Lecture 12 2013_
Download as PPT, PDF1 like1,888 views
The document discusses key concepts related to laser emission and operation, including: 1. Stimulated emission cross section is a constant that determines the relationship between gain and stored energy in a laser medium. It depends on emission wavelength. 2. Homogeneous and inhomogeneous broadening contribute to the linewidth of laser emission. 3. Threshold requirements refer to the gain needed for a laser beam to reach saturation intensity after passing through an amplifier multiple times with mirrors. 4. Resonator stability depends on mirror curvature, with stable resonators keeping light near the axis and unstable resonators producing doughnut-shaped output beams. 5. Pumping techniques include direct, optical, and particle pumping to excite the
![Cavity Modes
Longitudinal Laser Cavity Modes
This expression is valid for almost all gas lasers, as well as
for solid-state and dye lasers in which the mirrors are
placed immediately at the ends of the gain medium. If a
laser has a space of length d - L between the gain medium
and the mirrors, and if that cavity space has a different
value for the index of refraction nc than the index nL of the
laser gain medium, then a specific laser mode frequency
associated with a mode number m can be expressed as,
ö
ù
1
[ ] ÷ ÷ø
æ
ç çè
úû
é
êë
- +
=
n d L n L
m c
c L
2
n](https://image.slidesharecdn.com/lecture122013-140828061613-phpapp01/85/Lecture-12-2013_-18-320.jpg)
Lecture 12 2013_
- 2. Emission Cross Section Definition: material parameters for quantifying the likelihood or rate of optical transition event Stimulated Emission Cross Section It is a constant for a specific laser transition in a specific gain medium It is strongly dependent on the emission wavelength Is essential for calculations of the expected performance because it determines the relationship between the gain and the energy stored Homogeneous Broadening æ 1 ( ) ÷ ÷ø H ul n s n 2 Inhomogeneous Broadening ö ç çè = ul ul H D o A n l p 2 4 2 ö 1/ 2 2 ln 2 æ 1 = æ D ö çè ( ) ÷ ÷ø ç çè D D ul n s n 2 ÷ø ul ul o A n l p p 4 Linewidth of emission
- 3. Threshold Requirement Definition The necessary requirements for the beam to grow to the point at which it reaches the saturation intensity Isat The saturation intensity, Isat is arbitrarily defined as the intensity at which the stimulated rate downward equals the normal radiative decay rate, I c ul ( ) u sat B n n t =
- 5. Threshold Requirement Laser With No Mirror The beam would meet the threshold gain requirement if, = ( )D @ 12 ± 5 th sat ul ul sat g L s n N L This is to ensure that the beam can develop a well defined direction before Isat is reached It is shown that, 2 ö æ e th sat L 16 ÷ ÷ø ç çè g L sat = a d Diameter of amplifier Threshold gain Laser beam divergence
- 6. Threshold Requirement Laser With One Mirror Adding a mirror can be thought of as adding a second amplifier Assuming that the beam just reaches Isat after two passes through the amplifier, the gain medium would meet the threshold gain requirement if, g L = g (2L) = g L = ( )DN (2L) @ 12 ± 5 th sat th th eff ul ul s n oThe beam is narrower, as it emerges from the end of the amplifier
- 7. Threshold Requirement Laser With Two Mirrors Placing a mirror at each end of the amplifier effectively adds an infinite series of amplifiers behind the original amplifier A slight amount of light is allowed to leak out the end by using a mirror with 99.9% reflectivity Two factors determine if a two-mirror laser can reach Isat 1. Net gain per trip 2. Sufficient gain duration The beam emerges with a very narrow angular divergence
- 8. Threshold Requirement Net Gain per Round Trip The minimum round-trip steady-state requirement for the threshold of lasing is that the gain exactly equal the loss, The solution for the threshold gain is then,
- 10. Resonator Stability Stable Resonators The curvatures of the mirrors keep the light concentrated near the axis of the resonator The only way light can escape from the resonator is to go through one of the mirrors
- 11. Resonator Stability Unstable Resonators The light rays continue to move away resonator axis until eventually they miss convex mirror altogether The output beam from this resonator doughnut-like shape with a hole in the middle The advantage is that they usually produce larger beam volume inside the gain medium
- 13. Pumping Techniques Direct Pumping The excitation flux is sent directly to the upper laser level u from a source or target state j, in which the source state is the highly populated ground state 0 of the laser species
- 14. Pumping Techniques Optical Pumping Often used for solid-state and organic dye lasers Particle Pumping Generally used for gas lasers and also semiconductor lasers
- 15. Pumping Techniques Direct Pumping Disadvantages Several effects can prevent direct pumping from being an effective excitation process for many potential lasers. These effects are listed as follows. 1. There may be no efficient direct route from the ground state 0 to the laser state u. For optical pumping, that would mean that the B0u associated with pump absorption is too small to produce enough gain; for particle pumping, it would mean that the electron collisional excitation cross section σ0u is too small. 2. There may be a good direct route from 0 to u, but there may also be a better route from 0 to l (the lower laser level) by the same process. In this case Γ0l/Γ0u may be too large to allow an inversion. 3. Even though there may be a good probability for excitation - via absorption either of the pump light associated with B0u for optical excitation or of σ0u e for electron excitation - there may not be a good source of pumping flux available. That is, there may be insufficient intensity, I for optical pumping, or insufficient density Np (or electron density ne) for particle pumping, at the specific energies necessary for pumping population from level 0 to level u.
- 16. Pumping Techniques Indirect Pumping Indirect pumping processes all involve an intermediate level q and can be considered in three general categories as diagrammed in the figure below: transfer from below, transfer across, and transfer from above.
- 17. Cavity Modes Longitudinal Laser Cavity Modes We have seen that one or more longitudinal laser mode frequencies can occur when a two-mirror cavity is placed around the laser gain medium and sufficient time (typically 10 ns to 1 μs) is allowed for such modes to develop. The total number of modes present is determined by the separation d between the mirrors, as well as by the laser bandwidth and type of broadening (homogeneous or inhomogeneous) that is present. The actual laser mode frequencies can be obtained by, m c 2 ö çè ÷ø = æ nd n for lasers in which the index of refraction n is the same throughout the pathway of the laser beam within the optical cavity, as shown in the figure on the next slide. Remember that m is a positive integer so as to satisfy the standing-wave conditions of the Fabry-Perot resonator.
- 18. Cavity Modes Longitudinal Laser Cavity Modes This expression is valid for almost all gas lasers, as well as for solid-state and dye lasers in which the mirrors are placed immediately at the ends of the gain medium. If a laser has a space of length d - L between the gain medium and the mirrors, and if that cavity space has a different value for the index of refraction nc than the index nL of the laser gain medium, then a specific laser mode frequency associated with a mode number m can be expressed as, ö ù 1 [ ] ÷ ÷ø æ ç çè úû é êë - + = n d L n L m c c L 2 n