Terahertz-field-induced optical birefringence in common window and substrate materials Mohsen Sajadi,* Martin Wolf, and Tobias Kampfrath Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany * [email protected]
Abstract: We apply intense terahertz (THz) electromagnetic pulses with field strengths exceeding 2 MV cm−1 at ~1 THz to window and substrate materials commonly used in THz spectroscopy and determine the induced optical birefringence. Materials studied are diamond, sapphire, magnesium oxide (MgO), polymethylpentene (TPX), low-density polyethylene (LDPE), silicon nitride membrane (SiN) and crystalline quartz. We observe a Kerreffect-type transient birefringence in all samples, except in quartz and Si, where, respectively, a linear electrooptic signal and a response beyond the perturbative regime are found. We extract the nonlinear refractive indices and the electrooptic coefficient (in the case of quartz) of these materials and discuss implications for their use as windows or substrates in THz pumpoptical probe spectroscopy. ©2015 Optical Society of America OCIS codes: (040.2235) Far infrared or terahertz; (190.0190) Nonlinear optics.
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1. Introduction Owing to recent technological progress in terahertz (THz) photonics [1–3], pulsed electromagnetic fields with several MV cm−1 peak strength can routinely be generated with tabletop sources over a spectral range from 1 to tens of THz [4,5]. Such high fields have opened the field of nonlinear THz spectroscopy where low-frequency modes of matter are driven into unexplored large-amplitude regimes [6–8]. Examples are vibrational ladder climbing in molecular crystals [9], transient birefringence of liquids [10], control over molecular rotations in gases [11], charge-carrier generation by impact ionization in semiconductors [12,13], excitation of the Higgs mode in superconductors [14] and control over spin dynamics in magnets [15,16]. In THz spectroscopy, samples (such as thin solid films) are often attached to substrates or kept inside cryostats or cuvettes that comprise windows for the incident and outgoing THz and (possibly) optical radiation. While the linear THz and optical properties of a large number of THz transparent materials are known [17], the responses of such materials to intense THz radiations have not yet been studied systematically. Filling this gap of knowledge is critical to THz pump-optical probe experiments in which the pump-induced signal from windows and substrates has to be as small as possible. Here, we measure the transient optical birefringence of the most common THz window/substrate materials induced by an intense THz pulse. For most of the materials studied, we find the birefringence scales with the square of the THz electric field (Kerr effect). Only in the case of quartz, the signal is proportional to the THz field (Pockels effect).
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Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28986
2. Experimental details Our experimental setup is schematically shown in Fig. 1(a). Intense electromagnetic pulses at ~1 THz center frequency are generated by optical rectification in a MgO-doped (1.3 mol-%) stoichiometric LiNbO3 crystal with the tilted-pulse-front technique [4,18]. The LiNbO3 is driven by laser pulses (energy of 4.5 mJ, center wavelength of 800 nm, duration of 40 fs, repetition rate of 1 kHz) from an amplified Ti:sapphire laser system (Coherent Legend Elite Duo). A grating (2000 lines mm−1) and two cylindrical lenses (focal lengths of 250 mm and 150 mm) are used to tilt the intensity front of the 800-nm generation pulse by 62° inside the crystal. The beam cross section on the input face of the crystal is 3 mm and 9 mm (full width at half maximum) in horizontal and vertical direction, respectively. The emitted THz pump pulse is focused on the sample surface by means of three off-axis parabolic mirrors (focal lengths of 0.5”, 3” and 2” with 1” = 25.4 mm). The pump-induced birefringence of the sample is measured by a temporally delayed probe pulse (2 nJ, 780 nm, 8 fs) derived from the seed laser oscillator (Venteon One). The probe pulse is linearly polarized before the sample and subsequently acquires elliptical polarization owing to the birefringence induced by the co-propagating THz pulse. The ellipticity is detected with a combination of a quarter-wave plate and a Wollaston prism which splits the incoming beam in two perpendicularly polarized beams with power P1 and P2. The normalized difference ( P1 − P2 ) / ( P1 + P2 ) is twice the probe ellipticity and measured by two photodiodes as a function of temporal delay between THz pump and optical probe pulse. To vary the THz intensity on the samples, a pair of wire-grid polarizers is used. 800 nm, 8 fs, 2 nJ
ZnTe and quartz ETHz
ETHz
Eprobe
Eprobe
E0
(b)
amplitude (normal.)
(a)
ǀǀ ┴ sample
λ/4
PD1
THz field amplitude
45°
Δτ
0
1
2
frequency (THz)
E0 =2.1 MV/cm
PD2
PM
WP
-1
0
1
2
3
time (ps)
Fig. 1. (a) Schematic of the THz-induced optical birefringence setup. Probe pulses are incident on samples with 45° polarization, except for quartz and ZnTe (see figure). Optical components: PM: 90° off-axis parabolic mirror, λ/4: quarter waveplate, WP: Wollaston prism, PD: photodiode. (b) Temporal profile of the THz field generated with the LiNbO3 source (blue) and its Fourier spectrum (inset). By using a calibration method based on power and beam-profile measurements (see main text), we have determined the field scaling factor to be E0 = 2.1 MV cm−1.
The materials selected are a polycrystalline diamond window (thickness of 0.5 mm), Si (silicon, 10 μm), SiN (amorphous silicon nitride Si3N4) membrane (200 nm), MgO(100) (magnesium oxide, 0.5 mm), Al2O3(0001) (z-cut sapphire, 0.5 mm) and SiO2(001) (z-cut crystalline quartz, 1 mm) [17]. We also study two polymers, TPX (polymethylpentene, 2 mm) and LDPE (low-density polyethylene, ~10 µm). LDPE is a stretchable sheet of plastic wrap with high THz transmission [17]. As indicated in Fig. 1(a), for all samples, the angle between the linear pump and probe polarizations is set to 45°, except for quartz and the ZnTe electrooptic (EO) crystal (see below), where both polarizations are chosen to be parallel. As knowledge of the pump pulse parameters is critical to the accurate extraction of nonlinear optical constants, we characterize the transient electric field ETHz(t) in the THz beam focus as a function of time t by a combination of EO sampling and power measurements #247370 © 2015 OSA
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of the THz beam subject to a knife edge. For EO sampling, we place a 300 μm thick GaP(110) EO crystal in the THz focus [19]. To avoid saturation of the detector, we attenuate the incident THz field with two wire-grid polarizers (field transmission of 7%) and one teflon sheet (thickness of 2 mm, field transmission of 89%). A typical THz EO signal as a function of pump-probe delay is shown in Fig. 1(b). Note that the signal has been corrected for the detector response [20,21] and is, therefore, proportional to the transient THz electric field. At the field maximum, the probe ellipticity amounts to 31% which corresponds to a field strength of E0 = 1.8 MV cm−1 without attenuation. Note that the detector response function given in ref [21]. takes the dispersion and the shape of the sampling pulse into account. An often-used simpler detection model assumes THz fields to behave like DC fields [22] and yields E0 = 1.6 MV cm−1. While EO sampling permits reliable extraction of the shape of the transient electric field [21], absolute field amplitudes are prone to systematic errors. For example, the detector response depends on the quality of the EO crystal and the shape and spectrum of the probe pulse used [20]. As a consequence, we independently calibrate the absolute field scale E0 (Fig. 1(b)) by measuring the total energy and focus size of the THz pulse [23]. More precisely, a knife edge is placed in the THz focus, followed by a calibrated THz power meter (Ophir 3AP-THz). By measuring the THz power as a function of the knife position, we are able to determine the total THz power and the shape of the THz focus. We find a THz pulse energy of 7.6 μJ and, assuming a Gaussian beam profile, a focus diameter of a≈500 μm and b≈700 μm full width at half intensity maximum in the vertical and horizontal direction, respectively. 2 Using these numbers, Fig. 1(b) and the fact that 0.3622π abε 0 c dt EΤΗ z equals the THz pulse
energy, we obtain a value of E0 = 2.1 MV cm−1 for the peak THz field. (Here, c is the vacuum speed of light, and ɛ0 is the permittivity of vacuum.) Although the THz field strengths obtained with the two methods agree fairly well, we will in the following use E0 = 2.1 MV cm−1 as obtained with the knife-edge method, for the reasons mentioned above. 3. Results and discussion
Figure 2(a) shows ellipticity signals of diamond (thickness of 0.5 mm), LDPE (~10 µm), TPX 2 (2 mm) and SiN (200 nm). For comparison, the squared THz field EΤΗ z is also shown (dashed 2 red curve), and we observe that the ellipticity and EΤΗ z traces have quite similar shape. However, as seen in Fig. 2(b), distinctively different birefringence signals are observed for MgO (0.5 mm) and sapphire (0.5 mm). They exhibit a box-like shape and longer duration of ~2 ps. Nevertheless, for all materials of Figs. 2(a) and 2(b), we find that the maximum amplitude of the transient birefringence scales quadratically with the peak field of the THz pulse. This observation is displayed for the example of diamond in the inset of Fig. 2(a). Therefore, the transient birefringence of all materials of Fig. 2 arises from a so-called χ (3) 2 that causes an anisotropic change in the refractive index scaling with EΤΗ z (t ) [10]. As the window materials of Fig. 2 have either cubic (diamond, MgO, sapphire) or even isotropic (TPX, LDPE, SiN) symmetry in the planes parallel to their surfaces, it can be shown [24,25] that the normally incident THz field induces an anisotropic refractive-index change whose in-plane major axes are parallel and perpendicular to the THz electric-field direction.
#247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28988
5.7
0
diamond (×1.4) LDPE (×23) TPX (×1) THz intensity SiN (×40)
(a)
1
2
3
diamond quadratic fit
THz field strength (normal.)
0 0
phase shift Δϕ (mrad)
4
1
Δϕ (normal.)
-1
1
0
(b)
sapphire (×28) simulation MgO (×18) simulation
-1
0
1
time (ps)
2
3
4
Fig. 2. Transient optical birefringence of (a) LDPE, diamond, TPX, SiN, (b) sapphire and MgO induced by the THz pump pulse of Fig. 1(b). For comparison, the squared pump field is also shown (dashed line). Note that signal amplitudes are rescaled for clarity by the scaling factors indicated. Cyan and red solid curves in (b) represent the simulated birefringence signal of MgO and sapphire. The inset shows the peak values of the birefringence signal of diamond (full circles) as a function of pump amplitude along with a parabolic fit.
The difference of the refractive-index changes along these two major axes is given by 2 Δn( x, t ) = n2 I ΤΗz = n2 cε 0 EΤΗ z ( x, t )
(1)
where n0 is the refractive of the medium at the probe frequency. The nonlinear refractiveindex coefficient n2 describes the strength of the nonlinear response [24,25]. By writing Eq. (1), we have assumed an instantaneous material response, neglecting any memory effects. We note that for cubic materials, n2 depends on the angle between crystal axes and the direction of the THz field [24]. Since here we are interested in characterizing window performance, we set the azimuthal angle of the samples such that always maximum signals are obtained. In contrast to Eq. (1), the birefringence signals of MgO and sapphire do not 2 follow EΤΗ z (t ) . The reason for this apparent discrepancy is that Eq. (1) only describes a local relationship that does not take the propagation of THz pump and optical probe pulses into account. In fact, there is a large velocity mismatch of pump and probe in MgO and sapphire. The refractive index of MgO (sapphire) is 3.11 (3.08) at 1 THz and 1.72 (1.76) at 800 nm. Therefore, after propagation through L = 0.5 mm of MgO or sapphire, the THz pulse lags behind the probe by about 2 ps [26,27]. To confirm that the box-like shape of the signals of Fig. 2(b) arises from propagation effects, we model the signal generation process by only considering the different group velocities v ΤΗz and vpr of pump and probe. We assume the probe pulse is much shorter than the THz pump, enters the crystal at position x = 0 at time t and subsequently travels to the exit face at x = L. The phase difference Δϕ between the two probe polarization components along
#247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28989
1
2.1 MV/cm 1.2 0.7 0.4 0.2 0.02 THz intensity
Δϕ (normal.)
phase shift Δϕ (mrad)
5.1
0
-1
0
0
THz field strength (normal.)
1
1
2
time (ps)
Fig. 3. THz-pump-induced transient optical birefringence in 10-µm-thick Si at various THz field amplitudes. The dashed line is the square of the THz electric field. The inset shows the signal peak values of the signal as a function of THz peak field. The red line is a guide to the eyes.
the major axes of the transient birefringence (Fig. 1(a)) is then given by [28]
λpr L L Δϕ (t ) = dx Δn( x, t + x / vpr ) = dx Δn(0, t + β x) 0 0 2π
(2)
−1 Where λ pr is the probe center wavelength. The inverse-velocity mismatch β = vpr−1 − vΤΗ z
quantifies the temporal walk-off of pump and probe pulses per propagation length. In the second step of Eq. (2), we have neglected dispersion of the THz pump pulse by assuming. inc inc EΤΗz ( x, t ) = t12 EΤΗz (t − x / vΤΗz ) Here, EΤΗz is the incident THz field, and the Fresnel coefficient t12 = 2/(nTHz + 1) quantifies the pump transmission through the air-sample interface with nTHz being the window refractive index at 1 THz. The phase shift Δϕ leads to elliptical probe polarization with ellipticity Δϕ / 2 , such that the normalized photodiode signal ( P1 − P2 ) / ( P1 + P2 ) (see above) equals Δϕ [20]. Note that Eq. (2) represents a convolution of Δn( x = 0, t ) with a rectangular function of temporal width β L , which may indeed lead to box-like signals as observed in the experiment (Fig. 2(b)). Table 1. Linear-optical and third-order nonlinear-optical parameters of the window/substrate materials studied in this work (except quartz). Material
Δn (10−6)
Diamond TPX LDPE SiN MgO Al2O3
1.03 0.36 3.15 0.05 0.7 0.6
n2 for 1 THz pump/ 800 nm probe (10−16 cm2 W−1) 3 0.3 2 0.08 0.5 0.7
Si
65
56
β (ps mm−1)
nTHz at 1 THz
0.04 0.01 >0.01 2.5 4.6 4.4
2.38 [31] 1.46 [17] 1.51 [17] 2.75 [32] 3.11 [26] 3.08 [27]
n2 for 800 nm pump/ 800 nm probe [25] (10−16 cm2 W−1) 13 0.7 [29] 2.93
0.85
3.42 [27]
270
Equations (1) and (2) and the incident field (Fig. 1(b)) are now used to calculate the simulation curves shown in Fig. 2(b). We find good agreement with the experimental curves, confirming that the measured transient birefringence can be reproduced by only considering the velocity mismatch between pump and probe pulses. Comparison of the amplitudes of #247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28990
modeled and experimental data (Fig. 2) also allows us to derive values of the n2 coefficient [Eq. (1)] of the window materials studied. The resulting n2 values of the samples of Fig. 2 are summarized in Table 1. Given the uncertainties related with determining the THz field strength, the THz n2 values are comparable to the values obtained with near-infrared pump radiation [25–29]. We now turn to Si, another often-used window material in THz spectroscopy. The 10-µmthick silicon window studied here has a power transmittance of ~25% averaged over the spectrum of our 800-nm probe pulses. The measured signals of Si are displayed in Fig. 3 for multiple THz peak fields. In general, the signals exhibit a double-peak structure reminiscent 2 of the Kerr-type response; they are, however, substantially broader than EΤΗ z (t ) (dashed line). In contrast to MgO and sapphire (see Fig. 2(b)), velocity mismatch between pump and probe pulses cannot account for the peak broadening as the Si window is only 10 µm thick. In addition, the shape of the signal, in particular the relative height of the two maxima varies nontrivially with the THz field strength. Along these lines, the fluence dependence (inset of Fig. 3) suggests more complicated processes, whose investigation is beyond the scope of this report. Nevertheless assuming that the dominant nonlinear effect follows a Kerr process, we estimate the lower limit of its nonlinear refractive index in Table 1. 23
quartz (1 mm) ZnTe (8 μm) simulation (1 mm) phase shift Δϕ (mrad)
divided by 420
-3
-2
-1
0
1 2 time (ps)
3
4
5
Fig. 4. THz-pump-induced transient birefringence of a 1-mm thick z-cut quartz window (black curve) along with the simulated signal (green curve, see text). For comparison, the rescaled EO signal from an 8 μm thick ZnTe crystal is also shown (dashed red curve).
Our final sample is a 1 mm thick z-cut crystalline quartz window that delivers the birefringence signal shown in Fig. 4 (black curve). In this measurement, the polarization of the THz pump is chosen parallel to that of the 800-nm probe pulse (see Fig. 1(a)), for a reason that will become clear shortly. Distinct from all other samples, the induced birefringence signal from quartz exhibits both positive and negative peaks resembling a THz field, yet it is almost two times broader than the incident THz field (red curve). This observation suggests a χ (2) process, which is allowed in non-centrosymmetric quartz in electric-dipole approximation. To test this conjecture, we assume birefringence owing to the linear EO effect, Δn( x, t ) = EΤΗz ( x, t ),
(3)
and model the expected signal using Eq. (2). As with MgO and sapphire, there is considerable pump-probe velocity mismatch in quartz, which has an ordinary refractive index of 2.11 and 1.538 at 1 THz and 800 nm, respectively [27]. The simulated signal for 1 mm thick quartz is shown in Fig. 4 (green line), and we see that the main features of the signal are well captured by the simulation. The minor differences may again originate from the fact that dispersion #247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28991
was neglected in the simulation. In addition, the THz beam enters the quartz with a relatively large cone such that part of the pump may encounter the extraordinary refractive index of quartz (2.156 at 1 THz), thereby traveling with different velocity. In addition, the small angle between pump and probe beams may cause a deviation of the expected and the measured signals for a 1 mm thick sample because the effective spectrum of the THz pump seen by the probe pulse may change while traversing the sample. By comparing the EO sampling signal of quartz with that from ZnTe under otherwise identical experimental conditions and taking the known optical constants of ZnTe [19], we estimate the EO coefficient of quartz to be r11 = 0.29 pm V−1, a value that agrees well with 0.23 pm V−1 from Ref [30]. We finally comment on the uncertainty of the n2 values derived from our experimental data. The major error contribution to n2 emanates from the uncertainty in the determination of the THz intensity [see Eq. (1)]. We determine this error by fitting the data points from the size measurement of the THz focus by the knife-edge method to an error function. Thus we obtain the associated error to the THz intensity to be less than 10%, which can be taken as the upper limit of the errors to n2. There is also a minor statistical contribution to n2 error through the noise of the ellipticity signal which is estimated to be less than 1% for strong signals such as those from TPX and diamond. This contribution increases accordingly for the weaker signals obtained with MgO, sapphire and SiN. 4. Conclusion
In conclusion, we have measured the transient optical birefringences of window/substrate materials commonly used in THz spectroscopy, following excitation with intense THz fields exceeding 2 MV cm−1 at ~1 THz. A Kerr-type response proportional to the square of the THz field is observed in diamond, TPX, LDPE, SiN, MgO and sapphire. It is temporally broadened in MgO and sapphire due to the large velocity mismatch between pump and probe pulses in these materials. While a highly nonlinear response beyond the perturbative regime is seen for Si, the transient birefringence of quartz is dominated by the linear EO effect. Our data allow us to discuss the feasibility of the materials studied as windows or substrates in THz pump-optical probe spectroscopy. Diamond and TPX exhibit the highest n2 values, and the small pump-probe velocity mismatch leads to strong signals localized around pump-probe delay around time zero. Both materials could still be useful for samples whose pump-probe signal components of interest are significantly longer-lived than the pump pulse duration. In contrast, MgO and sapphire exhibit a significantly smaller n2. In addition, the poor pump-probe velocity mismatch reduces the transient birefringence amplitude by an order of magnitude but results in longer-lived, box-shaped signals. Such behavior is acceptable for samples either delivering sufficiently strong or short-lived pump-probe signals, localized around the excitation field. Finally, owing to their small thickness, LDPE and SiN exhibit a small and temporally localized response, which makes them particularly interesting window/substrate materials, provided such thin substrates do not pose an issue for the sample used. Acknowledgment
We acknowledge financial support by the German Research Foundation (priority program SPP 1666, Grant No. KA 3305/3-1).
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Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28992
Abstract: We apply intense terahertz (THz) electromagnetic pulses with field strengths exceeding 2 MV cm−1 at ~1 THz to window and substrate materials commonly used in THz spectroscopy and determine the induced optical birefringence. Materials studied are diamond, sapphire, magnesium oxide (MgO), polymethylpentene (TPX), low-density polyethylene (LDPE), silicon nitride membrane (SiN) and crystalline quartz. We observe a Kerreffect-type transient birefringence in all samples, except in quartz and Si, where, respectively, a linear electrooptic signal and a response beyond the perturbative regime are found. We extract the nonlinear refractive indices and the electrooptic coefficient (in the case of quartz) of these materials and discuss implications for their use as windows or substrates in THz pumpoptical probe spectroscopy. ©2015 Optical Society of America OCIS codes: (040.2235) Far infrared or terahertz; (190.0190) Nonlinear optics.
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Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28985
15. T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mahrlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent THz control of antiferromagnetic spin waves,” Nat. Photonics 5(1), 31–34 (2011). 16. T. Kampfrath, M. Battiato, P. Maldonado, G. Eilers, J. Notzold, S. Mahrlein, V. Zbarsky, F. Freimuth, Y. Mokrousov, S. Blugel, M. Wolf, I. RaduI, P. M. Oppeneer, and M. Munzenberg, “THz spin current pulses controlled by magnetic heterostructures,” Nat. Nanotechnol. 8(4), 256–260 (2013). 17. Y. S. Lee, Principles of THz Science and Technology: Proceedings of the International Conference, Held in Mainz, Germany, June 5–9, 1979. (Springer-Verlag). 18. J. Hebling, K. L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power THz pulses by tilted-pulse-front excitation and their applications,” J. Opt. Soc. Am. B 25(7), B6–B19 (2008). 19. A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectores and sources for ultrabroadband electro-optic sampling: experiment and theory,” Appl. Phys. Lett. 74(11), 1516–1518 (1999). 20. G. Gallot and D. Grischkowsky, “Electro-optic detection of THz radiation,” J. Opt. Soc. Am. B 16(8), 1204– 1212 (1999). 21. T. Kampfrath, J. Nötzold, and M. Wolf, “Sampling of broadband THz pulses with thick electro-optic crystals,” Appl. Phys. Lett. 90(23), 231113 (2007). 22. N. C. J. van der Valk, T. Wenckebach, and P. C. M. Planken, “Full mathematical description of electro-optic detection in optically isotropic crystals,” J. Opt. Soc. Am. B 21(3), 622–631 (2004). 23. F. Blanchard, L. Razzari, H.-C. Bandulet, G. Sharma, R. Morandotti, J.-C. Kieffer, T. Ozaki, M. Reid, H. F. Tiedje, H. K. Haugen, and F. A. Hegmann, “Generation of 1.5 µJ single-cycle terahertz pulses by optical rectification from a large aperture ZnTe crystal,” Opt. Express 15(20), 13212–13220 (2007). 24. M. Cornet, J. Degert, E. Abraham, and E. Freysz, “THz Kerr effect in gallium phosphide crystal,” J. Opt. Soc. Am. B 31(7), 1648–1652 (2014). 25. R. W. Boyd, Nonlinear Optics. (Academic Press, 2009). 26. D. Grischkowsky and S. Keiding, “THz time‐domain spectroscopy of high Tc substrates,” Appl. Phys. Lett. 57(10), 1055–1057 (1990). 27. D. Grischkowsky, S. Keiding, M. Vanexter, and C. Fattinger, “Far-infrared time-domain spectroscopy with THz beams of dielectrics and semiconductores,” J. Opt. Soc. Am. B 7(10), 2006–2015 (1990). 28. H. J. Bakker, G. C. Cho, H. Kurz, Q. Wu, and X. C. Zhang, “Distortion of THz pulses in electro-optic sampling,” J. Opt. Soc. Am. B 15(6), 1795–1801 (1998). 29. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, Inc.). 30. D. D. Eden and G. H. Thiess, “Measurement of the Direct Electro-Optic Effect in Quartz at UHF,” Appl. Opt. 2(8), 868–869 (1963). 31. A. J. Gatesman, R. H. Giles, G. C. Phillips, J. Waldman, L. P. Bourget, and R. Post, (1989). “Far-Infrared spectroscopic study of diamond films,” MRS Proceedings, 162, 285 (1990). 32. G. Cataldo, J. A. Beall, H.-M. Cho, B. McAndrew, M. D. Niemack, and E. J. Wollack, “Infrared dielectric properties of low-stress silicon nitride,” Opt. Lett. 37(20), 4200–4202 (2012).
1. Introduction Owing to recent technological progress in terahertz (THz) photonics [1–3], pulsed electromagnetic fields with several MV cm−1 peak strength can routinely be generated with tabletop sources over a spectral range from 1 to tens of THz [4,5]. Such high fields have opened the field of nonlinear THz spectroscopy where low-frequency modes of matter are driven into unexplored large-amplitude regimes [6–8]. Examples are vibrational ladder climbing in molecular crystals [9], transient birefringence of liquids [10], control over molecular rotations in gases [11], charge-carrier generation by impact ionization in semiconductors [12,13], excitation of the Higgs mode in superconductors [14] and control over spin dynamics in magnets [15,16]. In THz spectroscopy, samples (such as thin solid films) are often attached to substrates or kept inside cryostats or cuvettes that comprise windows for the incident and outgoing THz and (possibly) optical radiation. While the linear THz and optical properties of a large number of THz transparent materials are known [17], the responses of such materials to intense THz radiations have not yet been studied systematically. Filling this gap of knowledge is critical to THz pump-optical probe experiments in which the pump-induced signal from windows and substrates has to be as small as possible. Here, we measure the transient optical birefringence of the most common THz window/substrate materials induced by an intense THz pulse. For most of the materials studied, we find the birefringence scales with the square of the THz electric field (Kerr effect). Only in the case of quartz, the signal is proportional to the THz field (Pockels effect).
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Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28986
2. Experimental details Our experimental setup is schematically shown in Fig. 1(a). Intense electromagnetic pulses at ~1 THz center frequency are generated by optical rectification in a MgO-doped (1.3 mol-%) stoichiometric LiNbO3 crystal with the tilted-pulse-front technique [4,18]. The LiNbO3 is driven by laser pulses (energy of 4.5 mJ, center wavelength of 800 nm, duration of 40 fs, repetition rate of 1 kHz) from an amplified Ti:sapphire laser system (Coherent Legend Elite Duo). A grating (2000 lines mm−1) and two cylindrical lenses (focal lengths of 250 mm and 150 mm) are used to tilt the intensity front of the 800-nm generation pulse by 62° inside the crystal. The beam cross section on the input face of the crystal is 3 mm and 9 mm (full width at half maximum) in horizontal and vertical direction, respectively. The emitted THz pump pulse is focused on the sample surface by means of three off-axis parabolic mirrors (focal lengths of 0.5”, 3” and 2” with 1” = 25.4 mm). The pump-induced birefringence of the sample is measured by a temporally delayed probe pulse (2 nJ, 780 nm, 8 fs) derived from the seed laser oscillator (Venteon One). The probe pulse is linearly polarized before the sample and subsequently acquires elliptical polarization owing to the birefringence induced by the co-propagating THz pulse. The ellipticity is detected with a combination of a quarter-wave plate and a Wollaston prism which splits the incoming beam in two perpendicularly polarized beams with power P1 and P2. The normalized difference ( P1 − P2 ) / ( P1 + P2 ) is twice the probe ellipticity and measured by two photodiodes as a function of temporal delay between THz pump and optical probe pulse. To vary the THz intensity on the samples, a pair of wire-grid polarizers is used. 800 nm, 8 fs, 2 nJ
ZnTe and quartz ETHz
ETHz
Eprobe
Eprobe
E0
(b)
amplitude (normal.)
(a)
ǀǀ ┴ sample
λ/4
PD1
THz field amplitude
45°
Δτ
0
1
2
frequency (THz)
E0 =2.1 MV/cm
PD2
PM
WP
-1
0
1
2
3
time (ps)
Fig. 1. (a) Schematic of the THz-induced optical birefringence setup. Probe pulses are incident on samples with 45° polarization, except for quartz and ZnTe (see figure). Optical components: PM: 90° off-axis parabolic mirror, λ/4: quarter waveplate, WP: Wollaston prism, PD: photodiode. (b) Temporal profile of the THz field generated with the LiNbO3 source (blue) and its Fourier spectrum (inset). By using a calibration method based on power and beam-profile measurements (see main text), we have determined the field scaling factor to be E0 = 2.1 MV cm−1.
The materials selected are a polycrystalline diamond window (thickness of 0.5 mm), Si (silicon, 10 μm), SiN (amorphous silicon nitride Si3N4) membrane (200 nm), MgO(100) (magnesium oxide, 0.5 mm), Al2O3(0001) (z-cut sapphire, 0.5 mm) and SiO2(001) (z-cut crystalline quartz, 1 mm) [17]. We also study two polymers, TPX (polymethylpentene, 2 mm) and LDPE (low-density polyethylene, ~10 µm). LDPE is a stretchable sheet of plastic wrap with high THz transmission [17]. As indicated in Fig. 1(a), for all samples, the angle between the linear pump and probe polarizations is set to 45°, except for quartz and the ZnTe electrooptic (EO) crystal (see below), where both polarizations are chosen to be parallel. As knowledge of the pump pulse parameters is critical to the accurate extraction of nonlinear optical constants, we characterize the transient electric field ETHz(t) in the THz beam focus as a function of time t by a combination of EO sampling and power measurements #247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28987
of the THz beam subject to a knife edge. For EO sampling, we place a 300 μm thick GaP(110) EO crystal in the THz focus [19]. To avoid saturation of the detector, we attenuate the incident THz field with two wire-grid polarizers (field transmission of 7%) and one teflon sheet (thickness of 2 mm, field transmission of 89%). A typical THz EO signal as a function of pump-probe delay is shown in Fig. 1(b). Note that the signal has been corrected for the detector response [20,21] and is, therefore, proportional to the transient THz electric field. At the field maximum, the probe ellipticity amounts to 31% which corresponds to a field strength of E0 = 1.8 MV cm−1 without attenuation. Note that the detector response function given in ref [21]. takes the dispersion and the shape of the sampling pulse into account. An often-used simpler detection model assumes THz fields to behave like DC fields [22] and yields E0 = 1.6 MV cm−1. While EO sampling permits reliable extraction of the shape of the transient electric field [21], absolute field amplitudes are prone to systematic errors. For example, the detector response depends on the quality of the EO crystal and the shape and spectrum of the probe pulse used [20]. As a consequence, we independently calibrate the absolute field scale E0 (Fig. 1(b)) by measuring the total energy and focus size of the THz pulse [23]. More precisely, a knife edge is placed in the THz focus, followed by a calibrated THz power meter (Ophir 3AP-THz). By measuring the THz power as a function of the knife position, we are able to determine the total THz power and the shape of the THz focus. We find a THz pulse energy of 7.6 μJ and, assuming a Gaussian beam profile, a focus diameter of a≈500 μm and b≈700 μm full width at half intensity maximum in the vertical and horizontal direction, respectively. 2 Using these numbers, Fig. 1(b) and the fact that 0.3622π abε 0 c dt EΤΗ z equals the THz pulse
energy, we obtain a value of E0 = 2.1 MV cm−1 for the peak THz field. (Here, c is the vacuum speed of light, and ɛ0 is the permittivity of vacuum.) Although the THz field strengths obtained with the two methods agree fairly well, we will in the following use E0 = 2.1 MV cm−1 as obtained with the knife-edge method, for the reasons mentioned above. 3. Results and discussion
Figure 2(a) shows ellipticity signals of diamond (thickness of 0.5 mm), LDPE (~10 µm), TPX 2 (2 mm) and SiN (200 nm). For comparison, the squared THz field EΤΗ z is also shown (dashed 2 red curve), and we observe that the ellipticity and EΤΗ z traces have quite similar shape. However, as seen in Fig. 2(b), distinctively different birefringence signals are observed for MgO (0.5 mm) and sapphire (0.5 mm). They exhibit a box-like shape and longer duration of ~2 ps. Nevertheless, for all materials of Figs. 2(a) and 2(b), we find that the maximum amplitude of the transient birefringence scales quadratically with the peak field of the THz pulse. This observation is displayed for the example of diamond in the inset of Fig. 2(a). Therefore, the transient birefringence of all materials of Fig. 2 arises from a so-called χ (3) 2 that causes an anisotropic change in the refractive index scaling with EΤΗ z (t ) [10]. As the window materials of Fig. 2 have either cubic (diamond, MgO, sapphire) or even isotropic (TPX, LDPE, SiN) symmetry in the planes parallel to their surfaces, it can be shown [24,25] that the normally incident THz field induces an anisotropic refractive-index change whose in-plane major axes are parallel and perpendicular to the THz electric-field direction.
#247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28988
5.7
0
diamond (×1.4) LDPE (×23) TPX (×1) THz intensity SiN (×40)
(a)
1
2
3
diamond quadratic fit
THz field strength (normal.)
0 0
phase shift Δϕ (mrad)
4
1
Δϕ (normal.)
-1
1
0
(b)
sapphire (×28) simulation MgO (×18) simulation
-1
0
1
time (ps)
2
3
4
Fig. 2. Transient optical birefringence of (a) LDPE, diamond, TPX, SiN, (b) sapphire and MgO induced by the THz pump pulse of Fig. 1(b). For comparison, the squared pump field is also shown (dashed line). Note that signal amplitudes are rescaled for clarity by the scaling factors indicated. Cyan and red solid curves in (b) represent the simulated birefringence signal of MgO and sapphire. The inset shows the peak values of the birefringence signal of diamond (full circles) as a function of pump amplitude along with a parabolic fit.
The difference of the refractive-index changes along these two major axes is given by 2 Δn( x, t ) = n2 I ΤΗz = n2 cε 0 EΤΗ z ( x, t )
(1)
where n0 is the refractive of the medium at the probe frequency. The nonlinear refractiveindex coefficient n2 describes the strength of the nonlinear response [24,25]. By writing Eq. (1), we have assumed an instantaneous material response, neglecting any memory effects. We note that for cubic materials, n2 depends on the angle between crystal axes and the direction of the THz field [24]. Since here we are interested in characterizing window performance, we set the azimuthal angle of the samples such that always maximum signals are obtained. In contrast to Eq. (1), the birefringence signals of MgO and sapphire do not 2 follow EΤΗ z (t ) . The reason for this apparent discrepancy is that Eq. (1) only describes a local relationship that does not take the propagation of THz pump and optical probe pulses into account. In fact, there is a large velocity mismatch of pump and probe in MgO and sapphire. The refractive index of MgO (sapphire) is 3.11 (3.08) at 1 THz and 1.72 (1.76) at 800 nm. Therefore, after propagation through L = 0.5 mm of MgO or sapphire, the THz pulse lags behind the probe by about 2 ps [26,27]. To confirm that the box-like shape of the signals of Fig. 2(b) arises from propagation effects, we model the signal generation process by only considering the different group velocities v ΤΗz and vpr of pump and probe. We assume the probe pulse is much shorter than the THz pump, enters the crystal at position x = 0 at time t and subsequently travels to the exit face at x = L. The phase difference Δϕ between the two probe polarization components along
#247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28989
1
2.1 MV/cm 1.2 0.7 0.4 0.2 0.02 THz intensity
Δϕ (normal.)
phase shift Δϕ (mrad)
5.1
0
-1
0
0
THz field strength (normal.)
1
1
2
time (ps)
Fig. 3. THz-pump-induced transient optical birefringence in 10-µm-thick Si at various THz field amplitudes. The dashed line is the square of the THz electric field. The inset shows the signal peak values of the signal as a function of THz peak field. The red line is a guide to the eyes.
the major axes of the transient birefringence (Fig. 1(a)) is then given by [28]
λpr L L Δϕ (t ) = dx Δn( x, t + x / vpr ) = dx Δn(0, t + β x) 0 0 2π
(2)
−1 Where λ pr is the probe center wavelength. The inverse-velocity mismatch β = vpr−1 − vΤΗ z
quantifies the temporal walk-off of pump and probe pulses per propagation length. In the second step of Eq. (2), we have neglected dispersion of the THz pump pulse by assuming. inc inc EΤΗz ( x, t ) = t12 EΤΗz (t − x / vΤΗz ) Here, EΤΗz is the incident THz field, and the Fresnel coefficient t12 = 2/(nTHz + 1) quantifies the pump transmission through the air-sample interface with nTHz being the window refractive index at 1 THz. The phase shift Δϕ leads to elliptical probe polarization with ellipticity Δϕ / 2 , such that the normalized photodiode signal ( P1 − P2 ) / ( P1 + P2 ) (see above) equals Δϕ [20]. Note that Eq. (2) represents a convolution of Δn( x = 0, t ) with a rectangular function of temporal width β L , which may indeed lead to box-like signals as observed in the experiment (Fig. 2(b)). Table 1. Linear-optical and third-order nonlinear-optical parameters of the window/substrate materials studied in this work (except quartz). Material
Δn (10−6)
Diamond TPX LDPE SiN MgO Al2O3
1.03 0.36 3.15 0.05 0.7 0.6
n2 for 1 THz pump/ 800 nm probe (10−16 cm2 W−1) 3 0.3 2 0.08 0.5 0.7
Si
65
56
β (ps mm−1)
nTHz at 1 THz
0.04 0.01 >0.01 2.5 4.6 4.4
2.38 [31] 1.46 [17] 1.51 [17] 2.75 [32] 3.11 [26] 3.08 [27]
n2 for 800 nm pump/ 800 nm probe [25] (10−16 cm2 W−1) 13 0.7 [29] 2.93
0.85
3.42 [27]
270
Equations (1) and (2) and the incident field (Fig. 1(b)) are now used to calculate the simulation curves shown in Fig. 2(b). We find good agreement with the experimental curves, confirming that the measured transient birefringence can be reproduced by only considering the velocity mismatch between pump and probe pulses. Comparison of the amplitudes of #247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28990
modeled and experimental data (Fig. 2) also allows us to derive values of the n2 coefficient [Eq. (1)] of the window materials studied. The resulting n2 values of the samples of Fig. 2 are summarized in Table 1. Given the uncertainties related with determining the THz field strength, the THz n2 values are comparable to the values obtained with near-infrared pump radiation [25–29]. We now turn to Si, another often-used window material in THz spectroscopy. The 10-µmthick silicon window studied here has a power transmittance of ~25% averaged over the spectrum of our 800-nm probe pulses. The measured signals of Si are displayed in Fig. 3 for multiple THz peak fields. In general, the signals exhibit a double-peak structure reminiscent 2 of the Kerr-type response; they are, however, substantially broader than EΤΗ z (t ) (dashed line). In contrast to MgO and sapphire (see Fig. 2(b)), velocity mismatch between pump and probe pulses cannot account for the peak broadening as the Si window is only 10 µm thick. In addition, the shape of the signal, in particular the relative height of the two maxima varies nontrivially with the THz field strength. Along these lines, the fluence dependence (inset of Fig. 3) suggests more complicated processes, whose investigation is beyond the scope of this report. Nevertheless assuming that the dominant nonlinear effect follows a Kerr process, we estimate the lower limit of its nonlinear refractive index in Table 1. 23
quartz (1 mm) ZnTe (8 μm) simulation (1 mm) phase shift Δϕ (mrad)
divided by 420
-3
-2
-1
0
1 2 time (ps)
3
4
5
Fig. 4. THz-pump-induced transient birefringence of a 1-mm thick z-cut quartz window (black curve) along with the simulated signal (green curve, see text). For comparison, the rescaled EO signal from an 8 μm thick ZnTe crystal is also shown (dashed red curve).
Our final sample is a 1 mm thick z-cut crystalline quartz window that delivers the birefringence signal shown in Fig. 4 (black curve). In this measurement, the polarization of the THz pump is chosen parallel to that of the 800-nm probe pulse (see Fig. 1(a)), for a reason that will become clear shortly. Distinct from all other samples, the induced birefringence signal from quartz exhibits both positive and negative peaks resembling a THz field, yet it is almost two times broader than the incident THz field (red curve). This observation suggests a χ (2) process, which is allowed in non-centrosymmetric quartz in electric-dipole approximation. To test this conjecture, we assume birefringence owing to the linear EO effect, Δn( x, t ) = EΤΗz ( x, t ),
(3)
and model the expected signal using Eq. (2). As with MgO and sapphire, there is considerable pump-probe velocity mismatch in quartz, which has an ordinary refractive index of 2.11 and 1.538 at 1 THz and 800 nm, respectively [27]. The simulated signal for 1 mm thick quartz is shown in Fig. 4 (green line), and we see that the main features of the signal are well captured by the simulation. The minor differences may again originate from the fact that dispersion #247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28991
was neglected in the simulation. In addition, the THz beam enters the quartz with a relatively large cone such that part of the pump may encounter the extraordinary refractive index of quartz (2.156 at 1 THz), thereby traveling with different velocity. In addition, the small angle between pump and probe beams may cause a deviation of the expected and the measured signals for a 1 mm thick sample because the effective spectrum of the THz pump seen by the probe pulse may change while traversing the sample. By comparing the EO sampling signal of quartz with that from ZnTe under otherwise identical experimental conditions and taking the known optical constants of ZnTe [19], we estimate the EO coefficient of quartz to be r11 = 0.29 pm V−1, a value that agrees well with 0.23 pm V−1 from Ref [30]. We finally comment on the uncertainty of the n2 values derived from our experimental data. The major error contribution to n2 emanates from the uncertainty in the determination of the THz intensity [see Eq. (1)]. We determine this error by fitting the data points from the size measurement of the THz focus by the knife-edge method to an error function. Thus we obtain the associated error to the THz intensity to be less than 10%, which can be taken as the upper limit of the errors to n2. There is also a minor statistical contribution to n2 error through the noise of the ellipticity signal which is estimated to be less than 1% for strong signals such as those from TPX and diamond. This contribution increases accordingly for the weaker signals obtained with MgO, sapphire and SiN. 4. Conclusion
In conclusion, we have measured the transient optical birefringences of window/substrate materials commonly used in THz spectroscopy, following excitation with intense THz fields exceeding 2 MV cm−1 at ~1 THz. A Kerr-type response proportional to the square of the THz field is observed in diamond, TPX, LDPE, SiN, MgO and sapphire. It is temporally broadened in MgO and sapphire due to the large velocity mismatch between pump and probe pulses in these materials. While a highly nonlinear response beyond the perturbative regime is seen for Si, the transient birefringence of quartz is dominated by the linear EO effect. Our data allow us to discuss the feasibility of the materials studied as windows or substrates in THz pump-optical probe spectroscopy. Diamond and TPX exhibit the highest n2 values, and the small pump-probe velocity mismatch leads to strong signals localized around pump-probe delay around time zero. Both materials could still be useful for samples whose pump-probe signal components of interest are significantly longer-lived than the pump pulse duration. In contrast, MgO and sapphire exhibit a significantly smaller n2. In addition, the poor pump-probe velocity mismatch reduces the transient birefringence amplitude by an order of magnitude but results in longer-lived, box-shaped signals. Such behavior is acceptable for samples either delivering sufficiently strong or short-lived pump-probe signals, localized around the excitation field. Finally, owing to their small thickness, LDPE and SiN exhibit a small and temporally localized response, which makes them particularly interesting window/substrate materials, provided such thin substrates do not pose an issue for the sample used. Acknowledgment
We acknowledge financial support by the German Research Foundation (priority program SPP 1666, Grant No. KA 3305/3-1).
#247370 © 2015 OSA
Received 5 Aug 2015; revised 7 Oct 2015; accepted 8 Oct 2015; published 28 Oct 2015 2 Nov 2015 | Vol. 23, No. 22 | DOI:10.1364/OE.23.028985 | OPTICS EXPRESS 28992
