lasers in chemistry - stemed.sitestemed.site/ncsu/ch437/lec19/pdf/laser_basics.pdf · lasers in...
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Lasers in Chemistry
Light Amplification by Stimulated Emission of Radiation
I. Requirements for a laserII. Two state, three state, and four state systems.
III. Survey of tunable lasers.IV. Applications
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Requirements for a laser
• Gain (population inversion)• Laser cavity (reflecting mirrors)• Output coupler (semi-reflective mirror)• Standing waves can be obtained for nλ=2L• The bandwidth in the laser cavity can be
modulated using birefringent filters, etalons, or grating/prism combinations.
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Gain can only be achieved with a population inversion
• Gain represents the increase in photons emitted from the sample compared to a Boltzmann distribution.
• The Boltzmann distribution will never allow for more population in an excited state than in the ground state.
• Gain represents a non-Boltzmann distribution induced by optical or electrical pumping.
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Two Level System in Spectroscopy
• For states 0 and 1 the Einstein B coefficients are equal
• High fluence limit results in a ratio of populations determined by microscopic reversibility
• At equilibrium Wabsorption = Wemission
• Since Br is the same, in the limit of large r we have that n1 = n0, and there is no population inversion (i.e. n1 < n0).
Wemission=n1BρWabsorption=n0Bρ
0
1
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A Three Level System: Laser
• Optical or electrical pumping is used.• Pump to intermediate state that decays into long-
lived emissive state.• Ground state population must be overcome to
make a population inversion in the emissive state.• Example: the ruby laser, Cr:Al203 in which Cr d-d
transitions give a population inversion in a state that emits at 594 nm.
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A three-level system provides a route to a population inversion
• We can simplify the rate equations by assuming that
• If k21n2 >> n1Bρ then a population build-up in n1can lead to an population inversion n1 >> n0.
• Still has disadvantage that population in n0 is dominating at equilibrium.
k21
n1Bρ’n0Bρ
0
1
2
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Basic physical justificationThe figure shows why a population inversion is needed. It you want to get more photons out than you put in you need many molecules in the excited state to start a cascade of output photons.
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A four-level system produces superior results for laser design
• A four level system provides ease of creation of an inversion since state 3 is essentially unpopulated at equilibrium.
k12
n2Bρn0Bρ
k30Xe + Cl-
Xe+Cl-
Xe+ + Cl-
Xe:Cl
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A four-level system produces superior results for laser design
• A four level system provides ease of creation of an inversion since state 3 is essentially unpopulated at equilibrium.
• In order for this scheme to work the rate
• Rate from 1 to 2 is rapid• Rate from 3 to 0 is rapid.
k12
n2Bρn0Bρ
k30Xe + Cl-
Xe+Cl-
Xe+ + Cl-
Xe:Cl
1
2
3 0
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1
2
3 0
A four-level system produces superior results for laser design
• A four level system provides ease of creation of an inversion since state 3 is essentially unpopulated at equilibrium.
• In order for this scheme to work the rate
• Rate from 1 to 2 is rapid• Rate from 3 to 0 is rapid. • The population inversion is
set up between 2 and 3.
k12
n2Bρn0Bρ
k30Xe + Cl-
Xe+Cl-
Xe+ + Cl-
Xe:Cl
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Comparison of thermal and pumped population
Thermal Pumped
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The laser cavity
The partial reflector is usually called the output coupler.
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The gain bandwidthAlthough laser light is perhaps the purest form oflight, it is not of a single, pure frequency. All lasersproduce light over some natural bandwidth orrange of frequencies. A laser's bandwidth ofoperation is determined primarily by the gainmedium that the laser is constructed from, and the range of frequencies that a laser may operate over is known as the gain bandwidth. For example, a HeNe gas laser has a gain bandwidth of1.5 GHz Ti:sapphire has a bandwidth of about 128 THzExercise: convert these to wavenumbers!
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Longitudinal modesThese standing waves form a discrete set offrequencies, known as the longitudinal modes of the cavity. These modes are the only frequencies of light which are self-regenerating and allowed to oscillate by the resonant cavity; all other frequencies of light are suppressed by destructive interference. For a simple plane-mirror cavity, the allowed modes are those for which the separation distance of the mirrors L is an exact multiple of half the wavelength of the light λ, such that L = Nλ/2, when N is an integer known as the mode order.
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Longitudinal modesIn practice, the separation distance of themirrors L is usually much greater than the wavelength of light λ, so the relevant values of N are large (around 105 to 106). Of more interest is the frequency separation between any two adjacent modes N and N+1; this is given (for an empty linear resonator of length L) byΔν:
where c is the speed of light (≈3×108 m·s−1).
∆ν = c2L
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Output modesThe figure on the right shows the combination of the gain bandwidth and longitudinal modes. This leads to a discrete set of wavelengths that are output from the laser within the bandwidth.
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Gaussian beam optics
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Transverse resonator modes
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A Gaussian beam has a transverse electric field and intensity distribution that are well represented by a Gaussian function. This is observed when the laser operates using the fundamental transverse mode (TEM00 mode) of the optical resonator.
When refracted by a diffraction-limited lens, a Gaussian beam is transformed into another Gaussian beam (characterized by a different set of parameters). This optical model is a convenient model used in laser optics.
Introduction to the Gaussian beam
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Intensity profile of TEM00
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The concept of a beam waist