Laser & HolographyUnit-IV (B.Tech-II sem)

Dr. Vishal JainAssistant ProfessorDepartment of Physics

Introduction

LASER Light Amplification by Stimulated Emission of Radiation

A laser is a device that produce an intense, concentrated and highly parallel beam of coherent light. The first successful built by Townes and his associates at Colombia University between 1951 to 1954.

Or

A laser is a device that emits coherent light beam through a process of optical amplification based on the stimulated emission of electromagnetic radiation.

Red (660 & 635 nm), green (532 & 520 nm) and blue-violet (445 & 405 nm) lasers

He-Ne Laser

Properties of Laser• Monochromatic:- Concentrate in a narrow range of

wavelengths (one specific colour). • Coherent: - All the emitted photons bear a constant phase

relationship with each other in both time and phase • Directional:- A very tight beam which is very strong and

concentrated.

Early History of Laser• 1917 Einstein’s paper on Quantum Theory of Radiation• 1954-58 basic idea’s about laser by Townes and associates.• 1960 laser coined by Gould • 1960 first ruby laser by Maiman

Basic concepts for a laser(1) Absorption (2) Spontaneous Emission (3) Stimulated Emission (4) Population

inversion

Atom is initially in state 1, it will be raised to state 2 by absorbing a photon of light whose frequency is hν =E2-E1 . This process is called Absorption. (as shown in first figure)

The probability of such a transition depends on the energy density of incident photo

P12 = B12 u(ν) --------------------Eq 1

where P12 is the probability of absorption , u(ν) is the spectral energy density and B12 is the Einstein Constant.

The rate of absorption will be given by

R12 = N1 B12 u(ν) ----------------Eq 2

where N1 is the number of atoms in lower energy level

Atom present in Higher Energy level E2 has a small life time (10-8 sec) so it can be spontaneously jump from state E2 to state E1 by emitting a photon as shown in figure two. This process is called Spontaneous Emission.

It is independent of the presence of any photon present in the system. Therefore any of electron can jump to lower state randomly and the photon emitted are never be in phase. So spontaneous emission provides incoherent photons. Thus the probabilty here (P21)s is always constant

(P21 )s = A21 --------------------Eq 3

Where (P21 )s is the probability of Spontaneous emission , u(ν) is the spectral energy density and A21 is the Einstein Constant.

The rate of Spontaneous emission will be given by

(R21 )s = N2 A21 ------------------Eq 4

where N2 is the number of atoms in excited state.

Einstein proposed that of a photon of appropriate frequency is present, it is not essential that it may always be absorbed. It can also interact with Atom present in Higher Energy level E2 and induce that atom to emit a new photon. Such a process is known as Induced or Stimulated Emission.

This type of emission is in phase, directional and energy of the emitted photo is same as that of incident photon. It means both the photons are coherent with each other. This type of emission is preferred to get a highly coherent laser light. The probability of induced emission will be given as

(P21 )i = B21 u(ν)--------------------Eq 5

Where (P21 )i is the probability of Stimulated emission , u(ν) is the spectral energy density and B21 is the Einstein Constant.

The rate of Stimulated emission will be given by

(R21 )i = N2 B21 u(ν) --------------Eq 6

where N2 is the number of atoms in excited state.

Relation between Einstein Co-efficient A and B for Spontaneous and Stimulated emission

The total rate of emission from state 2 to state 1 is given by adding eq 4 and eq 6 we get

)]([ 2121221 uBANR ------Eq 7

In thermal equilibrium, the rate of emission must be equal to the rate of absorption

)]([)( 21212121

2112

uBANuBNRR

Solving for u(ν) we will get

][)(

)()(

212121

212

212212121

BNBNANu

ANuBNuBN

Dividing up and down right hand side by N2/B21, we get

------Eq 81

)(

21

12

2

1

21

21

BB

NN

BA

u

Now applying Maxwell’s Boltzmann Distribution Law in thermal equilibrium.

,/

2

1

/

21 kThvEE

kTE

eeNNso

eN

1)(

21

12/

21

21

BBe

BA

ukThv

The above expression of spectral energy density can be compared with planck’s radiation law, accordingly

,1

/8)( /

33

kThve

chu 3

3

21

21 8ch

BA

When B21 = B12 ------Eq 8

Let us now compare the probability of spontaneous emission to that of stimulated emission

)1()()(

)( /

21

21

21

21 kThvevuB

AiPsP

------Eq 9

Now applying two conditions(i) If hv >>kT, (P21)s>>(P21)I, then spontaneous emission will be much more probable than

induced emission. This is ordinarily true for electronic transitions in atoms and molecules and in radiative transition in nuclei.

(ii) If hv <<kT, (P21)s<<(P21)I, then the stimulated emissions no more negligible and it even predominant over spontaneous emission (Whatch This Link Video)

https://www.youtube.com/watch?v=1LmcUaWuYaohttps://www.youtube.com/watch?v=-YPixpL6Rnc

Threshold Condition for Laser Action For laser action, two conditions (Threshold Conditions) should be satisfied

(i) The probability of spontaneous emission which produced incoherent radiations should be much smaller than the probability of stimulated radiations i.e. A21 << B21u(v).

(ii) The emission rate should be larger than the absorption rate. R12 << (R21)s+ (R21)i. This condition can be achieved by following steps.1. The Situation in which the number of atoms in the higher energy state exceeds with

that in the lower energy state is known as population inversion.2. The method adopted to achieve population inversion is called pumping. There are

several methods of pumping such as (A) Optical Pumping, (B) Electron Impact (C)In elastic atom-atom collision (D)

Chemical Pumping (E) Gas Dynamic Pumping.

E2

E1Ordinary Condition N1>N2 Population Inversion N2>N1

The higher probability of stimulated emission is achieved by the following methods

(1) The spectral energy density of incident radiation must be made very large, means u(ν) must be largeTo increase u(ν), the emitted radiations are reflected coherently again & again between two parallel mirrors facing each other in a cavity containing active medium.

(2) The life time of excitation τc must be very large To minimize the value of τc metastable state of higher energy is chosen for stimulated transition of because transition from metastable state spontaneous emission are not allowed but life time τc is very large

Metastable states :- There are some energy states whose life times are much longer (10 -3 sec) than the life of usual excited states (10-8 sec). Such relatively long lived states are called metastable states.

Einstein coefficient of spontaneous emission is given by A21=1/ τc For metastable states the value of τc is very large so A21 is comparatively very small. So spontaneous emission from metastable states are forbidden. Hence an atom from metastable state can jump to ground state through by stimulated emission. That’s why in laser, transition from metastable states are chosen for laser action.

Main Component of a LASERA LASER requires three main components for operation

•It is a material which achieves the condition of population inversion & through stimulated emission produces LASERs. The active medium may be solid, liquid and gas.

Active Medium

•It is energy source which is used to raise the system to an excited states to achieve population inversion in active mediumPumping

Source•It consist of two mirror facing each other. The active medium is enclosed

by this cavity. One of the mirror is fully reflecting and another is partially transparent. Optical resonator cavity

Optical Resonator or cavity

Amplifying Medium

Fully Reflected Mirror

Pumping Source Partially Transmitted Mirror

Laser Beam

He-Ne Laser Ali Javan, Bennett and Harriott in1961

A Helium Neon LASER, usually called He-Ne laser is a small gas laser generally used in laboratory to demonstrate optics experiments. Its usual operation wavelength is 632.8nm, in the red portion of visible spectrum.Construction:-He-Ne laser consists of a narrow discharge tube of length 10 to 100cm with a diameter of order of 5mm to 10mm. The tube is filled with a mixture of helium and neon gases approximately in the ratio of 85% helium and 15% Ne contained at low pressure upto 2-3 torr. The positive high voltage connected to the anode and cathode which provide electrical discharge around 1000Volt. The LASER tube enclosed in between two mirrors, one will totally reflecting mirror and second is partially reflecting mirror mounted at the output end. Inside the tube LASER also has Brewster’s window to produced linearly polarized light.

Working:-

Metastable states

Helium Atom Neon AtomGround State Ground State

Laser Transition6328 Å..

Spontaneous Emission

Radiation less Transition [by collisions from walls]

Inelastic Collision 20.66eV

18.70eV

20.61eV

HeE1

HeE2

HeE3

Ener

gy

19.81eV

Fast Radioactive Transition [spontaneous emission]

6000 Å..

NeE1

NeE2

NeE3

NeE4

NeE5

NeE6

33900 Ang.

11500 Å.

When the voltage is applied, an electric discharge causes the ionization some of the atoms in the mixture of He-Ne gases. The electron and ion so created are accelerated towards anode and cathode respectively. Due to lighter mass of He-atoms, electrons to strike the Helium atoms and raise them to the excited state E2 and E3 He which lies at 19.81 eV and 20.61eV respectively above the ground as shown fig. The energy states are metastable states so transition from these states to ground states by spontaneous emission are forbidden. The energy excited to He atom to E2 and E3 is almost exactly same as the energy needed to excite Ne atom in to E4 and E6 energy state. Once the He population is successfully inverted, excite He atom strikes to Ne atoms and transfer their energy to the Neon atom. This process is given by the reaction

EHeNeNeHe **

Where * represent an excited state and ΔE is the small energy difference between the energy states of two atoms of the order of 0.05eV. This additional 0.05 eV provided by kinetic energy of He atom. Thus the role of He atom in the LASER is to provide the pumping medium to neon atom to attain the necessary population inversion

Since E6 and E4 excited state of Ne atom is more stable than other states. The transition from E6 to E5 and E4 to E3 emission the radiation having wavelength of 33900Å and 11500Å, but these transition falls in infrared region, However the transition from E6 to E3 generate a laser beam of red colour of wavelength 6328Å in the visible range. At last Ne aton comes to ground states though the collision with walls of tube from E2 states.

Brewster window in a LASER cavity:- Brewster windows are used in laser cavities to ensure that the laser light after bouncing back between cavity mirrors emerged as linearly polarized light.

Advantage:-

(i) It is most common and inexpensive gas laser

(ii) Typical He-Ne laser can generate a few mill watts of output power ranging fro 1W to

100mW in continuous wave operation.

(iii) Beam quality is usually excellent. It is often used for alignment purpose.

Semiconductor Diode LaserHall and Its Co-Workers in 1962

• A semiconductor diode laser is a specially fabricated p-n-junction device that emits coherent light when it is forwarded biased.

Construction:- A schematic diagram of the simplest type of GaAs LASER in shown in figure. It is a solid state device that consists of two outer semiconductor layers separated by a middle layer and generated LASER radiation, when charge carriers of opposite polarity, one to each from the top and bottom layers meets in the middle layer. Such LASER consists of two basic components and optical amplifier and a resonator. Excitation is provided by current flow through the device as the top and bottom layers are metalized and metal contact are provided

Principle of operation (Working)

The radioactive recombination of electron-hole pairs can be used for the generation of electromagnetic radiation by the electric current in a p-n junction. This effect is called electroluminescence.

When a diode is forward biasd, holes from p-junctions are injected into the n-region, and the electron from the n-region are injected into the p-region. As electrons and holes are present in same region, they may radioactively recombine and emits a photon with the energy of bandgap. This is called spontaneous emission. If before the spontaneous recombination a photo will interact with them, than stimulated emission will be happened and as a result we obtained a photon with same frequency, same direction same as the incident photon.

As the mirror are provided for total and partial reflection to obtained a coherent electromagnetic radiation with all photon in same phase with each other.

Advantage:- (i) Small size and weight, low current voltage and power required(ii) Low intensity.(iii) Wide angle beam

Application of LASER

a) Holography: Holography is a technique to record the complete picture of an object, that is it will produce the three dimensional picture. The process of holography will be discussed in detail later on.

b) Measurement of long distance: The beam spreading in the laser light is very small, laser can travel along distances, without appreciable spreading. The time taken by laser pulse to  travel from laser source to a given target and back is measured. As the velocity of light is known, the distance of the target can be calculated using the relation 2d =  c x  t where d is the distance of the target and c is the velocity of light.

c) Applications in scientific research: Due to the coherent nature of laser light, many new optical phenomenon have been observed using laser. Using laser light we investigate the basic  laws of interaction of atoms and molecules with electromagnetic waves.

d) Application in communication:  In the fibre communication system, laser beam is used. The rate at which information is transmitted is proportional to the band width of the information carrier signal.The bandwidth is proportional to the frequency of the carrier. Since the frequency range of laser signal is quite high compared to the microwaves, large bandwidth can be obtained using  optical region as compared to the microwave region.

e) Applications in Industry: Due to the high intensity of  laser beam, laser can be used in welding, cutting and in producing very high temperatures. The other advantage of laser is that the beam can be focused onto a fine spot. The small spot size implies that high energy densities are possible. Lasers are also found suitable for machining and  drilling holes.

f) Lasers in Isotope separation: The light emerging from a laser is extremely monochromatic. When laser light falls on a mixture of two isotopes, the laser light  excites the atoms of only one of the isotopes thus separating it from the other  isotope.In addition to the high monochromaticity, the high intensity of the laser is also responsible for  its application for  isotope  separation because with low intensity beams the separation rate would be too low for practical  use.

g) Applications in Medicine:i) Laser Surgery: The focused laser beam is capable of bloodless surgery, since the beam not only cuts but also welds blood vessels being cut. Laser surgery is painless because operations are very fast and there is not enough time for the patient to respond to the incision and sense pain.

ii) Laser Therapy:  He-Ne laser has produced curing effect on trophic ulcers, poorly healing wounds, and bone fractures. Laser can also be guided through optical fiber into blood  vessels to remove the  clothings, in case of  heart patients, through heating. It has also found application in treating the  decaying teeth. Laser  can replace dental drills.

HolographyHolography is a technique that allows the light scattered from an object to be recorded and later reconstructed so that it appears as if the object is in the same position relative to the recording medium as it was when recorded. The image changes as the position and orientation of the viewing system changes in exactly the same way as if the object was still present, thus making the recorded image (hologram) appear three dimensional. Holograms can also be made using other types of waves.The technique of holography can also be used to optically store, retrieve, and process information. While holography is commonly used to display static 3-D pictures, it is not yet possible to generate arbitrary scenes by a holographic volumetric display.

History of Holography

Holography was invented in 1947 by Hungarian physicist Dennis Gabor (1900–1979), work for which he received the Nobel Prize in Physics in 1971.

Gabor's research focused on electron optics, which led him to the invention of holography. The basic idea was that for perfect optical imaging, the total of all the information has to be used; not only the amplitude, as in usual optical imaging, but also the phase. In this manner a complete holo-spatial picture can be obtained.

"Train and Bird" is the first hologram ever made with a laser using the off-axis technique. This pioneer image was produced in 1964 by Emmett Leith and Juris Upatnieks at the University of Michigan only four years after the invention of the laser

In 1983 MasterCard International, Inc. became the first to use hologram technology in bank card security.

Dr. Stephen A. Benton, Massachusetts Institute of Technology, seen through "Crystal Beginning," a white light transmission hologram produced at the Polaroid Corporation in 1977.(Photo by Michael Lutch for WGBH, Boston)

Two photographs of a single hologram taken from different viewpoints

Difference between Holography and Photography

1. In photography, only intensity is recorded  so photography produces two dimensional picture of the  object whereas in holography, both intensity as well as phase of light wave is recorded, thus holography gives three dimensional picture of the object.

2. Negative is prepared first in photography whereas in holography no negative is required. The hologram is negative and image  it gives is positive.

3. A holographic recording requires a second light beam (the reference beam) to be directed onto the recording medium.

4. If  the  hologram  is  broken  into parts, each part is capable of reconstructing the  entire object. But in photography the destruction of even very small portion of negative or photography results in a irrepareable loss of information.

5. Holography has high information capacity as compared to photography6. A photograph can be viewed in a wide range of lighting conditions, whereas

holograms can only be viewed with very specific forms of illumination.

Construction of a Hologram

https://www.youtube.com/watch?v=lJVhWwINovY

Construction of a Hologram

Recording  of hologram. The recording of hologram  is based on the  phenomenon of interference.  It requires a laser source, a plane  mirror or beam splitter, an object and a photographic plate. A laser beam from the laser source is incident on a plane mirror or beam splitter. As the name suggests, the function of the beam splitter is to split the laser beam. One part of splitted beam, after reflection from the beam splitter, strikes on the photographic plate. This  beam is called reference beam. While other part of splitted beam  (transmitted from beam splitter) strikes on the photographic plate after suffering reflection from the various points of object. This beam is  called object beam.The object beam reflected from the object interferes with the reference beam when both the beams reach the photographic plate. The superposition of these two beams produces an interference pattern (in the form of dark and bright fringes) and  this pattern is recorded on the photographic plate. The photographic plate with recorded interference pattern is called hologram. Photographic plate is also known as Gabor zone plate in honour of Denis Gabor who developed the phenomenon of holography.Each and every part of the hologram receives light from various points of the object. Thus, even if hologram is broken into parts, each part is capable of reconstructing the whole object

2. Reconstruction of image.. In the reconstruction process, the hologram is illuminated by laser beam and this beam is called reconstruction beam. This beam is identical to reference beam used in construction of hologram. The hologram acts a diffraction grating. This  reconstruction beam  will undergo phenomenon of diffraction during passage through the hologram. The reconstruction beam after passing through the  hologram produces a real as well as virtual image of the object. One of the diffracted beams emerging from the hologram appears to diverge from an apparent object when project back. Thus, virtual  image is formed behind the hologram at the original site of the object and real image in front of the hologram. Thus an  observer sees light waves diverging from the virtual image and the image is identical to the  object. If the observer moves round the virtual image then other sides of the object which were not noticed earlier would be observed. Therefore, the virtual image exhibits all the true three  dimensional characteristics. The real image  can be recorded on a photographic plate.

Holographic Microscopy

Digital Holographic Microscopy (DHM) is digital holography applied to microscopy. Digital holographic microscopy distinguishes itself from other microscopy methods by not recording the projected image of the object. Instead, the light wave front information originating from the object is digitally recorded as a hologram

To create the necessary interference pattern, i.e., the hologram, the illumination needs to be a coherent (monochromatic) light source, a laser for example. As can be seen in Figure 2, the laser light is split into an object beam and a reference beam. The expanded object beam illuminates the sample to create the object wave front. After the object wave front is collected by a microscope objective, the object and reference wave fronts are joined by a beam splitter to interfere and create the hologram. Using the digitally recorded hologram, a computer acts as a digital lens and calculates a viewable image of the object wave front by using a numerical reconstruction algorithm.

Commonly, a microscope objective is used to collect the object wave front. However, as the microscope objective is only used to collect light and not to form an image, it may be replaced by a simple lens. If a slightly lower optical resolution is acceptable, the microscope objective may be entirely removed.

Previous RTU 2014, 2015 Questions

Thank You