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 Goal: Laser cavity where L = m /2n 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.

Coherence Factors that compromise coherence: 1. thermal fluctuations 2. vibrational fluctuations 3. emission of multiple wavelengths 4. multiple longitudinal modes Temporal Coherence – How long do the light waves remain in phase as they travel? Coherence Length = 2 /n 

Coherence Spatial Coherence – Over what area does the light remain in phase?

Are you getting the concept Calculate the coherence length for the sources below using n air = 1.00: (a)light bulb emitting from nm (b)semiconductor laser emitting from – nm (c)He-Ne laser emitting from – nm

Laser Wavelengths Factors influencing monochromaticity of laser light: 1. transitions responsible for emission 2. nature of transition determines bandwidth 3. resonance cavity characteristics Doppler bandwidth:  = [5.545 kT/Mc 2 ] ½ where M is the mass of the atom/molecule

Limiting Emitted s with a Fabry-Perot Etalon Insert a pair of reflective surfaces that form a resonant cavity tilted at an angle to the axis of the laser medium. Transmitted  depends on: 1.the angle the light travels through the etalon (  ) 2.the thickness of the etalon (l) 3.the refractive index of the material between the 2 surfaces (n)

Are you getting the concept? Calculate the minimum pulse length for a laser with a 1-nm emission bandwidth at a center wavelength of 500 nm.

Are you getting the concept? Calculate the best spectral resolution (in cm -1 ) that can be achieved with a pulse length of 368 fsec. Recall: ħ = x Js

Output Power Output power will depend on: 1.variations in power level with time 2.efficiency of converting excitation energy into laser energy 3.excitation method 4.laser size What is wall-plug efficiency? A practical measurement of how much energy put into the laser system (from the wall plug) comes out in the laser beam. Active Medium power supply

Pulsed Laser Power Considerations Consider a Gaussian beam profile: Peak Power FWHM Rise Time Fall Time Power Time If power was constant: E = Pt In this case, E = ∫P(t)dt Average Power = ΣE/t or Peak Power x Duty Cycle Duty cycle = Pulse Length x Repetition Rate

Controlling Laser Pulse Characteristics There are 3 primary methods to control laser pulse time: Q Switched Lasers – cavity mirrors are temporarily unavailable so the laser medium stores energy rather than releasing it. When the mirror is made available, a high energy pulse is released. Cavity dumped lasers – an extra cavity mirror momentarily diverts photons from a fully reflective cavity after photon energy has accumulated for awhile Modelocked lasers – “lock” together multiple longitudinal modes so that a laser simultaneously oscillates on all of them to emit very short pulses

Q-Switching Build up population inversion by preventing lasing while pumping. Systemis momentarily realigned to allow lasing. System is momentarily realigned to allow lasing. Results in short (~ nsec), high-intensity (up to MW) pulse. Only possible if the laser can store energy in the excited state longer than the Q-switched pulse. Demtröder, W. Laser Spectroscopy, Springer, Berlin: switch

Cavity Dumping Laser cavity has to “fully” reflective mirrors. A steady power grows inside the cavity during normal operation. Momentarily, a third mirror enters the light path and directs the beam out of the cavity. All energy is dumped in one pulse lasting as long as it takes the light to make a round trip in the laser cavity. Demtröder, W. Laser Spectroscopy, Springer, Berlin: 1996.

Mode - Locking Edward Piepmeier, Analytical Applications of Lasers, John Wiley & Sons, New York, Method for producing very short pulse widths (~ s). Synchronize longitudinal modes.

Are you getting the concept? A laser has a bandwidth of 4.4 GHz (4.4 x 10 9 Hz). What is the shortest modelocked pulse it can generate, according to the transform limit?

Accessible Wavelengths Lasers have also been prepared for the vacuum UV (VUV, nm) and XUV (eXtreme UltraViolet; also called the ultrasoft X-ray region; <100 nm). The shortest wavelength laser produced so far emits at 3.5 nm. Projects to extend this range to 0.1 nm by 2011 are in progress. Why x-ray lasers are so difficult to build: A ji /B ij = 8  h 3 / c 3 Intensity of stimulated emission (B) is proportional to intensity of spontaneous emission (A). Tallents, G.J. J. Phys. D 2003, 36, R259. Dattoli, G.; Renieri, A. Nucl. Inst. Meth. Phys. Res. A 2003, 507,

Characteristics of a Few Commercial Lasers Data from Typical Characteristics HeNeIon (Ar, Kr, mixed gas) He-CdDiodeDiode- pumped solid state P/mW0.1–404–4002– –5000 Efficiencygoodpoorgoodexcellentvery good Battery operation yesno yes Current supply (for typical P) na Vac na60– Vdc Noise<0.05% to <3% na<2%na<2% (peak to peak) Weight / kgna –10.9na Beam diver- gence / mrad 0.7–2.41.0–2.00.5–2.9<1.5x0.5<1.25 Warm-up time<15 min <15 min to <30 min <5 min<15 min Price0.5–4 k$6–11 k$8–25 k$0.8–4 k$4–33 k$