Transient Birefringence in Molecular Gases

Experiment

A strong, short pump pulse causes an impulsive alignment and the generation of a rotational wave packen in a gas of linear molecules (such as CO₂) inside a hollow-core capillary. The time evolution of the wave packet causes subsequent transient alignments or rotational revivals several picoseconds after the pump pulse.

During the revivals, the macroscopic polarizability becomes anisotropic, causing an interrogating probe pulse to experience spectral and polarization state changes. The spectral shear depends on the polarization of the probe as well as the pump pulses.

Theory

The ensemble molecular alignment state can be described as a superposition of spherical harmonics, where the expansion coefficients b vary with time. We have developed analytic and numerical models to calculate the b(t) coefficients. The model is valid not only for arbitrary linear polarization of the pump pulse, but also circularly and elliptically polarized pump fields.

Single-Shot Phase Measurement

In this experiment, we demonstrate a single-shot measurement of the transient phase modulation due to field free molecular alignment at the revival times of a rotational wave packet. The wave packet is excited by an arbitrarily polarized ultrashort laser pulse in CO₂ at room temperature. With this technique the time dependence along the eigenpolarization directions of the linear susceptibility tensor, i.e., the time dependence of its principle components, can be directly observed with high sensitivity.

In order to measure the transient phase due to the molecular alignment in a single shot, we utilize a technique which is based on the idea originally suggested by J. Valdmanis (Ultrafast Phenomena V, 1986), where a linearly-chirped ultrafast probe pulse is used to map temporal dynamics onto the probe pulse spectrum. Since then, this time-spectrum mapping has been realized in many different physical systems.

The technique uses spectral interferometry between two identically chirped broad bandwidth laser pulses. This probe-reference pulse pair is sent into a molecular gas in which a pump pulse has excited a rotational wave packet, leading to a transient optical susceptibility. To measure the time-varying phase modulation imposed on a probe pulse by the transient optical susceptibility, the probe pulse is time delayed with respect to the pump pulse as to coincide with a revival of the rotational wave packet. It thus accumulates phase as a function of time.

For a circularly polarized pump pulse there is no birefringence expected due to the molecular alignment, since the alignment direction is along the direction of propagation. The phase accumulated for this case by a linearly-polarized probe-reference pair oriented along x (dashed line), z (dotted line), and along 45° relative to z (solid line), as indicated by the insets. The measured phase along those three directions is essentially identical, confirming an absence of birefringence as expected.

References

• K. Hartinger and R. A. Bartels, "Pulse polarization splitting in a transient wave plate," Opt. Lett. 31(23), 3526-3528 (2006).
• Klaus Hartinger and Randy A. Bartels, "Single-shot measurement of ultrafast time-varying phase modulation induced by femtosecond laser pulses with arbitrary polarization," Appl. Phys. Lett. 91 (2007)