Problem

• Precise control of Nonlinear Optical effects is the limiting factor for controlling spectral broadening and pulse compression for high-powered laser systems (short pulses have large bandwidth)
• A consistent method to obtain uniform spectral broadening and pulse compression will provide direct access to extreme NLO’s

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Findings

• They showcase a method for controlling the broadening of the SH spectrum of a 4.55-μm mid-IR pulse during filamentation in a mixture of Kr and O2 (molecular gases)
• They independently adjust the spectrum generation by altering physical properties of the gas mixture and focusing conditions

Methods

• They present data for 4 different experiments
• They obtain and analyze the SH spectrum produced in Kr and O2 separately
• Then, they obtain the SH spectrum for the gas mixture of Kr and O2
• Finally, the alter the setup of the mixture experiment to achieve pulse compression at the laser’s full energy

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Experimental Setup

• ID – iris diaphragm: Controls the numerical aperture (NA) which was varied (.005-.03)
• F1 –focusing lens: f=20cm
• F2–culminating lens: f=15cm
• 17cm long gas cell
• Setup was altered for different experiments

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• B integral was lower than 1 rad for all NA values used (measure of nonlinear phase shift of light) and both mixture experiments

SHG-FROG

• Note. SHG is a special case of SFG when the frequency of the two beams are identical
• FROG also generalizes to arbitrary NLO’s (Self diffraction, SPM, etc.)
• Sensitivity of .001nJ

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Signal Pulse

XFROG

• A spectrogram uniquely determines the intensity and phase of a waveform within a given time interval

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What is a Spectrogram

Setup

SHG/SFG FROG

An Algorithm

• Essentially a 2-D phase retrieval algorithms (unique solution)
• Use algorithm to obtain E(t) (waveform) from it’s spectrogram
• There is an analogous algorithm for XFROG where we can determine the phase and intensity of an unknown beam from a known beam

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• Going to need Phase matching in either SHG and SFG for efficient generation

Pressure Dependent SHG

• Krypton
• Higher Pressure Blue shift dominates due to self-steepening and plasma generation
• They attribute the red-shifting to low-order harmonics mixing with mid-IR driver and four-wave mixing creating symmetric broadening up to ~21 bar

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Krypton

Oxygen

• Note. Krypton starts broadening symmetrically until about 25 bar (blue-shift)
• Critical power of 96GW at 1 bar
• Reduces linearly for higher pressure
• Using 160 fs 4.55-μm with NA=.03 at 20 GW

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Cont.

• Oxygen
• They attribute redshift of the output to Stimulated Raman Scattering under mid-IR filamentation in molecular gases. Ref. 10 and 12.
• There is spectral broadening in both KR and O2.
• Somewhat striking as Oxygen has a lower ionization energy (12 eV) as compared to Krypton (14 eV) yet we see more blue shifting in Krypton.

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Krypton

Oxygen

• Critical Power of 41 GW at 1 bar
• Reduces linearly with pressure
• Using 160 fs 4.55-μm with NA=.03 and 20 GW

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Stimulated Raman Scattering

• The red-shifting of the spectrum of the beam can be attributed to the inelastic collision of photons with the molecular gas.
• The photons impart momentum onto the molecules and they in turn gain rotational and vibrational kinetic energy.

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• Specifically, from a QM point of view we can imagine the pump photon excites a molecule to a virtual state and then the molecule relaxes to a rotational mode of lower energy releasing a “Stokes” (weaker) photon

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SH spectra For Oxygen

Main Takeaways (Oxygen)

• The shaded lower diagram is the SH spectrum of the input pulse
• The SH spectrum clearly broadens in both red and blue regimes
• For lower NA’s they were able to reduce the spectral breadth and blue-shifting to the initial spectrum

NA vs Bandwidth (Oxygen)

• Fundamental beam profiles at far-field vs NA
• Ultrashort pulses have large bandwidths–their bandwidth is 5.4THz with pulse duration: 160fs
• They claim the spectral broadening in O2 mainly due to Self-Phase Modulation and SRS

The Mixture

• They use a 2:1 mixture of Kr to O2
• 20 bar of Kr and 10 bar of O2
• A 5mm aperture to increase broadening
• To achieve a higher compression ratio and use the full energy the then upgraded the experiment

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SH spectra for Gas Mixture

• SH spectrum 3 different NA’s
• The SH spectrum spans from 1.76-2.5μm
• Dips attributed to strong SPM and atmospheric CO2 absorption due to long optical path of SHG-FROG set up

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Upgraded Experiment

• They increased the length of the cell to 32 cm with weaker focusing lens (30cm)
• The input beam size was reduced to use almost the entire energy
• They used a NA=.004

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• They obtained a 62 fs pulse from the original 160 fs pulse for a compression factor of 2.6
• They then reconstructed the time evolving envelope and the spectrum using XFROG

SFG-XFROG

• From the Algorithm we can reconstruct the output pulse spectrum, accumulated phases and pulse envelopes
• A and B are in 17-cm cells
• C and D are in 32-cm cells
• Solid lines in A and C indicate the pulse envelopes
• Solid lines in B and D show the spectra
• Dashed lines are the accumulated phases

Conclusion

• Precise control of the spectral content of the mid-IR radiation through the gas pressure, composition, and numerical aperture of the focusing optics is demonstrated.
• Pulse compression by a factor of 2.6 is also revealed.
• They claim in general: inert molecular gases provide an easily adjustable medium for uniform spectral broadening in a low plasma density self-channeling regime