Some quantum properties of light Blackbody radiation to lasers

Density of Field Modes in a Cavity x y z Perfectly conducting walls. Tangential component of E must vanish at bondary L

kxkx kyky kzkz Lattice points in the positive octant of k-space

Density of States for Radiation The number of field modes per unit volume having their wavenumber between k and k +  k or angular frequency between  and 

Each mode has total energy of: n k is the number of photons in a specific mode Quantization of electromagnetic modes produces energy levels just like that of the harmonic oscillator. Note that if n k = 0 the energy is: This is called the “energy of the vacuum.

In thermal equilibrium at temperature T the probability P n that the mode is thermally excited to the nth state is given by the Bolzmann factor

The mean number, of photons excited in a particular mode at temperature T is: Planck thermal excitation function

What is the mean energy density of the radiation in these modes at temperature T? Planck’s Law for radiative energy density

Energy Density of Radiation Units of J/m 3

Stefan-Bolzmann Law  What is intensity of radiated blackbody light.

Maximum of distribution found by taking derivative with respect to , and equate to zero. Wien’s Displacement Law

Cosmic Microwave Background

Einstein A & B Coefficients E 2, N 2 E 1, N 1 A 21 spontaneous emission absorption stimulated emission Consider N atoms in a cavity where the energy density of the radiation is:

From Planck: Thermal Equilibrium implies:

Note that: Thermal-stimulated emission rate is equal to the spontaneous emission rate multiplied by mean number of photons of frequency .

Spontaneous emission, or is it stimulated emission that was “stimulated” by the vacuum!??! Atom in a cavity?!?

In general, W(  ) tends to be small. In order to excite atoms one needs a powerful source of light, like a laser. N atoms Say at t=0 N=N 1 (all atoms in ground state) N2N2

Lasers Gain Medium L R~.999 R~.95 Standing light wave between mirrors. If 1W exits laser, 20W inside cavity Pump

1 2 E1E1 E2E2 For laser to work we need pump to provide “Population Inversion” Normally relative populations are small: Say  E~2eV, T=300K => N 2 /N 1 =3x Way small!

Real laser: pumping process typically something like E 1 Ground State E 3 Pump State E 2 Metastable state with lifetime t s hf 0 pump input fast decay hf laser output In order for one to achieve population inversion the lifetime of the metastable state must be greater than time atom spends in ground state or pump state during the pumping process.

Pulsed Lasers Gain Medium Periodic Switch Pump gain media but do not let light flow out until you say so. All energy released as a high power pulse when “lasing” is allowed. 1)Put mirror on a rotating shaft 2)Voltage signal to an electro-optic crystal. Optical properties change with applied voltage.

Mode Locking Periodic loss Periodic loss modulated at frequency equal to time for pulse to travel distance of 2L. Pulse propagates when losses are minimal.