II Laser operation In this section, we discuss how do the laser elements (pump, medium and resonator) work?

Consider the following figures;

In the above figure ( 3 )

Step (1)

An energy from an appropriate pump is coupled

into the laser medium. The energy is sufficiently high to

excite a large number of atoms from the ground state o

to several excited states 3. Then the atoms

spontaneously decay and back to the ground state o.

But some of them back by a very fast (radiationless)

decay from 3 to a very special level 2.

Step (2)

The level E2 labeled as the “upper laser level”, has a

long lifetime. Whereas most excited levels in atom

decay with lifetime of order 10-8 sec. Level E2 is

metastable, with a typical lifetime of order of 10-3 sec.

So that the atoms being to pile up at this metastable

level (E2), which functions as a bottleneck. N2 grows to a

large value, because level E2 decays slowly to level E1

which labeled by “ lower laser level ” and level E1

decays to the round state rapidly, so that N1 cannot

build to a large value. The net effect is the population

inversion (N2>N1) between the laser levels E1 and E2.

When the population inversion has been established, a

photon of resonant energy (h=E2-E1) passes by one of

the N2 atoms, stimulated emission can be occurred.

Then, laser amplification begins. Note carefully that a

photon of resonant energy (E2-E1) can also stimulate

absorption from E1 to E2. Then the light amplification

occurs and there is a steady increase in the incident

resonant photon population and lasing continues.

Step (3)

Step )4) One of the inverted N2 atoms, which dropped to level E1 during the

stimulated emission process, now decays rapidly to the ground state o. If the pump is still operating the atoms is ready to repeat

the cycle, there by insuring a steady population inversion and constant laser beam output.

Figure (3) shows the same action of figure (2(.

In (a) the laser medium is situated between the

resonator (two mirrors) in which most of the atoms are

in the ground state (black dots).

In (b) An external energy (pumping) raising most of

the atoms to the excited levels (as 3). The excited

states are shown by circles. During this pumping

process, the population inversion is established.

In (c) the light amplification process is initiated, in

which many of the photons leave through the sides of

the laser cavity and are lost. Since the remainder (seed

photons) are directed along the optical axis of the

laser.

In (d) and (e) As the seed photons pass by the

inverted 2 atoms, stimulated emission adds identical

photons in the same direction, providing an ever –

increasing population of coherent photons that bounce

bake and forth between the mirrors.

In (f) A fraction of the photons incident on the mirror

(2) pass out through it. These photons constitute the

external laser beam.

Characteristic of Laser Light Monochromaticity. The light emitted by a laser is

almost pure in color, almost of a single wavelength or

frequency. Although we know that no light can be truly

monochromatic, with unlimited sharpness in wavelength

definition, laser light comes far closer than any other

available source in meeting this ideal limit.

The monochromaticity of light is determined by the

fundamental emission process where atoms in excited

states decay to lower energy states and emit light. In

blackbody radiation, the emission process involves

billions of atoms and many sets of energy-level pairs

within each atom. The resultant radiation is hardly

monochromatic, as we know.

If we could select an identical set of atoms from this

blackbody and isolate the emission determined by a

single pair of energy levels, the resultant radiation,

would be decidedly more monochromatic. When such

radiation is produced by non-thermal excitation, the

radiation is often called fluorescence. Figure 1 shows

such

Figure (1) fluorescence and its spectral content for a

radiative decay process between two energy levels in

an atom. (a) Spontaneous decay process between well-

defined energy levels. (b) Spectral content of

fluorescence in (a), showing line shape and linewidth.

an emission process. The fluorescence comes from

the radiative decay of atoms between two well-defined

energy levels 2 and 1. The nature of the fluorescence,

analyzed by a spectrophotometer, is shown in the

lineshape plot, a graph of spectral radiant existence

( ) versus wavelength. 2mW

Note carefully that the emitted light has a wavelength

spread about a center wavelength , where

= c/and h . While most of the light

may be emitted at a wavelength , it is an

experimental fact that some light is also emitted at

wavelengths above and below , with different relative

existence, as shown by the lineshape plot. Thus the

emission is not monochromatic, it has a wavelength

spread given by 2 , where is often referred

to the linewidth. When the linewidth is measured at the

half maximum level of the lineshape plot, it is called the

FWHM linewidth, that is, “ full width at half maximum “

In the laser process, the linewidth shown in figure

(1) is narrowed considerably, leading to light of a much

higher degree of monochromaticity. Basically this

occurs because the process of stimulated emission

effectively narrows the band of wavelengths emitted

during spontaneous emission. This narrowing of the

linewidth is shown qualitatively in figure (2). To gain a

quantitative appreciation for the monochromaticity of

laser light, consider the data in table (1), in which the

linewidth of a high quality He-Ne laser is compared to the

linewidth of the spectral output of a typical sodium

discharge lamp and to the linewidth of the very narrow

cadmium red line found in the spectral emission of a

low-pressure lamp. The conversion from to is

made by using the approximate relationship.

where V0C.

2o

c

The data of table (1) show that the He-Ne laser is 10

million times more monochromatic than the ordinary

discharge lamp and about 100,000 times more so than

the cadmium red line. No ordinary light source, without

significant filtering, can approach the degree of

monochromaticity present in the output beam of typical

lasers.

Figure (2) Qualitative comparison of linewidths for laser

emission and spontaneous emission involving the same pair

of energy levels in an atom. The broad peak is the line shape

of spontaneously emitted light between levels E2 and E1

before lasing being. The sharp peak is the line shape of laser

light between levels E2 and E1 after lasing beings.

Table (1) comparison of linewidths

Light source Center

Wavelength

( A)

FWHM

Linewidth

( A)

FWHM linewidth

(HZ)

Ordinary discharge lamp

5896 1 9X1010

Cadmium low-pressure lamp

6438 0.013 9.4X108

Helium-neon laser 6328 10-7 7.5X103

Coherence. The optical property of light that most

distinguishes the laser from other light source is coherence.

The laser is regarded, quit correctly as the first truly

coherent light source. Other light source, such as the sun or

a gas discharge lamp, are at best only partially coherent.

Coherence, simple stated, is a measure of the degree of

phase correlation that exists in the radiation field of a light

source at different location and different times. It is often

described in terms of temporal coherence, which is a measure

of the degree of monochromaticity of the light, and a spatial

coherence, which is a measure of the uniformity of phase

across the optical wavefront.

To obtain a qualitative understanding of temporal and

spatial coherence, consider the simple analogy of water

waves created at the center of a quite pond by a regular,

periodic disturbance. The source of disturbance might

be a cork bobbing up and down in regular fashion,

creating a regular progression of outwardly moving

crests and troughs, as in figure (3). Such a water wave

filed can be side to have perfect temporal and spatial

coherence. The temporal coherence is perfect because

there is but a single wavelength; the crest–to-crest

distance remains constant.

As long as the cork keeps bobbing regularly, the

wavelength will remain fixed, and one can predict with

great accuracy the location of all crests and troughs

on the pond's surface. The spatial coherence of the

wave filed is also perfect because the cork is a small

source, generating ideal waves, circular crests, and

troughs of ideal regularity. Along each wave then, the

spatial variation of the relative phase of the water

motion is zero that is the surface of the water all along

a crest or trough is in step or in one phase.

Perfect temporal coherence

Perfect spatia

coherence uniform

ity of phase

Temporal coherence

phase difference time independent (temporal coherence

Spatial coherence

Figure (3) portion of a perfectly coherent water wave field created by a regularly bobbing cork at S. the wave field contains perfectly ordered wave fronts, C (crests) and T (troughs), representing water waves of a single wavelength

The water wave field described above can be

rendered temporally and spatially incoherent by the

simple process of replacing the single cork with a

hundred corks and causing each cork to bob up and

down with a different and randomly varying periodic

motion. There would then be little correlation between

the behavior of the water surface at one position and

another. The wave fronts would be highly irregular

geometrical curves, changing shape haphazardly as the

collection of corks continued their jumbled,

disconnected motions.

It does not require much imagination to

move conceptually from a collection of corks

that give rise to water waves to a collection of

excited atoms that give rise to light.

Disconnected, uncorrelated creation of water

waves results in an incoherent water wave

field. Disconnected, uncorrelated creation of

light waves results, similarly, in an

incoherent field.

To emit light of high coherence then, the radiating region

of a source must be small in extent (in the limit, of course. a

single atoms) and emit light of a narrow bandwidth (in the

limited, with equal to zero). For real light sources, neither

of these conditions is attainable. Real light sources, with the

exception of the laser, emit light via the uncorrelated action

of many atoms, involving many different wave lengths. The

result is the generation of incoherent light.

To achieve some measure of coherence with a non-laser

source, two notifications to the emitted light can be made.

First, a pinhole can be placed in front of the light source to

limit the spatial extent of the source. Second, a narrow-band

filter can be used to decrease significantly the linewidth of

the light. Each modification improves the coherence of the

light given off by the source-but only at the expense of a

drastic loss of light energy.

In contrast, a laser source, by the very nature of its

production of amplified light via stimulated emission,

ensures both a narrow-band output and high degree of

phase correlation. Recall that in the process of

stimulated emission, each photon added to the

stimulated radiation has a phase, polarization, energy,

and direction identical to that of the amplified light wave

in the laser cavity. The laser light thus created and

emitted is both temporally and spatially coherent. In fact,

one can describe or model a real laser device as a very

powerful, fictitious “point source” located at a distance,

giving off monochromatic light in a narrow cone angle.

Figure 4 summarizes the basic ideas of coherence for

non-laser and laser source.

For typical laser, both the spatial coherence and

temporal coherence of laser light are far superior to

that for light from other sources. The transverse spatial

coherence of a single mode laser beam extends across

the full width of the beam, whatever that might be. The

temporal coherence, also called “longitudinal spatial

coherence,” is many orders of magnitude above that of

any ordinary light source. The coherence time tc of a

laser is a measure of the average time interval over

which one can continue to predict the correct phase of

the laser beam at a given point in space. The coherence

length Lc, is related to the coherence time by the

equationLc ctc where c is the speed of light.

Thus the coherence length is the average length of

light beam along which the phase of the wave

remains unchanged. For the He-Ne laser described in

table 1 the coherence time is of the order of

milliseconds (compared with about 10-11s for light

from a sodium discharge lamp), and the coherence

length for the same laser is thousands of kilometers

(compared with fractions of a centimeter for the

sodium lamp).

Improve temporal coherence

Improve spatial coherence

Figure 4. A tungsten lamp requires a pinhole and filter

to produce coherent light. The light from a laser is

naturally coherent. (a) Tungsten lamp. The Tungsten

lamp is an extended source that emits many wavelength.

The emission lacks both temporal and spatial

coherence. The wave front are irregular and change

shape in a haphazard manner. (b) Tungsten lamp with

pinhole. An ideal pinhole limits the extent of the

tungsten source and improve the spatial coherence of

the light. However the light still lacks temporal

coherence since all wavelengths are present. Power in

the beam has been decreased.

(c) Tungsten lamp pinhole and filter. Adding

a good narrow –band filter further reduces the

power but improves the temporal coherence.

Now the light is "coherent" but the available

power that initially radiated by the lamp. (d)

Laser. Light coming from the laser has a high

degree of spatial and temporal coherence. In

addition, the output power can be very high.

Directionality. When one sees thin, pencil-like beam of

a He-Ne laser for the first time, one is struck

immediately by the high degree of beam directionality.

No other light source, with or without the help of

lenses or mirrors, generates, a beam of such precise

definition and minimum angular spread.

The astonishing degree of directionality of a laser

beam is due to the geometrical design of the laser

cavity and to the monochromatic and coherent

nature of light generate in the cavity. Figure (5)

shows a specific cavity design and an external

laser beam with an angular spread signified by the

angel .

The cavity mirrors shown are shaped with surfaces

concave toward the cavity, thereby “focusing” the

reflecting light back into the cavity and forming a beam

waist at one position in the cavity.

Figure 5. external and internal laser beam for a given cavity. Diffraction or beam spread, measured by the beam divergence angle appears to be caused by an effective aperture of diameter D, located at the beam waist.

The nature of the beam inside the laser cavity and its

characteristics outside the cavity are determined by solving

the rather complicated problem of eectromagnetic waves in

an open cavity. Although the details of this analysis beyond

the scope of this discussion, several results are worth

examining. It turns out that the beam- spread angel is

giving by the relationship

D

27.1 (1)

Where is the wavelength of the laser beam and D is the

diameter of the laser beam at its beam waist. One cannot

help but observe that Eq. (1) is quite similar to that

obtained when calculating the angular spread in light

generated by the diffraction of plane waves passing

thought a circular aperture .

The pattern consists of a central, bright circular

spot, the Airy disk, surrounded by a series of bright

rings. The essence of this phenomenon is shown in

figure (6). The diffraction angle , tracking the Airy

disk, is given by

D

44.2 (2)

Figure (6). Fraunhofer diffraction of plane waves through a circular

aperture. Beam divergence angle is set by the edges of the Airy

disk.

where is the wavelength of the collimated.

Monochromatic light and D is the diameter of the circular

aperture. Both Eqs. (1) and (2) depend on the ratio of a

wavelength to a diameter. They differ only by a constant

coefficient. It is tempting, then, to think of the angular

spread inherent in laser beams and given in Eq. (1) in

terms of diffraction.

If we treat the beam waist as an effectives circular

aperture located inside the laser cavity, then by

controlling the size of the beam waist we control the

diffraction or beam spread of the laser. The beam waist,

in practice, is determined by the design of the laser

cavity and depends on the radii of curvature of the two

mirrors and the distance between the mirror.

Therefore, one ought to be able to build lasers with a given

beam waist and, consequently, a given beam divergence or

beam spread in the far field, that is, at sufficiently great

distance L from the diffracting aperture that L >> area

aperture/. Such is indeed the case.

With the help of Eq. (1), one can now develop a feel

for the low beam spread, or high degree of

directionality, of laser beams. He-Ne lasers (632.8 nm)

have an internal beam waist of diameter near 0.5 mm.

Equation (1) then yields

sr102radian106.1)m105(

)m108.632)(27.1(

D

27.1 634

9

This is a typical laser-beam divergence, indicating that

the beam width will increase about 1.6 cm every 1000cm.

Since we can control the beam waist D by laser cavity

design and “select” the wavelength by choosing

different laser media, what lower limit might we expect

for the beam divergence? How directional can lasers

be? If we design a laser with a beam waist of 0.5 cm

diameter and a wavelength of 200 nm, the beam

divergence angle becomes about radian,. This beam

would spread about 1.6cm every 320m.

Clearly, if beam waist size is at our command and

lasers can be built with wavelength below the

ultraviolet, there is no limit to how parallel and

directional the laser beam can be made.

The high degree of directionality of the laser, or any

other light source, depends on the monochromaticity

and coherence of the light generated. Ordinary sources

are neither monochromatic nor coherent. Lasers, on

the other hand, are superior on both counts, and as a

consequence generate highly directional, quasi-

collimated light beams.

Laser Source Intensity. It has been that a 1-mW

He-Ne laser is hundreds of times “brighter” than the

sun. As difficult as this may be to imagine, calculations

for luminance or visual brightness of a typical laser,

compared to the sun, substantiate these claims. To

develop an appreciation for the enormous difference

between the radiance of lasers and thermal sources we

consider a comparison of their photon output rates

(photons per second).

Small gas lasers typically have power outputs P of

1mW. Neodymium-glass lasers, such as those under

development for the production of laser-induced

fusion, boast of power outputs near 1014 W!. Using

these two extremes and an average energy of 10-19 J

per visible photon (Eh), the photon output of laser

(Ph) varies from 1016 photons/s to 1033 photons/s. For

comparison, consider a broadband thermal source

with a radiating surface equal to that of the beam waist

of a 1-mW He-Ne laser with diameter of 0.5 mm, an

area of A2X103 cm2.

Let the surface emit radiation at a wavelength of 633 nm

with a linewidth of 100nm (or7x1013HZ) and

temperature T1000K. The photon output rat for the

broadband source can be calculated from the equation

sec/photon10A1e

11s/photonsthermal 9

KT/h2

(3)

Substituting the values given above into Eq. (3), we

find that the thermal photon output rat is only about 109

photons/s! This value is 7 orders of magnitude smaller

than the photon output rat of low-power 1-mW He-Ne

laser and 24 orders of magnitude smaller than a powerful

neodymium-glass laser. The comparison is summarized

in figure 7.

Figure (7). Comparison of photon output rates between a low-power He-Ne gas laser and a hot thermal source of the same radiating surface area. (a) 1-mW He-Ne laser (=633nm), A=2x10-3cm2,

o=633nm =100nm. Note that the laser emits all of the photons in a small solid angle (2x10-6 sr) compared with the 2 solid of the thermal source.

We see also from figure 7 that the He-Ne laser emits 1016

photons/s into a very small solid angle of about 2X10-6sr.

whereas the thermal emitter, acting as a Lambertian source,

radiates 109 photons/s into a forward, hemispherical solid angel

of 2 sr. If we were to ask how many thermal photons/second

are emitted by the thermal source into a solid angel equal to

that of the laser, we would find the answer to be 320 photons/s:

s/photons320sr

7

222

sr10210

sr2

sr102)s/photons10(

69

69

The comparison between 1016 photons/s for the laser

source and 320 photons/s for the thermal source is now

even more dramatic.