1. Ruby Laser
Crystal structure of sapphire: -Al2O3 (aluminum oxide). The shaded atoms make up a unit cell of the structure. The aluminum atom inside the dashed hexagonal prism experiences an almost cubic field symmetry from the oxygen atoms on the prism.
Schematic energy level diagram for ruby – Cr3+ ions in sapphire.
Taken from Lasers and Electro-Optics: Fundamentals and Engineering by Christopher Davis, Cambridge University Press, 1996

2. Ruby Laser: Absorption Spectra
Absorption coefficient and absorption cross-section as a function of wavelength for pink ruby. These absorption spectra are slightly different depending on whether the incident polarized light being absorbed is linearly polarized with its electric vector parallel, or perpendicular, to the c symmetry axis of the crystal.
Detailed absorption spectrum of pink ruby in the 686 – 702 nm region showing the absorption peaks corresponding to the R1 and R2 components of the ruby laser transition.
Taken from Lasers and Electro-Optics: Fundamentals and Engineering by Christopher Davis, Cambridge University Press, 1996

3. Ruby Laser Simple electrical circuit for driving a flashlamp
Schematic energy level diagram of three- and four-level lasers
Taken from Lasers and Electro-Optics: Fundamentals and Engineering by Christopher Davis, Cambridge University Press, 1996

4. Ruby Laser: Pumping
Schematic arrangement of Maiman’s original ruby laser
Elliptical reflector arrangement for optical pumping a laser crystal by a linear flashlamp
Taken from Lasers and Electro-Optics: Fundamentals and Engineering by Christopher Davis, Cambridge University Press, 1996

5. Helium-Neon Laser: Pumping by Collision
Calculated variation of energy transfer cross-section for a collision between two atomic species as a function of the energy discrepancy E∞. The probability of excitation transfer is linearly dependent on the cross-section
Taken from Lasers and Electro-Optics: Fundamentals and Engineering by Christopher Davis, Cambridge University Press, 1996

6. Helium-Neon Laser: Energy Level Diagram
Taken from Lasers and Electro-Optics: Fundamentals and Engineering by Christopher Davis, Cambridge University Press, 1996

7. Helium-Neon Lasers Schematic arrangement of the first gas laser.
Typical schematic design of a modern laser.
Taken from Lasers and Electro-Optics: Fundamentals and Engineering by Christopher Davis, Cambridge University Press, 1996

8. Introduction to Optical Electronics
Quantum (Photon) Optics (Ch 12)
Resonators (Ch 10)
Electromagnetic Optics (Ch 5)
Wave Optics (Ch 2 & 3)
Ray Optics (Ch 1)
Photons & Atoms (Ch 13)
Laser Amplifiers (Ch 14)
Lasers (Ch 15)
Photons in Semiconductors (Ch 16)
Semiconductor Photon Detectors (Ch 18)
Semiconductor Photon Sources (Ch 17)
Optics
Physics
Optoelectronics

9. Putting it all together Theory of Laser Oscillation
Laser Amplification Medium +
Optical Resonator =
Laser

10. Population Difference Depletion of the steady-state population difference1 2

11. Population Inversion Population Difference Steady-State Difference
Saturation Time Constant*
Four-Level Laser
Three-Level Laser
*What is the small-signal approximation?

12. Amplifier Nonlinearity Gain Coefficient
Note: 0() is called the small-signal gain coefficient. Why?

13. Amplifier Nonlinearity Gain

14. Saturable Absorbers

15. Saturated Gain Coefficient
small-signal
region
large-signal
region
small-signal:
large-signal:

16. Gain Coefficient Inhomogeneously Broadened Medium 

17. Laser Amplification Medium

18. Optical Resonator
Optical Resonator
Resonator
response I

19. Conditions for Laser Oscillations
Gain Condition: Laser Threshold
Phase Condition: Laser Frequencies

20. Exercise 15.1-1 Threshold of a Ruby Laser
At the line center of the 0 = nm transition, the absorption coefficient of ruby in thermal equilibrium (i.e., without pumping) at T = 300 K is (0) = - (0) ≈ 0.2 cm-1. If the concentration of Cr3+ ions responsible for the transition is Na = 1.58 x 1019 cm-3, determine the transition cross section 0 = (0).
A ruby laser makes use of a 10-cm-long ruby rod (refractive index n = 1.76) of cross-sectional area 1 cm2 and operates on this transition at 0 = nm. Both of its ends are polished and coated so that each has a reflectance of 80%. Assuming that there are no scattering or other extraneous losses, determine the resonator loss coefficient r and the resonator lifetime p.
As the laser is pumped, (0) increases from its initial thermal equilibrium value of -0.2 cm-1 and changes sign, thereby providing gain. Determine the threshold population difference Nt for laser oscillation.

21. Saturated Gain Coefficient
Laser Turn-On
Time
Steady State
r Loss Coefficient
() Gain Coefficient
 (Photon-Flux Density)

22. Steady-State Population DifferenceNt
2Nt s 
Flux Density
Photon N0 N
Population
Difference
Pumping Rate

23. Output Flux Density vs. Transmittance
Laser 
Transmittance
Output Photon-Flux Density

24. Characteristics of Laser Output
Internal Photon-Number Density
Output Photon Flux & Efficiency

25. Laser Oscillations B
Resonator modes
allowed modes

26. Exercise 15.2-1 Number of Modes in a Gas Laser
A Doppler-broadened gas laser has a gain coefficient with a Gaussian spectral profile given by
where is the FWHM linewidth.
Derive an expression for the allowed oscillation band B as a function of D and the ration 0(0)/r where r is the loss coefficient.
A He-Ne laser has a Doppler linewidth D = 1.5 GHz and a midband gain coefficient 0(0) = 2 x 10-3 cm-1. The length of the laser resonator is d = 100 cm, and the reflectances of the mirrors are 100% and 97% (all other resonator losses are negligible). Assuming that the refractive index n = 1, determine the number of laser modes M.

27. Homogeneously Broadened Medium

28. Inhomogeneously Broadened Medium
Typical
Doppler

29. Doppler Broadening Laser Line (atomic) Transverse Mode Polarization
Brewster
Window
Polarization

30. Longitudinal Mode Selection
Etalon d1 d
Gain
Resonator Modes
Etalon Modes
Laser Output

31. How to Pulse Lasers
Modulator
Modulator
Peak Power
Average
Power t

32. Pulsed Lasers t Gain Switching t t Q-Switching t Modulated absorber
Loss
Pump t t
Laser
Output
Q-Switching
Modulated
absorber t
Laser
Output
Loss
Gain

33. Gain Switched Laser

34. Q-Switching

35. Pulsed Lasers Cavity Dumping t Mode Locking Optical Modulator Gain
Output
Gain
Loss
Mirror
Transmittance
Cavity Dumping
Optical
Modulator
Mode Locking

36. Mode-Locked Laser TF
M = 5
M = 15
M = 25

37. Exercise 15.4-3 Demonstration of Pulsing by Mode Locking
Write a computer program to plot the intensity I(t)=|A(t)|2 of a wave whose envelope A(t) is given by the sum
Assume that the number of modes M = 11 and use the following choices for the complex coefficients Aq.
Equal magnitudes and equal phases.
Magnitudes that obey the Gaussian spectral profile |Aq| = exp[-1/2 (q/5)2] and equal phases.
Equal magnitudes and random phases (obtain the phases by using a random number generator to produce a random variable uniformly distributed between 0 and 2.

38. (a) Equal magnitudes and equal phases.
(b) Magnitudes that obey the Gaussian spectral profile and equal phases.
(c) Equal magnitudes and random phases (obtain the phases by using a random number generator to produce a random variable uniformly distributed between 0 and 2.