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

Light Amplification by Stimulated Emission of Radiation What is a laser? Light Amplification by Stimulated Emission of Radiation www.laserglow.com

Overall Ingle and Crouch, Spectrochemical Analysis

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.

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

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

Overall Ingle and Crouch, Spectrochemical Analysis

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

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

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

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

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

Better for pulsed mode operation 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 Commercial ruby laser operates with efficiency ~ 1% Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

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 Ingle and Crouch, Spectrochemical Analysis

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

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

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.

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? Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

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.

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 http://micro.magnet.fsu.edu/primer/java/lasers/gainbandwidth/index.html

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

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. www.wikipedia.org and www.lexellaser.com