Einstein’s Coefficients

Einstein’s Coefficients:

                                            Possibility of laser action:  Consider an atomic medium like a monoatomic gas, sealed in an enclosure. Let the e closure be maintained at a constant temperature, T. Let us define two energy states of Energies E1 and E2, such that E2>E1.

Let N1 and N2 = number of atoms in lower and upper energy states i.e. E1 and E2 respectively.

When an atom is in the lower energy state E1, it would be in a position to absorb a photon of energy, E2-E1=hv.

Let the enclosure be irradiated with an isotropic radiation of frequency, v or angular frequency w. Where, w=2πv.

                        

[where h=h/2π; h= Plank’s constant]

Let U(w)= Radiation density such that, U(w) dw is radiation density in frequency range w and (w+dw)

Therefore,    {The rate of absorption of radiation, per unit time, per unit volume}∞ N1 and U(w)

ð  [Number of photon absorptions per unit, volume] B12 N1 U(w)

Where B12=Constant of proportionality (Einstein’s coefficient)

Now we consider the two possible processes of emission.

(i)                  Spontaneous emission  is independent of the external radiation, therefore it depends only on N2.

ð  [Number of spontaneous emission per unit time, per unit volume] A21N2

Where A21=another Einstein’s coefficient

(ii)               Stimulated emission depends on the external radiation. Therefore rate of the stimulated emission would depend on N2 and U(w) both

ð  [Number of stimulated emission per unit time, per unit volume]= B21N2U(w)

Where B21= another Einstein’s coefficient

Thus A21, B12 and B21 are the Einstein’s co-efficients. We would now define the required conditions in terms of these co-efficient. When a thermo dynamical system is in equilibrium.

ð  upward transition rate= downward transition rate

Therefore,  B12 N1 U(w)= A21 N2 + B21 N2 U(w)

Semiconductor Laser:

The most popular form of the semiconductor laser is the laser printer. Almost everyone has a first hand experience of this device. But it must be realized that this stage has come after a long research and development. Initially the intrinsic semiconductor Laser was developed but it could never become a popular and usable device. The doped semiconductor laser was developed but it could never become a popular and usable device. The doped semiconductor lasers were a success story. Though these lasers are crticised for their poor coherence, astigmatic beam spots and many more bad features, but they have captured the market, to almost entirely fill in their own suitable domain.

Intrinsic semiconductor Lasers:   When a beam of light, having energy slightly more than the forbidden band gap energy is passed through a pure or intrinsic semi conductor, there are two notions,

(i)                 If there is a probability that an electron at the top of valance band absorbs this energy and goes to the conduction band.

(ii)               Then there is an equal probability that an electron already present at bottom of the conduction band is persuaded by the incident photon to move down to the valance band.

When this happens, the electron jumping down to the valance band recombines with a hole an in this process releases a photon; which is in the same state as that of the incident photon. Thus the radiation is amplified.

In order to create such an amplification it is required  that the population must be inverted. This physically means that NCB >NVB must be attained, where NCB and NVB are populations of conduction band and valance band respectively. Such a condition can be created in a semiconductor by optical pumping. The cadmium sulphide laser was developed on these ideas. An electron beam of about 100 keV was used for pumping. The major problem in this process is that the 100keV electron beam tends to heat up the semiconductor. This spoils the degree of population inversion, since the electrons now tend to jump from conduction band to the higher levels. Thus a super cooling became essential. It was found that the US laser world operate properly only at the liquid helium temperature i.e. at 4.2 kelvin. This proposition spoils the entire economics of an academic research or even a commercial research project. Thus these finds of lasers were not popular.

Doped semiconductor lasers: The doped semiconductor laser or an injection (carrier injection laser) is just a pn junction diode provided with some specific design features. It is the practical semiconductor laser which is in use. The basic idea is similar to the principle of operation of an optical light emitting diode (LED). It is well know that in a forward biased pn junction, there is a. Large probability of recombination of electors and holes. This amounts to a release of energy. In case of germanium and silicon diodes, the refractive index is such that most of the energy released ultimately goes to merely heat up the diode. But in gallium arsenide (GaAs) and many other compound semiconductor the pn junctions are able to emit the recombination energy in the form of UV, IR or visible radiation. By using a suitable design and by providing mirrors to make an optical resonator, the GaAs laser diode to explain and project the concepts of a semiconductor laser. The laser was developed by Hall et.al.