Stimulated radiation is a process in which an incoming photon of a certain frequency can interact with an excited atomic electron (or other excited molecular state), causing it to drop to a lower energy level. The released energy is transferred to the electromagnetic field, creating a new photon with a phase, frequency, polarization and direction of motion, which are identical to the photons of the incident wave. And this happens in contrast to spontaneous radiation, which works at random intervals, without taking into account the surrounding electromagnetic field.
Induced radiation conditions
The process is identical in form to atomic absorption, in which the energy of the absorbed photon causes an identical but opposite atomic transition: from a lower to a higher energy level. In normal environments, in thermal equilibrium, absorption exceeds stimulated emission, because in states with lower energy there are more electrons than in states with higher energy.
However, when population inversion is present, the stimulated emission rate exceeds the absorption rate and pure optical amplification can be achieved. Such a gain medium, along with an optical resonator, underlies a laser or a maser. Without a feedback mechanism, laser amplifiers and superluminescent sources also operate on the basis of stimulated emission.
What is the main condition for obtaining induced radiation?
Electrons and their interactions with electromagnetic fields are important in our understanding of chemistry and physics. In the classical representation, the energy of an electron rotating around an atomic nucleus is greater for orbits remote from the nucleus of an atom.
When an electron absorbs the energy of light (photons) or heat (phonons), it receives this incident quantum of energy. But transitions are only allowed between discrete energy levels, such as the two shown below. This leads to the appearance of emission and absorption lines.
Energy aspect
Further, we will discuss the main condition for obtaining induced radiation. When an electron is excited from a lower to a higher energy level, it is unlikely to remain so forever. An electron in an excited state can decay to a lower energy state, which is not occupied, in accordance with a certain time constant characterizing this transition.
When such an electron decays without external influence, emitting a photon, this is called spontaneous emission. The phase and direction associated with the emitted photon are random. Thus, a material with many atoms in such an excited state can lead to radiation that has a narrow spectrum (centered around one wavelength of light), but individual photons will not have common phase relationships and will also be emitted in random directions. This is the mechanism of fluorescence and heat release.
An external electromagnetic field at a frequency associated with the transition can affect the quantum-mechanical state of an atom without absorption. When an electron in an atom makes a transition between two stationary states (none of which shows a dipole field), it enters the transition, which has a dipole field and acts like a small electric dipole that oscillates at a characteristic frequency.
In response to an external electric field at this frequency, the probability of the transition of an electron to this state increases significantly. Thus, the transition rate between two stationary states exceeds the value of spontaneous emission. The transition from a higher to a lower energy state creates an additional photon with the same phase and direction as the incident photon. This is the process of forced emission.
Opening
Stimulated radiation was Einstein's theoretical discovery in the framework of the old quantum theory, in which radiation is described in terms of photons, which are quanta of the electromagnetic field. Such radiation can also occur in classical models without reference to photons or quantum mechanics.
Stimulated radiation can be mathematically modeled taking into account an atom, which can be in one of two electronic energy states, a state of a lower level (possibly a ground state) and an excited state, with energies E1 and E2, respectively.
If the atom is in an excited state, it can decay to the lower state as a result of the spontaneous emission process, releasing the energy difference between the two states in the form of a photon.
Alternatively, if an atom of an excited state is perturbed by an electric field with a frequency ν0, it can emit an additional photon of the same frequency and in phase, thereby increasing the external field, leaving the atom in a state with a lower energy. This process is known as stimulated emission.
Proportionality
The proportionality constant B21, which is used in the equations for determining spontaneous and induced radiation, is known as the Einstein coefficient B for this particular transition, and ρ (ν) is the radiation density of the incident field at a frequency ν. Thus, the radiation velocity is proportional to the number of atoms in the excited state N2 and the density of incident photons. Such is the essence of the phenomenon of induced radiation.
At the same time, an atomic absorption process will take place, which removes energy from the field, raising electrons from the lower to the upper state. Its speed is determined by a substantially identical equation.
Thus, the net power is released into the electric field, equal to the photon energy, h times higher than this net transition speed. In order for this to be a positive number, indicating the total spontaneous and induced radiation, there should be more atoms in the excited state than at the lower level.
Differences
The properties of induced radiation compared to conventional light sources (which depend on spontaneous emission) is that the emitted photons have the same frequency, phase, polarization and direction of propagation as the incident photons. Thus, the involved photons are mutually coherent. Therefore, inversion results in optical amplification of the incident radiation.
Energy change
Although the energy generated by stimulated radiation is always at the exact frequency of the field that stimulated it, the above description of calculating the speed only applies to excitation at a specific optical frequency, the strength of the stimulated (or spontaneous) radiation will decrease in accordance with the so-called line shape. Given only homogeneous broadening affecting atomic or molecular resonance, the spectral line shape function is described as the Lorentz distribution.
Thus, stimulated emission decreases by this factor. In practice, there may also be an expansion of the line shape due to inhomogeneous broadening, primarily due to the Doppler effect resulting from the distribution of velocities in the gas at a certain temperature. This has a Gaussian shape and reduces the peak strength of the line shape function. In a practical task, the total line shape function can be calculated by convolving the individual involved line shape functions.
Induced radiation can provide a physical mechanism for optical amplification. If an external energy source stimulates more than 50% of the atoms in the ground state to transition to an excited state, then what is called population inversion is created.
When light of the appropriate frequency passes through an inverted medium, the photons are either absorbed by the atoms, which remain in the ground state, or stimulate the excited atoms to emit additional photons of the same frequency, phase and direction. Since there are more atoms in the excited state than in the ground state, the result is an increase in the input intensity.
Radiation absorption
In physics, the absorption of electromagnetic radiation is the way that photon energy is absorbed by matter, usually by the electrons of an atom. Thus, electromagnetic energy is converted into the internal energy of the absorber, for example thermal. A decrease in the intensity of a light wave propagating in a medium due to the absorption of part of its photons is often called attenuation.
Usually the absorption of waves does not depend on their intensity (linear absorption), although under certain conditions (usually in optics), the medium changes transparency depending on the intensity of the transmitted waves and saturable absorption.
There are several ways to quantify how quickly and efficiently radiation is absorbed in a particular medium, for example, the absorption coefficient and some closely related derivatives.
Attenuation coefficient
Several features of the attenuation coefficient:
- The attenuation coefficient, which is sometimes, but not always, synonymous with the absorption coefficient.
- The molar absorption capacity is called the molar extinction coefficient. It is an absorption coefficient divided by molarity.
- The mass attenuation coefficient is the absorption coefficient divided by density.
- The absorption and scattering cross sections are closely related to the coefficients (absorption and attenuation, respectively).
- Extinction in astronomy is equivalent to the attenuation coefficient.
Constants for Equations
Other measures of radiation absorption are penetration depth and skin effect, propagation constant, damping constant, phase constant and complex wave number, complex refractive index and extinction coefficient, complex dielectric constant, electrical resistivity and conductivity.
Absorption
Absorption (also called optical density) and optical depth (also called optical thickness) are two interrelated indicators.
All of these quantities measure, at least to some extent, how much the medium absorbs radiation. However, practitioners of various fields and methods usually use different values taken from the list above.
The absorption of an object quantifies how much incident light is absorbed by it (instead of reflection or refraction). This can be connected with other properties of the object through the Beer – Lambert law.
Accurate absorption measurements at many wavelengths allow the substance to be identified using absorption spectroscopy, where the sample is illuminated on one side. Some examples of absorption are ultraviolet-visible spectroscopy, infrared spectroscopy, and X-ray absorption spectroscopy.
Application
Understanding and measuring the absorption of electromagnetic and induced radiation has many uses.
When distributed, for example, by radio, it is presented out of line of sight.
Induced laser radiation is also well known.
In meteorology and climatology, global and local temperatures partially depend on the absorption of radiation by atmospheric gases (for example, the greenhouse effect), as well as the surface of the land and ocean.
In medicine, x-rays are absorbed to different degrees by different tissues (in particular, bone), which is the basis for radiography.
It is also used in chemistry and material science, since different materials and molecules will absorb radiation to different degrees at different frequencies, which allows the material to be identified.
In optics, sunglasses, color filters, dyes and other similar materials are specially designed taking into account what visible wavelengths they absorb and in what proportions. The structure of the glasses depends on the conditions under which the induced radiation appears.
In biology, photosynthetic organisms require that light of the appropriate wavelength be absorbed in the active region of the chloroplasts. This is necessary so that the energy of light can be converted into chemical energy inside sugars and other molecules.
In physics, it is known that the D-region of the Earth’s ionosphere significantly absorbs radio signals that fall into the high-frequency electromagnetic spectrum and are associated with induced radiation.
In nuclear physics, the absorption of nuclear radiation can be used to measure fluid levels, densitometry, or thickness measurements.
The main fields of application of induced radiation are quantum generators, lasers, and optical devices.