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Third order nonlinear optics 1. Two Photon pumping 2.. Third harmonic generation 3. Doppler free spectroscopy 4. Lambda structures

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Two-photon absorption and optical pumping ri W Purpose: create a two photon population inversion As before: But we need to be ON resonance Adiabatic approximation breaks down!

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Two-photon absorption and optical pumping ri W Alternate to pi pulse pumping:

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Two-photon absorption and optical pumping The dilemma: if The adiabatic approximation breaks down, and the energy Gets stored in the intermediate levels by absorption!? Too high powers are required to reach an inversion If Is there a solution? Is there a problem worth looking for a solution? “Light travels undisturbed for billions of years - only to get its wavefront distorted in the last few milliseconds” Yes, there is a problem: atmospheric distortion of out of space radiation:

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What are the solutions to atmospheric distortions? Send an observer into space …they selected Mr. Hubble

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2nd solution: Correct for the atmosphere a) Correct the telescope to minimize the size of the image of the point source. Choose/create a point source within 2 arcsec of the object to be observed. b) But how?

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Two-photon absorption and optical pumping 2 photon coherent excitation of Sodium Which we approximate by The ideal solution: create an artificial star by optical pumping of Na

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now 1 st approach: off-resonance zero area pulse excitation

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now

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1 st approach: off-resonance zero area pulse excitation now

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1 st approach: off-resonance zero area pulse excitation The purist will tell you that you have to include the full hyperfine structure

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1 st approach: off-resonance zero area pulse excitation The result of listening to the purist: t = 650 ps = 100 ps F 589 =.90 J/cm 2 F 1140 = 2.2 J/cm 2 = 14.6 GHz = 2.39 GHz => 3.1 mW / cm 2

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Second approach: the two-photon “pi pulse” 10 ps, 4.58 J/cm 2 (each) 1 = 1.91 GHz and 2 = 2.39 GHz.

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Full hyperfine structure (including Doppler-distribution) = 25 ps F 589,1140 = 14.1 J/cm 2 = 58.6 MHz = 0 => 30 mW / cm 2

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Sodium temperature: 190 K. Pulse duration: 10 ps, Single pulse fluence: 4.58 J/cm 2 (each) Detunings: 1 = 1.91 GHz and 2 = 0 GHz. -pulse yields 5 times more signal than cw excitation at roughly the same energy expenditure Photon return is 25 times above detection limit for an un-cooled PMT -pulse excitation leads to a signal per excitation Comparison of coherent excitation versus cw More details in J.~Biegert and J.~C.~Diels, “Feasibility study to create a polychromatic guidestar in atomic sodium", Physical Review A, 67: (2003). Much

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2. Third harmonic generation Bloch vector model for two-photon resonance Max value of = 1,, therefore Shortest two photon absorption length Shortest harmonic generation length Linear absorption length Linear absorption length for 3rd harmonic

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Shortest two photon absorption length Shortest harmonic generation length Linear absorption length Linear absorption length for 3rd harmonic Maximum conversion efficiency L 0 0 L L photon resonance Low efficiency, but low power needed small large small + 3 photon resonance Highest efficiency, but highest power needed 2. Third harmonic generation

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Simple characteristics: Reversibility Zero-area pulse excitation E F=E P d=P Mechanical analogy Do we need to look at a 2 level-system? Each successive cycle of the pulse constitutes a zero-area pulse sequence Cumulative (coherent) effects in the attosecond scale!

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Intracavity interaction in a mode-locked laser Atomic beam pulse ZERO-AREA PULSE What are they good for?

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2. Third harmonic generation Exploit coherent propagation effects to minimize the two-photon absorption losses. U V W

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Third order nonlinear optics 1. Two Photon pumping 2.. Third harmonic generation 3. Doppler free spectroscopy 4. Lambda structures Does it apply to ultrashort pulses?

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3. Doppler Free two-photon spectroscopy PMT Tunable laser Doppler cancels – one measures lines with their natural linewidth

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Doppler Free two-photon spectroscopy PMT Doppler cancels – one measures lines with their natural linewidth Tunable short pulse laser Shorter pulses stronger signal? But… can one get better resolution than the pulse bandwidth? Yes… continuous train of pulses

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Doppler Free two-photon spectroscopy PMT Tunable short pulse laser “Transit time” broadening Shorter pulses stronger signal? Doppler does not cancel anymore i[ v]t c e i[ v]t c e cc v

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Third order nonlinear optics 1. Two Photon pumping 2.. Third harmonic generation 3. Doppler free spectroscopy 4. Lambda structures

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