Einsteian relatioiin and other modern physics topics

Einstein reltions andd other modern physics tpoics

1. Einstein Relations - A and B Coefficients:

2. Introduction The distribution of atoms in the two energy levels will change by absorption or emission of radiation. The Einstein A coefficients are related to the rate of spontaneous emission of light, and the Einstein B coefficients are related to the absorption and stimulated emission of light.

3. Types 1- Einstein Coefficient for Stimulated Absorption 2- Einstein Coefficient for S pontaneous Emission 3- Einstein Coefficient for Stimulated Emission

4. - If is the probability (per unit time) of absorption of radiation, the population of the upper-level increases. The rate is proportional to the population of atoms in the lower level and to the energy density of radiation in the system. Thus the rate of increase of population of the excited state is given by where is a constant of proportionality with dimensions m /s -J. 1-Einstein Coefficient for Stimulated Absorption

5. The population of the upper level will decrease due to spontaneous transition to the lower level with emission of radiation. The rate of emission will depend on the population of the upper level If is the probability that an atom in the excited state will spontaneously decay to the ground state, Einstein Coefficient for Spontaneous Emission

6. where it gives the average lifetime of an atom in the excited level before the atom returns to the ground state. Thus the spontaneous emission depends on the lefetime of the atom in the excited state. The process is statistical and the emitted quanta bear no phase relationship with one another, i.e. the emission is incoherent . The equation above has the solution

7. Stimulated or induced emission depends on the number of atoms in the excited level as well as on the energy density of the incident radiation. If be the transition be the transition probability per unit time per unit energy density of radiation, the rate of decrease of the population of the excited state is . The rate equation for the population of the upper level is Since constant, Stimulated Emission

8. The emitted quanta under stimulated emission are coherent with the impressed field. The spontaneous emission, being incoherent, is a source of noise in lasers. When equilibrium is reached, the population of the levels remains constant, so that and the rate of emission equals the rate of absorption, so that Using the Boltzmann factor and simplifying, we get

9. If we regard the matter to be a blackbody and compare the above expression for the energy density with the corresponding energy density expression derived for the blackbody radiation, viz., AND

10. The last equation shows that n the absence of degeneracy, the probability of stimulated emission is equal to that of absorption. In view of this we replace the two coefficients by asingle coefficient and term them as B- coefficient. The spontaneous emission coefficient will be called the A- coefficient. The ratio of spontaneous emission probability to the stimulated emission probability is so that for low temperatures, when , spontaneous emission is much more probable than induced emission and the latter may be neglected. For high enough temperatures, stimulated emission probability can be significant though for optical frequencies, this requires very high temperature. For microwave frequencies the stimulated emission processes may be significant even at room temperatures.

11. Blackbody Radiation

12. When the black body is extremely hot, the wavelength it emits could even shift to invisible ultraviolet light. On the other hand, if it’s really cold, the wavelength it emits might shift towards infrared or microwaves. In this case, the black body does appear black, as our eyes can’t see those types of light.

13. This is an illustration of how blackbody radiation would behave with electromagnetic radiations

14. Boltzmann Statistics SANA IQTADAR QURESHI

15. Two level system

16. If the atoms are in thermal equilibrium with the surrounding at a temperature , the relative population in the two levels are given by Boltzmann distribution.

17. Results: — Population of excited state increases, with the increase in temperature. — the population of an excited state always lies lower than the population of the ground state, under equilibrium condition. — For large energy gaps such that , the ratio above is close to zero so that very few of the atoms are in the upper energy state.

18. Population Inversion Population inversion is a key concept in lasers. It occurs when there are more atoms or molecules in a higher energy level than in a lower energy level within a laser's medium. This condition is crucial for amplifying light in a laser and understanding how lasers work. Muhammad Ahmad (L1F20BSPH0040)

19. Principles of Laser Operation 1 Stimulated Emission Stimulated emission is the process by which an electron in an excited state releases a photon of specific wavelength. This amplifies existing photons, leading to the coherent and intense beam of light that characterizes laser output. 2 Optical Cavity Lasers use an optical cavity, typically consisting of two mirrors, to trap and amplify light. Photons bouncing back and forth between the mirrors interact with the lasing medium, causing more stimulated emission and further amplification of the light. 3 Pumping Mechanism To achieve population inversion, the lasing medium must be actively pumped, usually through an external energy source such as an electrical current or a flash of light. This excites the atoms or molecules in the medium, creating the necessary population inversion.

20. Principles of Laser Operation 1 Stimulated Emission Stimulated emission is the process by which an electron in an excited state releases a photon of specific wavelength. This amplifies existing photons, leading to the coherent and intense beam of light that characterizes laser output. 2 Optical Cavity Lasers use an optical cavity, typically consisting of two mirrors, to trap and amplify light. Photons bouncing back and forth between the mirrors interact with the lasing medium, causing more stimulated emission and further amplification of the light. 3 Pumping Mechanism To achieve population inversion, the lasing medium must be actively pumped, usually through an external energy source such as an electrical current or a flash of light. This excites the atoms or molecules in the medium, creating the necessary population inversion.

21. Principles of Laser Operation 1 Stimulated Emission Stimulated emission is the process by which an electron in an excited state releases a photon of specific wavelength. This amplifies existing photons, leading to the coherent and intense beam of light that characterizes laser output. 2 Optical Cavity Lasers use an optical cavity, typically consisting of two mirrors, to trap and amplify light. Photons bouncing back and forth between the mirrors interact with the lasing medium, causing more stimulated emission and further amplification of the light. 3 Pumping Mechanism To achieve population inversion, the lasing medium must be actively pumped, usually through an external energy source such as an electrical current or a flash of light. This excites the atoms or molecules in the medium, creating the necessary population inversion.

22. Drawbacks of 3-stage Inversion Three-stage lasers require more pumping power compared to some other systems. This is because they need to push a large number of atoms to a higher energy level before achieving population inversion (necessary for laser action). They can suffer from inefficiency due to spontaneous transitions from the upper level (E2) back down to the ground state (E1). This wasted energy is often released as heat, reducing the overall laser output

23. Drawbacks of 3-stage Inversion Three-stage lasers require more pumping power compared to some other systems. This is because they need to push a large number of atoms to a higher energy level before achieving population inversion (necessary for laser action). They can suffer from inefficiency due to spontaneous transitions from the upper level (E2) back down to the ground state (E1). This wasted energy is often released as heat, reducing the overall laser output

24. Drawbacks of 3-stage Inversion Three-stage lasers require more pumping power compared to some other systems. This is because they need to push a large number of atoms to a higher energy level before achieving population inversion (necessary for laser action). They can suffer from inefficiency due to spontaneous transitions from the upper level (E2) back down to the ground state (E1). This wasted energy is often released as heat, reducing the overall laser output Thank you