may be, to higher levels to create population inversion and consequent generation of laser. Commonly used excitation techniques are optical pumping (solid state lasers), electrical discharge / radio frequency excitation (gas lasers), electron beam / injection current (semiconductor lasers), chemical (chemical lasers), thermal (Gas Dynamic Lasers), high-energy electrons from accelerator (free electron lasers) etc. Lasers, with output in the spectral region matching the absorption band of the active media, are also employed for excitation. The type of excitation techniques used is decided by the nature of the active laser media. The different types of excitation mechanisms are optical, electrical, chemical, thermal, laser etc.

Optical

In solid-state lasers (SSLs), the laser media are in the form of optically transparent solid materials with active ions having strong absorption bands in the visible or near infrared region. A pump source, giving maximum emission at wavelengths to excite fluorescence in the laser material, is most suited for SSLs. Noble gas filled flash lamps, metal vapour discharge lamps, tungsten-halogen filament lamps, semiconductor lasers, etc. are all used in this connection. Xenon flash lamps for pulsed operation and CW arc lamps for CW operation of lasers are the most commonly employed optical pumps. An optical reflector cavity is required to couple the high intensity light output efficiently from the flash lamp to the laser rod. Various reflecting geometries have been employed for this purpose. Elliptical reflector, with the laser rod at one focus and the flash lamp at the other, cylindrical reflector with the lamp and the rod in close proximity or the rod surrounded by the helical flash lamp, have all been used for efficient coupling of light on to the rod. End pumping as well as side pumping geometries have been employed for diode laser pumping of solid-state lasers. Examples of optically pumped SSLs are Nd:YAG, Nd: Glass and Alexandrite, to sight a few.

Electrical

In gas lasers (helium-neon, argon ion and carbon dioxide lasers), electrical discharge is employed to excite neon atoms, argon ions and CO₂ molecules respectively to higher levels to create population inversion. The most common type of excitation is either a direct current electrical discharge or a radio frequency discharge. For high power CO₂ lasers, instead of having the discharge along the length of the laser tube, a transverse excitation, with a series of electrodes spaced along the gas tube, is employed.

Chemical

In chemical lasers, the chemical reaction generates a large amount of excited molecules and then another gas is introduced in to the system. Now depending on the system, one of the two following things can happen. Either it takes energy from the excited molecule, as in the case of COIL (iodine molecules from singlet oxygen) or it reacts with those particles, producing an excited molecule, as in the case of DF / HF laser (deuterium or hydrogen respectively with fluorine radicals) These excited molecules produce population inversion. COIL, DF and HF lasers are some of the examples of chemical lasers.

Thermal

In gas dynamic laser, adiabatic expansion cooling of hot gases is utilized to produce population inversion. The technique is to expand hot gases through specially shaped nozzles from a high pressure, high temperature chamber into a low-pressure chamber, thus creating a highly non-equilibrium state in the resonator. Due to adiabatic expansion, the upper level population is frozen and the lower level population is depleted, resulting in strong population inversion. Carbon dioxide gas dynamic laser (CDGDL) is an example of a thermally excited laser.

Laser

Ti: Sapphire laser is a good example of a laser pumped laser. As the peak of the absorption band of Ti: Sapphire is around 500 nm, frequency doubled Nd: YAG laser (532 nm) for pulsed operation and Argon ion laser (514 nm) for CW mode of operation are used for excitation to create population inversion and subsequent laser emission. Diode laser pumping of Nd: YAG laser is another example of a laser being employed for excitation.

These pumping techniques have been discussed in greater details in the next chapter, which deals with specific type of lasers.

Resonators

The two mirrors, between which the gain medium is situated is referred to as the laser resonator. Resonator plays a very important role in controlling small signal gain as well as total gain of the laser system and developing transverse and longitudinal modes. It is responsible for generating special types of laser beam profiles and also gives the laser its unique property of directionality and coherence. The spectral characteristics of the laser, like beam diameter, divergence and energy distribution are controlled primarily by transverse modes. Line width and coherence length are basically determined by longitudinal modes. Various types of resonators were discussed in the earlier section and the same will not be repeated. Further, the intention of this site is only to give an insight into the subject and to provide references for a serious study.

Different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them. The most common types of optical cavities consist of two flat or spherical mirrors. The simplest of these is the plane-parallel or Fabry-Perot cavity, consisting of two flat mirrors separated by some distance L. These arrangements of flat mirrors are usually not preferred because of the difficulty of their alignment with required accuracy, which is typically few seconds of arc. Fabry-Perot cavities suffer from another type of problem, which further results in increased losses. The plane waves that exist in F-P cavities generate large diffraction losses at the edges of the mirrors. Losses, in general, are very carefully monitored in laser cavities because they can wipe out the gain of the active medium. The resonator geometry must be chosen so that the beam remains stable. By stability, we mean that the size of the beam does not continually grow with multiple reflections. However, this problem is much reduced for very short cavities with a small mirror separation distance (L < 1 cm). Plane-parallel resonators are therefore commonly used in microchip and semiconductor lasers. In these cases, rather than using separate mirrors, the laser medium itself is suitably coated at both the ends to serve as fully reflecting and partially reflected mirror.

The plane-parallel cavity (shown in the above figure) is an important component in pulsed solid lasers and some other pulsed lasers as well because its high mode volume makes efficient use of the active medium. Though, the cavity has the highest diffraction loss of any configuration, but this loss is overcome easily in pulsed lasers by the additional gain achieved by the larger mode volume. It has the additional advantage of not focusing the laser beam inside the active medium. Such internal focusing can damage solid laser rods. As mentioned earlier, the plane parallel cavity is, however, the most difficult to align.

Optical cavities are designed to have a large Q factor, so that the beam can reflect large number of times without any significant attenuation. As such, the frequency and thus the line width of the beam are very small as compared to the frequency of the laser.

For the type of lasers we are discussing, flat mirror geometries are not feasible. Only certain ranges of values for R₁, R₂, and L produce stable resonators in which periodic refocusing of the intra-cavity beam is produced. If the cavity is unstable, the beam size will grow without limit, eventually growing larger than the size of the cavity mirrors and being lost. The stability criterion in terms of R₁, R₂ and L is given as:

The stability criterion can be shown graphically by plotting g₁ against g₂ as shown. Areas bounded by the line g₁ g₂ = 1 and the g₁ g₂ axes are stable. Cavities at points exactly on the line are marginally stable. Even a little variation in cavity length can cause the resonator to become unstable. The plane-parallel cavity corresponds to point (1,1) in the stability diagram.

For a resonator with two mirrors with radii of curvature R₁ and R₂, there are a number of common cavity configurations. Some of these configurations are discussed below:

If the two curvatures are equal to half the cavity length (R₁ = R₂ = L / 2), a concentric or spherical resonator results. This type of cavity produces a diffraction limited beam waist in the centre of the cavity, with large beam diameters at the mirrors, filling the whole mirror aperture. This type of configuration corresponds to point (-1,-1) in the stability diagram.

The spherical cavity is shown in the adjoining figure and is basically functionally opposite to the plane- parallel cavity. It is easiest to align, has the lowest diffraction loss, and has the smallest mode volume. CW dye lasers usually employ this type of cavity because a focused beam is necessary to cause efficient stimulated emission of these lasers. The spherical cavity is not commonly used with any other type of laser.

The confocal cavity is a compromise between the plane-parallel and the spherical cavities. The confocal cavity combines the ease of alignment and low diffraction loss of the spherical cavity with the increased mode volume as in case of flat and parallel mirror configuration. This configuration corresponds to a point (0,0) in the stability diagram. Confocal cavities can be utilized with almost any CW laser for moderate power levels. A common and important design is the confocal resonator, with equal curvature mirrors equal to the cavity length (R₁ = R₂ = L). This design produces the smallest possible beam diameter at the cavity mirrors for a given cavity length, and is often used in lasers where the purity of the transverse mode pattern is important. In case of confocal resonator the foci F1 and F2 of mirrors are coincident. In this case, the center of curvature of one mirror lies on the surface of another mirror as L=R.

Resonators formed by two spherical mirrors of the same radius of curvature R and separated by a distance L such that R<L<2R, i.e., in between confocal and concentric, are called Generalized Spherical Resonators, which is also often used.

Resonators formed by two spherical mirrors of the same radius of curvature R and separated by a distance L such that R<L<2R, i.e., in between confocal and concentric, are called Generalized Spherical Resonators, which is also often used.

The hemispherical cavity, which is actually a half of the spherical cavity, has characteristics similar to that of spherical. This configuration corresponds to point (0,1) in the stability diagram. The advantage of this type of cavity over the spherical cavity is the cost of the mirrors. The hemispherical cavity is used with most low-power HeNe lasers because of low diffraction loss, ease of alignment, and reduced cost.

Cavities can be identified as stable or unstable according to whether a particular configuration allows the cavity oscillations to remain within the cavity or the laser beam spreads out of the cavity. The output mirror of the laser resonator is precisely coated to achieve the required reflection into the cavity. In case the beam is too intense, the mirror may suffer damage, which may result in the cessation of laser action. Generally, for low powers typically less than a kilowatt, lasers mainly use stable cavity configurations. The laser output is from the center of optical axis. Stable cavity design allows the beam to oscillate many times inside the cavity to get high gain, and also the focal property and directionality are also improved.

However, for high power lasers, unstable cavity configurations are usually preferred as shown in the adjoining figure. The laser output comes from the edge of the output mirror, which is often a totally reflecting metal mirror. This concave-convex cavity normally is used only with high power lasers. In practice, the diameter of the convex mirror is smaller than that of the beam. The output beam is formed by the part of the beam that passes around the mirror and, consequently, has a "doughnut" configuration. The beam must pass around the mirror because mirrors that will transmit the intense beams of these high-power lasers cannot be fabricated. The ring shaped beam reduces the intensity of the beam, thus reduces the risk of damaging the mirror. In this cavity configuration, the ring shaped beam is however, poor for focusing. Unstable cavities are suitable for high gain per round trip laser systems, which don't require large numbers of oscillation between the mirrors.

Thermal problems

Efficiency of most of the laser systems is very poor (less than 5%) and as such the unutilized input energy goes as heat. To understand effect of thermal problems on the resonator, let us consider a solid-state laser. Since most of the input energy goes up in heating the laser rod, fluid cooling is employed to get the rod with in the thermal limit of working. During the cooling cycle, radial temperature gradient arises between the center of the rod and its surface i.e. center of the rod is at higher temperature than the periphery, as the surface gets cooled faster than the central region. Consequently, refractive index variation in the material takes place, resulting in thermal lensing. We can say that the input power of the optical pump controls the beam radius with in the laser rod in the resonator. Thus, thermally induced birefringence occurs and depolarization effects become a hindrance for power scaling or increasing the repetition rate of the laser. It becomes imperative to know the compensation of depolarization in order to design a resonator for high power lasers. Further, the finite size of the resonator mirrors and inherent in-homogeneity of the laser crystal also produce aberration of the output beam. Resonator dielectric mirrors in the lasers are passive structures and they cannot correct the aberration introduced. The use of self-correcting adaptive resonators and phase conjugate mirrors has reduced these aberrations to a great extent.

Q-switching techniques

The losses associated with the modes generated in the resonator are radiation losses produced by scattering and absorption due to impurities in the laser material, diffraction losses associated with the finite dimensions of the laser material, mirrors, other optical components etc and reflection losses produced by the imperfect mirrors. It is necessary to overcome these losses by way of building up gain with the feed back between the mirrors, while the population inversion and stimulated emission exist. The Q or quality factor of an optical cavity describes the ability of the cavity to store light energy in the form of standing waves. The Q factor is the ratio of energy contained in the cavity divided by the energy lost during each round trip in the cavity:

This means that a cavity with high losses dissipates a lot of energy per cycle hence it has a low Q value; a high Q cavity means the energy loss per cycle is small in the given cavity. Hence higher the quality factor, lower is the losses.

This implies that by controlling Q, one can control the output of the laser. Q-switching or Q-spoiling is a technique to generate high power laser output by controlling the quality factor in a laser cavity i.e. controlling the losses. Q-switch, located in the cavity can change temporal and power characteristics of the laser beam.

Q switching technique can be defined as a method to create high power / energy laser pulses. It modulates the Q of laser cavity to build population inversion first, and then release the accumulated energy suddenly, in this way high-energy pulses can be created.

If a closed shutter is kept inside the laser cavity during pumping, the optical feedback between mirrors will be prevented. Consequently, the population inversion caused by energy stored in the material, as well as the gain increases to a high value. But the losses are also high (low Q) and due to the absence of feedback, the increase in gain to overcome the losses are not available and consequently the laser action is inhibited. When the shutter is suddenly opened, high Q (low loss) is restored and the excess energy stored is discharged in a very short time, resulting in a high power laser pulse, which is several orders of magnitude higher than the normal pulse. The basic idea is that for only a brief time is the beam allowed to pass back and forth between the mirrors to achieve the laser action, but the pumping action is continuous so that a large population inversion is already build up when the lasing condition is satisfied. Since the power of the pulse is very high it is called a giant pulse. Q-switched lasers normally emit only one giant pulse in an operational cycle. The pulse typically has time duration of nanoseconds and the peak intensity is of 10⁶ - 10⁹ watts. The extremely short, high-energy output pulses make the Q-switched lasers an ideal transmitter source for rangefinders and surveillance radar applications.

A good Q-switch should reduce the loop gain to zero when closed and should introduce no loss in the cavity when opened. It should switch from one condition to the other as fast as possible, and the switching should be synchronized to external events.

There are a number of techniques employed for the generation of high power laser pulses, which are discussed briefly below:

Mechanical

In the mechanical Q-switching technique, rotational, oscillatory or translational motion of optical components are used to create a situation, where laser action is inhibited during pump cycle either by putting a shutter between mirrors or by misaligning mirror itself i.e. to introduce high loss during pumping for storing the excess energy in the material. Pulse widths of the order of few tens of nano-seconds have been obtained with this technique.

The simplest type of Q-switch uses a rotating mirror or prism to form one end of the optical cavity. A sensor triggers the pump source i.e. flash lamp just before the mirror or other optical element rotates into position such that the resonator mirrors are parallel to each other. Usually the maximum-reflectivity mirror is rotated so that the mirror is tilted out of alignment. The system is Q-switched when the mirror rotates back into alignment. This alignment happens once in each revolution. Rotating mirror Q-switches offer 100% dynamic loss and 0% insertion loss. This is fairly easy to do with ruby as the lasing medium with its long (3 ms) fluorescence lifetime. However, the corresponding value for Nd: YAG is only 230 ms.

Thus, only 100 to 200 ms is available once the flash lamp fires and sensing the position of a rotating optical element to this precision would be somewhat more difficult. For example, at 6,000 rpm or 100 rps, one revolution is completed in 10-4 sec. Thus 100 microseconds correspond to 1/100th of a full rotation. However, if rotating mirror can be made multifaceted or the Q-switch speed can be made fast enough by rotating the mirror at high speed typically 20,000 to 60,000 rpm, even lasers like Nd: YAG can be Q-switched and switching time typically of a few nanoseconds can be achieved. However, rotating mirror Q-switches are prone to alignment difficulties because each face of the mirror must be aligned to within a fraction of milliradian. Thus, roof prisms are often used as rotating elements. As long as the roof of the prism is perpendicular to the axis of rotation, reflection is guaranteed at some angle of rotation. Simple set ups are shown in the adjoining figures.

Mechanical Q-switches are simplest and least expensive of the Q-switches. They have the additional advantages of polarization and wavelength insensitivity. However, the high rotational speeds mean that the devices are noisy and possess relatively short lifetimes. Furthermore, mechanical components are not robust in harsh environments.

Electro-optical

Probably the most reliable and commonly used Q-switches employ electro-optical (E-O) effect in crystals (Pockels effect) and liquids (Kerr effect). An E-O element like the properly oriented lithium niobate crystal, under the influence of electric field, becomes birefringent, producing 'fast' and 'slow' axes orthogonal to each other, with different refractive indices. A plane polarized optical beam at 45o to these axes and incident normal to their plane, will split in to two orthogonal components, traveling along the same path, but with different velocities, causing a phase difference between the them. Depending on the voltage applied to the E-O element (eg. Lithium niobate crystal), the combination of the two beams will produce a linearly, circularly or an elliptically polarised beam. E-O Q-switch is formed by the combination of a polariser and an E-O element in the resonator cavity. These are called Pockels cell Q-switches also, since the working is based on Pockels effect.

This common arrangement for an electro-optic Q-Switch in which the Q-Switch is placed between a linear polarizer and the rear mirror is shown in the figure. The applied voltage across the Q-Switch is chosen so as to cause a l/4 difference in the phases of the emerging components. If linearly polarized light enters the crystal, then circularly polarized light will emerge. In other words, when voltage is applied to the Q-Switch, it acts like a quarter-wave plate. Initially, the beam passes through the linear polarizes. It enters the electro-optic crystal and emerges as right circularly polarized light. After it reflects from the mirror, it converts into left circularly polarized light. When the beam passes through the electro-optic crystal, it emerges as linear polarized light but perpendicular to the direction of the original light polarization. In other words, the l/4 Q-switch plus the mirror reflection plus the l/4 Q-switch again, acts like a l/2 or half-wave plate that will convert linear polarization in one direction to linear polarization in the orthogonal direction. This orthogonal polarized beam is then ejected from the cavity by the polarizer. When the voltage is removed from the Q-Switch, the crystal is no longer birefringent. Thus, the emerging beam from the crystal is unchanged and is not affected by the polarizer. Therefore, this Q-Switch only produces a pulse when the voltage is off.

Another method is to place the E-O element between two crossed linear polarisers. Initially, the beam passes through the linear polarizer. It enters the electro-optic crystal and emerges as linear polarized light rotated by 90 degrees (orthogonal to the original polarization). It then can pass through the second polarizer. When the voltage is removed from the Q-Switch, the crystal is no longer birefringent and emerging beam from the crystal is unchanged. The beam has the same polarization as original beam and is ejected from the cavity. Thus, this Q-Switch only produces a pulse when the voltage is on. This configuration is shown in the adjoining figure.

Electro-optical Q-switches have high dynamic loss (99%) and relatively high insertion losses (15%) because of the losses in the optical elements. Switching time is fast; typically less than a nanosecond, and synchronization is good. Laser pulse widths of the order of few nano-seconds can be obtained using this method. Crystals, like lithium niobate, potassium di-deuterium phosphate etc are used for making E-O Q-switches as Pockels effect is shown only by crystals, which lack center of point symmetry.

Few words about the power drivers for the Pockels cell Q-switches may be of interest here. Depending on the material used for the Q-switches, the voltage may vary from 3 to 15KV, with the current requirement of the order of 10 to 20 mA and having a rise time of few nano-seconds. Krytrons are best for fast switching.

Acousto-optical

When an ultrasonic wave passes through a transparent material, say fused quartz, it acts like an optical phase grating, due to photo-elastic effect. Acousto-optic Q-switches employ these quartz like materials which exhibit a change in the refractive index when the material is acoustically excited via photo elastic effect. The idea is to create an acoustic standing wave in the crystal by means of a piezo-electric transducer bonded to the crystal. The acoustic standing wave generates a corresponding standing wave in the refractive index. This refractive index variation behaves like an acoustic grating. If a light beam is incident on this grating, part of the intensity will be switched out of the resonator cavity. With a little more ingenuity most of the diffracted beam can be deflected out of the laser cavity, thus spoiling the Q of the cavity. The resulting optical phase grating deflects the beam out of the laser cavity thus creating a low Q value.

Acousto-optic Q-switches are often operated in the Bragg scattering regime. In this regime, the interaction path is large and the zeroth and first-order diffraction beams need to be considered. In the Bragg regime of the operation, the acoustic grating is oriented at an angle q with respect to the incoming light ray. The angle is typically defined inside the acousto-optic modulator, and is given as

Where n is the index of the refraction and L is the acoustical wavelength.

This configuration is shown in fig. The scattering angle 2q and the diffracted beam intensity is given as:

Where P_ac is the acoutic power, 'l' and 'w' are the length and width of the transducer respectively. M₂ is the acousto-optic figure of merit.

By cutting off the driving voltage to the transducer, the acoustic wave is removed and the diffraction effect disappears, the cavity is again aligned. The laser system returns to the high Q value, with consequent generation of laser.

As compared to E.O. devices, where dynamic loss of almost 100 % can be achieved, acousto-optic devices have low dynamic loss typically 50 - 60 %. However, the insertion loss can be almost zero. As mentioned earlier, EO devices can be switched off faster typically in the nanosecond range, in case of AO devices; on the other hand, the switching time is determined by the time the acoustic wave requires to cross the optical beam. Since 6 km/s is a typical acoustic velocity, so the switching time is about 170 ns per mm beam diameter. This slow switching time at 100 ns or greater is a drawback of these devices.

On the other hand, AO devices can be modulated much faster thus implying that the repetition rate can be very high. Though the switching time is slow, one can have 100s of kHz repetition rate in these devices. EO devices, on the other hand suffer from these considerations. EO devices need a certain recovery time. Typically these devices are good for a few 100 Hz rep rate.

An additional advantage of AO Devices is that they require only low voltages

Acousto-optic Q-switches are ideally suited for use with CW pumped Nd:YAG laser systems They cannot be used with most pulse pumped systems because their low dynamic loss will not prevent lasing.

Magneto-optical

Magneto-optic (M-O) effect or Faraday effect manifests in most of the optically transparent solids and liquids, when they are subjected to strong magnetic fields. The induced optical activity so generated is able to rotate the plane of polarization of an optical beam, which propagate parallel to the direction of the magnetic field in the material. The devices working on M-O effect can produce rotation of the plane of polarization for any input polarization angle, which is not the case with the electro-optic devices and are used in the development of isolators and rotators. This device produces a clockwise rotation of the polarization of the optical beam's axis through 45° when the beam propagates in one direction. When the beam passes back through the same assembly, it will not reverse this effect, but will produce an additional rotation of 45° for the reverse beam, thus making the total rotation by 90°. This will then be at 90° to the input polarization axis. Faraday isolators are used to prevent damage to the laser oscillators from enhanced back reflection from amplifiers as well as from targets. Rotators are used to ensure unidirectional response in ring laser systems in conjunction with other intra-cavity polarization selective element. Faraday isolators are rarely used for Q-switching applications.

Dye

Unlike all the other Q-switches, dye Q-switch is a passive element, since it does not need an external agency for its working. It is either a cell filled with dye or dye molecules embedded in polyurethane, placed between the rear mirror and the laser medium. During pumping, the initial fluorescent emission from the laser medium is absorbed by the dye and isolates the rear mirror from the system, thus inhibiting the laser gain build up. As the intensity of the fluorescent emission increases, the dye gets bleached and becomes transparent allowing laser oscillation to begin and subsequent generation of laser. The property of the dye is such that its absorption coefficient decreases with increasing intensity. The dye in solution or polyurethane matrix is a non-linear optical material. This has an absorption coefficient, which is a function of incident light intensity: the material is opaque (absorbing) until the intensity of the light in the cavity reaches a critical value, at which point the material suddenly becomes transparent. No external signal is needed to trigger a passive Q switch. As the intensity in the cavity reaches a critical value at which the dye saturates, the cavity Q is switched. The result is a very short of the order of nanosecond length output pulse. The saturable absorber then returns to its absorbing state and if the pumping continues, the process will repeat generating a series of short pulses.

The dye based Q-switch is also called a saturable absorber because its absorption saturates at high intensities. Basically, the dye molecules absorb photons and are transferred to a higher state and once the sufficient number of ground level molecules is pumped up, the dye becomes transparent i.e. in the beginning the dye is opaque (shutter closed) and in the end it is transparent (shutter opened). Important points to remember while selecting the dye, are that the dye cross section should be much larger than the laser cross section and the dye should be able to absorb radiation at the specific wavelength of the laser. Another important aspect is the dye relaxation time, as the spectral and temporal characteristics are very much dependant on it. If the dye has a short relaxation time, it will mode-lock the pulses instead of Q-switching it, as it can follow the fast oscillations in intensity.

Crypto cyanine and Kodak 9860 and 9740 dye solutions have very short relaxation times, where as Kodak 14015 dye (for Q-switching of neodymium lasers) has much lower relaxation time. Power output and the pulse width of the laser will depend on the dilution level of the dye with the solvent i.e. by controlling the transmission level, which is around 40% to 60%. Various lasers require different types of dyes due to the reasons given above.

Bleachable dye Q-switches rate very high in dynamic loss (>99%) and insertion loss is typically few percent. Their switching time is fast. There are virtually no synchronization issues involved at all. Dye cell Q-switches can be used with pulse pumped systems only because a CW pumped laser never produces sufficient fluorescence to bleach the dye. This can be used to provide a means of easily controlling the pulse rate of a diode or arc lamp pumped laser with excellent consistency of pulse energy as the Q-switch only activates when its threshold is reached. Since no complex mechanical and/or electronic systems are involved, this is an excellent approach, especially for compact lower power systems. Schematic of dye Q-switch is shown in the adjoining figure.

Cavity dumping

As discussed earlier, Q-switch works as an optical shutter and is used to prevent lasing so that the energy from the pump source can be stored in the active medium of the laser in the form of excited atoms. Pulsed output can be obtained from many lasers using this type of Q-switching, however, this technique does not work with lasers whose upper-state lifetime is too short to store the sizeable energy. Cavity dumping is another method to generate short, powerful pulses. It is different from Q-switching in the sense that in this case the energy is stored in the form of the optical waves in the cavity and not in the population of excited states of the active medium.

The cavity of a laser to be used for cavity dumping consists of two high reflective mirrors. That is, this cavity has no partially transmitting mirror, the so-called output coupler. Light is totally confined within the cavity. Lasing begins when the intra-cavity shutter is opened for maximum transmission. As there is no light leaving the cavity, the Q factor of the cavity is very high.

As the laser begins to oscillate, the optical energy builds up in the cavity in the form of the E.M. waves. All the light energy is stored inside a cavity. A component called the 'cavity dumper', which is placed inside the cavity, is suddenly switched-on so that it deflects the light out of the cavity. That is, this component 'dumps' all the stored light energy out of the cavity in one pulse. In other words, we first build up the light energy inside the cavity, and than dump all the stored energy in one go out of the cavity. Simple set up is shown in adjoining figure.

The component that may work as cavity dumper can be a transparent electro-optic or acousto-optic switch, which, when switched on, can deflect the light out of the cavity with high efficiency. Cavity dumpers can be used practically with any laser. The only point to see is that the optics should have a high damage threshold? Pulse duration in cavity-dumped lasers is typically 1-2ns.

Mode locking

In a laser resonator cavity, light waves reflect between the two mirrors continuously and as such they interfere constructively and destructively with it self to form standing waves. We already know from the previous section that standing waves that form a discrete set of frequencies are called longitudinal modes. These modes are the only frequencies, which are allowed to oscillate by the resonat cavity, the rest being suppressed by destructive intereference. If we consider a plane-plane mirror geometry, only those modes, for which the the distance between the mirrors is an exact multiple of half the wavelength of the light, will be allowed to oscillate. Even though the laser is in fact nearly monochromatic, the modes are so close together that there can be many thousands of modes within that narrow frequency range. A typical in-homogeneously broadened laser cavity may support oscillations in many modes simultaneously. The output of such a laser as a function of time depends on the relative phases, frequencies and amplitudes of the modes. If these parameters are random and vary all time, the modes are incoherent. Further if there is no means to choose modes, then random quantum "noise" will trigger modes randomly and laser action can occur essentially continuously and with random phases with respect to other longitudinal modes. A laser can oscillate on many longitudinal modes, with frequencies that are equally separated by inter-modal spacing of n_F = c/2L, where c and L are velocity of light and the distance between the resonator mirrors respectively. Normally, these modes oscillate independently without any fixed phase relationship with each other. Although these modes oscillate independently and are usually called free running modes, however external means can be used to couple them and lock their phases together. If a mode operates with the other modes with a fixed phase relationship, then all the modes will periodically interfere with each other constrctively, generating an intense pulse of light. The laser is now said to be mode-locked or phase-locked. These high intensity pulses repeat themselves in a time ( t ) taken by the light to make exactly one round trip of the laser cavity. This time corresponds to t = 1/n_F = 2L/c.

Difference between mode locking and Q-switching

• Mode locking is a technique for producing periodic, high power, short duration laser pulses. Mode locking is achieved by forcing the longitudinal modes to maintain fixed phase relationships. This can be accomplished by modulating the loss (or gain) of the laser cavity at a frequency equal to the inter-modal frequency separation n_F = c/2L. The basis of the technique is to induce a fixed phase relationship between the modes of the laser's resonant cavity. The laser is then said to be phase-locked or mode-locked. Interference between these modes causes the laser light to be produced as a train of pulses. Depending on the properties of the laser, these pulses may be of extremely brief duration, as short as a few femtoseconds.
• Major difference between Q switching and mode locking is that in case of mode locking, before generation of the output pulse the energy is stored in the intra-cavity light field, whereas in case of Q- switching it is stored in the gain medium. The most important advantage of mode locking is that this energy can be extracted within just one round-trip time, independent of the time required for building up the intra-cavity power. Therefore, the pulse duration achievable is more or less determined by the resonator length (provided that the switching time of the modulator is not longer than the resonator round-trip time), and is decoupled from the laser gain. This means that even for very high pulse repetition rates, e.g. several megahertz, pulse durations of a few nanoseconds are still achievable.
• In case of Q switching, the number of radiation transits through the switch whether active or passive, are usually few; in most cases just once. Whereas, in case of mode locking the radiation transits through the switch large number of times.
• In case of Q-switching, the laser output is turned off by increasing the resonator loss i.e. by spoiling the resonator quality factor Q periodically with the help of a modulated absorber inside the resonator. Thus Q-switching is loss switching. Because the pump continues to deliver constant power at all time, energy is stored in the atoms in the form of accumulated population difference during the off (high loss) times. When the losses are reduced during the on times, the large accumulated population difference is released, generating short intense pulses of light.
• In case of mode locking, pulsed laser action is attained by coupling together the modes of lasers and locking their phases to each other. For example, the longitudinal modes of a multimode laser, which oscillates at frequencies that are equally separated by the inter-modal frequency, n_F = c/2L, may be made to behave in this fashion.

Mode locking Techniques

The method used to obtain these operating conditions consists in using a rapid light modulator that can chop the light in the cavity into periods of exactly the same length as a round trip. Thus, only those photons allowed to pass through the modulator in its on state will be amplified and will always find the modulator in this state after each round trip. The other photons elsewhere in the cavity will be subject to losses when they travel through the modulator Active as well as passive techniques have been employed to generate mode-locked laser pulses.

In case of active techniques, suppose that an optical switch for example, an electro-optic or acousto-optic is placed inside the resonator, which blocks the light at all the times, except when the pulse is about to cross it, whereupon it opens for the duration of the pulse. Since the pulse itself is permitted to pass, it is not affected by the presence of the switch and the pulse train continues uninterrupted. In the absence of phase locking, the individual modes have different phases that are determined by the random conditions at the onset of their oscillation. If the phases, by chance, happen to take equal of fixed values, the sum of the modes will form a giant pulse that would not be affected by the presence of the switch. Any other combination of phases would form a field distribution that is blocked by the switch, which adds to the losses of the laser system. Therefore in the presence of a switch, only case where there is lasing is that the modes have equal phases. The laser waits for the lucky accident of such phases, but once the oscillation starts they continue to be locked.

As discussed earlier, in case of acousto-optic modulators, the devices usually work in the Bragg regime. In such cases, the Bragg diffraction is given by

Where l₀, n and L are the wavelength of the light, refractive index and the acoustic wave, respectively. This equation implies that the diffraction angle q is inversely proportional to acoustic wavelength or in other words is linearly proportional to the acoustic frequency. It is also directly proportional to the optical wavelength; thus, for a given acoustic frequency, higher the optical wavelength, the larger the diffraction angle.

During the time the acoustic wave is produced, the incident laser light is scattered into a certain direction (the first diffraction order); thus, it is lost for the direct pass of the laser light between the mirrors of the cavity. About 90% of the incident light can be deflected. To obtain pulses, we must switch the acoustic waves on and off. Devices operating in the range up to GHz frequencies are available from industrial manufacturers.

In case of electro-optic shutters, the device, when placed in a laser cavity and driven with an electrical signal, induces a small, sinusoidal varying frequency shift in the light passing through it. If the frequency of modulation is matched to the round-trip time of the cavity, then some light in the cavity sees repeated up-shifts in frequency, and some repeated downshifts. After many repetitions, the up-shifted and downshifted light is swept out of the gain bandwidth of the laser. The only light, which is unaffected, is that which passes through the modulator when the induced frequency shift is zero, which forms a narrow pulse of light.

A shutter or modulator whose timing is accurately controlled externally is not necessary in passive mode locked systems. If some material or mechanism could be used which automatically opens to allow the pulses through but is closed otherwise, a self-adjusting modulator could be constructed. In other words, the light pulse would open its own shutter when it arrived, rather than depending on it being open upon arrival. Hence, if the pulse arrived early or late, the shutter would still open, allow the pulse to pass through and then close. This method is referred to as passive mode locking.

A saturable absorber is an optical device that exhibits an intensity-dependent transmission. What this means is that the device behaves differently depending on the intensity of the light passing through it. For passive mode-locking, ideally a saturable absorber will selectively absorb low-intensity light, and transmit light which is of sufficiently high intensity.

When placed in a laser cavity, a saturable absorber will attenuate low-intensity constant wave light. However, because of the somewhat random intensity fluctuations experienced by an un-mode-locked laser, any random, intense spike will be transmitted preferentially by the saturable absorber. As the light in the cavity oscillates, this process repeats, leading to the selective amplification of the high-intensity spikes, and the absorption of the low-intensity light. After many round trips, this leads to a train of pulses and mode-locking of the laser.

Saturable absorbers are commonly liquid organic dyes, but they can also be made from doped crystals and semiconductors. Semiconductor absorbers tend to exhibit very fast response times (~100 fs), which is one of the factors that determines the final duration of the pulses in a passively mode-locked laser

The advantage here is that both Q-switching and mode-locking can be carried out with th same dye. Without going in to theoretical aspects, the following experimental points are note worthy. In a configuration for obtaining mode-locked lasers, it is essetial that reflections from the two resonator mirrors only should be confined in the laser cavity and the reflections from all the other surfaces of components, should go out of the cavity. Therefore, the laser rod should be cut at a small angle (and not perpendicular to the rod axis) and the dye cell containing saturable absorbable should be kept at an angle to the laser axis or the dye cell should be in optical contact with the fully reflecting mirror, to avoid etalon effects as well as avoiding spurious reflections from the surfaces of other components. To reduce the stringent alignment requirements, one can employ curved mirrors. The generation of TEMoo mode can be fecilitated by the use of a pin hole in the laser cavity.

The minimum laser pulse width that can be obtained by Q-switching technique is around 10 nanoseconds by pulse reflection mode technique (limitation due to the pulse buildup time requirement) and about a nano-second employing pulse transmission mode technique (limited by the length of the cavity). Generation of pico-second and femto-second pulse widths is possible with mode-locking technique.

Some important points regarding mode locked lasers

• Inter-modal frequency separation n_F = c/2L, where c and L are velocity of light and the distance between the resonator mirrors respectively. Typically for a solid-state laser, if the value of 'L' is 15 cm, so the inter-modal frequency separation is 1 GHz.
• Time ( t ) taken by the light to make exactly one round trip of the laser cavity is given as t = 1/n_F = 2L/c . This value is typically a nanosecond.
• No of modes present in the cavity are M, where
  
               M = Dn / n_F, where Dn is the atomic line width
• The period of pulse train is t = 2L/c. This is just the time for a single round trip of reflection within the resonator.
• The mode locked pulse width t_pulse is given as t_pulse = t / M.
• The maximum output irradiance is equal to (ME₀) ², where we have assumed for simplicity that all M modes have the same amplitude E₀.
  
• Typically an Nd³⁺: YAG laser having a line width of 100 GHz can support 100 modes and the minimum mode locked pulse width can be 10 ps.
• For Ti³⁺: Al₂O₃ laser, having a line width of 100 THz, can support 100,000 modes and the minimum mode locked pulse width can be 10 fs.

A simple mode locked laser pulse train is shown in the adjoining figure.

Gain, Small signal gain and Saturation Intensity

Since this section is discussing various aspects of gain, it is only appropriate to define small signal gain, laser threshold, threshold pump power, saturation power, gain band width etc, understanding of which are essential for the development of lasers.

• Small signal gain of a laser medium is the optical gain obtained for a weak input signal, which does not produce gain saturation.
• The input power for which the small signal gain is equal to the total cavity losses, is defined as the laser threshold and the pump power for which the laser threshold is reached is called threshold pump power. One has to reach a compromise between high slope efficiency and low threshold power for optimization of the output.
• Loop gain is defined as the total net gain that is obtained for a round trip transmission through the laser, after taking into account the losses.
• The saturation power is defined, as the power of that input signal, which in the steady state produces a gain equal to one half of the value of its small signal gain.
• Gain bandwidth is the finite range of frequencies, in which gain is available.

Let us discuss these terms in detail.

We may recall that the stimulated laser cross-section R₂₁(n) is given as

Where l is the wavelength, n is the refractive index, A₂₁ is the Einstein coefficient and L (n) is the spectral line shape function.

Under favorable conditions, stimulated emission can result in optical amplification. An external source of energy such as flash lamp stimulates atoms from ground state to excited state. Under certain conditions, it may create population inversion. When light of appropriate frequency passes through this medium having population inversion, the incident photons stimulate the excited atoms to emit additional photons of the same frequency, phase and direction resulting in an amplification of the input intensity.

The population inversion is given as

Where g₁ and g₂ are degeneracy of energy levels 1 and 2 respectively.

We know that the population difference, DN₂₁ ≈ (N₂ - N_l), is a function of E.M. energy density I_incident, i.e. the intensity of the E.M. radiation in the material.

This is so because both the stimulated emission and the absorption rates depend on I_incident, and these two processes determine the population difference. As I_incident (or the intensity) increases in the amplifier, it stimulates more and more excited atoms to emit photons.

This can only go on as long as the number of stimulating photons is less than the number of excited atoms. Once the number of photons overtakes the number of excited atoms, the exponential growth comes to an end

In terms of population of different levels, the population difference, DN₂₁ ≈ (N₂ - N_l), can be written in terms of intensity as:

Where I_s is the saturation intensity and is given as

(N₂ - N_l)_o represents the population difference (population inversion) before interaction with the E.M. radiation intensity, 'I' : 'h' is the Plank's constant, n is the frequency of light, R₂₁ is the stimulated emission cross-section and t_u is the upper state life time of the laser gain medium.

• It is clear from equation (2) that the population difference (N₂ - N_l) decreases with increasing intensity. When the incident intensity is equal to I_sat, the population difference is reduced to half of its original value.

Similar expression for the intensity dependent gain can be written in the following manner:

The output intensity of the stimulated emission, for small enough input intensity I(z), is given as

The product of R₂₁(n) and DN₂₁ is known as small signal gain per unit length 'g_o'

The small-signal gain coefficient represents the gain at very low intensities, at which the population inversion has not been significantly affected (depleted) by the radiation.

Therefore,

In case we also consider the losses in the material and a denotes the loss coefficient of the laser material, then this equation becomes

The general gain coefficient equation for a laser-amplifying medium is given as

Where g_o is the laser small signal gain coefficient, I is the intensity of the incident light on the gain medium and I_s is the gain medium saturation intensity, which is given as

Where h is the Plank's constant, n is the frequency of light, R₂₁ is the stimulated emission cross-section and t_u is the upper state life time of the laser gain medium.

Equation (1) indicates that for very small values of intensity 'I', gain 'G' is equal to small signal gain 'g_o' . As intensity increases, the gain decreases; when it is equal to 'saturation intensity', the gain becomes half.

As such, the saturation intensity IS is defined as the input intensity at which the gain of the optical amplifier drops to exactly half of the small-signal gain.

With further increase in intensity, the gain further reduces drastically.

To summarize, as the intensity in the material increases, so does the rate of stimulated emission, which acts to remove population from the upper level. This means that the degree of population inversion is reduced with increasing intensity, which in turn means that the gain is also reduced. The steady state condition corresponds to the case when the level of stimulated emission is just sufficient to balance the increase due to pumping.

Importance of Saturation Intensity

The output of a laser depends on the energy stored in the laser material. The stored energy density (J/cm²) E_st in a laser material, is directly related to the pump energy E_pump and is also modified by:

• The overlap of the pump spectrum to the absorption spectrum of the material
• The intrinsic efficiency of the material
• Lifetime of upper excited energy laser level.
• Saturation effects for very high pump energy densities.
• The small signal gain g_o is directly proportional to population inversion, which in turn depends on the stored energy. Under small signal gain conditions, the maximum extractable energy is the product of stored energy E_st and area.
• If E_st is far greater than the saturation energy, the degree of stimulated emission increases thereby reducing the population inversion and thus the reduction in output energy.
• If E_st is less than the saturation energy, the degree of stimulated emission is less and thus the output energy is not optimum.
• For efficient operation, lasers must operate with stored energy densities roughly comparable their saturation energy density.

Saturation energy density of common laser materials:

Nd: YAG:	0.7 J/cm2
Nd: Glass:	5 J/cm2
Ti: Sapphire:	0.9 J/cm2
Alexandrite:	30 J/cm2

Higher saturation energy density in Nd: Glass and Alexandrite suggest that higher output energies are possible in these materials.

Threshold Gain

Letter 'a' in laser stands for amplification and obviously various aspects related to amplification is the key to laser generation. Amplification or optical gain in the laser medium is hindered by the cavity losses. The losses in the laser cavity make part of the available radiation not to take part in the lasing process. The necessary condition for lasing is that the total gain in the system should be a little higher than all the losses. This input energy is referred to as laser threshold. Although lasing is supposed to start immediately when the input energy reaches above laser threshold, useful, stable low noise performance and significant output can be obtained only much above laser threshold, since for achieving low threshold and low cavity losses as well as high gain are a must.

The cavity losses are:

Absorption and scattering losses in the gain medium, mirrors and other optical components

• Spontaneous emission losses
• Diffraction losses due to finite sizes of components
• Radiation losses through the output coupler, it being a partial reflector (unavoidable as partial reflectivity is essential for extracting the power from the laser)

In order to have a lower threshold and subsequent operation of an efficient laser system, one can employ high optical quality components with low absorption and scattering, to reduce losses. Radiation losses through the output coupler can be minimised by optimising its reflectivity. Thus one can achieve a low loss situation.


Let us estimate the threshold gain condition.

As already stated, at laser threshold, the gain equals losses.

Let us consider a laser media of length 'l', reflectivity of output coupler R₂ and that of rear mirror as R₁ = 100% or unity.

Let us imagine a wave of initial radiant power E_o at the rear mirror.

Then the radiant power, E, without feedback is given as

Where g_o is the single pass gain.

After one pass through the gain medium, the radiant power at the output coupler is E₁ is given as

Where a_i is the loss coefficient. After reflection from output coupler, the radiant power is E₂, which is

After the next pass through the gain medium, the radiant power is E₃, which can be written as

The beam has made one complete roundtrip pass through the system, after reflection from the rear mirror (reflection coefficient =1).

To sustain laser oscillations, the new radiant power E₃ should be either equal or more than the initial value. That is

Which is the loop gain with feedback.

We already know that unless gain equals the loss, the steady state oscillations cannot be sustained.

The above equation can be rewritten as,

After rearranging and taking log on both sides,

This is the threshold gain condition below which no laser oscillations can be sustained.

Therefore, threshold gain, g_o (threshold) is

The above equation can be rewritten as,

Laser parameter characterization

Basic laser parameters are beam width, divergence, beam propagation factor, power, energy, temporal characteristics, power and energy distribution. Accurate measurements of these parameters are essential for the users as well as the manufacturers, to get the required results from the laser products. Lasers are very expensive devices and lasers procured for a certain job will fail, if the parameters expected from the systems are not met with, incurring heavy losses to the user. Taking all these aspects in to account, International Standards have been generated to characterize various parameters of lasers and optical components for the benefit of all concerned, under the EUREKA project entitled Characterization of Optical Components Laser Beams (CHOCOLAB). The aim of the EUREKA project is to develop accurate test methods for these standards and to implement the same in the industry for various applications. Under the Vienna agreement, draftm standards have been published both as EN ISO and ISO standards, to evaluate the technical performance of both pulsed and CW lasers as well as to measure very accurately the parameters mentioned above.

The standards listed below, are for laser equipments and optical components, the details of which can be obtained from web site of American National Standards Institute.

ISO/DSO 11146 - This standard describes methods for accurate measurements of laser beam properties like laser beam diameter, divergence angle and beam propagation factors.

ISO/DIS 11554 - This standard specifies methods for the evaluation of laser power, energy and temporal characteristics for the accuracy and performance of the measurement system.

ISO/DIS 11670 - This standard is basically meant for laser beam positional stability for testing and characterizing of lasers along with related symbols and terms.

ISO/DIS 12005 - This standard provides test methodology for quick measurement of not only the polarization characteristics, but also the degree of polarization.

ISO/CD 13694 - This standard is meant for the measurement and characterization of spatial properties power and energy density distribution functions at a given plane.

References

• Koechner, W.K., Solidstate Laser Engineering, Springer-Verlag, London, 1998.
• Siegman, A. E., Lasers, University Science Books, Mill Valley, California, 1986.
• Kogelnik, H., in Lasers I, ed. Levine, A. K., p. 295-347, Dekker, New York, 1966.
• Svelto, O., Principles of Lasers, Plenum, New York (1998)
• Silfvast, W.T., Laser Fundamentals, Cambridge University Press, Cambridge (1996)
• Sam's Laser FAQs
• Site of American National Standards Institute, ISO ICS Electronics (Laser equipment etc.)
• http://www.rp-photonics.com
• http://en.wikipedia.org/wiki/Q-switching
• http://hyperphysics.phy-astr.gsu.edu/
• http://www.ligo.caltech.edu/
• http://www.mrl.columbia.edu/
• http://prn1.univ-lemans.fr/prn1/siteheberge/optique/