1. EM Radiation Sources 1. Fundamentals of EM Radiation 2. Light Sources
3. Lasers

2. Light Amplification by Stimulated Emission of Radiation
What is a laser?
Light Amplification by Stimulated Emission of Radiation

3. Overall
Ingle and Crouch, Spectrochemical Analysis

4. Stimulated Absorption
Einstein Coefficient for Absorption Bij (cm3 J-1 s-1 Hz):
with Un: energy density of the field at the appropriate frequency n (J cm-3 Hz-1)
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

5. Spontaneous Emission
Einstein Coefficient Aji for Spontaneous Emission (s-1):
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

6. Stimulated Emission Einstein Coefficient for Stimulated Emission:
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

7. Overall
Ingle and Crouch, Spectrochemical Analysis

8. BijUnni = Ajinj + BjiUnnj
For an ideal black body, the rate of absorption and emission must be balanced:
BijUnni = Ajinj + BjiUnnj
Rearrange:

9. Are you getting the concept?
Determine the population ratio for atoms/molecules in two energy states spaced by 1 eV at T = 300 K: nj ni

10. Spectral Energy Density
We know:
Set equal and solve for Uv:
Looks similar to Planck’s Radiation Law:

11. Population Inversion
Goal: More atoms or molecules in the upper energy level than the lower energy level.
Heating the lasing medium will not work:
nj = nie-(Ej-Ei)/kT
Must selectively excite atoms/molecules to particular energy levels. Most common approaches:
*light
*electricity

12. Optical Pumping Intense light source at h (e.g. flash lamp)
Excites to a metastable state to achieve population inversion
With fast flashing, initial photons start chain reaction
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

13. Electrical Discharge
Accelerated e- and ions excite atoms/molecules into higher energy states
Common in gas lasers
Ingle and Crouch, Spectrochemical Analysis

14. Better for pulsed mode operation
Three - Level System
No saturation
Not very efficient
Better for pulsed mode operation
Ingle and Crouch, Spectrochemical Analysis

15. The ruby laser is a three – level laser
Commercial ruby laser
operates with efficiency ~ 1%
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

16. Four - Level System More efficient than 3-level
Laser transition does not involve ground state or most highly excited state
Easier to achieve population inversion
Ingle and Crouch, Spectrochemical Analysis

17. The He – Ne laser is a four – level laser
He* + Ne → He + Ne* + ΔE
Ingle and Crouch, Spectrochemical Analysis

18. Resonance Cavity and Gain
Gain = degree of
amplification based
on positive feedback
Ingle and Crouch, Spectrochemical Analysis

19. Gain Gain (G) = es(nj-ni)b s = transition cross-section
b = length of active medium
Oscillation begins when:
gain in medium = losses of system
r1r2G2 = 1
Threshold population inversion:
Ingle and Crouch, Spectrochemical Analysis

20. Light Amplification in Resonance Cavity
Highly collimated beam
Typically ~mm beam width, ~mrad divergence
A typical photon travels about 50 times forward and backward within the cavity
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

21. Mirror Arrangements
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

22. Are you getting the concept?
Knowing that the purpose of the resonance cavity is to direct the majority of the photons back through the active medium, what cavity characteristics will be most important?
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

23. Achieving Resonance
Stimulated emission is coherent (all light waves in phase)
If the cavity is an integer multiple of the wavelength, each wave will be at the same phase when it reflects from one of the cavity mirrors (recall that a photon make many round trips in a laser cavity before it is emitted).
This allows constructive interference between all photons.
Want: ml = 2nL
Other wavelengths will not be strongly amplified, and thus, will die out.
In practice, laser transitions have gain over a range of wavelengths – the gain bandwidth… so that resonance cavity lengths are not impossible to achieve.

24. Achieving Resonance Goal: Laser cavity where L = ml/2n
Estimate amplification factor:
Amp = (1+Gain)L
This condition is not as strict as it sounds because:
Laser transitions have gain over a range of wavelengths
Any integer multiple (longitudinal mode) of l will work

25. Longitudinal Modes
Actual  is the convolution of the transition bandwidth and the  of the longitudinal modes.
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

26. Transverse Modes
Transverse modes determine the pattern of intensity distribution across the width of the beam.
TEM00 has a Gaussian distribution and is the most commonly used.
The resonator geometry of many commercial lasers is designed to obtain “single transverse mode” operation.
and