LASERS - 1V Sharma

Principle:

Light Amplificated by Stimulated Emission of

Radiation (LASER)

Important property that makes laser special?

CoherenceTemporal Coherence (also k/a longitudinal coherence):

Coherence time Tc is the time between phase interruptions.

The average distance from one phase interruption to the next in a wave is called the longitudinal coherence

length, Lc, and can be thought of as the average distance (in the direction of propagation) over which the wave is

coherent.

Lc = cTc (longitudinal coherence length)

The high degree of coherence of laser

light is important for applications such

as holography that involve interference of two beams.

The coherence length of a laser can be increased by

reducing the spectral width.

The high degree of coherence has an important consequence for the spread of wavelengths in laser

light, known as its spectral width or linewidth.

Power spectral distribution for light with coherence time Tc.

Question: A laser operates at a free-space wavelength of 790 nm, and has a longitudinal coherence length of

1 mm. Determine the linewidth in terms of both frequency and wavelength.

Solution: The frequency linewidth is

The wavelength linewidth is obtained by taking the differential of = c/l,

The linewidth is then 0.62 nm.

Spatial Coherence (also k/a transverse coherence):

The degree of coherence along a wave front (perpendicular to the direction of wave propagation) is referred

to as transverse or spatial coherence.

Spatially coherent light has smooth and continuous wave fronts, and the E fields at points A and B

are correlated.

Light with partial spatial coherence has interruptions in phase along the wave fronts, and the E fields at

points A and B are uncorrelated for separation greater than Dc. The divergence angle is similar to that of

a coherent beam passing through an aperture of width Dc.

A figure of merit that is often used to describe a partially coherent beam is the M2 parameter,

defined as the ratio of its divergence to that of a perfectly coherent beam. It can be related to the

spatial coherence length by

Since Dc ≤D, then M2 ≥1, with M2 = 1 corresponding to a perfectly coherent beam.

Brightness:

The brightness of a light source is the power emitted per unit solid angle, per unit emitting area.

For perfectly coherent laser beam of diameter D, the emitting area is As ~ D2 and the

solid angle of emission is DW = pq2

q~ l/D for coherent light

The Brightness

For Partially coherent light:

q~ l/Dc

The brightness will be reduced by the factor (Dc/D)2

IMPORTANT: The brightness of a laser is independent of

the beam diameter, depending only on the power and the

wavelength. Shorter-wavelength lasers have a greater brightness, for the same optical power.

Brightness theorem:Light from a source with emitting area As and brightness B is imaged with a lens into a spot of area A’s

The brightness of an optical beam is not changed by

passing through any combination of lenses, mirrors, or

other passive optical elements.

W and W’ are the solid angles corresponding to the linear

angles q and q’.

To achieve the highest intensity, W (and hence q) should be made as large as possible. q > 45° give rise to

significant aberrations, so a practical maximum value for the solid angle is = 2 (1 – cos 45°) ~ 2 sr.

Therefore, maximum intensity at the focus is then ~2B.

Summary of different types of coherence for laser light.

Optical Resonator

-∞ ∞τ

t

Df0

f

Black Box

Oscillator

HOW to make an oscillator?

e-t/t

Δf

fof

Df=1/t = losses

Z

Decay time effects the line width. If we improve the losses we improve the line width means the narrow width.

Lower the friction, lower will be the width

To make an oscillator, we need

• A resonator (low loss) fo

The laser resonator

LMM

L= l1/2l1=2L

lf = cf1 = c/2L

f1

f

LMM

l1=2L

f1 = c/2L

l2=2L/2

f2 = 2. c/2L

l3=2L/3

f2 = 3. c/2L

Other mode of oscillations

f1

ff3

c/2L

f2

LMM

l1=2L

f1 = c/2L

l2=2L/2

f2 = 2. c/2L

l3=2L/3

f2 = 3. c/2L

lq=2L/q

fq = q. c/2L

f1

f or

f3f2

fq

lq=2L/q

fq = q. c/2L

Que: Estimate the mode number and mode spacing for a laser oscillating at 514 nm in a cavity of

length 1 m. Assume n = 1.

Solution: The frequency of the laser light 5.84 × 1014 Hz

The mode spacing c/2L = 1.5 × 108 Hz

The number of modes 3.89 × 106

Mode width:

We assumed that the modes were perfectly sharp, with well-defined frequencies. In practice, there is always some spectral broadening of the modes.

fq

Df

Photon Lifetime:

Assume that the light has initial intensity I at point A in the cavity. After getting reflected from right

mirror having reflection coefficient R2, the intensity is R2I and after further reflection from the left

mirror the intensity is R1R2I.

Change in intensity in one round trip (distance 2L) is

Here, Dt = 2L/c round trip time

The rate of change of intensity is given by,

We can approximate I(t) as continuous function as the mirror reflectivities are usually very high, therefore the losses per round trip are <<<1

tc photon or cavity lifetime

The light intensity in the cavity decays exponentially in time, with a decay time equal to the photon lifetime tc.

The measurement of this decay time is one method of making

accurate determinations of mirror reflectivity.

The time dependence of E is that of a damped sinusoid.

Time decay is characterized by the uncertainty relation

Dw1/2 = full width at half maximum (FWHM) of angular

frequency.

Using Dn= Dw1/2/ 2p, the frequency width of the modes can be written as

Quality Factor

The quality factor Q of a resonance is defined as the centre frequency divided by the width,

Sharpness of the modes is greatest for very high reflectivity mirrors and long cavity lengths.

Cavity Finesse

As the laser cavity length L increases, the modes become narrower, but the spacing

between modes also decreases.

A useful parameter that gives the mode width compared with the mode spacing is the finesse,

Independent of cavity length, and dependent on reflectivity

Finesse and quality factor are related by

Light Amplificated by Stimulated Emission of Radiation (LASER)

-General layout

-1 Active media

-2 External pump source

-3 and 4 optical resonator

-5 Laser light