Coherent Raman Umklappscattering Luqi Yuan 1,* , Aleksandr A. Lanin 2 , Pankaj K. Jha 1,3, * , Andrew J. Traverso 1 , DmitriV. Voronine 1 , Konstantin E. Dorfman 1 , Andrei B. Fedotov 2 , George R. Welch 1 , Alexei V. Sokolov 1 , Aleksei M. Zheltikov 1,2† and Marlan O. Scully 1,3 1 Texas A&M University, College Station, TX 77843, USA 2 M.V. Lomonosov Moscow State University, Moscow, Russia 3 Princeton University, Princeton, NJ 08544, USA We identify the conditions for coherent Raman scattering to enable the generation of phase-matched, highly directional, nearly-backward-propagating light beams. Our analysis indicates a unique possibility for standoff detection of trace gases using their rotational and vibrational spectroscopic signals. We demonstrate spatial selectivity of Raman transitions and variability of possible Umklapp scattering implementation schemes and laser sources. I. INTRODUCTION The universal requirement of momentum conservation in coherent light matter interactions imposes stringent limita- tions on the range of wave-vector directions allowed for the coherent signals [1–3]. Specifically, generation of backward- propagating beams in nonlinear wave-mixing processes has been a long-standing problem in optical science, impeding the application of wave-mixing-based techniques to standoff de- tection [4, 5]. When applied to a generic third-order process generating a field with a frequency ω 4 through the coherent mixing ω 1 ± ω 2 ± ω 3 of light fields with frequencies ω 1 , ω 2 , and ω 3 , momentum conservation translates into the following requirement for the wave vectors k i = n i ω i /c of the optical fields i =1, 2, 3 involved in the wave-mixing process (c is the speed of light in vacuum and n i = n(ω i ) is the index of refraction at the frequency ω i ): Δk = k 4 ± (k 1 ± k 2 ± k 3 )= 0. With properly designed periodic structures, this phase- matching condition can be satisfied by picking up the mo- mentum deficit from the reciprocal lattice of the structure. This approach has been successfully demonstrated with a va- riety of photonic structures [6, 7]. In the standoff detection mode, however, creation of subwavelength lattices, needed to phase-match the backward wave, is technically difficult re- quiring a complex arrangement of auxiliary high-power laser beams [5] or modulating the index of refraction [8]. In the mi- croscopy mode, backward coherent anti-Stokes Raman scat- tering (CARS) becomes possible [9] due to the specific geom- etry of tightly focused light beams scattered by microinhomo- geneities in a biotissue. None of such epi-CARS microscopy beam-interaction geometries, however, seems to suggest a re- alistic way of scaling to larger beam propagation paths that are needed for optical standoff detection. Recent experimental demonstrations of backward stimu- lated emission from atomic oxygen produced by UV laser pulses in the air [10], yielding a highly directional backward- propagating light beam with an excellent quality and an aver- age power well above the microwatt level [11], offer a pow- erful tool for standoff spectroscopy. Still, in order to bene- * Equal contribution † Electronic address: zheltikov@physics.tamu.edu fit from the chemical selectivity provided by the Raman ef- fect, and to obtain efficient (coherent) signal generation, the Δk =0 momentum conservation (phasematching) needs to be satisfied. The main goal of this paper is to demonstrate that coherent Raman scattering of laser fields can give rise to a highly directional (phase-matched) nearly backpropagating CARS signals, and to use phasematching to resolve individual signal components in space. This regime of the Raman effect, referred to hereinafter as coherent Raman Umklappscattering, by analogy with phonon-phonon and electron-phonon Umk- lappscattering in solids [12], is shown to be well suited for standoff detection applications, including remote sensing of trace gases in the atmosphere and on the surfaces of distant objects, paving the way for the development of a new class of security and ecological safety monitoring systems. Coherent anti-Stokes Raman scattering by molecular vibra- tions [9, 13] and molecular rotations [14, 15] has a broad range of applications. For example, the real-time detection of a low concentration of bacterial endospores (≈ 10 4 spores) via CARS was demonstrated [16, 17]. The waveguide Raman effect in a variety of specialty fibers[18–21] is promising for bio and chemical sensing applications. We note that the tradi- tional CARS cannot be used in a standoff mode in scenarios involving perfectly parallel forward and backward propagat- ing laser beams, because of the phasematching constraints. However, we show that under certain conditions, a small an- gle between laser beams satisfies phasematching. Moreover, the angled geometry provides a convenient spatial separation of the applied laser and generated signal beams [22, 23]. The corresponding spatial separation of various Raman transition lines allows improving detection capabilities which in conven- tional spectrally separated methods may be limited by detector resolution or by spectral line broadening. II. IMPLEMENTATION SCHEMES We consider a coherent Raman scattering process where optical fields with frequencies ω 1 and ω 2 , referred to as the pump and Stokes fields, are used for a coherent selective ex- citation of a Raman-active mode with the frequency Ω in a medium. The third field, with frequency ω 3 , is used to probe this coherence, giving rise to Stokes and anti-Stokes signal fields with frequencies ω 4 = ω 3 - (ω 1 - ω 2 )= ω 3 - Ω and