 ## Laser

Subject: Physics

#### Overview

Heisenberg’s uncertainly principle states that in any simultaneous determination of a pair of complementary variables of a particle, the product of the uncertainties of the variables is greater than and equal to Planck’s constant (h). This note provides us an information on Laser.
##### Laser

Werner Heisenberg is best known in quantum physics for his discovery of the uncertainty principle, which has the consequence that to make measurements of very short distances — such as those required by string theory — very high energies are required.

The uncertainty principle states that the more precisely you measure one quantity, the less precisely you can know another associated quantity. The quantities sometimes come in set pairs that can’t both be completely measured.

What Heisenberg found was that the observation of a system in quantum mechanics disturbs the system enough that you can’t know everything about the system. The more precisely you measure the position of a particle, for example, the less it’s possible to precisely measure the particle’s momentum.

The degree of this uncertainty was related directly to Planck’s constant — the same value that Max Planck had calculated in 1900 in his original quantum calculations of thermal energy. Heisenberg found that certain complementary quantities in quantum physics were linked by this sort of uncertainty: • Position and momentum (momentum is mass times velocity)

• Energy and time

This uncertainty is a very odd and unexpected result from quantum physics. Until this time, no one had ever made any sort of prediction that knowledge was somehow inaccessible on a fundamental level. Sure, there were technological limitations to how well a measurement was made, but Heisenberg’s uncertainty principle went further, saying that nature itself doesn’t allow you to make measurements of both quantities beyond a certain level of precision.

If a coordinate x has an uncertainty Δx ,and if the corresponding momentum component px has an uncertainty Δpx ,then uncertainties are found to be related in general to the inequality,

$$\Delta x\Delta p\geqslant \hslash$$

This is the Heisenberg uncertainty principle for position and momentum.

$$where \; \hslash =\frac {h}{2\pi}$$

#### The Laser

The LASER stands for “Light Amplification by Stimulated Emission of Radiation”. A laser is a device which produces a highly concentrated monochromatic, coherent and unidirectional beam of light.

##### Principle of Laser

Suppose that we have an assembly of atoms whose metastable state is $h\mu$. If we somehow raise the atoms to the metastable stable and let a light of frequency $\mu$ fall upon them, there will be more stimulated emission than the stimulated absorption. As a result, we get an amplification of the original light. This is the principle of the laser.

#### Laser Action

Metastable state

An excited atom cannot stay in excited state for a long time. It comes back to the ground state by emitting a proton. The average time for which the excited atom stays in the excited state is called the mean life time which is characteristics of the energy state. The mean life time for different energy state is different. The energy states having the mean life time of more than 10-3 sec are known as metastable states.

Spontaneous Emission

An excited atom cannot stay in excited state for a long time. It comes back to the ground state by emitting a proton. If E1 is the energy in the ground state and En is the energy in the nth state, the frequency of photon emitted when an electron jumps from En to E1 is given by $\mu = \frac {E_n – E_1}{h}$. This kind of emission of photons is known as spontaneous emission.

Stimulated or induced absorption

If the incident photon forces the excited atom E2 to move the ground state E1 by emitting the photon of energy $hf = E_2 – E_1$ the emitted photon has the same energy as that of incident photon and they are in the same phase and they move in the same direction as the incident photons. This type of emission is called stimulated emission or induced emission.

Population Inversion

At ordinary room temperature, the number of atoms (N2) in the excited state (E2) is much less than the number of atoms (N1) in the ground state N1. When light photons of frequency($\mu$)are incident on a large collection of such atoms, the ground state atoms are excited to the excited state (E2). The excited atoms then return to the ground state either by spontaneous state and stimulated emission. +In order to achieve the higher probability of stimulated emission for laser action the population of the atoms in the excited state must be greater than the population of the atoms in the ground state. Achieving more number of atoms in the higher energy state (excited state)than the lower energy state (ground state) is called the population of inversion.

##### Types of Laser

Solid laser, the gas laser, semi-conductor laser, chemical laser etc. are types of laser. The most commonly used solid laser is ruby laser and gas laser is the helium-neon gas laser.

Ruby Laser

It consists of a ruby rod whose ends are optically flat surrounded by a glass tube. The glass tube is surrounded by a helical xenon flash tube which acts as the optical pumping system. Ruby rod is a crystal of aluminum oxide (Al2O3) doped with 0.05% chromium oxide (Cr2O3) so that some of the aluminum atoms in the crystal lattice are replaced by Cr3+ ions. The energy level diagram of these chromium ions is as shown in the figure.

Helium-Neon Laser

He-Ne laser tube is approximately 0.5 m long and 5 mm in diameter. The tube is filled with the mixture of the helium and neon gas in the ratio is 5:1 at the total pressure of 1torr. The ends of the tube are cut at Brewster's angle. The tube has two parallel mirrors at its two ends one being partially transparent. The spacing of the mirrors is equal to an integral number of half wavelengths of the laser height. There are two electrodes which are connected to power supply. The mixture of gas is ionized by passing the electric current through it.

##### Uses of Laser
1. The laser is used in radio communication in outer space.
2. It is used in welding and perching holes in metals.
3. It is used in detecting and ranging objects at great distances.
4. It is used in medicine and scientific research.
##### Properties of Laser
1. The light is very nearly monochromatic.
2. The laser beam diverges hardly at all.
3. The lights are coherent and are in phase with each other.
4. The beam is extremely intense.

References

Manu Kumar Khatry, Manoj Kumar Thapa, etal. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

##### Things to remember

Heisenberg’s uncertainly principle states that in any simultaneous determination of a pair of complementary variables of a particle, the product of the uncertainties of the variables is greater than and equal to Planck’s constant (h).

A laser is a device which produces a highly concentrated monochromatic, coherent and unidirectional beam of light.

The energy states having mean life time of more than 10-3 sec are known as metastable states.

Achieving more number of atoms in the higher energy state (excited state)than the lower energy state (ground state) is called population of inversion.

The most commonly used solid laser is ruby laser and gas laser is the helium neon gas laser.

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