Fundamentals of Laser Dynamics
Fundamentals of Laser Dynamics.
ABSTRACT
The thesis presents the modeling and simulation of three types of lasers namely; Semicondoctor laser, Solid state laser and CO2 laser. The rate equations were derived and simulated to examine the dynamic behaviour of the three types of lasers under investigation.
The result shows that the Semicondoctor laser has the longest latency period, highest intensity spikes and takes a longer time to come to relaxation oscillation (RO) while the CO2 laser has the shortest latency time, the lowest intensity spikes and takes a shorter time to come to relaxation oscillation (RO).
The solid state laser lies between the semiconducor laser and the CO2 laser.
It was also observed from the results that as the pump power A increases the latency time decreases, the intensity increases and it takes a shorter time for the laser to come to relaxation oscillation.
TABLE OF CONTENTS
1 Introduction 1
1.1 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Concept of stability . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Aims of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Laser operation 4
2.1 How Laser Emits Light . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Active Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Spontaneous Emission . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.5 Population Inversion . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.6 Non Radiactive Deexcitation . . . . . . . . . . . . . . . . . . . . . 7
2.7 Pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.8 Stimulated Emission . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.9 Lasing Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Models of Laser Dynamics 10
3.1 Simple one-dimensional models . . . . . . . . . . . . . . . . . . . 10
3.2 The two-dimensional dynamics . . . . . . . . . . . . . . . . . . . . 14
3.3 Three-Dimensional Model . . . . . . . . . . . . . . . . . . . . . . 19
3.3.1 Physical considerations . . . . . . . . . . . . . . . . . . . . 19
3.3.2 Model of ruby laser . . . . . . . . . . . . . . . . . . . . . . 20
3.3.3 CO2 laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Fundamentals of Laser Dynamics CONTENTS
4 Simulation Results 28
4.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Switch-on Transient and phase portrait . . . . . . . . . . . . . . . 29
4.3 Comparison of the linear approximation vs. exact numerical solution 41
5 Conclusion and Recommendations 45
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Recommendation . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
INTRODUCTION
1.1 Lasers
The origin of laser can be traced back to the Einstein’s concept of stimulated emission. The presence of a photon, with appropriate frequency, can stimulate an excited atom to emit a photon, with identical phase, frequency and propaga- tion direction than the incident one [2].
Three components are fundamental in any laser: a medium proving gain/amplification, a pump generating population inversion, and a cavity confining the optical field.
The first population inver- sion was attained in ammonia molecules passing through an electrostatic focuser by Townes and Shawlow [3] in 1958. The constructed device, originally called MASER, emitted light in the microwave range.
The first successful laser, oper- ating in the visible spectrum, was constructed by Maiman [4] and consisted of a ruby crystal surrounded by a helicoidal flash tube. This advert was followed, at the ends of the same year, by experimental demostration of working He-Ne gas laser.
Lasers have important applications in communications signal processing and medicine, including optical interconnects, RF links, CD ROM, gyroscopes, surgery, printers and photocopying (to mention but a few).
Compared with other optical sources, lasers have a high bandwidth and higher spectral purity, they function as bright cohenrent sources.
BIBLIOGRAPHY
Manus J. Donahue The Chaos Theory.
Haken, Light (North-Holland, Amsterdam, 1985)
A.L Schawlow and C.H Townes, phys. Rev. 112, 1958
T.H Maiman, Nature 187, 493 (1960)
Bernard, Jaffe. A compact Science Dictionary. Edited by G. E speck. London: Ward, Lock and Co, 1954.
