A Glimpse in Science

By Prof. (Dr.) Rajmani Pd. Sinha (rtd.) and Prof. (Dr.) Bijoyendra Narayan (rtd.)

Articles presented here are mostly in the field of laser, plasma and spectroscopy which happens to be our field of research and teaching. The purpose of these articles is to popularize the new emerging fields of Science. All these fields are somehow or other related with one another. Spectroscopic devices are invariably used in  generation and application of laser and plasma.Recently laser has been used for fusion reaction leading to the production of plasma resulting first time output energy more than the input one where spectroscopic devices are used to measure such a high temperature.

• Language: English
• Publisher: Authors Click Publishing
• Release date: May 13, 2024
• ISBN: 9788119368440

Book preview

CHAPTER-1

Introduction to Laser

1. Laser — A radiation and a technology

Laser is an extension of optics i.e. science of light.

A year wise account of development in this field —

1666:  Newton

Newton for the first time in 1666 observed solar spectrum with the help of a prism. This was the beginning of a new science, and thus laid the foundation of spectroscopy. He further studied the nature of light with the conclusion that light consists of light particles known as corpuscles.

1676: Huygen

Huygen in 1676 gave a new theory of light known as wave theory of light. He stated that light is a wave.

1801: Young

Obviously, a new debate came to the fore as to the characteristics of light. Whether it was a wave or particles arrested the attention of the scientists. It was Young who resolved in 1801 the uncertainty between the wave and the particle theory with the introduction of Double Slit Experiment, known as Young double slit experiment. With this experiment he was able to show the production of interference pattern using two coherent light sources that proved that light is a wave.

1913: Neil Bhor

The great scientist, Neil Bhor, added in 1913 a new leaf to the world of light by introducing the concept of (spontaneous emission). He worked on the origin of light. 1n 1913 he introduced the concept of quantized orbit and quantum emission. He stated that light emission passes through three stages—

(i) absorption of energy by an atom

(ii) electron moving from a lower orbit to a higher one in an atom

(iii) release of energy in the form of photon in course of the

electron coming to a lower orbit from a higher one.

Fig.1: A schematic diagram of spontaneous emission of light

In this type of photon emission all probable directions of emission are possible, and one does not know in advance the possible direction of emission. This type of emission (Fig.1) is known as spontaneous or random emission. Light from all natural sources — the Sun, or stars, and artificial sources such as fire and lamps—are in the class of spontaneous emission.

1917: Einstein

1n 1917 the great scientist Einstein came forward with a new concept of stimulated emission. For this to occur there has to be collision of the excited atom with a proper photon emitted by the atom itself. The striking photon decides the direction, phase, and polarization of the emitted photon, which is, one can say, just a clone of the striking photon. The following figure (Fig. 2) schematically demonstrates the process of stimulated emission.

A further insight into the concept of having a clone in the field of light can be understood better by seeking an analogy from the science of Biology. The cloning concept came into being in 1952 in the area of biological science, and it got materialized in 1997 by giving an artificial birth to a lamb named Dolly. Similarly, an analogous concept developed in the field of physics that was termed stimulated emission. It was realized in 1954 by having MASER and later in 1960 by having LASER. ‘Photoelectric effect’ and ‘Stimulated emission’ were the two important research papers that Einstein got published in 1905 and 1917 respectively. The former paper fetched him a Nobel Prize. The latter one showed us the way to laser production.

Laser is a man-made device, and to realize it in practice a proper technology is required. One must keep in mind that laser is a radiation as well as a technology. To put on a more stronger footing one can say that laser is an ordered emission that resembles, one may say, a march of army in which their movements are in phase. This phase characteristic eludes the spontaneous emission, and a crowd movement after the (cinema) show break, where the movements are in all directions, can illustrate what one finds in this type of emission. Laser is an acronym for Light Amplification by Stimulated Emission of Radiation. To note, the first two words in ‘Light amplification by stimulated emission of radiation represent the product while the last three words in it represent the process.

Fig. 3: Production of stimulated emission &photon amplification

Similarly, MASER is another important achievement preceding the birth of laser, which reads in full as ‘Microwave Amplification by stimulated Emission of Radiation’.

2. Einstein A & B Coefficients:

Coefficients A & B are related with spontaneous and stimulated emissions respectively that were developed by Einstein in1917.To explain them we consider the two states of an atom with energy levels Em, En as is shown in Fig. 4.

Fig. 4: Two states, m and n, of an atom

Let us assume that at a time, the number of atoms in the state, n is Nn and in the state m is Nm. Let the photon density be , where ν is given by

―— (1)

It must be noted that emission, or absorption in the presence of a proper photon is known as stimulated emission, or stimulated absorption. To emphasize, there are two processes through which atoms may emit radiation— the spontaneous and the stimulated, but only the absorption is called the stimulated as it takes place in the presence of photons.

In order to calculate the number of atoms going up from the statem ton per second, and also the number of atoms going down from the state n to mper second we make the following assumptions —

is the coefficient of the stimulated absorption per atom per photon per second; is the coefficient of the stimulated emission per atom per photon per second; is the coefficient of spontaneous emission per atom per second. So the number of atoms going from statem to n per second is:

—(2 )

Similaly, the number of atoms coming down per second to the level m from n is:

―(3)

It is further added that in the steady state situation of the absorption/emission process the number of atoms going up is equal to those going down.

Hence,

— (4 )

Since the same atoms are involved in absorption and emission the respective probabilities do not change during both the processes, one can take, .Taking into account this particul are quality one finds that

— (5)

Now, as per the Boltzmann distribution law—

and , where Nois the total number of atoms

Now, we have

= —  (6)

Hence equn.(5) becomes

[Since

(7)

Two cases of interest:

Case 1 ― Microwave region:

In this region,

It means,

It is concluded that the stimulated emission dominates over the spontaneous emission in the microwave region.

Case 2 :— Visible region :

For this region, =6000

From,

one gets,

It means ― (9)

In other words the spontaneous emission dominates over the stimulated emission in the visible region. If the Boltzmann law of distribution of molecules holds it is not possible to achieve the domination of the latter over the former in the visible region.

3. Population inversion:

Fig.5: Two energy levels of an atom

As per the Boltzmann law of distribution of molecules (ref. to Fig. 5) the number of atoms, Nn in the upper energy state En is less than the number Nm in the lower state with energy Em. But for the population inversion to materialize one must have the condition, Nn >Nm.

4. Maser:

To move on the path of deeper insight in the field we revisit the historical experiment for the production of Maser. Undoubtedly, it was to the credit of Townes and his co-workers that Maser was made in 1954 using Ammonium gas (NH3). The molecule NH3 has a tetrahedral structure with N at its two positions— the top & the down. But the two positions are not exactly similar, and the respective vibrational energies differ slightly. To be specific the ground vibrational energies differ by 0.8 cm-1i.e.

Fig.6: Tetrahedral structure of NH3molecule

Fig. 6 (a): Two states of a NH3 molecule and their vibration energy levels

Fig. 6(b): A quadrupole is formed with two dipoles

NH3 and N’H3 have different electrical properties. The point of difference arises due to their quadrupole moment. But what is a quadrupole moment? Two dipoles form a quadrupole and a dipole is formed when two equal and opposite charges are quite close.

5. Experimental arrangement:

For an experimental arrangement to have Maser, the two provisions must be made: one for the isolation of NH3 molecules having slightly higher ground vibrational energy level and the other, for managing the interaction of those molecules with a weak signal of a microwave having wavelength 1.25 cm.

Fig.7: Experimental arrangement for production of Maser

Refer to Fig. 7andfind that A is a NH3-gas container out of which a pencil of gas ray comes out through an outlet ‘O’. Further find that B and C are the two slits which are employed to ensure a fine stream of flow of NH3 molecules that enters a nonuniform electric field set-up after emerging from the slit C. NH3 molecules with two vibrational states separate due to the non uniform electric field ‘D’ set up there. Management of the experimental situation is such that NH3 molecules with slightly higher ground state vibrational energy enter through ‘E’ and move to the cavity resonator and others with lower ground state vibrational energy get deflected. The weak signal, =1.25 cm enters into the waveguide from the wing, F of the waveguide (see Fig, 7). After a violent interaction with NH3 molecules it comes out as a strong microwave signal ( =1.25 cm) from the wing G of the waveguide.

The emitted wave from the NH3 molecules move in the direction of propagation of the weak wave. To mark, it was for the first time that amplification of a wave through stimulated emission was demonstrated. Undoubtedly, it was a success achieved after many failures. On the other hand it was a big-ticket project of £ 30000. Even if Townes ’endeavor was visited by the success, the opposition camp of scientists was quick to describe Maser in his self –styled acronym, though interesting, of ‘Means of Acquiring Support for Expensive Research’. Despite being a costly business the experiment finally verified the theoretical concept of Einstein about the stimulated emission.

6. Ruby Laser:

It was Maiman Group who had obtained Laser in 1960 using Cromium doped Ruby crystals.

(i) Energy level diagram of Cr+++ ion is given below:

Fig.8: Energy level diagram of Cr+++ ion

(ii) Negative temperature:

To effect population in version i.e. N1> N0 between the energy levels E0and E1it requires a proper pumping arrangement

Now where E=E1 - E0

.........................( 10 )

i.e. provided is positive.

But this is possible only for

.........................................( 11 )

i.e. population in version means nothing but a negative temperature.

( iii ) No independent existence of Cr +++ ion in the atmosphere:

Cr+++ ion cannot exist freely in the atmosphere. This is why it is embedded in the Ruby crystal lattice (Al2 O3) by replacing some of its Al+++ ions through the doping technique. As we know Ruby is pink in colorist turns deep red after having been doped with Cr2O3 in a proportion of 0.05%. It amounts to replacement of 5 Al+++ by Cr+++for every 10000 Al+++ . Ions store energy for a time interval of 10-3 sec in the energy level, E1.

(iv) Heisenberg’s uncertainty principle:

It is expressed in the energy and the time co-ordinates in the following form:

—(12)

or,

— (13)

i.e.

— (14)

and

—(15)

For ie —(16)

Fig. 9: Atomic or molecular transitions

Thus the energy levels, , are very narrow, and so any transition between them produces quite a narrow or, if alternatively called, a monochromatic transition as shown in(b)of Fig. 9. Fig.9 (a) shows the normal broad transition.

(v) Cavity resonator:

Fig: 10: Multiplication of photons due to Cavity or Fabri-Perot Resonator

A cavity resonator is the hub of the photon management scheme where the stimulated emission is monitored with a window—a mirror of required reflectivity and transmittivity—such that radiation comes out from the enclosure (Fig. 10).

Construction:

The two mirrors ML and MR are placed parallel to each other, also normal to the axis of the cylindrical Ruby rod. MLis a 100 % reflecting mirror whereas MR is only 50 % reflecting and 50 % transmitting too. This characteristic of the mirrors works for the amplification of photons, and what we obtain is a stimulated emission that comes out of the enclosure through the window, MR

(b) Action:

Suppose that a photon produced due to the spontaneous emission moves along the axis of the resonator towards the mirror ML; it strikes the mirror, and is normal to the plane of the mirror. Since this mirror is 100 % reflecting the photon that strikes bounces back exactly in the opposite direction. If the photon happens to strike an excited atom on its bounce back journey through the active medium the stimulated emission results due to the very fact that the new photon obtained is found to be exactly similar— similarity is in terms of phase, polarization, direction, and frequency to the striking photon. What we have now is a pair of photons propagating along the axis of the resonator towards the mirror MR. Since this mirror is 50% reflecting and 50% transmitting only one (2⁰) photon out of the two comes out through it(mirror), and the remaining trapped photon further contributes to the ongoing process of the stimulated emission. Next time the reflected photons reaching at the mirror, MR are four in number due to the stimulated emission having taken place in course of propagation of the two photons, in the active medium, and their 100% reflection from the mirror ML. To mark, with two photons remaining in the resonator after their first encounter with MR the two pairs of photons, are actually obtained due to the stimulated emission. Here, the assumption is that each photon strikes at least the one excited atom, and there is no loss of any photon during its passage through the active medium. The process, of photons’ striking the excited atoms, followed by the consequent increase in the number of photons, and again the photons getting reflected, continues. While the process is on, the number of photons coming out of the mirror, MR, second time is 2 i.e. 2¹ (ref. to Fig. 10). Finally, one finds that the number of photons coming out of the mirror, MR grows in a particular order i.e.

From the growing number of photons in the series it appears that photons are found to have been produced due to the stimulated emission in the 70th oscillation of photons. It must be noted that the growth in number of photons is fast if a photon strikes more than one excited atoms during its passage through the axis of the Ruby rod, and all photons coming out in a bunch are along the axis. Of course, photons that come out through the mirror, MR, are in phase. Photons coming out from the axis of the Cr-rod, and not parallel to the axis, get lost after reflection from mirrors.

(vi)Calculation for time taken for the completion of 70 oscillations for a 50 cm long system:

Time = ( )/1.7where 1.7 is the refractive index of Ruby.

[the distance covered by the photon in one oscillationis1m (50 cmx2 =1m)]

=3.961 x which is10-4 secless than the lifetime of the excited molecule in level, E1 i.e. the large photon amplification takes place within a fraction of lifetime of E1 energy level of Cr+++ ion.

Energy of the pulsed beam:

E=

[ Photons ≈ photons]

[ the wavelength of Ruby laser is 6943 Å ]

.............................................( 17 )

Energy of the laser beam in a real Ruby laser system is 100 Joules per pulse.

(vii)Actual Ruby laser:

Fig. 11: Actual Ruby Laser

In an actual Ruby laser system mirrors are developed at the two ends of the Ruby rod applying the thin film deposition technique using silver material. Secondly, Laser Pumping is done using a xenon flash lamp, which is made in a helical form. The Ruby rod is placed inside the xenon flash lamp as shown inFig.11. The Xenon lamp produces a flash of light through the technique of condenser charging and discharging, which lies in the blue –green region of the spectrum. It normally produces 10 pulses per second. Each pulse of light is laser of 100 Joules. Thus energy per second of 10 pulses per second is 1000Joules.It means the power of this laser system is 1kwatt (1000Joules/s) . Also, the laser pulse life is of second. So, a simple calculation gives the power of a pulse equal to , which can be obtained by dividing 100Joules by second.

(a) Dimension of a Ruby laser system:

Length of the Ruby rod — 5 cm to 50 cm

Diameter of the rod — 2mm to 50 mm

Laser beam cross-section—2mm²

The laser is operated in the pulse mode using flash pumping scheme keeping in view the heat dissipation in the system. But it can also be produced in the continuous mode using arc-flash pumping scheme.

(b)It is a three energy level scheme such as Fig. 8:

E3, E1, E0 and E2, E1, E0

(c) The power of the laser system is not very large as the ground energy level, E0, does not allow a large population inversion.

(d) The power of a pulse can be increased using a rotating mirror scheme. In fact this scheme reduces the lasing time from to , and also the energy of a pulse from 100 Joules to 10 Joules. It means the power of a pulse is 10⁹ watt that one obtains by the division of 10 Joules by 10-8 sec.

(vii) Intensity of laser radiation:

A comparison of laser intensity with the intensity of solar radiation

If we take the intensity of solar radiation to be1000 watt/m²

Actual solar radiation intensity above the atmosphere, known as solar radiation constant is 1370 watt/m² .It comes equal to 1000watt/10⁶mm²

=1x10⁶mwatt/10⁶ mm²=1mwatt/mm²

If the cross-sectional area of 1mw laser beam is 1mm².then the solar radiation intensity is equal to the intensity of1mw laser beam. Light intensity becomes dangerous for our eyes if its intensity is above 10

=

Thus, both 1mw laser having intensity equal to 0.05Mw² , where beam cross-sectional area is 2mm² ,and solar radiation( equal to 1 m Watt/mm²) are equally dangerous for our eyes. As the laser power increases, the danger for our eyes increases.

Let us see it from another angle

Let us compare 1mw laser intensity with the intensity of 3 watt LED light source when kept at a distance of 0.1meter.

1mw laser=0.001watt

Spot size =1mm=(0.0005m) radius

Intensity

Now the intensity of 3w LED at a distance of 0.1m

It means has its intensity higher by about 40 times.

(viii) Coherency of a laser beam:

In order to consider coherency of a laser beam we describe the two famous experiments —

one is the Young double slit experiment and the other, the Michelson interferometer experiment.

(a)Young’s double slit experiment:

This famous experiment demonstrates the wave nature of light, which was originally conceptualized by Huygen in 1676.

Fig. 12: Young double slit experiment

The slit, S, allows monochromatic light to fall on the other two slits, S1& S2 . Positions of slits are such that SS1 =SS2 due to which they act like the coherent light sources. One observes on the screen an interference fringe pattern that consists of equally spaced dark and bright fringes. Let ‘O’ be the middle point between S1& S2, and P beany point on the screen in the region of shadow. Also, let

S1P=d1

OP = d0

S2P =d2

S1O=S2O= d

S1Mis the normal drawn from S1 on to OP, and ON the normal drawn from O on to S2P.

Thus,

OM = dcosθ =d0—d1 ................ (a)

S2N=d cosθ =d2—d0 ......... ( b)

Adding ( a ) & (b) one gets the optical path difference, , equal to 2d cosθ, which is (d2— d1) from the diagram . In other words the optical path difference is the difference of path lengths of light reaching at P from the secondary sources of light, S1& S2.

For the constructive interference the condition, = 2n holds.

For the destructive interference the condition, =(2n+1) holds,

Where n=0, 1, 2.3...........

Apart from meeting the conditions for the interference pattern to take place one has to ensure that ‘S’ is a narrow slit. If the slit, S, is enlarged a general illuminations found within the shadow region. The reason is that the larger Sis equivalent to a number of narrow slits, each producing its own interference pattern. But if S is a laser source, the requisite limitation of the slit for the formation of the interference pattern has no meaning, and the entire (laser) beam cross-section, or its extended form, may be used for producing the interference pattern. Suppose an office pin is placed in the laser path, then there appears an interference pattern on the screen in the shadow region. Thus, it is easier to produce interference with a laser source. This is known as the spatial coherence of a laser beam.

(b) Michelson interferometer (1889):

In Young double slit experiment one observes different fringes by shifting one’s eye position. In case one wishes to fix the eyes and yet have the delight of observing different fringes the only option to realize it practically is through Michelson approach. Refer to Fig.12(a). G1& G2 are two glass plates made out of the same (glass) plate. The back-silvered surface of the glass plate, G1 acts as a beam splitter, splitting beam in a ratio of 50:50. The