FAQ - General Lasers

LASER is the acronym for Light Amplification by Stimulated Emission of Radiation.

Einstein postulated that, when the population inversion exists between upper and lower levels among atomic systems, it is possible to realize amplified stimulated emission and the stimulated emission has the same frequency and phase as the incident radiation.

Though the idea of stimulated emission was given by Albert Einstein way back in 1917, but Theodore Maiman invented the laser as such in 1960. He realized the first Laser using ruby as a lasing medium that was stimulated using high energy flashes of intense light.

MASER stands for Microwave Amplification by the Stimulated Emission of Radiation. Charles H Townes of Columbia University, Alexander Prokhorov and Nikolai G Basov of Moscow University and Joseph Weber of University of Maryland invented it simultaneously in 1951.

The ratio of probability of spontaneous to stimulated light emission is given by the relation: where ρ is the radiation energy density and is equal to Nhn, N being the number of photons of frequency n per unit volume and k is Boltzmann constant.
It is evident that this probability of spontaneous to stimulated light emission depends directly on the frequency of emission or inversely to the wavelength. Thus in the microwave region, stimulated emission is more probable than spontaneous, hence the early production of the maser.

Laser beam has following three basic characteristics:

1. Monochromaticity
2. Coherence
3. Directionality

Wavelength of the emission is longer than the absorption wavelength and the emission stops the moment the excitation ceases

Laser out put can be generated only from those laser materials, which show the property of fluorescence and laser action is possible only at that wavelength, where the fluorescence emission occurs. Scientists examine the energy levels spectroscopically to find fluorescence and evaluate the fluorescence efficiency of the new laser active media. In fluorescence, the emitted wavelengths are always longer than the absorbed wave lengths and emission stops the moment the excitation of the material stops.

In this process, the emission lasts much after the absorption has ceased to exit.

1. Laser light consists of essentially one wavelength, having its origin in stimulated emission from one set of atomic energy levels. This is possible because laser transition, in principle, involves well-defined energy levels.
2. EM wave of frequency n = (E₂ - E₁) only can be amplified, n has a certain range which is called line width. This line width is decided by various broadening factors such as Doppler effect of moving atoms and molecules.
3. The generation of laser is such that the laser cavity forms a resonant system and laser oscillation is sustained only at the resonant frequencies of the cavity. This leads to the further narrowing of the laser line width. So laser light is usually very pure in wavelength, we say it has the property of monochromatic.

No, laser light is not truly monochromatic. This line width is decided by various broadening factors such as Doppler effect of moving atoms and molecules.
Typically, the frequency bandwidth of a commercial He-Ne laser is about 1500MHz (full width at half-maximum, FWHM). In terms of wavelength, it means that at a wavelength of 632.8 nm, this means a wavelength bandwidth of about 0.01nm. On the other hand, the bandwidth of a typically diode laser with a wavelength of 900nm is about 1nm as compared to LED, which has a bandwidth of approximately 30-60 nm.

Coherence is of two types: temporal and spatial.
Temporal coherence is a measure of the correlation between the phases of a light wave at different points along the direction of propagation.
Spatial coherence is a measure of the correlation between the phases of a light wave at different points transverse to the direction of propagation. Spatial coherence tells us how uniform the phase of the wave front is.

Temporal coherence tells us how monochromatic a source is. Suppose the laser emits wavelength λ and λ + Δλ. These waves with slightly different wavelengths would continue to interfere constructively and destructively in space at points dependant on the magnitude of Δλ. Smaller is the value of Δλ, larger will be the distance between points where constructive and destructive interference will take place. This optical path between these two positions is called coherence length lc.
This is mathematically represented as: In terms of time, Δt, the time taken by the waves to cover the above-mentioned two positions, it can be given as:
where c is the speed of the light wave.

As we know that in case of stimulated emission, atoms in an upper energy level are triggered or stimulated in phase by an incoming photon of a specific energy. The incident photon must have an energy corresponding to the energy difference between the upper and lower states. The emitted photons have the same energy as incident photon. These photons are in phase with the triggering photon and also travel in its direction. This leads to directionality in case of a laser.
Further, the mirrors placed at opposite ends of a laser cavity enables the beam to travel back and forth in order to gain intensity by the stimulated emission of more photons at the same wavelength, which results in increased amplification due to the longer path length through the medium. The multiple reflections also produce a well-collimated beam, because only photons traveling parallel to the cavity walls will be reflected from both mirrors. If the light is the slightest bit off axis, it will be lost from the beam. The resonant cavity, thus, makes certain that only electromagnetic waves traveling along the optic axis can be sustained, consequent building of the gain.

For a Gaussian beam propagating in free space, the spot size w (z) will be at a minimum value w₀ at one place along the beam axis. This minimum position is known as the beam waist. The position of the beam waist for a typical laser resonator mode occurs either at a point of focus after it has passed through the lens, or in the region between the two mirrors of an optical resonator. For example, in case of confocal resonator (R₁ = R₂ = length of cavity, d), it occurs exactly in the middle.

In case of Gaussian beams, it is the distance from the beam waist where the mode area is doubled. In terms of beam radius, it is the distance, from the beam waist where the beam radius is increased by a factor of √2. Mathematically, it can be written as:

The region between the beam waist and the Rayleigh range is known as the near field. Or for near field conditions,

The distance beyond near field is known as far field. Divergence is always specified in the far field, which is usually chosen to begin around 10 to 100 times the Rayleigh range.

For near field conditions, For far field conditions

The optical intensity is a function of axial and radial distances. Axial distances are the distances along the propagation direction, whereas radial distances are the distances in the transverse plane. On the beam axis, it varies as: Where I_o is the maximum value at z=0 i.e. beam waist and drops gradually with increasing z, reaching half its value at z = z_R i.e. Rayleigh distance. When z>> z_R, The intensity decreases with the distance in accordance with the inverse square law.
In the transverse plane, the intensity distribution is of the form: Where I_max is the value of intensity at that value of z, r is the radial distance from the axis and w_or is the beam waist radius.
Maximum intensity is at a point where z = 0 and r = 0, i.e. at the center of the beam waist.

Peak pulse power (W) = Pulse energy (Joules) / Pulse width (sec)
Average Power (W) = : Pulse Energy (Joules) x Pulse Repetition Rate (Hz)
Average Power (W) = : Peak pulse power (W) x pulse width (sec) x Pulse Repetition Rate (Hz)

Far from the beam waist, i.e. z >>z_R, the beam radius increases approximately linearly with z, defining a cone with an angle θ. About 86% of the beam power is confined within this cone. The divergence arises because of the diffraction effects associated with the cavity bore. The diffraction-limited divergence is given as: where angle θ is in radians, and both λ and w_o are either in meter or centimeter. Higher the diameter of the beam waist, lower is the divergence.

Absorption, spontaneous emission, population inversion, stimulated emission, gain build up and finally laser action.

As we know that for laser action, an incident photon must have a higher probability of causing stimulated emission than of being absorbed which is possible only if N₂ > N₁. The number of photons emitted through stimulated emission process depends upon two factors i.e. N₂ and the incident energy. However, after stimulated emission, the atoms return from the excited state to the ground state, reducing the number of N₂, thus the capacity of the gain medium for further amplification. The effect is more pronounced, if he incident or pumping energy is large. Small signal gain is defined as the gain in the system under the conditions that the depletion of the excited species are negligible.

For laser action, population inversion i.e. N₂ > N₁ is required. A population inversion cannot be achieved with just two levels because the probability for absorption and for spontaneous emission is exactly the same. The lifetime of a typical excited state is about 10 ^-8 - 10 ^-9 seconds, so in practical terms, the electrons revert back to ground level through spontaneous emission of photon almost as fast as we pump them up to the upper level.

Radiance is usually to the source. It is power divided by the area of the laser beam and the solid angle within which the power is confined. Its units are Watts / m²-steradian. It is also referred as brightness.

For small angle, the relation between planar angle θ and the solid angle ρ is given as One milirad corresponds to

It is defined as the power per unit area of laser light falling on the target. It is usually referred as power density and expressed as Watt / cm². Suppose one kilowatt of laser power is falling on a target having a spot size of 10 cm. The irradiance can be estimated as:

Intensity = Laser Power / Area of the spot.
One can see that this is the same relation as that of Irradiance. The term irradiance is usually used when we consider a distant target and the actual power is the one reaching the target. This must take care of factors like attenuation in atmosphere etc. On the other hand, the term intensity is used for targets kept very near to the laser source i.e. typically for material applications point of view. So one can assume the power of the laser as the power falling on the work sample.

Wavelength: λ (m)
Frequency: n (Hz)
Time period: T (sec^-1)

c = n λ
n = c / λ
λ = c / n
n = 1 / T

The wavelength of Nd:YAG laser is 1.064 micron or 1.064 x 10^-6m. Frequency is given as:

Quantum efficiency of a laser is defined as the ratio of the energy of the output photon and the input energy necessary to produce that photon, for a perfect system. The operating efficiency is the ratio of the output energy to the input energy expressed in percentage. Taking Nd:YAG laser as an example, its quantum efficiency is about 80% while its operating efficiency is only few percentage.

As we know that when light passes through any medium, its velocity changes depending on the refractive index, n, of the medium. In the present case, the velocity in glass would be:

The frequency of the laser does not change and this velocity change is reflected in the wavelength change. In the present case, the wavelength in the medium will be reduced in the following manner:
For Nd:YAG laser, the wave length in the medium will be reduced from 1.064 micron to 0.71 micron.

The energy of a photon is given as E = h n, where h is Plank's constant and n is the frequency of laser radiation. The wavelength of Nd:YAG and CO₂ lasers are 1.064 and 10.6 micron respectively. The corresponding frequencies are The corresponding energies are given as: Or in terms of other familiar units "electron volts (eV)", these energies are: It is clear that photon emitted by Nd:YAG laser is an order more energetic than that emitted by CO₂ laser.

Please refer to following figures of three level and four level laser systems;
We know that the laser action is initiated only when the population inversion condition is achieved i.e. N₂ > N₁ where N₁ and N₂ are the population of the two levels involved in laser action. Further higher is the probability of stimulated emission as compared to absorption, if the difference N₂ - N₁ is large. In case of three level laser systems, the laser action is initiated only when the excited atoms in level 2 are significantly higher than the number of atoms in ground state at level 1. Since the lifetime of level 3 is of the order of nanoseconds, the excited atoms emit spontaneously and come to a metastable level 2, which has a higher lifetime. In other words, more than half of the atoms should be shifted to level 2 via level 3 to initiate laser action. This requires very strong pumping source. On the other hand, in case of four level lasers, laser action is achieved between levels 3 and 2; both of them are completely empty to start with. So if pumping were able to excite even a fraction of the total ground level atoms, these would shift to metastable level 3 via level 4, which has a short lifetime of the order of nanoseconds. This results in immediate establishment of population inversion condition and thus the laser action.
Since the number of atoms to be excited is far smaller in case of four level lasers as compared to three level lasers, the pump power requirements are much smaller too. This leads to higher efficiency in four level lasers.

1. Scattering and absorption due to impurities in the active laser material produce radiation losses
2. The finite dimensions of the laser material, end mirrors and other components produce diffraction losses
3. Imperfect end mirrors produce reflection losses

• Population inversion
• Fluorescence efficiency, line width and shape of the spontaneous emission in the wavelength of interest
• Resonant cavity

Active gain in the laser media should exceed the losses in a complete round trip path of the photons between the end mirrors.

After achieving population inversion, gain build up takes place and laser is generated. Due to laser generation, depletion of population inversion occurs and laser emission ceases. i.e. laser kills it self, unless population inversion and gain are achieved again. In normal lasing, laser output comes in bursts. A typical view of a normal solid-state laser output is shown in the figure below.