26 Properties of Laser Light

Devendra Mohan

Contents of this Unit

 

1.  Difference between laser light and ordinary light:

2.  Properties of laser light:

(a). Directionality

(b). Intensity

(c). Monochromaticity

(d). Coherence

3. Self focusing of laser light

 

Learning Outcomes

  • From this module students may get to know about the following:
  • Difference between laser light and ordinary light Self focusing of laser light

 

Properties of Laser Light

 

Let us understand the difference between a laser light and an ordinary light

 

1.  Directionality:

 

The ordinary light sources emit in all directions while Laser light emit only in one direction.

 

The directionality of laser beam is expressed in terms of the ‘Full Angle Beam Divergence’ that is twice the angle that the edge of the beam makes with the axis of the beam. The outer edge of the beam is defined as the p[point at which the strength of the beam is dropped to 1/e times its value at the centre.

 

As the beam moves straight and only in one direction, the laser beam can be sharply focused, while light from an ordinary source travels in all directions and in latter case, the energy intensity rapidly decreases as one moves away from the source similar to the fact the sun’s intensity diminishes when it finally reaches the earth.

 

This simply means that a laser beam can give very high energies to a very small area.

 

It is also important to note the spread of the beam. The spread of the beam on the surface of moon is a few kilometers though the moon is ~380000 Kms. Thus the beam has a too little divergence. If a laser beam is sent from the earth to a mirror on the moon, the beam will be reflected to the earth again with no divergence.

 

2.  Intensity:

 

The intensity of a laser beam is quite high in comparison to any other light source. As the laser gives light into a narrow beam, its energy is concentrated in a very small region and this lead to great intensity.

 

Now we have output intensity per unit area that is highly directional and very large.

 

Flux densities for focused laser light of 1015 W cm-2 are achievable. However, An oxyacetylene flame has a flux density of only 103Wcm-2

 

An object needs to be heated to a temperature at ~ 1030 K to radiate with an intensity of a typical laser source. It is worth noticing that a tungsten lamp, while radiating is only ~3000 K in temperature and our sun is only about 108 K.

 

Intensity is the power transferred per unit area (Watts per square meter), where the area is an imagined surface that is perpendicular to the direction of propagation of the energy.

 

Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area.

 

If a point source is radiating energy in all directions producing a spherical wave, and is assumed that no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to distance from the object squared because of the inverse-square law.

Applying the law of conservation of energy

where P is the power radiated, I is the intensity as a function of position, and dA is a differential element of a closed surface that contains the source.

Integrating over a surface of uniform intensity I, may be over a sphere centered around the point source

 

where I is the intensity at the surface of the sphere, and r is the radius of the sphere.

For a monochromatic propagating wave of Gaussian beam, if E is the complex amplitude of the electric field then the time-averaged energy density of the wave is given by:

and the local intensity is obtained by multiplying this expression by the wave velocity, c/n:

where n is the refractive index, c is the speed of light in vacuum and  is the vacuum permittivity.

 

For non-monochromatic waves, the intensity of different spectral components is to be simply added. The treatment above does not hold for arbitrary electromagnetic fields. In general, an evanescent wave may have finite electrical amplitude and may not transferring any power.

 

3.   Monochromaticity:

A laser source is highly monochromatic means comes with a precise wavelength, while ordinary light source has a broad spectral output. The spread in frequency of aline is characterised by the line width. The laser light has a high degree of monochromaticity. A typical laser emits line of linewidth as 3Ao. It is almost the purest monochromatic light available so far. In fact Lasers can be generated with short time durations from pico second to femto seconds and this can be considered dual property of mono chromaticity. This means the energy concentrated in wavelength.

 

4.  Coherence:

 

Laser Light has high degree of coherence whereas the ordinary light is not coherent.

 

This is the unique property of laser beam. It has arisen due to stimulated emission process. The emitted photons have a definite phase relation to each other. This coherence is of two types: temporal coherence and spatial coherence, both of which are important.

 

Ordinary light is not coherent because it comes from independent atoms which emit on time scales of about 10-8 seconds. Though there is a good degree of coherence in sources like the mercury green line and some other useful spectral sources, but their coherence is not comparable with that of a laser.

 

It will be of interest to introduce the two types of Coherence: Spatial and Temporal

 

If we consider two points S1 and S2 in such a way that at time t=o, these lie on the same wave front of given Electromagnetic wave, where E1(t) and E2(t) be the corresponding electric fields. The difference between phases at these two fields at time t=0 is zero and if it remains zero at t>0, there exist perfect coherence between these points. The wave will be said to be spatially coherent if even otherwise any two points of the wavefront are considered. The idea can be understood through Double slit experiment. Spatial coherence implies a fixed phase relationship between the electric fields at different locations across the wavefront of beam. Spatial coherence is the essential prerequisite of the strong directionality of laser beams

 

To define temporal coherence, consider the electric field of electromagnetic wave at a given point S at times t and t+ τ. Now for a delay time of τ, the phase difference for two field values remains the same for any time t, then it is understood that there is temporal coherence over a time τ. If this remains same for any value of τ, there exists perfect time coherence. The idea can be understood through Michelson Interferometer experiment.Temporal coherence implies a strong correlation between the electric fields at one location but different times.

 

Lasers generate the Gaussian beams with very high spatial coherence, and this is the fundamental difference between laser light and radiation from other ordinary light sources. High spatial coherence arises from the existence of resonator modes that define spatially correlated field patterns.

 

The difference between spatial and temporal coherence can be presented by the following figure that depicts a monochromatic Gaussian beam, exhibiting perfect spatial and temporal coherence.

 

(Electric field distribution around the focus of a Gaussian laser beam with perfect spatial and temporal coherence)

 

The figure below shows a beam with high spatial coherence, but poor temporal coherence. The wave fronts are formed as above, and the beam quality is also very high, but the amplitude and phase of the beam varies along the propagation direction. It is to observe that both the local amplitude and the spacing of the wave fronts vary to some extent.

(A laser beam with high spatial coherence, but poor temporal coherence)

The figure below depicts a laser beam with poor spatial coherence, but high temporal coherence. The wave fronts are deformed, and this results in a high beam divergence and poor beam quality. On the other hand, the beam is monochromatic, so that the spacing of the deformed wavefronts remains constant.

(A laser beam with poor spatial coherence, but high temporal coherence)

 

In conclusion, The high degree of collimation has arise due to the fact that the cavity of the laser has very nearly parallel front and back mirrors which constrain the final laser beam to a path which is perpendicular to those mirrors. The back mirror is almost perfectly reflecting while the front mirror is ~90% reflecting. But the light has passed back and forth between the mirrors many times in order to gain intensity by the stimulated effect of more photons at the same wavelength.

 

The highly collimated nature of the laser beam contributes both to its danger and to its usefulness. One should never look directly into a laser beam, because the highly parallel beams focused on the retina of the eye will cause instant damage to the retina.

 

Self-Focusing of Laser Light

 

The laser is known to be a non-linear phenomenon and therefore has a unique property of Self-focusing.

 

It is well known that the refractive index of a material is related to the susceptibility by the relation.

 

As the susceptibility x is a function of the field E, depends on E. This dependence of the refractive index on the field strength gives rise to a nonlinear effect.

 

A dielectric medium when placed in an electric field, it gets polarized. Each constituent molecule acts as a dipole, with a dipole moment Pi. The dipole moment vector per unit volume P is given by

Here, the summation is over the dipoles in the unit volume. It is evident that the orienting effect of the external field on the molecular dipoles depends both on the properties of the medium and on the field strength. Thus,

P  = ε0 x E

 

Here x is called the polarizability or dielectric susceptibility of the medium.

 

The quantity x is a constant only in the sense of being independent of E; its magnitude is a function of the frequency. With sufficiently intense laser radiation the relation does not hold good and has to be generalized to

 

 

Here x (1) is the same as x, the coefficients x(2), x(3), … define the degree of nonlinearity and are known as nonlinear susceptibilities. If the field is low, as it is in the case of ordinary light sources, only the first term is retained. The higher order terms become more significant with the increased value of the electric field. Thus, dielectric permittivity, refractive index, etc., that depend upon susceptibility, also become functions of the field strength E, Now the medium is called a “nonlinear medium.”

 

Therefore, considering

The expression for the refractive index is

That gives the dielectric permittivity of the linear medium, and

is a nonlinear increment in the expression for dielectric permittivity.

This implies that the refractive index of a nonlinear medium is proportional to the square of the amplitude of the field, that is, to the intensity. Now the intensity of a laser beam is not constant over its cross-section. It peaks at the axis of the beam and falls off gradually away from the axis. The velocity of the light wave is given by c /n . As decreases owing to the falling of the intensity of the light beam, plane wave-front incident on material becomes concave as it propagates through the medium and contracts towards the axis and self-focuses.

 

References:

  1. Principles of Lasers By ORAZIO Svelto (Plenum publication cooperation)
  2. Lasers and Nonlinear Optics By B. B. Laud (New Age International Publishers Ltd. , INDIA)
  3. Physics for engineers By N.K.verma(PHI learning Private limited,Delhi)
  4. Optics by Ajoy Ghatak,The McGraw Hill companies