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Chapter 11. Laser
Chapter 11
Laser
§11.1 The fundamental principles of laser
• Laser: The word LASER is an acronym for “light amplification by stimulated
emission of radiation”. The output of laser is a monochromatic, coherent light beam.
• Atomic Energy levels: There are many energy levels in atoms. The lowest one
is called normal or ground state and others are called excited states. At the room
temperature, most of atoms are in their ground states if it is under thermal equilibrium.
-7
But the excited states have very short lifetime (10 ~ 10-7 second). If the lifetime of a
-3
state is within 10 ~ 10-2 second, it is called metastable state.
• Absorption
If the atom is initially in the lower state E0, it can be raised to E1 by absorbing a
photon of energy E1 – E0 = hv. This process is called induced absorption which is
depicted schematically in Fig. 10.1a.
• Spontaneous emission
After absorbing the photon, the atom becomes an excited atom A*. A short time
later, spontaneous emission takes place and the excited atom becomes normal again
by emitting a photon of the same frequency as that which was originally absorbed but
in a random direction and with a random phase as shown in Fig. 10.1b.
• Stimulated emission:
There is also a third process, first proposed by Einstein, called stimulated
emission. Stimulated emission takes place when a photon encounters an excited atom
and forces it to emit another photon of the same frequency, in the same direction, and
in the same phase. The two photons go off together as coherent radiation.
• Maxwell-Boltzman distribution law:
Consider an absorption cell containing a large number of atoms. In the absence of
an external beam of radiation, most of the atoms are in the ground state; there are only
a few excited atoms present in the cell. The ratio of the number nE of excited atoms to
the number n0 of normal atoms is extremely small as they are distributed according to
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Medical Physics
the Maxwell-Boltzman distribution law.
ni  n 0 e

Ei
kT
,
f ( Ei )  Ae

(11.1)
Ei
kT
(11.2)
• Population inversion:
Now suppose a beam of radiation is sent through the cell with frequency v
corresponding to the energy difference E. The ratio of the numbers nE and n0, that is,
the ratio of the populations of the energy levels, will increase. Since the population of
the normal state was so much larger than that of the excited state, an enormously
intense beam of light would be required to increase the population of the excited
states to a value comparable to or greater than that of the normal state.
Therefore, the rate at which energy is extracted from the beam by absorption of
normal atoms far outweighs the rate at which energy is added to the beam by
stimulated emission of excited atoms.
If a condition can be created in which nE is substantially increased compared to
the normal equilibrium value, known as population inversion, the rate of energy
radiation by stimulated emission may exceed the rate of absorption.
The system then acts as a source of radiation with photon energy E. Furthermore,
since the photons are the result of stimulated emission, they all have the same
frequency, phase, polarization, and direction. The resulting radiation is therefore very
much more coherent than light from ordinary sources, in which the emissions of
individual atoms are not coordinated (同等的).
It is known that the electron transitions between energy levels are like two-way
street, such a “back and forth” are alternatively called absorption and emission
according to their gaining or losing energies.
The necessary population inversion can be achieved in a variety of ways. As an
example, we consider the helium-neon (氦-氖) laser, a simple, inexpensive laser
available in many universities.
• Helium-neon Laser machine
A mixture of about 7 part of helium and 1 part of neon at a low pressure of the order
of 10^2 Pa (or 10^(-3) atm, or ~ 1mm of mercury), is sealed in a glass tube provided
with two electrodes. When a sufficiently high voltage is applied, a glow discharge
occurs. Collisions between ionized atoms and electrons carrying the discharge current
EXCITE atoms to various energy states.
Figure 10.2 shows the an energy level diagram for the system. Helium atoms
excited to the 1s2s state cannot return to the ground state by emitting a 20.61eV
photon, as might be expected, because both the states have zero total angular
momentum, while a photon must carry at least one unit (h/2p) of angular momentum
(selection rules of spectrum). Such a state, in which radiative decay is impossible, is
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Chapter 11. Laser
Neon
Heliu
1s2s
metastable
Collisio
5
20.61eV
4p
20.66e
20.30eV
4
19.78eV
3p
632.8nm laser
18.70eV
Electron
impact
3s
16.70eV
Diffusion to walls
1s2 ground state
2p
ground
Fig.10.2 Energy level diagram for Helium-neon
called a metastable state (亚稳态). The helium atom can, however, lose energy by
energy–exchange collisions with neon atoms initially in the ground state.
A 1s2s helium atom, with its internal energy of 20.61eV and a little additional
kinetic energy, can collide with a neon atom in the ground state, exciting it to the 5s
excited state at 20.66eV and leaving the helium atom in the 1s2 ground state. Thus we
have necessary mechanism for a population inversion in neon, with the population in
the 5s state substantially enhanced. Stimulated emission from this state then results in
the emission of highly coherent light at 632.8nm, as shown on the diagram.
• Optical resonator
In practice the beam is sent back and forth through the gas tube many times by a pair
of parallel mirrors, so as to stimulate emission from as many excited atoms as possible.
One of the mirrors is partially transparent, so a portion of the beam emerges as an
external laser beam. On the other hand, the spacing of the two mirrors must be equal
to an integer number of half-wavelength of the laser light as this is the condition for
standing waves in such a case.
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Medical Physics
§11.2 The characteristics of laser
The net effect of all the processes taking place in a laser tube is a beam of
radiation that has several special properties:
(1) Good directionality.
Laser is almost perfectly parallel. This means that it has good directionality. For
the same power, normal light can travel very small distance before it is diverted but
laser could travel very large distance almost without diversion, the distance between
the moon and the earth, for example.
(2) High brightness and high intensity.
Laser is the brightest light source in the world now. its brightness (40W for
example) can be 1011 times higher than the normal light.
(3) Good monochromatic;
This factor is determined by the width of spectrum (10-8nm) . This characteristic
is very useful in medical treatment because the biological effect is strongly related to
the wavelength of light.
(4) Good coherence (相干性)
Time coherence: Coherent light are emitted in the same place but in different time
with interval tc which is called coherent time and
Lc = c tc is called coherent length. It is known that from wave optics the
coherent time is the continuous emitting time of the light. For stimulated emission,
it is the average life-span of the atom in the metastable state. For normal lights, the
coherent length is less 100cm and for laser it can be tens or hundreds of kilometers
Spatial coherence: It is defined that the phase relations of the two beams of lights
emitted from two different places do not vary with time. This is called the spatial
coherence of light. This concept can be extended to the coherent area.
To understand this characteristic, we recall the simple double-slit interference
experiment. A mercury arc (弧光) placed directly behind the double-slit would not
give rise to interference fringes because the light issuing from the two slits would
come from different parts of arc and would not retain a constant phase relationship.
In the use of the usual laboratory arc-lamp sources, it is necessary to use the light
from a very small portion of the source to illuminate (not eliminate) the double slit.
The slightly diverging beam from a laser, however, may be allowed to fall directly on
a double slit because the light rays from any two points of a cross section are in phase ,
and are said to exhibit “spatial coherence”.
(5) Good polarization (偏振).
As different material allows different light with specially polarized light to
penetrate, the polarization of light is also quite useful in experiments and applications
to human life.
• Comparison: Laser and normal light.
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Chapter 11. Laser
§11.3 Laser applications to medicine
The biological functions of laser
The biological functions (生物作用) of laser contain a lot of useful aspects in medical
treatment. These functions can be summarized as heating, mechanical, actinic (光化),
electromagnetic field and biological stimulation.
• Heating or thermal function: Biological tissues can be heated under the
irradiation of laser. Its temperature will get higher. These functions can be controlled
by doctors in order to do some treatments to patients.
• Mechanical function: Biological system can be evaporated and produces
mechanical waves by the laser energy.
•Actinic (光化) function : Big biological molecules absorbing laser photon could be
stimulated and cause a series of chemical reactions together with biological tissues.
This phenomenon is call actinic reaction it has two laws (absorption law and quantum
law)
• Electromagnetic function
• biological stimulating function.
• Laser applications to the fundamental theoretical studies of medicine
On the other hand, laser is also useful for the fundamental theoretical studies of
medicine. As laser some special functions to the biological molecules, cells and
tissues, you could use it to do a lot of studies about the treatment to patients.
• Clinical applications of Laser
(1) Laser diagnosis methods (laser spectroscopic analysis, laser interference
(scattering, diffraction, transmission) analysis and laser polarization.
(2) Laser treatment methods (laser operation, weak laser treatment which includes:
laser physical therapy (理疗), laser acupuncture (针灸), laser photon dynamical
treatment and laser endoscope (内镜) treatment.
• Medical laser:
Variety of laser have been obtained and they are used in different purpose
according to their properties. Most of these lasers and their functions are given in your
text book on pages 358-9.
• Safety protection against laser
Laser can cause harmful effect to human beings. It can damage eyes, skin, nerve
system and internal organs. The protection method can be obtained from your book
and proper training should be given before hands.
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Medical Physics
Problems
1. How fast must an electron be moving if all its kinetic energy is lost to a single
x-ray photon (a) at the high end of the x-ray electromagnetic spectrum with a
wavelength of 1.00  10-8 m; (b) at the low end of the x-ray electromagnetic
spectrum with a wavelength of 1.00  10-13 m?
Solution: According the first sentence, that all the kinetic energy are
transformed into X-ray photon energy will give the following equation using
relativistic theory:




1

 hc
E k  mc 2  m0 c 2  h  m0 c 2 
 1 
2

 1 u



c2


where u is the speed of electrons,  is the corresponding wavelength, h is Planck’s
constant, c is the light speed and m0 is the rest mass of electron. Solving the above
equation, the speed of electron could be found:
u
c 2m0 ch  h 2
m0 c  h
Substituting the different value of wavelengths at high and low ends into above
formula, we have:
(a) u high  6.603  10 6 m  s 1
(b)
u low  2.995  10 8 m  s 1
2. What minimum accelerating voltage would be required to produce an x-ray with a
wavelength of 0.0300 nm?
Solution: eU  hv 
hc


4.136  10
15


eV  s 3  10 8 m / s
 4.13  10 4 eV
3  1011 m
3. Calculate the minimum wavelength x-ray that can be produced when a target is
struck by an electron that has been accelerated through a potential difference of (a)
15.0 kV; (b) 1.00  105 V.
4. The extremes of x-ray portion of the electromagnetic spectrum range from
approximately 1.0  10-8 m to 1.0  10-13 m. Find the minimum accelerating
voltage requires to produce wavelength at these two extremes.
5. If the voltage of the x-ray machine is 80 kV, find that the maximum energy of the
x-ray photon and the minimum wavelength of the x-rays.
6. The attenuation coefficient of a matter with density of 3 g/cm3 is 0.03 cm2g-1 for
a monochromatic x-rays. Find the percentage of density with respect to the
original density of the x-rays after penetrating the absorbing layers of 1mm, 5mm
and 1cm thickness respectively.
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