Introduction

1. Atomic/Molecular jet Atomic/Molecular jet HHG HHG Cavity Buildup x250 Cavity Buildup x250 Imaging Molecular Structure With High HarmonicsDonald Willcox, Melanie Reber, Yuning Chen, Karabi Halder and Thomas AllisonStony Brook University, Stony Brook, NY Heterodyne HHG Spectroscopy Introduction Gain Narrowing Calculations High harmonic generation (HHG) from molecules is sensitive to the molecular electronic and nuclear structure, yet experimental systematics have presented a challenge to tomographic imaging of molecules. In part this is due to the difficulty of measuring the phase of the resulting harmonics, which existing techniques measure imprecisely or not at all. We propose to perform HHG spectroscopy on molecules using extreme ultraviolet (XUV) frequency combs [1]. Measurement of the heterodyne beat signal between two XUV combs will provide access to the amplitude and phase of the HHG from molecules with high fidelity. RF phase will permit us to precisely explore the systematics of high harmonic generation from aligned molecules and its potential for molecular tomography. [1] A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye. Direct frequency comb spectroscopy in the extreme ultraviolet.  Nature482, 68 (2012). Amplifier gain narrowing reduces bandwidth, increasing pulse duration and making fs pulses more difficult to achieve. We explore this effect and thus find the appropriate laser wavelength. • Doing HHG requires pulses. With a 100MHz laser, this is 5kW. • We can’t build a 5kW laser, so instead use passive enhancement (x250) in a cavity. Thus, a 40W laser will be sufficient for both cavity arms. • Coupling a frequency comb into a cavity requires matching cavity resonances with comb frequencies and depends on finesse . Yb Laser Output Yb-doped LMA Fiber Stretcher Yb-doped Rod Oscillator Compressor Fiber Rod Comb-Cavity Coupling First Beat Results from JILA Time domain picture: HHG From Molecules HHG Dipole Factorization (Additional pulses orient and excite molecules) Frequency domain picture: Comb Cavity The Brewster plate is oriented to transmit p-polarized harmonics with minimal reflection. Brewster Pierced Plate Mirror • Each IR half-cycle produces an attosecond burst of XUV light. A single attosecond burst consists of a broad continuum of frequencies, but the periodic train of bursts every half-cycle forms odd harmonics of the IR laser frequency. Or a small () pinhole through a mirror at the cavity output transmits the HHG light. Extreme UV Combs • In the three step model, HHG originates from a high frequency dipole moment between the returning free electron and the bound molecular orbital. If the amplitude and phase of this dipole is measured in the molecular frame, the data can be inverted to give the molecular wavefunction. • Inverting the harmonic spectrum requires measurement of the phase of the XUV light. Measurement of HHG amplitudes is straightforward, but phases are difficult. Gain narrowing arises since is narrower than simply • B Integral: B < 0.5 • Amplifier spectra demonstrate redshifting of the signal spectrum due to higher absorption of the shorter wavelength content compared to longer wavelengths. • A tradeoff exists between gain narrowing and amplifier gain depending on wavelength. • offers more bandwidth than , but amplification to high powers () is inefficient. We use to obtain enough power for intracavity HHG. • In the first experimental reconstruction of the N2 HOMO by Itatani, et al, 2004, phases were assumed, along with many other assumptions. HHG Spectra N2 HOMO Fourier Transform • With accurate phase measurement and • varying experimental conditions, • can HHG spectroscopy be a robust method for molecular imaging? Itatani, J., et al. Tomographic Imaging of Molecular Orbitals. Nature 432, 867-871 (2004). Frequency Combs • Creating beats between high harmonics in the XUV gives a beat signal at a tunable RF difference frequency! • The beat signal provides a clear measurement of the phase of molecular HHG. • Beat signals of 9th through 17th harmonics have been measured at JILA. • Sub-hertz linewidths are possible with stabilization of the XUV interferometer. • Comb teeth frequencies are multiples of pulse repetition rate offset by the carrier-envelope offset frequency • and are RF frequencies and can be electronically measured and stabilized! • High harmonics generated from IR comb create XUV comb in a definite phase relationship. Funding Sources