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.

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

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

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

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

The He – Ne laser is a four – level laser He* + Ne → He + Ne* + ΔE

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

Gain Gain (G) = e  (n j -n i )b  = transition cross-section b = length of active medium Oscillation begins when: gain in medium = losses of system  1  2 G 2 = 1 Threshold population inversion: Ingle and Crouch, Spectrochemical Analysis

Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 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

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

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?

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: m = 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.

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

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

Transverse Modes and Transverse modes determine the pattern of intensity distribution across the width of the beam. TEM 00 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.