Chapter 11

Laser

June 8, 2005

Brief review to the last lecture• The production of x-rays

Good heat conductor

1% to x-rays99% to heat energy

What is the nature of x-rays?杨振东 ,李春梅 *

KL

These are the two ways of producing x-rays. How does it work based on your knowledge? 吴泽纯 *, 曾结霞 *,

• The spectrum of X-rays

How does the continuous spectrum produced how does the line spectrum produced?( 邓俊明

*, 朱春苗 *) . Why do we get cut-off frequency? ( 梁裕团 , 钟树林 )

• The basic properties of x-rays

Ionizing function,

Fluorescence function,

Actinic (光化 ) function,

biological effect,

high penetration capability;

• What does the intensity and hardness of x-rays depend on? ( 汤忠明 , 朱春苗 *)

• The attenuation of x-rays

xeII

0x is the thickness and is the attenuation coefficient.

2/1

2

1 ,

693.02ln02/1

x

x

IIx

Applications of x-rays to medicine

• Treatment,

• Diagnosis,

• Digital subtraction angiography (数字减影血管造影 ).

• X-CT, CT: Computerized Tomography (X射线断层摄影术 )　

11.1 The fundamental principles of laser

• Laser:

LASER is an acronym for “light amplification by stimulated emission of radiation”, a monochromatic, coherent light beam.

• Atomic Energy levels:

Ground state, Excited states, under thermal equilibrium, most atoms are in their ground states at room temperature.

• Lifetime

Excited states (10-9 ~ 10-7 second).

metastable state (10-3 ~ 10-2 second)

• Radiation transition

There are three interaction processes between atoms and radiation. They are absorption, spontaneous emission and stimulated emission.

(2) Spontaneous emission

same frequency, not the same direction, not the same phase, not coherent light, not amplified!

(1) Absorption

eg EhE h

Eg

Ee

Fig.10.1 Three interaction processes between an atom and a radiation.; (a) absorption, (b) spontaneous emission, (c) stimulated emission.

(3) stimulated emission

This idea was first proposed by Einstein, shown schematically in Fig.10.1c.

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. So it is amplified!

• Maxwell-Boltzman distribution law:

Consider a large number of atoms

No radiation, thermal equilibrium

most in the ground state no and few in the excited state nE

Distributions are based on the Maxwell- Boltzman distribution law.

kT

E

i

i

enn

0

1

69.110704.2

,300

3.65

0

19

en

n

eVJE

KT

E

For example, Neon, at room temperature, on 3S and 1S states

• Population inversion

h

Eg

EE

• Strong beam of light irradiate on the atoms

• making nE > n0

Not easy, as both the absorption of normal atoms and the stimulated emission of excited atoms exist! This is like a two-way street!

Metastable state!

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

7 helium to 1 neon atoms (Z=10) at a low pressure of the order of 10^(-3) atm are sealed in a glass tube provided with two electrodes. When a sufficiently high voltage is applied, a glow discharge ( 辉光放电 ) occurs. Collisions between ionized atoms and electrons carrying the discharge current ( 放电电流 ) EXCITE atoms to various energy states.

Electron impact

metastable

Helium (Z=2)

1s2s

1s2 ground state 2p ground state

20.61eV

Collision 5s4p

Diffusion to walls

20.66eV

3p632.8nm laser

4s

3s

Neon (Z=10)

Fig.10.2 Energy level diagram for Helium-neon laser

16.70eV

18.70eV

19.78eV20.30eV

selection rules of spectrum So: 1s2s 1s2 1

622 221 pss

Helium atoms are excited to the 1s2s state which is a metastable state ( 亚稳态 ).

The helium atom can lose energy by collisions with neon atoms initially in the ground state.

population inversion in neon,

5s 3p.

coherent light with wavelength 632.8nm,

Helium (1s2s, 20.61eV) + kinetic energy

Neon (5s, 20.66 eV)

• Optical resonator

Mirror Semi-transparent

2

nL Harmonic resonance

11.2 The characteristics of laser

(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 c. c is called coherent time and

Lc =c c

is called coherent length. It is known that from wave optics the coherent time is the continuous emitting time of the light (about 10-8

s).

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.

11.3 Laser applications to medicine

1. 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 called actinic reaction it has two laws (absorption law and quantum law) .

• Electromagnetic function

• biological stimulating function

2. Laser applications to the fundamental studies of medicine

On the other hand, laser is also useful for the fundamental studies of medicine. As laser has 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.

3. Clinical applications of Laser

(1) Laser diagnosis methods

laser spectroscopic analysis method

laser interference analysis method

Laser scattering analysis method

Laser diffraction analysis method

laser transmission analysis method

laser polarization method.

(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.

4. Medical laser:

lots of lasers 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.

5. 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.

Example 1: (a) if a laser emits 10 Joules of energy in a pulse lasting 5 10-11 s, what power is emitted? () (b) What is the intensity of the beam if it is 2 10-6 m2 in area?

)( 102105

10 1111

Ws

J

t

EP

Solution: (a) The power is defined as the amount of energy emitted per unit time. So, we can obtain that

(b) The intensity is defined as the amount of energies transmitted per unit time per unit area: ()

)(10102

102 21176

11

msJS

PI

17

1834

9

1049.3100.310626.6

104.6931.01.01.0

smsJ

mJ

hc

J

h

JN

Example 2: A ruby laser emits light at 693.4 nm. If the energy released in each 10-11 second pulse is 0.1 J, how many photons are there in the pulse? ()

Solution: (1) calculate one photon energy

(2) total energy / one photon energy

老师 : “中文本说： 各个电子到原子核的距离不同，速度变化情况也各不一样，所以每个电子损失的动能将不同，辐射出来的光子能量具有各种各样的数值，从而形成各种各样的连续 X射线

”谱。     原子轨道是量子化的，各个能级之间的电子跃迁而辐射出来光子能量应是量子化的（即辐射能量的数值并非连续的），那么为什么光谱是连续谱，是否辐射出来的光子能量完全取决于 X射线电子动能损失，而与耙原子本身能级差无关。谢谢！

Example 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 15.0 kV; ()

nmkVU )(

242.1min

hc

hveU