Nonlinear Terahertz Spectroscopy

Coherent Spectroscopy and Control of Various Material Systems Using THz Fields

Tristan Pitt and Zhuquan Zhang

This lab is located at 2-063.

1. Introduction

In recent years there has been great progress in the exploration of the electromagnetic spectrum between 0.1 and 10 THz, also known as the THz gap. This region gives access to many interesting physical properties of semiconductors, molecular crystals, ferroelectrics, gas molecules, superconductors and biological objects, whose spectroscopic signatures are largely to be discovered in the THz range. In our lab, we are focused on development of generation of broadband/tunable narrow band THz radiation with high field strengths and characterization of various material systems' nonlinear and collective behaviors induced by the intense THz fields.

2. High field THz generation

Nonlinear THz spectroscopy requires broad bandwidth/tunable narrow band, and high electric field strengths. We generate single- and multi-cycle THz pulses using optical rectification in LiNbO3 crystals via noncollinear phase matching with tilted pulse front excitation from a Ti:Sapphire amplifier system. THz pulses are characterized by electro-optic (EO) sampling in EO crystals such ZnTe. The single-cycle THz pulses we generated typically have electric field strengths exceeding 100kV/cm and spectra ranging through 0.1-3 THz. We also developed the chirp and delay method to generate multiple-cycle THz pulses with flexible tunability and high field strength. The THz electric fields can be further enhanced by an order of magnitude using metamaterial structures called split-ring resonators. These generation methods open up new possibilities of observation of nonlinear collective materials responses.


                                          (a)                                                                                                 (b)

Fig 2.1 (a) Schematic setup of THz generation using tilted-pulse-front pump. (b) Single cycle THz waveform and its FFT spectrum (inset), with the noise level shown in the corner.

Fig 2. 2  (a) Multi-cycle THz waveforms and (b) FFT spectra with central frequency from 0.3 to 1.1 THz generated by the chirp and delay method.

3. Nonlinear THz spectroscopy (To be continued)

(1) THz alignment and orientation of gas/liquid molecules

Orientation of gas phase molecules by THz fields

The interaction of a molecule with an electromagnetic field depends on the relative angle between the molecule and the field polarization. In samples lacking of long range order, as in the gas phase, one measures spectroscopic signals which are averages over all possible molecular orientations. This can be avoided by ‘ordering’ the molecular sample prior to its spectroscopic interrogation, by rotating all the molecules toward a desired direction in the lab frame. 

Cartoon 3.2.1: Perfect molecular orientation (left hand side), Perfect molecular alignment (right hand side) and ‘unordered’ isotropic angular distribution (in the middle). 

Intense optical fields (typically 800nm) induce coherent rotational motion in gas phase molecules and result in transient molecular alignment along the polarization axis of the optical field. In this case, however, the inversion symmetry of the molecular ensemble is conserved (as shown by the cartoon in cartoon 1 – alignment - half of the molecular dipoles point toward the +z direction, while the other half point toward –z.)

An intense terahertz field forces the molecular dipoles to transiently orient in the +z (or the –z direction), giving rise to periodic emission of radiation bursts (Free Induction Decay signals).

The harmonic energy spectrum of linear molecules results in periodic orientation of the ensemble - a phenomenon known as “quantum revivals”. The first three of these revivals are shown in figure 2.

Figure 3.2.2: Electro-optic sampling of the free induction decay signals, emitted from carbonyl sulfide molecules following their interaction with the terahertz field

Further reading – [12] " Molecular orientation and alignment by single-cycle THz pulses," S. Fleischer, Y. Zhou, R.W. Field, and K.A. Nelson, Phys. Rev. Lett. 107, 163603 (2011). [url]

Multiple THz – molecule interactions in multilevel rotational system

Multiple interactions between the field and the molecule invoke a broad range of coherences between the rotational states. For example, two field-molecule interactions result in alignment of the molecules,   and are described by the coherences induced between rotational states  and . Such coherences manifest as transient birefringence of the molecular medium, with characteristic time of appearance and magnitude that strongly depend on the time delay between the two interactions. We study these responses in a multiple-level system. For example, the measurements shown in figure 3 of carbonyl sulfide at ambient temperature includes ~50 thermally populated rotational levels (or ~2500  rotational states including the  multiplicity) 

Figure 3.2.3: Seven experimental data sets illustrate THz-induced time-dependent birefringence in 180 torr OCS at 300 K for seven different delays (color-coded) between two single-cycle THz excitation pulses. The arrows mark the arrival time of the second pulse. The inset shows the birefringence modulation at ½Trev (41ps for the carbonyl sulfide molecules) induced by the first THz pulse in each data set. 

Further reading: [16] "Commensurate two-quantum coherences induced by time-delayed THz fields," S. Fleischer, R.W. Field and K.A. Nelson, Phys. Rev. Lett. 109, 123603 (2012). [url]

(2) Ferroelectric phase transition and THz vibrational spectroscopy

(3) THz driven phase transition in strongly correlated electronic systems

(4) Nonlinear 2D THz Magnetic Resonance Spectroscopy of Magnons

Magnons are quantized low-energy excitations of electron spins. In many ferromagnetic (FM) and antiferromagnetic (AFM) materials, intrinsic magnetic fields in the same range put collective spin waves (magnons) in the THz range. Current ESR spectroscopy remains limited at THz frequencies because the weak sources used only permit measurements of free-induction decay (FID) signals that are linearly proportional to the excitation magnetic field strength. Here, we explore the nonlinearity of magnons using time-delayed intense THz pulse pairs. We develop 2D THz magnetic resonance spectroscopy, which can be understood in terms of multiple field-spin interactions that generate the nonlinear signal fields. Magnons are resonantly excited without promoting electrons to excited states (as in most spintronics excitation) and hence the observed nonlinearities are of purely magnetic origin. The material under study is single-crystal YFeO3 (YFO). The ground state has canted AFM order with Two THz-active magnon modes, the quasi-AFM (AF) and quasi-FM (F) modes, can be constructed based on different cooperative motions of sublattice spins.


Fig. (a) The canted AFM order in YFO leads to a net magnetization M along the crystal c axis and the AF mode is the amplitude oscillation of M. (b) AF mode magnon signals induced by THz pulse A (blue) and B (red) individually. (c) Magnon signal with the presence of both THz pulses with interpulse delay time 3.7 ps (black) and the nonlinear signal (magnified 50×, magenta). (d) FT magnitude spectrum of the oscillatory signal of the nonlinear signal reveals third and second order peaks. (e) 2D THz magnetic resonance spectra of the AF mode magnons in YFO.

4. References

[1]. ''Velocity matching by pulse front tilting for large area THz-pulse generation." J. Hebling, G. Almasi, et al. Optics Express 10, 1161-1166 (2002).

[2]. "Terahertz polaritonics: High power THz signal generation in ferroelectric crystals," J. Hebling, K.-L. Yeh, M. C. Hoffmann, and K. A. Nelson, Integrated Ferroelectrics 92, 87-94 (2007).

[3]. "High Power THz Generation, THz Nonlinear Optics, and THz Nonlinear Spectroscopy," J. Hebling, K.-L. Yeh, M. C. Hoffmann and Keith A. Nelson, IEEE J. Selected Topics in Quantum Electronics 14, 345-353 (2008). 

[4]. "Generation of high power THz pulses by tilted pulse front excitation and their application possibilities," J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, J. Opt. Soc. Amer. B 25, B6-B19 (2008). 

[5]. "Generation of high average power 1 kHz shaped THz pulses via optical rectification," K.-L. Yeh, J. Hebling, M. C. Hoffmann, and K. A. Nelson, Opt. Comm. 133567-3570 (2008).

[6]. "Impact ionization in InSb probed by terahertz pump-terahertz probe spectroscopy,"  M. C. Hoffmann, J. Hebling, H. Y. Hwang, K. L.Yeh, and K. A. Nelson, Phys. Rev. B 79, 161201(R) (2009).

[7]. "THz-pump/THz-probe spectroscopy of semiconductors at high field strengths [Invited]," M. C. Hoffman, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, J. Opt. Soc. Amer. B, 26, No. 9, A29 (2009).

[8]. "Collective coherent control: Synchronization of polarization in ferroelectric PbTiO3 by shaped THz fields," T. Qi, Y.-H. Shin, K.-L. Yeh, K.A. Nelson, and A.M. Rappe, Phys. Rev. Lett. 102, 247603 (2009).

[9]. "Terahertz Kerr effect," M.C. Hoffmann, N.C. Brandt, H.Y. Hwang, K.-L Yeh, and K.A. Nelson, Appl. Phys. Lett. 95, No. 23, 231105 (2009).

[10]. "Impact Ionization in InSb studied by THz-Pump-THz-probe spectroscopy," M.C. Hoffmann, J. Hebling, H.Y. Hwang, K.-L Yeh, and K.A. Nelson, in Ultrafast Phenomena XVI, P. Corkum, S. DeSilvestri, K. Nelson, Phys. Rev. B 79 121201 (2009).

[11]. "Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump-terahertz probe measurements," J. Hebling, M.C. Hoffmann, H.Y. Hwang, K.-L. Yeh, and K.A. Nelson, Phys. Rev. B 81, No. 3, 035201 (2010).

[12]. " Molecular orientation and alignment by single-cycle THz pulses," S. Fleischer, Y. Zhou, R.W. Field, and K.A. Nelson, Phys. Rev. Lett. 107, 163603 (2011).

[13]. "Generation of high power tunable multicycle terahertz pulses." Z. Chen, X. Zhou, C.A. Werly and K.A. Nelson, Appl. Phys. Lett. 99, 071102 (2011).

[14]. ''Nonlinear THz conductivity dynamics in CVD-grown graphene." H. Y. Hwang, N.C. Brandt, H. Farhat, A.L. Hsu, J. Kong and K.A. Nelson, arXiv:1101.4985 [cond-mat.mtrl-sci] (2011). 

[15]. "Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial," M. Liu, H.Y. Hwang et al, Nature 487, 345-348 (2012).

[16]. "Commensurate two-quantum coherences induced by time-delayed THz fields", S. Fleischer, R.W. Field and K.A. Nelson, Phys. Rev. Lett. 109, 123603 (2012).

[17]. "Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves," J. Lu, X. Li, H. Y. Hwang, B. K. Ofori-Okai, T. Kurihara, T. Suemoto, and K. A. Nelson, Phys. Rev. Lett. 118, 207204 (2017)