Laser: Introduction, Einstein’s Coefficients, Types and Applications

Laser: Introduction, Einstein’s Coefficients, Types and Applications!

Introduction to Laser:

Einstein in 1917 first predicted the fact that there should be two kinds of emissions, viz. spontaneous and stimulated. He suggested that both the emissions are required for getting the Planck’s radiation law. The phenomenon of stimulated emission was first used by Townes in 1954 for constructing a microwave amplifier device called ‘maser’.

In 1958, Schawlow and Townes extended the ‘maser’ principle to the optical frequencies which led to the device called ‘LASER’ (an acronym for light amplification by stimulated emission of radiation). In 1960, Maiman first successfully demonstrated the operation of a ‘LASER’ device using ruby crystal. Since then the laser action has been noted in a wide variety of materials including semiconductors, dyes, liquids, ionized gases, etc.

The present-day light-wave communication had its birth in 1960s. The first successful demonstration of the ruby laser in 1960 and then a demonstration of laser operation in 1962 were the early stepping stones. In the year 1966, an evolution of fibre technology was taking place, though at that time the existing fibres had a loss even more than 1000 dB/km. Research workers at Corning Glass Works in 1970 first produced the fibre with a loss below 20 dB/km. Since then fibre technology has advanced to the point of fabricating fibre with a loss less than 0.5 dB/km.

Einstein’s Coefficients of Radiation:

In 1970, Einstein predicted that there are two kinds of emissions. The first one is called spontaneous emission while the other is known as stimulated emission which is caused by the presence of the light radiation of the proper frequency. We have discussed below Einstein’s coefficients and also presented the original argument of Einstein which led to a relation between these coefficients. It has also been established how a light beam gets amplified in the presence of population inversion.

Let us assume that N₁ and N₂ are two numbers of atoms per unit volume in levels 1 and 2 respectively. As shown in Fig. 28.1, these levels correspond to energies E₁ and E₂. An atom in the lower energy level absorbs radiation and thereby gets excited to the level E₂. The process of excitation occurs in the presence of radiation only and is known as absorption. The rate of absorption depends on the density of radiation at a particular frequency separating the two levels.

In this case, the absorption process depends on the energy density of radiation at that frequency. These energy density may be represented by u(ω) and is defined such that u(ω)dω represents the radiation energy per unit volume in the frequency interval ω to ω + dω.

The rate of absorption is proportional to N₁ and also to u(ω). Hence, the number of absorptions per unit volume can be written as-

N₁B₁₂u(ω)

Where B₁₂ = the coefficient of proportionality.

Next, let us consider the reverse process, viz., the emission of radiation at a frequency ω when the atom de-excites from E₂ to E₁. Einstein postulated that in an excited level an atom makes a radiative transitions to a lower energy level either through spontaneous emission or through stimulated emission.

In spontaneous emission, the probability per unit time of the atom making a downward transition does not depend on the energy density of the radiation field but it depends only on the levels involved in the transition. Thus the rate of spontaneous emissions to the lower energy levels can be represented by-

N₁A₂₁

Where A₂₁ = coefficient of proportionality.

For stimulated emission, the rate of transition to the lower energy levels is directly proportional to the energy density of the radiation at a frequency co. So the rate of stimulated emission is represented by-

N₂B₂₁u(ω).

The quantities A₂₁, B₁₂ and B₂₁ are called Einstein’s coefficients.

The above coefficients are determined by the atomic system. The number of upward transitions at thermal equilibrium must be equal to the number of downward transitions. Hence, at thermal equilibrium, we may write-

Since for optical regions ω ∼ 4 x 10¹⁵ per second, at optical frequency the emission is mainly due to the spontaneous transitions and, therefore, the emission from usual light sources is incoherent.

Types of Laser:

i. Ruby Laser:

It was the first laser operated successfully by Maiman in 1960. It has a single crystal of ruby whose ends are flat. One of the ends is completely silvered while the other is partially silvered and thus the two ends form a resonant cavity. Ruby is an aluminium oxide with some of the Al atoms replaced by chromium (about 0.05%). The energy levels of the chromium ion are presented in Fig. 28.2.

The states E₁ and E₂ have very short lifetime (≤ 10^-9 second) while the metastable state M has a longer lifetime (∼ milliseconds). The ruby crystal is placed inside a flash lamp which is connected to a capacitor. The capacitor discharges a few thousand joules of energy in a few milliseconds.

This causes a power output from the flash lamp of a few megawatts order and a part of this energy is absorbed by the chromium ions resulting an excitation to the energy level inside the bands E₁ and E₂. Transitions to E₁ and E₂ arc caused by the radiation of wavelength ∼ 6600 Å and ∼ 4000 Å respectively.

Chromium ions make a fast non-radiative transition from the excited to the metastable state. They lead to a state of population inversion between M and G. Once a state of population inversion is achieved lasing action may be triggered by spontaneously emitted photons.

The flash-lamp operation provides a pulse output of the laser. As soon as the flash lamp stops operating, the population in the upper level is depleted and lasing action stops till the arrival of the next flash of the lamp. Even in the short period in which the ruby is lasing one may see that emission is measured as spikes of high intensity emissions. This phenomenon is known as spiking of the laser.

Such spiking occurs due to the following mechanism:

As soon as the flash-lamp power attains the threshold level, the laser oscillation sets in and depletes most atoms in the upper level to a stage when the laser action ceases. In this way the laser emission lasts for a few microseconds during which the flash lamp again pumps the ground state atoms to the upper level and thus further laser oscillation begins. The process repeats itself till the flash-lamp power falls below the threshold value and the lasing action stops.

Alternative methods for pumping may also be employed. An optical pumping scheme in which the laser rod and the flash lamp coincides with the focal lines of a cylindrical reflector of an elliptical cross-section. The property of an elliptical reflector is that all the energy emerging from one of its foci after reflection from the reflecting surface focuses to the other focus. As a result an efficient transfer energy occurs from the flash lamp to the laser rod.

The efficiency of pumping the lasers is increased by using the following two methods:

(i) The flash tube and the ruby rod may be mounted closely near the central axis of a circular mirror. Due to this arrangement a major portion of the radiated light comes back to the centre of the cylinder giving light illumination.

(ii) To increase the efficiency further, a cylindrical mirror with elliptical contours may be used. At one focus F₁ of the ellipse the flash lamp is placed while at the other focus F₂ the laser rod is kept. The light which radiates from one focus strikes the mirror and thereby it reflects to the other focus. Thus most of the light from flash lamp reaches the laser rod at the other focus.

ii. High-Power Laser:

The ruby lasers can generate very high power within a very short intervals of time. An important technique used for producing high-power lasers is called Q-spoiling. Between one end of the ruby rod and the mirror a fast-acting shutter is interposed. As the mirror at one end is obstructed, the internal reflections between the two mirror surfaces cannot take place. For most of the pumping cycle, the shutter is kept in closed positions permitting no laser action to take place. Consequently, many atoms are raised to an excited level.

Next, the shutter is quickly opened allowing the laser action to proceed. The energy built up within the rod is mainly emitted in one tremendous burst. The enormous energies (millions of watts) such achieved have been used to burn holes in diamonds and in about six-millimetre thick steel girders.

iii. Raman Laser:

A method of changing the laser frequencies was developed by E. J. Woodbury. A beam of ruby laser light was made to pass through a vessel containing benzene. Additional wavelengths were produced on either side of 6943 Å wavelength of the ruby laser. Like the main beam, the additional wavelengths were also highly parallel and coherent.

It was noted that the frequency shifts were equal to the multiples of natural vibration frequency of benzene molecule. A change in the frequency of light owing to the vibrational frequencies of a substance is known as the Raman effect. In Raman laser, the intensities of the new wavelengths were half of the main beam.

The Raman laser provides a valuable method for getting information about the natural vibrational frequencies of many molecules.

4. Applications of Laser:

i. Medical Uses:

Lasers have been successfully utilised in the treatment of detached retinas. Ophthalmologists find the possibility of using the laser as an improved tool for microsurgery and vision research. Lasers also show great promise in cancer treatment.

ii. Applications in Military:

Owing to the high amount of energy which the laser can concentrate, it can be used as ‘death-ray’ type of incendiary weapon for use against enemy missiles. However, the technology required for the purpose is not yet well-developed. Presently, the laser system can put out energy of the order of 1500 joules. By proper lens system, if that intensity is concentrated, it could set on fire inflammable material situated at a distance of two miles or 3.2 kilometres long.

iii. Uses in Science:

Laser has been used to repeat Michelson-Morley experiment showing that the velocity of light is constant and hence it proved the Einstein’s theory of relativity. Using gas lasers many experiments were performed by various scientists and some valuable results were achieved.

The use of lasers in computers is being investigated for various potential application, e.g., to transmit an entire memory bank from one computer to another.