Four-level system, lasers

The trivalent neodymium ion is a good example of a four-level laser system. The trivalent Nd3+ system is illustrated in Fig. 12.12 in a schematic fashion. 

Describe the advantage of a four-level laser system over a three-level type. 

The dominant single crystal for solid-state lasers is YAG, which is produced using the Cz melt-growth process [29]. Transition metal elements or lanthanide rare earth elements are used as laser active ions that are doped in YAG host material. Due to its narrow spectral width and high quantum efficiency, Nd ion, a four-level laser system has been acknowledged to be the most popular active ion. 

The principle processes within a four-level laser system are shown in Figure 3.B 1. Note that only those transition probabilities that are significant for the pump and laser processes are indicated. 

Clearly, this confirms mathematically the hand-waving arguments used in the description of a four-level laser system, namely that, in a four-level laser, population inversion is produced as soon as pumping commences. 

Figure 8 schematically illustrates a four-level laser system such as that for a Nd YAG laser. Population inversion and lasing is established between levels E2 and Ej. The optical pump populates level E3 that may be a broad range of closely spaced levels in practice. Decay from E3 down to the metastable upper laser level E2 may occur via radiative or nonradi-ative relaxation processes. Random radiative emission, or spontaneous emission, occurs without a stimulating electric field, in contrast to stimulated emission. Nonradiative relaxation implies energy transfer via lattice vibration also called phonon modes. 

Four-level laser systems by optical pumping, Nd ions are excited to a higher energy level (pump level), followed by a decay to a metastable level (laser level) generation of population inversion between upper and lower laser levels is the basic step for the laser process shown in Figure 6.2... 

Four-level lasers offer a distinct advantage over tlieir tliree-level counterjiarts, (figure C2.15.5). The Nd YAG system is an excellent example of a four-level laser. Here tlie tenninal level for tlie laser transition, 2), is unoccupied tlius resulting in an inverted state as soon as any atom is pumped to state 3. Solid-state systems based on tliis pumping geometry dominate tlie marketplace for high-power laser devices. 

Figure C2.15.5. (a) A four-level laser energy level diagram and (b) tire Nd YAG system.

Figure 3.B1 Schematic term level diagram of a four-leve laser system, including all relevant radiative processes...

Here we extend the simple three-level EIT system to mote complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced either constractive or destractive interfereiKe can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT confignration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system. 

The atomic coherence and interference phenomenon in the simple three-level system sueh as EIT can be extended to more eomplicated multi-level atomic systems. A variety of other phenomena and applications involving three or four-level EIT systems have been studied in reeent years. In particular, phase-dependent atomic coherence and interference has been explored [52-66]. These studies show that in multi-level atomic systems coupled by multiple laser fields, there are often various types of nonlinear optical transitions involving multiple laser fields and the quantum interference among these transition paths may exhibit complicated spectral and dynamic features that can be manipulated with the system parameters such as the laser field amplitudes and phases. Here we present two examples of such coherently coupled multi-level atomic systems in which the quantum interference is induced between two nonlinear transition paths and can be eontrolled by the relative phase of the laser fields. 

In Fig. 22(a), a four-level atomic system are driven by three laser pulses with carrier frequeneies of j, 3, and Rabi frequeneies Qj, 0.2, Q3, respectively. For simplicity, we suppose... 

The Nd-YAG laser is one of the most widely used solid-state lasers. The lasing medium consists of neodymium ion in a host crystal of yttrium aluminum garnet. This system offers the advantage of being a four-level laser, which makes it much easier to achieve population inversion than with the ruby laser. The Nd-YAG laser has a very high radiant power output at 1064 nm, which is usually frequency doubled (see page 175)... 

It was shown above that the normal two-level system (ground to excited state) will not produce lasing but that a three-level system (ground to excited state to second excited state) can enable lasing. Some laser systems utilize four- or even five-level systems, but all need at least one of the excited-state energy levels to have a relatively long lifetime to build up an inverted population. 

Laser action involves mainly the 3/2 hi/i transition at about 1.06 pm. Since is not the ground state, the laser operates on a four-level system (see Figure 9.2c) and consequently is much more efficient than the ruby laser. 

Fig. 1. Pumping methods for lasers where is the pump light frequency and is the laser frequency, wavy lines represent radiationless transitions, and the dashed line collisions (a) optical pumping in three-level systems (b) optical pumping in four-level systems (c) pumping by electron impact and...

Figure lb shows a four-level system. The terminal level, level 2, is ordinarily empty. Atoms are optically pumped to level 4. From level 4, the atoms make a rapid radiationless transition to level 3. The first few atoms to arrive begin to contribute to the population inversion. Therefore, laser operation can begin with much less intense pumping light. After the laser transition, the atoms return to the ground state (level 1) by a radiationless transition. 

Next, let us consider a four-level problem and try to excite the middle level 3 > among the three excited states (see Fig. 32). The laser pulse is the same as Eq. (170) with foe = 981.2fs and = 4.257ps . The system parameters are... 

Figure 2. Representations of two- (left), three- (middle), and four-level (right) laser systems. Key GS, ground state ULL, upper laser level and LLL, lower laser...

The condition for observing induced emission is that the population of the first singlet state Si is larger than that of So, which is far from the case at room temperature because of the Boltzmann distribution (see above). An inversion of population (i.e. NSi > Nso) is thus required. For a four-level system inversion can be achieved using optical pumping by an intense light source (flash lamps or lasers) dye lasers work in this way. Alternatively, electrical discharge in a gas (gas lasers, copper vapor lasers) can be used. 

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