Extremely large nonlinear response in crystalline quartz at THz frequencies Soheil Zibod Payman Rasekh Murat Yildrim Wei Cui Ravi Bhardwaj Jean-Michel M enard Robert

2025-04-27 0 0 677.94KB 8 页 10玖币

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Extremely large nonlinear response in crystalline quartz at THz

frequencies

Soheil Zibod* Payman Rasekh Murat Yildrim Wei Cui Ravi Bhardwaj Jean-Michel M´enard Robert

W. Boyd Ksenia Dolgaleva

S. Zibod, P. Rasekh

School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Ontario K1N

6N5, Canada

Email Address: szibo043@uottawa.ca

M. Yildirim, W. Cui, R. Bhardwaj, J.-M. M´enard

Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

R. W. Boyd

Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada; Institute of Optics,

University of Rochester, Rochester, New York 14627,United States

K. Dolgaleva

School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Ontario K1N

6N5, Canada; Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Keywords: THz radiation, Nonlinear refractive index, Crystal quartz, Vibrational modes

We report on the ﬁrst experimental observation of a very strong nonlinear response in crystalline quartz in the terahertz (THz)

frequency region through THz time-domain spectroscopy (THz-TDS). Theoretical modelling is presented and predicts a Kerr coeﬃcient

n2equal to 5.17×10−14 m2W−1. The time-domain analysis of the measured data shows that with increasing of the THz peak amplitude,

the pulse experiences a larger time delay in the sample. As the THz amplitude increases to values higher than 110 kV cm−1, the growth

rate of the delay decreases, indicating a saturation process. The value of the nonlinear refractive index calculated through the frequency-

response analysis is estimated to be on the order of 10−13 m2W−1, which is several orders of magnitude larger than typical values of the

nonlinear refractive index of solids in the visible region. Furthermore, a negative ﬁfth-order susceptibility on the order of 10−30 m4V−4

is measured.

1 Introduction

Terahertz (THz) radiation, deﬁned as a region of the electromagnetic spectrum between the microwaves

and far-infrared, is gaining a growing importance in applications such as biomedical sensing,[1, 2] security,[3]

spectroscopy and imaging,[4] and communications.[5] Furthermore, THz time-domain spectroscopy (THz-

TDS) systems are used for monitoring production processes,[6] art conservation,[7] and characterization of

materials.[8]

THz-TDS allows the simultaneous measurement of the magnitude and phase of the THz signal through

the linear electro-optic eﬀect, representing a suitable technique for measuring the complex refractive index

of a material at the THz frequencies.[9] The recent development of intense THz pulse generation techniques

opens the door to studying nonlinear behavior of diﬀerent materials in the THz region.[10] Nonlinear

eﬀects such as THz-induced impact ionisation and inter-valley scattering in semiconductors,[11, 12, 13, 14, 15]

THz high-harmonic generation by hot carriers,[16, 17, 18, 19] and THz-induced ferroelectricity and collective

coherence control have been demonstrated.[20, 21] A very large third-order nonlinearity has been reported

for water vapor,[22] where the stepwise multiphoton transitions in water molecules lead to a third-order

susceptibility of χ(3) = (0.4+6i)×102m2V−2. Extreme THz-induced Kerr eﬀects have been reported

for diﬀerent liquids,[23, 24, 25, 26] where the nonlinear refractive indices can be several orders of magnitude

larger than their values in the optical regime. Moreover, THz-induced Kerr eﬀects have been observed in

amorphous chalcogenide glasses such as arsenic trisulﬁde and arsenic triselenide.[27] Furthermore, it has

been theoretically predicted that crystals can exhibit an extremely large nonlinear refractive index in the

THz frequency range.[28] Crystalline solids such as quartz are predicted to show THz nonlinear refractive

indices that exceed the optical values by several orders of magnitude. However, there has not been any

experimental demonstration reported to date.

arXiv:2210.01926v1 [physics.optics] 4 Oct 2022

Figure 1: Theoretical modelling of the nonlinear refractive index caused by the dominant resonance at 37.2 THz (blue solid

lines) and the resonances at 7.9 THz (black dashed lines) and 3.9 THz (red dashed lines) in quartz. The top inset resolves the

values of the nonlinear refractive indices at around the low-frequency resonances. The bottom inset shows the contribution

from three resonances at the lower frequencies (1 THz and lower).

Here we report on the experimental observation of very strong nonlinear interactions in crystalline

quartz in the THz regime. First, a theoretical model for the nonlinear refractive index of quartz at

the THz frequencies is presented.[28] This model relies on the classical anharmonic oscillator, where the

nonlinear refractive index is given as a sum of contributions from diﬀerent vibrational modes. As predicted

by the model, the value of the nonlinear refractive index at the lower frequencies exceeds its typical values

in the visible range by several orders of magnitude. Then, we perform nonlinear THz-TDS on a 1-mm-

thick z-cut quartz sample. The time-domain analysis of the collected data demonstrates an increased

delay, experienced by the pulse as it propagates through the sample, with increasing THz beam intensity.

However, the growth rate of the delay decreases with the further intensity increase, revealing a phase

saturation process. Further, the analysis in the Fourier domain shows an increase in the nonlinear phase

and nonlinear absorption with the increase of the THz ﬁeld intensity. At higher signal levels, however, the

nonlinear phase grows with ﬁeld intensity increase at a declining pace, whereas the nonlinear absorption

tends to increase more rapidly. The data analysis revealed extremely large values of the nonlinear refractive

index and ﬁfth-order susceptibility, where the latter has a negative real part.

The manuscript is structured as follows: In Section 2, we describe a simple theoretical model for

calculating the contributions from the vibrational modes to the nonlinear refractive index of crystalline

quartz at THz frequencies, developed originally in Ref. [28]. We modify the model to include additional

vibrational resonances, which helps us to achieve a better agreement with the experimental results. In

Section 3, the experimental setup for the nonlinear THz-TDS is introduced. In section 4, we present the

experimental results. In addition to the time-domain analysis, the frequency response of crystalline quartz

is presented. Finally, the nonlinear parameters of the material are calculated and the result is compared

with the theoretical model.

2 Theory

An extremely large refractive index has been theoretically predicted for quartz in the THz regime, where

the nonlinear refractive index was predicted to be several orders of magnitude larger than its typical

visible and near-infrared values.[28] The model is based on the equation of motion of a classical anharmonic

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ExtremelylargenonlinearresponseincrystallinequartzatTHzfrequenciesSoheilZibod*PaymanRasekhMuratYildrimWeiCuiRaviBhardwajJean-MichelMenardRobertW.BoydKseniaDolgalevaS.Zibod,P.RasekhSchoolofElectricalEngineeringandComputerScience,UniversityofOttawa,Ottawa,OntarioK1N6N5,CanadaEmailAddress:szibo043@uot...

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Extremely large nonlinear response in crystalline quartz at THz frequencies Soheil Zibod Payman Rasekh Murat Yildrim Wei Cui Ravi Bhardwaj Jean-Michel M enard Robert

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