Elements of Modern Physics
192
up an intense photon beam (the effective path length is increased by a factor
equal to the number of reflections). One of the mirrors is partially transparent,
between 90% to 100% reflecting, which allows the beam to be taken out. If the
tube windows (Fig. 6.4) are at the Brewster angle, the emerging beam will be
plane polarized.
Apart from increasing the intensity of the beam, the mirrors help in producing
a monochromatic beam in that they serve as walls of a resonance cavity which
sustains only those wavelengths λ which satisfy the relation
pλ = 2t,
p = 1, 2, ...
(6.85)
where t is the distance between the mirrors. The separation between two
successive modes is
λ p – λ p + 1 ≈ λ
2
/2t,
≈ 0.002 Å for λ = 6328 Å, t = 1 m
(6.86)
which is quite a bit smaller than the spread in wavelength due to Doppler effect
[Eq. (6.79)]. Thus, there are several frequencies, each with a very narrow width,
supported by the resonance cavity, within the Doppler width of the central
frequency. Some special technique can be used to select one of these frequencies,
such as reducing t which will increase λ p – λ p + 1 , or lowering the temperature
which will decrease the Doppler width.
6.6 APPLICATIONS OF LASERS
Since the laser beam is made up of stimulated emission, it is monochromatic,
has a high temporal coherence, i.e., the phases at different times are related, and
a high spatial coherence, i.e., the phases at different positions are related. It is
parallel and has a very high intensity since the beam has a small cross section.
The temporal coherence is determined by the frequency width of the beam,
∆t ~ 1/∆ω
(6.87)
and can be as large as 10
–6
or larger in some lasers. Spatial coherence implies
that the beam is essentially described by a single plane wave with a width equal
to the cross-section of the beam. This gives rise to a directionality constrained
only by the width. If a beam with a cross-sectional area (∆x)
2
is travelling in the
z-direction, uncertainty relation implies
∆p x ≈ /∆x
(6.88)
so that the angular spread is
α =
x
z
p
p
∆ ≈
x h
λ
∆
(6.89)
≈ 10
–4
rad for λ ≈ 5000 Å, ∆x ≈ 10
–3
m
192
up an intense photon beam (the effective path length is increased by a factor
equal to the number of reflections). One of the mirrors is partially transparent,
between 90% to 100% reflecting, which allows the beam to be taken out. If the
tube windows (Fig. 6.4) are at the Brewster angle, the emerging beam will be
plane polarized.
Apart from increasing the intensity of the beam, the mirrors help in producing
a monochromatic beam in that they serve as walls of a resonance cavity which
sustains only those wavelengths λ which satisfy the relation
pλ = 2t,
p = 1, 2, ...
(6.85)
where t is the distance between the mirrors. The separation between two
successive modes is
λ p – λ p + 1 ≈ λ
2
/2t,
≈ 0.002 Å for λ = 6328 Å, t = 1 m
(6.86)
which is quite a bit smaller than the spread in wavelength due to Doppler effect
[Eq. (6.79)]. Thus, there are several frequencies, each with a very narrow width,
supported by the resonance cavity, within the Doppler width of the central
frequency. Some special technique can be used to select one of these frequencies,
such as reducing t which will increase λ p – λ p + 1 , or lowering the temperature
which will decrease the Doppler width.
6.6 APPLICATIONS OF LASERS
Since the laser beam is made up of stimulated emission, it is monochromatic,
has a high temporal coherence, i.e., the phases at different times are related, and
a high spatial coherence, i.e., the phases at different positions are related. It is
parallel and has a very high intensity since the beam has a small cross section.
The temporal coherence is determined by the frequency width of the beam,
∆t ~ 1/∆ω
(6.87)
and can be as large as 10
–6
or larger in some lasers. Spatial coherence implies
that the beam is essentially described by a single plane wave with a width equal
to the cross-section of the beam. This gives rise to a directionality constrained
only by the width. If a beam with a cross-sectional area (∆x)
2
is travelling in the
z-direction, uncertainty relation implies
∆p x ≈ /∆x
(6.88)
so that the angular spread is
α =
x
z
p
p
∆ ≈
x h
λ
∆
(6.89)
≈ 10
–4
rad for λ ≈ 5000 Å, ∆x ≈ 10
–3
m