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Amplification of laser light

We have seen how the stimulated emission can produce LASER light, to special properties: consistency, spectral purity, directional aspect. However you have to mind that trigger a stimulated emission is only a part of work to achieve a usable laser light source: without secondary amplification, it is not possible to generate a beam of LASER light at the exit of the cavity.

The only stimulated emission limits

The following scenario to understand why the amplification of the laser light to generate a beam out of the cavity.

We can imagine that once the reversal of population created in an environment, a first atom is greater spontaneously, causing a first photon. This photon has a great chance to meet in turn a second excited Atom, and cause the creation of a second photon. One of these photons can continue its journey and get out of the cavity - or be absorbed by one of the atoms not excited (even though their proportion is less than that of the excited atoms),.. .and the other cause a new delay, leading to the appearance of a new photon, before these two - here to come out of the middle. It will be then created 3 photons... there where there should be of the order of 10 19 to produce a light energy of one Joule!

Amplify and perpetuate the phenomenon of stimulated emission, to be able to maintain the photons generated by the show stimulated in the cavity containing the Middle excited; This phenomenon of stimulated emissions to reach a certain size. To achieve this goal, we use mirrors that you can place on part and on the other the Middle, on which the photons will bounce, and will be returned to the environment.

These mirrors are not truly the same as those of the bathrooms. their surface is not covered of a metal film but multiple layers, different refractive index, so as to create the necessary conditions so that the generated laser radiation-specific light wavelengths is reflected. We will see further the importance of that curvature and the distance separating these mirrors, between which the wavelike properties of the lights induce phenomena of "resonance". The laser cavity equipped with these two mirrors behaves then like a "resonator". One of these mirrors is partially transparent, so as to produce output laser radiation: this radiation can then be used for the required purposes: the radiation emitted at the exit of the cavity has been amplified between the mirrors; with the curvature and alignment are designed to facilitate the issuance of a directional light.

Loss and gain of the laser cavity

The radiation produced by the cavity to the outside is however 'lost' for the maintenance of the stimulated emission: If the transparency of the mirror is 5%, this means that out of 100 incident photons, 5 come out to generate laser radiation, 95 others will be reflected and returned towards the middle to produce new desexcitations and generate other photons. This means that the gain after this trip is at least 5% higher represented by the loss of the output mirror, lest the process of stimulated emission extinguish, "lack of fighters" (or rather lack of a sufficient number of photons).

In addition, factors other than the output of a certain number of photons have reduce the magnitude of the stimulated emission (i.e. the probability that a photon emitted by stimulation meets an excited Atom, and produce a second photon by delay). Indeed, when the photons emitted by stimulated emission encounter excited atoms, they in turn produce a new show stimulated, but... at the cost of a decrease in the number of excited atoms present in the environment. Therefore, constantly offset this reduction by an external input of energy (excitement of the environment). Photons produced by stimulated emission also also calling out of the cavity of the laser at any given time, and some are also absorbed, scattered, and thus lost to maintain the phenomenon of stimulated emission.

 

In total, this subtle antagonism losses and gain has two consequences:

-We need to reach a certain threshold of stimulated emission to gain, that is, the energy supplied in the Middle allows a population inversion and the beginning of a stimulated show maintained, i.e. higher than the cavity losses. In this case, the number of photons produced by stimulated emission grows gradually, but not indefinitely: it necessarily involved a "regulation" that makes the gain once the stimulated emission and resonance in the cavity remains constant (this gain is the difference between the contribution of the stimulated emission and losses by spontaneous absorption, diffraction, etc. in the cavity). This occurs regardless of the power supplied to the system. To understand this balance, it must be remembered that over there is desexcitations and stimulated emission, more produced identical photons, but fewer atoms likely to encounter these photons there...

 

-If one increases the energy supplied to the system, it does not increase the gain, but only the intensity (power) of output of the laser. It could be argued that simply to increase the transmission of the output mirror to increase the power obtained output: this may actually reduce the number of photons present in the cavity and thus reduce the rate of stimulated emission... There are for each laser optimum transmission, which allows to produce the maximum possible power without reducing the internal power of the laser.

For a constant power laser, the gain and therefore the power flowing in the laser range (oscillate) over time, because the increase in the production of photons by stimulated emission mechanically induced a reduction in the proportion of the excited atoms, and vice versa.

gain and power of the laser cavity

Schematic representation of the circulating power in a laser cavity: gain related to the stimulated emission, which occurs when the stream of photons meets the excited environment allows to compensate for losses related to the light emission output and absorption and diffusion phenomena.

 

We therefore understand why the cavity containing the excited environment had to be framed mirrors, because this allows the photons generated by the show stimulated to perpetuate it. However, in addition to its particle component (photons), light has wave properties (the energy of the photons is proportional to their "frequency"). Because it has a certain length in the axis of the mirrors; a cavity will serve of resonator for some frequencies of light, which has a significant impact on the quality of the produced radiation.

The following illustration is a picture of the cavity of an excimer laser used for refractive surgery (laser EX500, wavelight).

excimer laser cavity

Cavity Laser (excimer) and exit hole (EX500 Wavelight laser)

 

Characteristics of the resonator, consequences on the LASER radiation

 

Before addressing the characteristics in the frequency of the radiation produced by the cavity, back on the fact that inside the of the resonator, the photons emitted by stimulated emission circulate one mirror to another: the profile of energy created in a transverse plan marries a profile in "Bell", whose peak is located in the center of the cavity. This profile to a "Gaussian", one speaks of Gaussian profile. It presents noted wide 'w' (' for ' waist ' in English) which matches the width defined for the laser beam in energy terms.  The width of the LASER energy profile definition is arbitrary, because the beam has no sharp edges: by convention, when at a distance radiaire w of the central peak, the intensity is more than 13 per cent, the LASER energy is considered negligible.

profile Gaussian LASER light energy

The (RADIUS) within a cavity (main mode) laser Gaussian beam width is a function of the Gaussian peak of intensity measured in the transverse plane (perpendicular to the axis of the cavity and parallel to the axis of the mirrors). This width is defined as the radial distance at which the intensity of the beam is more than 13% of that of the central peak. In this representation, the profile is studied in cross-section (mirrors of the cavity would be directed vertically, in the corresponding axis in intensity)

The formula that provides the profile of the Gaussian beam intensity is I = Io exp (-2 x)2/w2).

Do not confuse the intensity of the Gaussian beam and its curvature: the intensity is equal to the square of the amplitude of the wave front coherent light that spreads into the cavity and "resonates" between the mirrors.

The radius of the Gaussian beam is its direction of propagation, and is one of the wave front formed by trains of coherent light (do not confuse the radius of curvature and the RADIUS which corresponds to the size of the beam). The radius of curvature is "infinite" at the level of the minimum diameter of the beam (diameter to for RADIUS w)o), and then decreases quickly before to grow again.

 

curvature of the beam in the cavity

Schematic representation of the curvature of the beam in the cavity.

 

 

A formula is used to calculate the width of the beam at a given propagation distance, if one knows its minimum radius (wo). This is important, because you can play on the w parametero to adjust the radius of the beam in such a way that it is the size you want when it reaches its target.

width of the laser beam

2W represents the width (diameter) of the laser beam after a spread over a distance of Z metres since its minimum diameter (w0). For a distance between instrument and eye, some cm, we can calculate only a beam of infra-red light (emitted by a laser Nd:YAG) wavelength equal to 1.06 microns is undergoing a significant expansion (of the order of a micron). If this bundle is progageait to the Moon, its diameter would however reach a few hundred kilometres. It is important to note that most Wo is big, and less the beam diverges, and vice versa.

 

It is also possible to calculate the radius of curvature of the beam propagating in the laser cavity Gaussian: this can be useful in designing the optimal geometry of the mirrors that surround the resonator. We built a cavity which we of course know the length: one can then calculate the curvature of the Wavefront of the oscillation laser at a given distance from the place where the Gaussian beam has a minimum radius (wo). Then simply make mirrors that have the same RADIUS. The Department of energy that circulates through the cavity is perpendicular to the envelope of the wave front, and at each point of the mirror thus designed, the reflected rays have the same angle as the incident rays. In this configuration, the resonance of the laser cavity will be known as "stable". There is a mathematical relationship between the radii of curvature of mirrors, the distance between them, with the possibility of inducing a stability at the level of the laser cavity.

It is interesting to note that this condition is independent of the wavelength, and therefore the type of radiation emitted by the excited middle. However, the wave nature of light is that only some radiation, specific wavelength, can be put in "resonance" in a same cavity.

 

Longitudinal LASER modes

For a given cavity length (L), the radiation that are likely to resonate in a longitudinal way (across the cavity) are those for which a whole number of half length of waves can register between the mirrors.

This condition is expressed as: n x (ʎ/2) = L where n is an integer.

Resonance mode, cavity

A radiation can be amplified between the mirrors (M1 and M2) if the position of these correspond to a 'mode '; the condition is met when the distance between the mirrors (L) is equal to a whole number of half wavelengths. The place of the modes, the amplitude of the electromagnetic field is zero.

The wavelengths can therefore resonate are given by:

ʎ = 2 L/n

We can convert this expression in the frequency domain:

Frequency and wavelength in vacuum are connected by: ʎ = c/F (c: speed of light)

We get the formula that provides the spectrum that can resonate in a cavity of length L:

Fn = n (c/2xL), where n is an integer

The resonant frequencies are separated by intervals of (c/2xL).

cavity and frequencies laser

The interval between the resonant frequencies located on part of the main frequency within a laser cavity only depends on the width of it, and not the medium used to generate laser radiation. More the cavity is short, and more the difference between the frequencies is important, and vice versa. To restrict the emitted frequency range, it is therefore necessary to use a longer cavity. For a 30 cm cavity, C / 2 L = 5 x 10-8 Hz, is 500 Mz. At this point, a question may be: what is the show stimulated in a cavity provides a range of wider radiation around the main peak 500 MH2? The answer is Yes!

As a result, a laser cavity has the geometry required to produce a spectrum of frequency corresponding to different longitudinal modes. This happens in practice because unlike the simplified model of the stimulated emission (restricted to an equivalent to a single resignation frequency energy transition), the phenomena of stimulated emission cause the emission of radiation whose frequency spectrum is not restricted to a frequency, but concerns a wide bandwidth. Here are a few of the reasons:

-The electrons are not as discrete energy levels that the simplified model suggests

-Complex phenomena such as the optical Doppler effect induce variations in frequency of the photons emitted for lasers which is gaseous: atoms or constituent molecules of these gases are fast moving, which leads to a broadening of the frequencies of Photonics show.

-Intra Cavitary pressure for gas lasers affects the probability of meeting of an excited Atom or molecule: lower this probability (less pressure, fewer molecules) and more bandwidth of the laser cavity is narrow, and vice versa.

For example, the gas (Helium Neon) laser emits a laser radiation composed of several frequencies, due to different transitions of the Neon Atom, which is excited by collision with the Helium atoms. The most intense matches a visible wavelength in the Red (632.8nm): enlargement by frequency related to the Doppler effect is close to 1.4 GHz: enlargement, however, allow a length of close coherence of 20 to 30 cm. If we can reduce this bandwidth 1 Mhz (by ' purifying' the emitted radiation), the coherence length can reach several hundred metres.

 

Depending on the application, various methods exist for 'purifying spectrally' the radiation emitted by the laser. For example, we can position a dispersive element to the center of the cavity (Prism, and/or Diffractive network), so as to deflect some radiation of wavelength (so a particular frequency) of the cavity axis.

Conversely, there is a type of laser emitting of pulse ultra brief, where the use of a range of radiation of different consecutive frequencies is desired, but these frequencies must be perfectly synchronized to generate of pulses very short: it's the principle of the technology of femtosecond laser.

 

Lasers pulsed lasers vs continuous

Lasers can deliver their (constant in time) continuously or pulsed radiation. Some lasers using a gaseous environment (ex: Helium Neon: no He) are lasers which provide a continuous program. Excimer lasers femtosecond lasers or even laser Nd: Yag used in ophtalmolgie are pulsed lasers.

With pulsed lasers, the delivered energy can be concentrated at the time: in other words, the emitted power (energy per unit of time) may be increased. A laser that emits 1 Joule in a second has a power of 1 Watt. If the Joule is emitted over a period of 10-6 seconds, the generated power is 1000 Watts. The issue period is the time between two pulses. Depending on the applications (medical or industrial) the power emitted by the excimer lasers varies between 0.50 and 50 Watt.

The peak power is equal to the energy delivered by the pulse on the duration of the pulse itself. The transmission time of pulses emitted by the femtosecond lasers is some hundreds of femtosecond (a femto second equals 10-15 seconds): this duration is very short in terms of the period (time between two pulses, of the order of 5-10)-6 seconds with a 200 KHz as the FS 200 Wavelight laser). The energy delivered in one pulse is weak, of the order of a joule (10 micro-6 (J), but extremely brief time of the show ensures a very high peak power, able to ionize matter by defeating the force between the electrons and atomic nuclei (see here for more information on the orders of magnitude)

One response to "laser light Amplification"

  1. BUI says:

    Hello
    Your explanations are very clear
    With my thanks
    Dr Yen BUI

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