stimulated emission

Examples of stimulated emission in the following topics:

• Lasers

  • A laser is a device that emits monochromatic light through a process of optical amplification based on the stimulated emission of photons.
  • It does so through a process of optical amplification based on the stimulated emission of photons.
  • This "induced" decay process is called stimulated emission.
  • In stimulated emission, the decaying atom produces an identical "copy" of the incoming photon.
  • In stimulated emission process, a photon (with a frequency equal to the atomic transition) encounters an excited atom, and a new photon identical to the incoming photon is produced.

• Oscillator Strengths

  • In an earlier equation, the final term could be important if the $E_i-E_f \approx -\hbar \omega$ this corresponds to stimulated emission of radiation.
  • Except for the degeneracy factors for the two states, the Einstein coefficients will be the same, so we can define an oscillator strength for stimulated emission as well,
  • We can also separate the emission from absorption oscillator strengths
  • Because the second term is for stimulated emission.

• Absorption

  • The positive contributions are true absorption and the negative ones correspond to stimulated emission.

• Emission

  • Generally material has two routes for the emission of radiation: stimulated emission and spontaneous emission.
  • The spontaneous emission is independent of the radiation field.
  • Let's define the spontaneous emission coefficient, $j$.
  • Often the emission is isotropic and it is convenient to define the emissivity of the material per unit mass

• Lasers

  • Having examined stimulated emission and optical amplification process in the "Lasers, Applications of Quantum Mechanics" section, this atom looks at how lasers are built.

• Problems

  • You may neglect scattering and assume that the emission is in the Rayleigh-Jeans limit.
  • Show that if stimulated emission is neglected, leaving only two Einstein coefficients, an appropriate relation between the coefficients will be consistent with thermal equilibrium between an atom and a radiation field with a Wien spectrum, i.e.
  • Compare the power from the surface emission to the power lost as the neutron star spins down.

• Einstein Coefficients

  • Kirchoff's law yields a relationship between the emission and absorption coefficients for a thermally emitting material, specifically $j_\nu = \alpha_\nu B_\nu$.
  • This relationship suggests some connection between emission and absorption at a microscopic level.
  • If we calculate the probability of absorption of a photon for example, we can use the Einstein relations to find the rate of stimulated and spontaneous emission.
  • Can you use the principle of detailed balance to say anything about the relationship between the stimulating and the stimulated photon?

• Microwaves

  • A maser is a device similar to a laser, which amplifies light energy by stimulating photons.
  • The maser, rather than amplifying visible light energy, amplifies the lower-frequency, longer-wavelength microwaves and radio frequency emissions.

• Calculating the Emission and Absorption Coefficients

  • We can write the emission and absorption coefficients in terms of the Einstein coefficients that we have just examined.
  • The emission coefficient $j_\nu$ has units of energy per unit time per unit volume per unit frequency per unit solid angle!
  • The Einstein coefficient $A_{21}$ gives spontaneous emission rate per atom, so dimensional analysis quickly gives

• Problems

  • What is the synchrotron emission from a single electron passing through a magnetic field in terms of the energy density of the magnetic field and the Lorentz factor of the electron?
  • What is the inverse Compton emission from a single electron passing through a gas of photons field in terms of the energy density of the photons and the Lorentz factor of the electron?
  • What is the total inverse Compton emission from the region if you assume that the synchrotron emission provides the seed photons for the inverse Compton emission?