Elements of Modern Physics
188
6.5 LASERS AND MASERS
It was noted in Secs. 6.3 and 6.4 that, for an atom (or a molecule) in the presence
of radiation, the stimulated probabilities for absorbing a photon of resonant
energy (ω = E m – E n ) or emitting a photon of the same energy are equal. This
is in addition to the probability for spontaneous emission of radiation. Neglecting
the spontaneous transitions, the net rate of absorption per unit time is
dE
dt
= (N n – N m ) B nm u (ω nm ), E m > E n
(6.81)
At thermal equilibrium one has
n
m
N
N
= exp ( ω nm /kT)
(6.82)
so that N n > N m , and radiation will be absorbed. However, if the initial condition
is such that N n < N m , known as population inversion, then
0
<
dE
dt
and there is
a net emission of radiation of frequency ω = (E m – E n )/ This leads to an
amplification of the incident wave and forms the basis of lasers and masers
(those words stand for light/microwave amplification by stimulated emission
of radiation). It is of importance to note that the emitted wave has the same
frequency, phase, and polarization as the incident wave, so that the amplification
is in the wave amplitude, not just the intensity.
Though population inversion is not an equilibrium condition, it is sometimes
convenient to think of it as corresponding to a negative temperature in Eq. (6.82),
for which N n < N m .
Similarly, since the radiation is increasing in intensity, the situation can be
described by the usual formula
I(x) = I(0) e
–αx
(6.83)
for the propagation through an absorbing medium but with a negative co-efficient
of absorption.
The mechanism of population inversion characterizes the different lasers
and masers. A few of them are discussed here.
The ammonia maser (Townes, 1954): This is based on the separation of the
components of an ammonia beam. The NH 3 molecule has a pyramidal structure
with N at the apex. However, the N atom can be on either side of the base and
can tunnel from one side to the other through the base. As a result, the two
degenerate ground states split into two closely-spaced energy levels, which are
described essentially by the even and odd linear combinations of the two states
and have an energy separation given by
188
6.5 LASERS AND MASERS
It was noted in Secs. 6.3 and 6.4 that, for an atom (or a molecule) in the presence
of radiation, the stimulated probabilities for absorbing a photon of resonant
energy (ω = E m – E n ) or emitting a photon of the same energy are equal. This
is in addition to the probability for spontaneous emission of radiation. Neglecting
the spontaneous transitions, the net rate of absorption per unit time is
dE
dt
= (N n – N m ) B nm u (ω nm ), E m > E n
(6.81)
At thermal equilibrium one has
n
m
N
N
= exp ( ω nm /kT)
(6.82)
so that N n > N m , and radiation will be absorbed. However, if the initial condition
is such that N n < N m , known as population inversion, then
0
<
dE
dt
and there is
a net emission of radiation of frequency ω = (E m – E n )/ This leads to an
amplification of the incident wave and forms the basis of lasers and masers
(those words stand for light/microwave amplification by stimulated emission
of radiation). It is of importance to note that the emitted wave has the same
frequency, phase, and polarization as the incident wave, so that the amplification
is in the wave amplitude, not just the intensity.
Though population inversion is not an equilibrium condition, it is sometimes
convenient to think of it as corresponding to a negative temperature in Eq. (6.82),
for which N n < N m .
Similarly, since the radiation is increasing in intensity, the situation can be
described by the usual formula
I(x) = I(0) e
–αx
(6.83)
for the propagation through an absorbing medium but with a negative co-efficient
of absorption.
The mechanism of population inversion characterizes the different lasers
and masers. A few of them are discussed here.
The ammonia maser (Townes, 1954): This is based on the separation of the
components of an ammonia beam. The NH 3 molecule has a pyramidal structure
with N at the apex. However, the N atom can be on either side of the base and
can tunnel from one side to the other through the base. As a result, the two
degenerate ground states split into two closely-spaced energy levels, which are
described essentially by the even and odd linear combinations of the two states
and have an energy separation given by