Page 320 - Electrical Properties of Materials

302 Lasers

this feedback mechanism, it is advisable to return to the language of classical
physics and talk of waves and relative phases. Thus, instead of a photon be-
ing emitted, we may say that an electromagnetic wave propagates in a way in
which any two points bear strict phase relationships relative to each other. This
phase information will be retained if we put perfect reflectors in the path of
the waves on both sides, constructing thereby a resonator. The electromagnetic
wave will then bounce to and fro between the two reflectors establishing stand-
ing waves, which also implies that the region between the two reflectors must
be an integer multiple of half wavelengths. Thus, in a practical case, we have
a relatively wide frequency band in which population inversion is achieved,
and the actual frequencies of oscillation within this band are determined by the
possible resonant frequencies of the resonator.
A resonator consisting of two parallel plate mirrors is known as a Fabry–
Perot resonator after two professors of the Ecole Polytechnique, who followed
each other (mind you, in the wrong order, Perot preceded Fabry).
∗
∗ What will determine the condition of oscillation in a resonator? Obviously,
In fact, lasers are nearly always used
as oscillators rather than amplifiers. So the loop gain must be unity. If we denote the attenuation coefficient by α (dis-
the phenomenon should be referred to as cussed previously in Sections 1.5 and 10.15—talking about lossy waves) the
light oscillation by stimulated emission
of radiation but, somehow, the corres- intensity in a resonator of length, l, changes by a factor, exp[(γ – α)2l]. Denot-
ponding acronym never caught on. ing further the two mirror’s amplitude reflectivity by R 1 and R 2 , respectively,
we find that the condition for unity loop gain is

R 1 R 2 exp[(γ – α)2l] = 1. (12.33)

We know what determines γ . How can we find α? It represents all the losses
in the system except mirror losses, which may be summarized as ohmic losses
in the material, diffraction losses in the cavity, and losses due to spontaneous
† emission. †
This is one of the reasons why it is
more difficult to obtain laser action in Just one more word on diffraction losses. If the resonator consists of two
the ultraviolet and soft X-ray region. Ac- parallel mirrors, then it is quite obvious that some of the electromagnetic power
cording to eqn (12.11) the coefficient of
spontaneous emission increases by the will leak out. In any open resonator there is bound to be some diffraction loss.
third power of frequency. Then why don’t we use a closed resonator, something akin to a microwave
cavity? The answer is that we would indeed eliminate diffraction losses, but on
the whole we would lose out because ohmic losses would significantly increase.

12.6 Some practical laser systems
How can we build a practical laser? We need a material with suitable energy
levels, a pump, and a resonator. Is it easy to find a combination of these three
factors which will result in laser oscillation? It is like many other things; it
seems prohibitively difficult before you’ve done it and exceedingly easy after-
wards. By now thousands of ‘lasing’ materials have been reported, and there
must be millions in which laser oscillations are possible.
There are all kinds of lasers in existence; they can be organic or inorganic,
crystalline or non-crystalline, insulator or semiconductor, gas or liquid, they
can be of fixed frequency or tunable, high power or low power, CW or pulsed.
They may be pumped by another laser, by fluorescent lamps, by electric arcs, by
electron irradiation, by injected electrons, or by entirely non-electrical means,
as in a chemical laser. You can see that a mere enumeration of the various