. The laser is a device which amplifies the light, hence the LASER is an acronym for light amplification by simulated emission of radiation. The operation of the device may be described by the formation of an electromagnetic standing wave within a cavity (optical resonator) which provides an output of monochromatic highly coherent radiation.
. Material absorb light rather than emitting. Three different fundamental process occurs between the two energy states of an atom.
1) Absorption 2) Spontaneous emission 3) Stimulated emission.
. Laser acting is the result of three process absorption of energy packets (photons) spontaneous emission, and stimulated emission. (These processes are represented by the simple two-energy-level diagrams).
Where, E1 is the lower state energy level.E2 is the higher state energy level.
. Quantum theory states that any atom exists only in certain discrete energy state, absorption or emission of light causes them to make a transition from one state to another. The frequency of the absorbed or emitted radiation f is related to the difference in energy E between the two states.
If E1 is lower state energy level.and E2 is higher state energy level.
E = (E2 – E1) = h.f.
Where, h = 6.626x 10-34 J/s (Plank's constant).
. An atom is initially in the lower energy state, when the photon with energy (E2 – E1) is incident on the atom it will be excited into the higher energy state E through the absorption of the photon.
. When the atom is initially in the larger energy state E2, it can make a transition to the lower energy state E providing the emission of a photon at a frequency corresponding to E = h.f. The emission process can occur in two ways.
A) By spontaneous emission in which the atom returns to the lower energy state in random manner.
B) By stimulated emission when a photon having equal energy to the difference between the two states (E2 – E1) interacts with the atom causing it to the lower state with the creation of the second photon.
. Spontaneous emission gives incoherent radiation while stimulated emission gives coherent radiation. Hence the light associated with emitted photon is of same frequency of incident photo, and in same phase with same polarization.
. It means that when an atom is stimulated to emit light energy by an incident wave, the liberated energy can add to the wave in constructive manner. The emitted light is bounced back and forth internally between two reflecting surface. The bouncing back and forth of light wave cause their intensity to reinforce and build-up the result in a high brilliance, single frequency light beam providing amplification.
Emission and Absorption Rates. If N1 and N2 are the atomic densities in the ground and excited states.
Rate of spontaneous emission
Rate of stimulated emission
Rate of absorption
Where,
A, B and B' are constants.
ρem is spectral density.
. Under equilibrium condition the atomic densities N1 and N2 are given by Boltzmann statistics.
Where,KB is Boltzmann constant.
T is absolute temperature.
. Under equilibrium the upward and downward transition rates are equal.
Spectral density ρem
Comparing spectral density of block body radiation given by Plank's formula,
. A and B are called Einstein's coefficient.
1 Fabry – Perot Resonator
. Lasers are oscillators operating at optical frequency. The oscillator is formed by a resonant cavity providing a selective feedback. The cavity is normally a Fabry-Perot resonator i.e. two parallel plane mirrors separated by distance L,
Light propagation along the axis of the interferometer is reflected by the mirrors back to the amplifying medium providing optical gain. The dimensions of cavity are 25-500 μm longitudinal 5-15 μm lateral and 0.1-0.2 μm transverse. Fig. 3 shows Fabry-Perot resonator cavity for a laser diode.
. The two heterojunctions provide carrier and optical confinement in a direction normal to the junction. The current at which lasing starts is the threshold current. Above this current the output power increases sharply.
2 Distributed Feedback (DFB) Laser. In DFB laser the lasing action is obtained by periodic variations of refractive index analog the longitudinal dimension of the diode. Fig. 4 shows structure of DFB laser diode.
Lasing Conditions and Resonant Frequencies
.The electromagnetic wave propagation in longitudinal direction is expressed as -
Where,
I(Z) is optical field intensity.
ω is optical radian frequency.
β is propagation constant.
.The fundamental expression for lasing in Fabry-Perot cavity is -
Where,
Γ is optical field confinement factor or the fraction of optical power in the active layer.
ᾱ is effective absorption coefficient of material.
g is gain coefficient.
hv is photon energy.
Z is distance traverse along the lasing cavity.
. Lasing (light amplification) occurs when gain of modes exceeds above optical loss during one round trip through the cavity i.e. z 2L. If R1 and R2 are the mirror reflectivities of the two ends of laser diode. Now the expression for lasing expression is modified as .
The condition of lasing threshold is given as –i) For amplitude : I(2L) = I (0)
ii) For phase : e-j2βL = 1
iii) Optical gain at threshold = Total loss in the cavity.
i.e. I' gth = αt
. Now the lasing expression is reduced to –
Where,
αend is mirror loss in lasing cavity.
. An important condition for lasing to occur is that gain, g ≥ gth i.e. threshold gain.
3 Power Current Characteristics
. The output optic power versus forward input current characteristics is plotted in Fig. 5 for a typical laser diode. Below the threshold current (Ith) only spontaneous emission is emitted hence there is small increase in optic power with drive current. At threshold when lasing conditions are satisfied. The optical power increases sharply after the lasing threshold because of stimulated emission.
. The lasing threshold optical gain (gth) is related by threshold current density (Jth) for stimulated emission by expression –
Where, β is constant for device structure.
4 External Quantum Efficiency.
. The external quantum efficiency is defined as the number of photons emitted per electron hole pair recombination above threshold point. The external quantum efficiency ηext is given by –
Where,ηi = Internal quantum efficiency (0.6-0.7).
gth = threshold gain.
ᾱ = Absorption coefficient.
.Typical value of ηext standard semiconductor laser is ranging between 15-20%.
5 Resonant Frequencies
. At threshold lasing
M is an integer.
. Gain in any laser is a function of frequency. For a Gaussian output the gain and frequency are related by expression –
Where,g(0) is maximum gain.
λ0 is center wavelength is spectrum.
σ is spectral width of the gair.
. The frequency spacing between the two successive modes is –
6 Optical Characteristics of LED and Laser
. The output of laser diode depends on the drive current passing through it. At low drive current, the laser operates as an inefficient LED, when drive current crosses threshold value, lasing action begins. Fig. 6 illustrates graph comparing optical powers of LED operation (due to spontaneous emission) and laser operation (due to stimulated emission).
7 Spectral and Spatial Distribution of LED and Laser
. At low current laser diode acts like normal LED above threshold current, stimulated emission i.e. narrowing of light ray to a few spectral lines instead of board spectral distribution, exist. This enables the laser to easily couple to single mode fiber and reduces the amount of uncoupled light (i.e. spatial radiation distribution). Fig. 7 shows spectral and spatial distribution difference between two diodes.
8 Advantages and Disadvantages of Laser DiodeAdvantages of Laser Diode
1. Simple economic design.
2. High optical power.
3. Production of light can be precisely controlled.
4. Can be used at high temperatures.
5. Better modulation capability.
6. High coupling efficiency.
7. Low spectral width (3.5 nm).
8. Ability to transmit optical output powers between 5 and 10 Mw.
9. Ability to maintain the intrinsic layer characteristics over long periods.
Disadvantages of Laser Diode
1. At the end of fiber, a speckle pattern appears as two coherent light beams add or subtract their electric field depending upon their relative phases.
2. Laser diode is extremely sensitive to overload currents and at high transmission rates, when laser is required to operate continuously the use of large drive current produces unfavourable thermal characteristics and necessitates the use of cooling and power stabilization.
9 Comparsion of LED and Laser Diode