An amplification of the Gaussian beams in an active gaseous medium, possesing a quadratic radial variation of the population inversion, is considered. The gain curve is shown to have an asymmetrical shape. For a given population inversion, the maximum gain is calculated to be attainable at higher frequency than that of the atomic resonance, both in unsaturated and saturated operations.
An amplification of the Gaussian beams in an active gaseous medium, possesing a quadratic radial variation of the population inversion, is considered. The gain curve is shown to have an asymmetrical shape. For a given population inversion, the maximum gain is calculated to be attainable at higher frequency than that of the atomic resonance, both in unsaturated and saturated operations.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
A calculation is made of the steady-state population inversion distribution in homogeneously pumped active media of spherical or cylindrical form. It is assumed that reflections from the boundaries of the active medium have been completely eliminated and it is shown that the inversion decrease, caused by the amplification of spontaneously emitted radiation, is mainly a function of the overall volume of the active medium. For active media of equal volume, the stored inversion is minimal for a sphere.
POPULATION RATE EQUATIONS From the discussion in the preceding chapter, it is clear that population inversion is the basic condition for an optical gain. For any system in its normal state in thermal equilibrium, a low-energy level is always more populated than a high-energy level, hence there is no population inversion. Population inversion in a system can only be accomplished through a process called pumping by actively exciting the atoms in a low-energy level to a high-energy level. If left alone, the atoms in a system relax to thermal equilibrium. Therefore, population inversion is a nonequilibrium state that cannot be sustained without active pumping. To keep a constant optical gain, continuous pumping is required to maintain population inversion. This condition is clearly consistent with the law of conservation of energy: amplification of an optical wave leads to an increase in optical energy, which is possible only if the required energy is supplied by a source. Pumping is the process that supplies energy to the gain medium for the amplification of an optical wave. There are many different pumping techniques, including optical excitation, electric current injection, electric discharge, chemical reaction, and excitation with particle beams. The use of a specific pumping technique depends on the properties of the gain medium being pumped. The lasers and optical amplifiers of particular interest in photonic systems are made of either dielectric solid-state media doped with active ions, such as Nd:YAG and Er:glass fiber, or direct-gap semiconductors, such as GaAs and InP. For a dielectric gain medium, the most commonly used pumping technique is optical pumping using either an incoherent light source, such as a flashlamp or a light-emitting diode, or a coherent light source from another laser. A semiconductor gain medium can also be optically pumped, but it is usually pumped by electric current injection. In this section, we consider the general conditions for pumping to achieve population inversion. Detailed pumping mechanisms and physical setups are not addressed here because they depend on the specific gain medium used in a particular application. The net rate of increase of the population density in a given energy level is described by a rate equation. As we shall see below, pumping for population inversion in any practical gain medium always requires the participation of more than two energy levels.
In the present work, an analytical calculation of the value of xo is presented for the same physical conditions as in [5, 6], with one additional approximation. In a gas laser, movement of the atoms has the result that the periodic structure of the standing wave field of the laser modes is weakly reflected in the spatial distribution of the population inversion [7]. On this basis we shall carry out the calculation of xo assuming that the intensity of the fields ml and ma is constant along the axis of the laser. We thus exclude from consideration a certain range of phenomena related to the effect of a spatial displacement between the standing waves m~ and ma on the mode competition. We consider this reasonable, since those phenomena were analyzed in sufficien.t detail in [3], where the basic attention of the work was directed at analysis of the competition effect for various values of q. Following Evseev et al. [5,6] we shall use the fact that, near the boundaries of the two-frequency and slngle-frequency regimes (x = the intensity of one of the modes is much larger than the intensity of the other, almost to the point of suppression. We shall assume at the outset that lasing takes place in one strong mode, for example m,, caused by saturation of the active medium. We shall initially assume the mode ma to be suppressed and '~eak, i.e., not saturating the active medium. In the steady state, the saturated amplification gt of the mode m~ in the active medium is equal to the losses T. The saturated amplification ga of the weak mode may be larger than, smaller than, or equal to T, depending on x. In the first case, the field of the mode ma will grow and two-frequency operation, not slngle-frequency, will be stable, while the third is realized for x = Based on the results of [8] it is possible to obtain the following expressions for gt and ga:
Introduction We were able to show in Chapter 3 that a medium in which we can obtain a population inversion (i.e. a situation in which the population density in the excited state is greater than that in the fundamental level) allows for optical gain of an electromagnetic wave having a frequency near to the resonant frequency of the system. By introducing feedback of the amplified signal into the medium, the system can be made to oscillate naturally, resulting in laser oscillations . To obtain this population inversion, we must introduce at least a third (and perhaps even a fourth) energy level into the system. (We saw how a two-level system under the influence of an intense pump beam will saturate with no resulting population inversion.) The aim then of this chapter is to introduce the concepts necessary to extend our two-level system into a working model capable of illustrating the phenomenon of laser oscillation. We will not spend too much time discussing atomic transition lasers as they do not figure readily in our treatment of quantum electronic properties of semiconductors. An exception will be made, however; we brush upon the particular topics of a diode pumped laser in Complement 4.E and a quantum cascade laser in Complement 13.H. Population inversion and optical amplification Population inversion We will show how population inversion can be achieved by carrier transfer from higher lying levels to the upper level of a two-level subsystem of interest.