Principles of Laser Action

The basic principle of the laser, as the name "light amplification by stimulated emission of radiation" indicates, is based on stimulated emission from a higher level f to a lower level i (not necessarily the ground state) (Svelto, 1998). As discussed in Chapter 4, this will require that a population inversion is created so that the number of atoms or molecules in level f is higher than that in level i (i.e., Nf > N). Most lasers utilize electronic levels for laser actions. A widely used carbon dioxide laser is an example of exceptions which utilize vibrational levels (f and i are vibrational levels with different quantum numbers, v). This population inversion is created either by electrical excitation of level f or by optical excitation (absorption) to a higher level f from which nonradiative relaxation stores the energy into state f to reach population inversion. The population inversion has also been achieved in chemical lasers by utilizing energy released in a chemical reaction (Basov et al., 1990). However, chemical lasers have not found applications in biophotonics and therefore will not be discussed here. Table 5.1 describes the various steps involved in laser action.

A simple diagram of laser design is shown in Figure 5.1. The components of a laser are:

• An active medium, also called a gain medium, in which an atom or a molecule can be excited by a suitable pumping mechanism to create population inversion so that the spontaneously emitted photons at some site in the medium stimulates emission at other sites as it travels through it.

TABLE 5.1. Various Steps in Laser Operation

An active medium consisting of atoms, ions, or molecules in gaseous, liquid, or solid form

Electrical or optical energy added

Pumping to an excited level

Nonradiative relaxation to a lower emissive state f

Population inversion between level f, in which excitation accumulates, and another yet lower energy level i

Active feedback (back and forth reflection) in a cavity formed by two coupling mirrors or one mirror and a wavelength selective reflector

Multipass amplifications and highly directional amplified stimulated emission (laser action)

Cavity Length

Cavity Length

Flow Cytometry Reflector
Figure 5.1. The schematics of a laser cavity. R represents percentage reflection.

• An energy pump source, which can be an electrical discharge chamber, an electrical power supply, a lamp, or even another laser.

• Two reflectors, also called rear mirror and output coupler, to reflect the light in phase (determined by the length of the cavity) so that the light will be further amplified by the active medium in each round-trip (multipass amplification). The output is partially transmitted through a partially transmissive output coupler from where the output exits as a laser beam (e.g., R = 80% as shown in Figure 5.1).

Both the process of stimulated emission and cavity feedback impart coherence to the laser beam. Only the waves reflected in phase and in the direction of the incident waves contribute to multipass amplification and thus build up intensity. Emission coming at an angle (like from the sides) does not reflect to amplify. This process provides directionality and concentration of beam in a narrow width, making the laser highly directional with low divergence and greater coherence. For an incident beam and reflected beam to be in phase in a cavity, the following cavity resonance conditions must be met (Svelto, 1998), as shown in equation (5.1):

where l = the wavelength of emission; l = the length of the cavity, and n is an integral number.

In the case where the fluorescence from the active medium is broadened inhomogeneously, different emitting centers in the medium may emit at different wavelengths that form a continuous band describing the fluorescence lineshape. However, the stimulated emission curve is generally much narrower because extremes of the emission profile cannot lase due to lack of sufficient population needed to create threshold population inversion. The range of wavelengths over which sufficient stimulated emission and lasing action can be achieved defines what is called the gain curve.

Within the gain curve of an active medium, equation (5.1) can be satisfied for many wavelengths with different integral numbers n. These are called the longitudinal cavity modes. Wavelength selection can be introduced by replacing the rear mirror in Figure 5.1 with a spectral reflector (grating or prism) that permits the return of only a certain narrow wavelength of light (monochromatic beam) to be multipass-amplified. However, these optical elements do not provide the resolution necessary to select a single longitudinal mode of the cavity (narrowest bandwidth possible). One introduces other optical elements such as a Fabry-Perot etalon or Liot filter in the cavity to isolate a single longitudinal mode. Lasers that provide the laser beam output in a single longitudinal mode and at the same time are stable so that the optical output

Etalon Laparoscopic Surgery

Single bright circle

Single light circle with a dark area in the center (an annulus)

Solid circular center, encircled by a dark ring, which is in turn encircled by a thinner, less bright ring.

Single bright circle

Single light circle with a dark area in the center (an annulus)

Solid circular center, encircled by a dark ring, which is in turn encircled by a thinner, less bright ring.

Figure 5.2. Transverse electromagnetic modes and the corresponding shapes of the laser beam.

does not undergo mode-hopping (jumping from one mode to another) or mode-beating (mode interference) are called single-frequency lasers.

Another feature of a laser is the spatial profile of its beam in the transverse direction (the plane perpendicular to its propagation direction). These profiles are called transverse modes and are represented in the form TEMmn, where m and n are small integers that describe the intensity distribution in the transverse x and y directions (the plane perpendicular to the beam). Some mode structures with the beam shape (intensity distribution) are shown in Figure 5.2. The beam with a TEM00 transverse mode characteristic is called a Gaussian beam because the intensity distribution from the center (the brightest point) to the edge of the beam falls off as a Gaussian function given by equation (5.2):

where I(r) is the intensity of the beam as a function of distance r in any direction from the center. The parameter w0 is called the beam radius or the spot size, which in the case of a TEM00 mode is the distance from the center where by the intensity has dropped by a factor of 1/e2.

The TEM00 beam has the minimum possible beam divergence and can be focused to a "diffraction limited" size, which is the minimum attainable beam spot possible. If a beam is not Gaussian (TEM00), the minimum spot it can be focused to is not diffraction limited. For this reason, it is preferable to use a Gaussian beam where a tight focus or a spatially uniform intensity distribution is needed (e.g., in microscopy).

Pump

Non-radiative decay

Non-radiative decay

Pump

Nonradiative Decay Symbol

Laser action at 694.3 nm

A three-level system in ruby laser for pulse laser operation

Laser action at 694.3 nm

Laser action at 1064 nm

A four-level system in a neodymium laser for CW laser operation

A three-level system in ruby laser for pulse laser operation

A four-level system in a neodymium laser for CW laser operation

Figure 5.3. Schematics of a three-level system for pulse operation and a four-level system for CW as well as pulse operation.

Depending on the energy levels scheme, the population inversion, a key step in lasing, can be achieved only for a short time or can be maintained continuously. They respectively produce a pulse laser or a continuous wave (termed CW) laser. The two possible schemes, as shown in Figure 5.3, determine pulse or CW operations. In Figure 5.3, the energy levels of the atoms (ions) are represented by their term symbols as defined in Chapter 2. In the three-level system, such as in ruby, the excitation is to a set of two closely spaced levels 4F1 and 4F2 from where the energy relaxes by nonradiative decay to a lower level 2E where excitation builds up to create a population inversion between it and the ground state. In the case of the neodymium laser, a continuous population inversion is maintained between two intermediate levels 4F and 4/.

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