Vorlesungen uber theoretische Physik Von Prof. Arnold Sommerfeld. Band 1: Mechanik. Vierte, neubearbeitete Auflage. Pp. xii + 276. 18 D. marks. Band 2: Mechanik der deformierbaren Medien. Pp. xv + 376 + 4 plates. 18 D. marks. Band 3: Elektrodynamik. Pp. xvi + 368. 18 D. marks. Band 6: Partielle Differentialgleichungen der Physik. Pp. xiii + 332. 18 D. marks. (Wiesbaden: Dieterich'sche Verlagsbuchhandlung, 1947–1949.)

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Lectures on Theoretical Physics

Elementary Theory of Angular Momentum. By M. E. Rose. Pp. x, 248. 80s. 1957. (Wiley)

Light is one of the most powerful and precise tools allowing us to control, shape and create new phases of matter. In this task, the magnetic component of a light wave has so far played a unique role in defining the wave's helicity, but its influence on the optical response of matter is weak. Chiral molecules offer a typical example where the weakness of magnetic interactions hampers our ability to control the strength of their chiral optical response. It is limited several orders of magnitude below the full potential. Here we introduce freely propagating locally and globally chiral electric fields, which interact with chiral quantum systems extremely efficiently. To demonstrate the degree of control enabled by such fields, we focus on the nonlinear optical response of randomly oriented chiral molecules. We show full control over intensity, polarization and propagation direction of the chiral optical response, enabling its background-free detection. This response can be fully suppressed or enhanced at will depending on the molecular handedness, achieving the ultimate limit in chiral discrimination. Our findings open a way to extremely efficient control of chiral matter and to ultrafast imaging of chiral structure and dynamics in gases, liquids and solids.

Locally and globally chiral fields for ultimate control of chiral light matter interaction

The fast and accurate analysis of chiral chemical mixtures is crucial for many applications but remains challenging. Here we use elliptically-polarized femtosecond laser pulses at high repetition rates to photoionize chiral molecules. The 3D photoelectron angular distribution produced provides molecular fingerprints, showing a strong forward-backward asymmetry which depends sensitively on the molecular structure and degree of ellipticity. Continuously scanning the laser ellipticity and analyzing the evolution of the rich, multi-dimensional molecular signatures allows us to observe real-time changes in the chemical and chiral content present with unprecedented speed and accuracy. We measure the enantiomeric excess of a compound with an accuracy of 0.4% in 10 min acquisition time, and follow the evolution of a mixture with an accuracy of 5% with a temporal resolution of 3 s. This method is even able to distinguish isomers, which cannot be easily distinguished by mass-spectrometry.

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Real-time determination of enantiomeric and isomeric content using photoelectron elliptical dichroism.

Using a model methanelike chiral system, we theoretically demonstrate a possibility to access photoelectron circular dichroism (PECD) by a single experiment with two overlapping laser pulses of carrier frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$, which are linearly polarized in two mutually orthogonal directions. Depending on the relative phase, the resulting electric field can be tailored to have two different rotational directions in the upper and lower hemispheres along the polarization of the $\ensuremath{\omega}$ pulse. We predict a strong forward-backward asymmetry in the emission of photoelectrons from randomly oriented samples, which has an opposite sign in the upper and lower hemispheres. The predicted PECD effect is phase and enantiomer sensitive, providing new insight in this fascinating fundamental phenomenon. The effect can be optimized by varying relative intensities of the pulses.

Photoelectron Circular Dichroism with Two Overlapping Laser Pulses of Carrier Frequencies ω and 2 ω Linearly Polarized in Two Mutually Orthogonal Directions

Photoelectron circular dichroism refers to the forward/backward asymmetry in the photoelectron angular distribution with respect to the propagation axis of circularly polarized light. It has recently been demonstrated in femtosecond multi-photon photoionization experiments with randomly oriented camphor and fenchone molecules [C. Lux et al., Angew. Chem., Int. Ed. 51, 4755 (2012) and C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)]. A theoretical framework describing this process as (2+1) resonantly enhanced multi-photon ionization is constructed, which consists of two-photon photoselection from randomly oriented molecules and successive one-photon ionization of the photoselected molecules. It combines perturbation theory for the light-matter interaction with ab initio calculations for the two-photon absorption and a single-center expansion of the photoelectron wavefunction in terms of hydrogenic continuum functions. It is verified that the model correctly reproduces the basic symmetry behavior expected under exchange of handedness and light helicity. When applied to fenchone and camphor, semi-quantitative agreement with the experimental data is found, for which a sufficient d wave character of the electronically excited intermediate state is crucial.

Theoretical description of circular dichroism in photoelectron angular distributions of randomly oriented chiral molecules after multi-photon photoionization

Photoelectron circular dichroism refers to the forward/backward asymmetry in the photoelectron angular distribution with respect to the propagation axis of circularly polarized light. It has recently been demonstrated in femtosecond multi-photon photoionization experiments with randomly oriented camphor and fenchone molecules [C. Lux et al., Angew. Chem. Int. Ed. 51, 5001 (2012);C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)]. A theoretical framework describing this process as (2+1) resonantly enhanced multi-photon ionization is constructed, which consists of two-photon photoselection from randomly oriented molecules and successive one-photon ionisation of the photoselected molecules. It combines perturbation theory for the light-matter interaction with ab initio calculations for the two-photon absorption and a single-center expansion of the photoelectron wavefunction in terms of hydrogenic continuum functions. It is verified that the model correctly reproduces the basic symmetry behavior expected under exchange of handedness and light helicity. When applied it to fenchone and camphor, semi-quantitative agreement with the experimental data is found, for which a sufficient d wave character of the electronically excited intermediate state is crucial.

R. E. Goetz

Papers

Theoretical description of circular dichroism in photoelectron angular distributions of randomly oriented chiral molecules after multi-photon photoionization

Theoretical description of circular dichroism in photoelectron angular distributions of randomly oriented chiral molecules after multi-photon photoionization