LASER THE PRODIGAL CHILD

LASER -THE PRODIGAL CHILD OF QUANTUM PHYSICS WHICH CHANGED OUR LIFE STYLE

It was on October 19th, 1900 when the German theoretical physicist Max Planck announced before the Berlin Physical society that light can travel in the form of energy particle or quanta. This announcement shook the very foundation of Physics. But 3rd March 1917 Albert Einstein published a treaties “On the Quantum Theory of Radiation”. In this influential work Einstein postulated that under certain conditions discrete packets of energy called “PHOTONS” could be emitted and absorbed by atoms. Einstein proposed that in isolation an excited atom ca return to a lower energy state by emitting photons, a process he named as “SPONTANOUS EMISSION”. To understand this, I shall give you two examples. Tomato fruits and green leaves.

Many properties of matter and phenomena in nature are directly related to atomic energy levels and their associated excitations and deexcitations. The colour of a material is due to the ability of its atoms to absorb certain wavelengths, while reflecting or reemitting others. For example a tomato fruit absorbs all visible wavelengths except RED, because the atoms of its hydrocarbon pigment LYCOPENE have levels separated by a variety of energies corresponding to all visible photon energies except red. Similar is the case of CHLOROPHYLL pigment in green leaves of plants. Atoms will only absorb photon of correct wavelength. When such a photon enters the atom, the photon is absorbed and the atom goes to a higher state which then allows for SPONTANEOS EMISSION.

Einstein extended his theory and postulated that photons prefer to travel together in the same state. If there is a large collection of atoms containing excess energy, they will be ready to emit a photon randomly. If a stray photon of correct wavelength passes by, its presence will stimulate the atoms to release their photons and the released photons will travel in the same direction with identical frequency and phase as the original stray photon. A cascading effect ensues as a multitude of identical photons move through the remaining atoms, emitting more photons to join them.

This inspirational piece of physics formed the CORNERSTONE for the development of the theory of stimulated emission of radiation which was expanded further by many scientists prominent among them was Gordon Gould of Colombia University who is widely recognized as the inventor of LASER.

LASER is an acronym of the phrase Light Amplification by Stimulated Emission of Radiation coined by Gordon Gould of Colombia University. He is also responsible for developing the optical resonator in the form of mirrors at ends of the lasing tube.

Theodore Harold Maiman used a synthetic pink ruby crystal as the lasing medium with a helical xenon flash lamp as exciting source.

On 16th May 1960 Maiman successfully fired the device and worlds’ first laser was born.

This is a basic ruby laser consists of a rod made of ruby crystals with a mirror on each end with a flash tube

A burst of light from a flashtube adds energy inside the rod exciting the ruby atoms and producing light particles called photons.

The photons strike the atoms creating more and more photons bouncing back and forth between the two mirrors within the rod.

The number of photons become so great that they pass through one of the mirrors which is partially reflective and the laser beam emerges

For laser amplification three things are important

1.POPULATION INVERSION

2.METASTABLE STATE OF THE ATOM

3.OPTICAL RESONANCE

When a gas in the lasing medium absorbs radiation electrons are elevated to different energy levels most electrons return immediately to the ground state but others linger in what is called

METASTABLE STATE. This state is required for laser production

 When a photon of energy disturbs an electron in a metastable state as shown in the figure above) the electron drops to the lower energy level and emits an additional photon, and the two photons procced off together. This process is called STIMULATED EMISSION. This occurs with relatively high probability when the energy of the incoming photon is equal to the energy difference between the excited and deexcited energy levels of metastable state electrons. These photons encounter more electrons in the metastable state and the process repeats.  The result is a chain reaction of similar deexcitation sharing same frequency and same phase which is the characteristic of laser.

The amplification process occurs in a laser cavity as shown here in the figure.

 The laser cavity consists of a gain medium typically a crystal or gas place between two mirrors. The gain medium is excited by a power source in the form of flash lamp which raises the atoms in the medium to an excited state to achieve the condition of population inversion. Population inversion is very crucial requirement in laser production.  Here majority of the atoms which are in the ground state are pushed to metastable state using an external power supply. POPULATION INVERSION is important to keep the stimulated photons in continuous supply for laser production

When a photon of laser signal passes through the gain medium it stimulates the emission of additional photons by the excited atoms in the metastable state resulting in the amplification of the laser signal.

The amplification process is governed by rate differential equation which describes the rate of change of population inversion of the gain medium as a function of time. (THE GAIN MEDIUM USED IN THE COMMERCIAL LASER SCANNER IS AMIXTURE OF HELIUM AND NEON GAS WHICH LASES IN THE WAVE LENTH OF 630nm). The equation is

dN/dt =BNP – AN -CN

BNP = rate of stimulated emission

AN = rate of absorption

CN = rate of spontaneous emission

 Population inversion is a condition in which the number of atoms in the excited state is greater than the number of atoms in the ground state. In order to achieve laser amplification POPULATION INVERSION must be maintained above the threshold level. The amplification factor of the laser cavity depends on several factors including the length of the gain medium the strength of the pump laser and the reflectivity of the mirrors. A high reflectivity mirror at one end of the amplifier will reflect the amplified laser signal back to the gain medium causing further amplification.

In addition to the creation of population inversion several other factors are required to amplify and concentrate light into a laser beam.

 The figure shows the stimulated emission in a mirrored laser cavity

In a longitudinal resonant cavity such as a ruby rod or gas filled tube light travelling along length of the laser medium generate far more stimulated emission than the perpendicular axis of the cavity. Placing mirrors at the opposite ends of the laser cavity enables the beam to travel back and forth which results in increased amplification due to longer path length through the medium. The multiple reflections also produce a narrowly focused beam an important laser characteristic. Because only photons travelling parallel to the cavity walls will be reflected from both mirrors. This arrangement is known as the OSCILLATOR. It is necessary because an equilibrium state is required for the laser to come out. The emission intensity grows with each pass of the light until it reaches an equilibrium level that is the cavity and mirror design. One cavity mirror reflects the entire incident light while the other the output mirror reflects some light and transmits a portion as LASER BEAM

In physics specifically statistical mechanics, A POPULATION INVERSION occurs when a system such as a group of atoms or molecules exist in a state with more members in an excited state than in lower energy states. The concept is of fundamental importance in laser science because the production of population inversion is a necessary step in the working of standard laser

BOLTZMANN DISTRIBUTION AND THERMAL EQUILIBRIUM

To understand the concept of population inversion it is necessary to understand thermodynamics and the way light interacts with matter. To do so it is useful to consider a very simple assembly of atoms forming a lasing medium.

Assume there are a group of N atoms each of which is capable of being in one of the energy states, either

THE GROUND STATE with energy E1 or

THE EXCYED STATE with energy E2

E2 > E1

The number of atoms in the ground state is designated as N1 and number in excited state N2.

Since there are N atoms in total

N1+N2 = N

The energy difference between the two states given by

Delta E = E2- E1

The characteristic frequency v12 which will interact with the atoms is given by the relation

E2 -E1 =Delta E = hv12

Where h is PLANCKS CONSTANT

If the group of atoms is in thermal equilibrium it can be shown from thermodynamics that the ratio of the atoms in each state is given by

BOLTZMAN DISTRIBUTION

N2/N1 = e – (E2 -E1) /kT

Where T is the thermodynamic temperature of the group of atoms and k is the BOLTZMANN CONSTANT

Now let us look into a sample problem and we consider a 2-atom molecule. The ground state has an energy E1and an excited state E2. If the system is in a thermal bath at temperature T, what is the probability that the atom will be seen in the excited state E2 compared to the probability that the atom will be found in the ground state E1? If the system is in room temperature kT = 250 meV and E2 – E1= 1.65eV what is the relative probability of finding the electron in the excited state? Since the probabilities of finding the electron in any state of energy En is

Pan= P0 e-En//kT

Where P0 is the normalizing factor. Then the ratio of the probabilities that the system is in the state E2 compared to in the state E1 is

P2 /P1= P0e-E2/ kT /P0e-E1 /kT

P0 cancels out and since ea/eb=ea-b our ratio is

P2/ P = e-(E2 -E1 ) /kT

For the numbers we are given,

Delta E =1650meV and kT = 250  deltaE/ kT

 1650/250 = 6.6

Interposing in the equation

P2/P1= e-6.6= 1.4x 10-3 or o.oo136  that is very low probability of finding in E2 state

that is there are no atoms in the exited state. When in thermal equilibrium it is seen that the lower energy is more populated than the higher energy state and this the normal state of the system. As T increases the number of electrons in the high energy state (P2) increases, but P2 never exceed P1 for a system at thermal equilibrium, rather at infinite temperature the populations P2 and P1 become equal. In other words, a population inversion (P2/P1 more than 1) can never exist for a system in thermal equilibrium. To achieve population inversion therefore requires pushing the system into non equilibrated state. This is achieved by flash light or electrical pumping.

Lasers today are used to read bar codes at stores and in libraries. Laser printers produce quality images at relatively low cost. Lasers send prodigious numbers of telephone messages, internet through optical fibers. Lasers are also used in surveying, weapons guidance, tumor eradication, welding detached retina, reading music on CDs and watching videos on blue ray DVDs.

The why do lasers have such varied use and applications. The answer is simple - lasers produce single wavelength electromagnetic radiation. Very coherent and the emitted photons are in phase. Thus, laser can be very precisely manipulated than incoherent wavelength of electromagnetic radiation from other sources

Now my strange title “LASER AS A PRODIGAL CHILD OF QUANTUM PHYSISICS”. Yes, one of the strong pillars of quantum physics is Paulis exclusion principle. This principle says that particles of the same energy cannot stay in the same energy level.

Laser photons have INTEGER SPINS and therefore can be called BOSONS. They do not obey PAULI’S exclusion principle and can stay at the same energy level. Laser light is the photon equivalent of a BOSE EINSTEIN CONDENSATION or rather BOSE EINSTEIN CONDENSAATE IS THE MATTER WAVE equivalent of laser light, both of which are a collection of BOSONS in the same quantum state

In 1924 SATYENDRANATH BOSE of DHAKA UNIVERSITY (present Bangladesh) made the seminal observation that it is possible to derive Planck’s radiation law from purely corpuscular or particle argument without invoking at all wave properties of light. The main ingredient in Bose’s argument was the indistinguishability of the particles in question and a new way of counting them – now universally known as the BOSE_EINSTEIN STATISTICS.

In statistical mechanics BOSE EINSTEIN STATISTCS means statistics of a system where you cannot tell the difference between any of the particles and the particles are BOSONS. BOSONS are the fundamental particles like the photons which make the laser light.

The aggregation of particles in the same state which is characteristic of particles obeying BOSE EINSTEIN STATISTICS accounts for cohesive streaming of laser light.

The photons in metastable state defies PAULI’S EXCLUSION PRINCIPLE. When the laser photons are random and based on probability, Einstein used a statistical calculation. Einstein’s statistical calculations were ably supported by SATYENDRANATH BOSE of University of Dhaka (present Bangladesh) in 1927 developed into what today we know as the famous BOSE EINSTEIN STATISTICS.  

The laser photons of the metastable state are also known as BOSONS in honour of SATYENDRANATH BOSE. I venture to re define laser rays as BOSON RAYS.

Professor K.A.Balasubramanian

Ph.D. (IARI NEW DELHI), Ph.D. (Imperial College London) DIC (Imperial College London)

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