Stimulated photons emission

It turns out (the development of this eoneept is beyond the seope of this text) that the rate at whieh an exeited level ean emit photons and deeay to a lower energy level is dependent on two faetors (i) the rate of stimulated photon emission as eovered above, and (ii) the rate of spontaneous photon emission. The former rate gf Ri,f (per moleeule) is proportional to the light intensity g(cofj) at the resonanee frequeney. It is eonventional to... 

If cof i is positive (i.e., in the photon absorption ease), the above expression will yield a non-zero eontribution when multiplied by exp(-i cot) and integrated over positive covalues. If cOf j is negative (as for stimulated photon emission), this expression will eontribute, again when multiplied by exp(-i cot), for negative co-values. In the latter situation, pi is the equilibrium probability of finding the moleeule in the (exeited) state from whieh emission will oeeur this probability ean be related to that of the lower state pf by... 

If we start with A + B the inverse process of stimulating photon emission will result in a transition from the upper into the lower potential, which means an energy transfer from B to A for the separated atoms. 

One more similarity between the conventional laser and the atom laser can be understood in terms of stimulated processes. In the conventional laser, the photon field stimulates the excited atoms to emit additional photons into the laser mode. If the laser photon field contains n photons, the stimulated photon emission is proportional to n + 1. In the atom laser, a similar process of bosonic stimulation produces more atoms in the ground state of the trap, that is, in the condensed state. If the condensed matter already includes N atoms, the bosonic stimulation is proportional to a factor A + 1. 

The acronym LASER (Light Amplification via tire Stimulated Emission of Radiation) defines the process of amplification. For all intents and purjDoses tliis metliod was elegantly outlined by Einstein in 1917 [H] wherein he derived a treatment of the dynamic equilibrium of a material in a electromagnetic field absorbing and emitting photons. Key here is tire insight tliat, in addition to absorjDtion and spontaneous emission processes, in an excited system one can stimulate tire emission of a photon by interaction witli tire electromagnetic field. It is tliis stimulated emission process which lays tire conceptual foundation of tire laser. 

Interaction of an excited-state atom (A ) with a photon stimulates the emission of another photon so that two coherent photons leave the interaction site. Each of these two photons interacts with two other excited-state molecules and stimulates emission of two more photons, giving four photons in ail. A cascade builds, amplifying the first event. Within a few nanoseconds, a laser beam develops. Note that the cascade is unusual in that all of the photons travel coherently in the same direction consequently, very small divergence from parallelism is found in laser beams. 

Other techniques in which incident photons excite the surface to produce detected electrons are also Hsted in Table 1. X-ray photoelectron Spectroscopy (xps), which is also known as electron spectroscopy for chemical analysis (esca), is based on the use of x-rays which stimulate atomic core level electron ejection for elemental composition information. Ultraviolet photoelectron spectroscopy (ups) is similar but uses ultraviolet photons instead of x-rays to probe atomic valence level electrons. Photons are used to stimulate desorption of ions in photon stimulated ion angular distribution (psd). Inverse photoemission (ip) occurs when electrons incident on a surface result in photon emission which is then detected. 

Stimulated emission Another form of photon emission is called stimulated emission, where a photon of the right energy can cause an excited state to emit an additional identical photon, that is,... 

The photons produced by stimulated emission are in phase with the stimulating photons and travel in the same direction that is, the light produced by stimulated emission is coherent light. Stimulated emission forms the basis of laser action. 

The radiative transitions of the previous descriptions have all been spontaneous Relaxation from the excited state to the ground state and emission of photons occur without external aid. In contrast, a stimulated emission occurs when the half-life of the excited state is relatively long, and relaxation can occur only through the aid of a stimulating photon. In stimulated emission, the emitted photon has the same direction as, and is in phase with, the stimulating photon. The example of Cr +-doped AI2O3 that we utilized earlier for our description of the color of ruby works equally well for a description of stimulated emission. Recall that the presence of chromium in alumina alters the electronic structure, creating a metastable state between the valence and conduction bands. Absorption of a blue-violet photon results in the excitation of an electron from... 

A photon with an energy that exactly spans two states can be absorbed to raise a molecule to an excited state. Alternatively, that same photon can stimulate the excited molecule to emit a photon and return to the lower state. This is called stimulated emission. When a photon emitted by a molecule falling from E2 to E( strikes another molecule in E2, a second photon can be emitted with the same phase and polarization as the incident photon. If there is a population inversion (n2 > nt), one photon stimulates the emission of many photons as it travels through the laser. 

FIGURE 22.24 (a) In this solid-state laser, photons emitted as electrons and holes recombine to stimulate the emission of additional photons, (b) Reflection by a mirror on the right side sends coherent waves back through the laser medium, (c) Further amplification occurs by stimulated emission, (d) Some of the waves pass through a partially reflecting mirror on the left side. 

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