Generation of THz and IR Radiation in DAST ... - SPIE Digital Library

Invited Paper

Generation of THz and IR Radiation in DAST crystals A. Schneider, M. Stillhart, and P. G¨ unter Nonlinear Optics Laboratory, Institute of Quantum Electronics, Swiss Federal Institute of Technology, CH-8093 Z¨ urich, Switzerland ABSTRACT Short THz pulses are commonly generated through the optical rectification of ultrashort laser pulses in nonlinear optical crystals. Our purpose is to discuss the controllability of the THz spectrum emitted from the polar organic salt DAST (4-N,N-dimethylamino-4-N-methyl stilbazolium tosylate) and also the efficiency of the THz generation. It does not only depend on different experimental parameters such as duration of the laser pulse and crystal thickness, but is also affected by absorption and dispersion caused by several resonances of the crystal in the THz range. Keywords: THz pulses, optical rectification, organic crystals, DAST, velocity-matching

1. INTRODUCTION Ultrashort electromagnetic pulses in the frequency range of 0.1 − 10 THz (THz pulses) have experienced growing interest in the past decade, both in basic research as well as in applications in the area of imaging and spectroscopy. The aspired part of the electromagnetic spectrum is situated between the range accessible with electronic methods and the optical range. In this intermediate position, the THz spectral range is not easily accessible. With the design and development of commercially available laser systems delivering sub-picosecond pulses, it has become possible to generate THz pulses that comprise only few cycles of the oscillation of the electric field. The processes are based on nonlinear conversion in solid state materials. One possibility is the use of semiconductors. An alternative method uses noncentrosymmetric crystals. In the first case, biased1 or unbiased2 semiconductors are illuminated with laser light with a photon energy above the bandgap. The acceleration of the excited electrons and holes in either the bias field or the built-in surface electric field leads to the emission of THz radiation. The resulting spectrum is mainly determined by intrinsic material properties, first of all by the lifetime of the electron-hole pairs. The generation processes take place only within an absorption length from the surface. Therefore, the amplitude will not be increased in a bulk material. In the second method to generate THz pulses, an ultrashort laser pulse induces a quasistatic polarization in a noncentrosymmetric material.3, 4 This polarisation follows in time the amplitude of the pump pulse and thus acts as a source for the THz pulse. This process is known as optical rectification (OR). In the following sections, we will demonstrate that the generation efficiency as well as the spectrum of the THz pulses can be controlled by varying experimental parameters such as crystal thickness or wavelength and duration of the generating laser pulse. A properly chosen wavelength significantly enhances the output by optimal phase-matching, i.e. by the equality of the phase velocity vp = c/n of the THz pulse and the group velocity vg of the optical pump pulse which is given by vg (λ) =

c c = ng (λ) n(λ) −

∂n ∂λ λ

,

(1)

where ng (λ) is the optical group index. In many nonlinear optical materials like LiNbO3 , velocity-matching cannot be achieved because the optical group index is significantly smaller than the refractive index at THz frequencies - given approximately by the square root of the dielectric constant ε. However, the dielectric constant of DAST is relatively low and velocity-matching has been observed in this material.5 Thus, the choice of a proper set of parameters allows us to generate THz pulses with optimum power in a desired frequency band, which is very promising for a number of applications, e.g. imaging for biomedical or security purposes,6 or time-resolved investigations of electronic processes in solids.7 Organic materials have been designed wih optical nonlinearities significantly higher than those of inorganic crystals8 and therefore are valuable candidates for highly efficient Solid State Lasers XV: Technology and Devices, edited by Hanna J. Hoffman, Ramesh K. Shori, Proc. of SPIE Vol. 6100, 61001C, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.661033

Proc. of SPIE Vol. 6100 61001C-1

THz generation, since the generation process scales with the second-order nonlinear susceptibility χ(2) of the material. Among these organic materials, the polar organic crystal DAST (4-N,N-dimethylamino-4-N-methyl stilbazolium tosylate) has been demonstrated to be very useful for THz generation.9

2. THE ORGANIC CRYSTAL DAST DAST (4-N,N-dimethylamino-4’-N’-methyl stilbazolium tosylate) is a molecular crystal that is composed of a cation that possesses a large molecular optical nonlinearity, and of an anion that is designed to force noncentrosymmetric packing in the crystalline phase. It crystallises in the monoclinic space group Cc (point group m) with four molecular units per unit cell. The crystals were grown from a supersaturated solution in methanol. By incorporating highly nonlinear molecules as cations one can, depending on the anion, obtain noncentrosymmetric crystals with large macroscopic second-order optical nonlinearity. DAST is one of the best examples. It is known for its very high nonlinear optical and electro-optic coefficients. Table 1. The two largest electro-optic coefficients rijk and nonlinear susceptibilities χOR kij of DAST. Values of r from Pan et al.,10 those of χOR calculated. Absolute values in units pm/V.

Wavelength

r111

r221

800 nm

77 ± 8

42 ± 4

1535 nm

47 ± 8

21 ± 4

χOR 111

χOR 221

800 nm

1230 ± 130

166 ± 16

1535 nm

490 ± 90

63 ± 13

The combination of low dielectric constant and high nonlinearity makes DAST crystals promising candidates for generation and detection of THz radiation. The optical refractive indices of DAST single crystals in the near infrared show extraordinarily high birefringence (n1 − n2 = 0.8 at 800 nm, where n1 and n2 correspond to polarisations along the dielectric x1 and x2 axes, respectively) as can be expected from the highly aligned arrangement of the chromophores. By THz time-domain spectroscopy, Walther et al.11 measured the THz index of refraction and the absorption coefficient of DAST. They observed a strong resonance at 1.1 THz, which is attributed to a transverse optical (TO) phonon, the anion-cation vibration. It dominates the linear properties in the THz range for polarisation of the pump beam along the x1 axis, resulting in a dispersion of n1 from 2.3 bo 3.0 below the resonance frequency and from 1.8 to 2.3 above it. The related absorption coefficient at 1.1 THz is very high (about 300 cm−1 ) and results in a gap in the emitted THz spectrum of DAST (See Sect. 5).

3. THEORY 3.1. Generation The field amplitude of a light pulse with angular frequency ω can be written as Eω (t) =

1 (A(t)eiωt + c.c) 2

(2)

where A(t) is the envelope of the pulse and c.c denotes the complex conjugate. For a material with an instantaneous response and negligible dispersion, the induced polarisation P (t) is given by P (t) = ε0 (χEω (t) + χ(2) Eω2 (t) + χ(3) Eω3 (t) + . . .) .


(3)

ε0 is the vacuum permittivity and χ(n) the n-th-order susceptibility. Because of symmetry, the odd-order susceptibilities are present in any material, whereas the even-orders only occur in noncentrosymmetric materials. The second term in brackets is the nonlinear polarization PN L . Inserting Eq. (2) one gets PN L (t) =

ε0 χ2 ([A2 (t)e2iωt + c.c] + 2|A(t)|2 ) 4

(4)

The terms including 2ω are known as second harmonic generation (SHG), while the ω-independent term is the optical rectified polarization POR , or simply referred to as optical rectification (OR). The induced polarization POR leads to the emission of a secondary electromagnetic wave E(t). A simple calculation12 reveals this field ˆ to be proportional to the second time derivative ∂ 2 /∂t2 POR (t). The according spectrum E(ω) of this secondary radiation can be calculated by a Fourier Transform: 2 (ω), ˆ E(ω) = S0 ω 2 |A|

(5)

where S0 is a factor which takes into account all constants and material parameters. Assuming a Gaussian 2 2 function |A(t)|2 = A0 e−t /2τ for the pump intensity, the spectrum in Eq. (5) becomes 2 2 S0 A0 ˆ E(ω) = √ ω 2 e−τ ω /2 2π

(6)

√ where τ is the full width at half maximum (FWHM) of the pump pulse intensity divided by 2 ln 4. The total THz radiation after the generation crystal corresponds to the integration of the emitted spectra originating from different positions in the crystal as the pump pulse passes over the crystal length. Using the non-depleted pump approximation and including the absorption α(ω), ET Hz (ω) is then given by −α(ω)l/2−iω(n(ω)−ng )l/c ˆT Hz (ω) = S√0 A0 ω 2 e−τ 2 ω2 /2 · 1 − e E = a(ω) · f (ω, l). ω(n(ω)−ng ) α(ω) 2π 2 +i c

(7)

ˆT Hz (ω) has a ng is the group velocity index at the optical pump wavelength. For any crystal length l, E maximum for the velocity-matched case ng = n(ω), where the THz amplitudes from all positions z within the crystal interfere constructively. For ng = n(ω), i.e. if the pump pulse has a group velocity that is not equal to the THz phase velocity (velocity-mismatching), the emitted THz pulse is distorted due to unequal propagation velocities. The peak of constructive interference will become narrower with increasing crystal thickness. It is now easy to see that the THz spectrum can be varied by changing the pump wavelength unless one uses a material without group velocity dispersion at optical frequencies. Eq. (7) shows that the center frequency of a THz pulse and its bandwidth are both directly related to the length of the pump pulse. As an example, a 100 fs pulses theoretically generates pulses centered around 5 THz. This is in fact highly ineffective, since DAST has a resonance at around 1.1 and 5 THz13 such that a large fraction of the THz energy is directly reabsorbed. This problem can only be circumvented if the pump pulse length is chosen such that most of the THz power is generated at frequencies below the first or between those two resonances. We found a pulse length of 150 fs (FWHM) to be more suitable.

3.2. Detection Electro-optic (EO) sampling is the standard method of measuring THz transients.14 This technique is in its standard configuration only applicable to non-birefringent materials, e.g. ZnTe. This compound is used as a standard material due to its excellent velocity matching within the tuning range of Ti:sapphire lasers. A typically measured THz spectrum will strongly differ from Eq. (7), since one has to consider propagation effects also in the detection crystal. An accurate calculation renders this term to be similar to the form of the fraction on the right hand side of Eq. (7). The influence of the finite length of the probe pulse causes a filtering effect for higher frequencies, such that the detection sensitivity using 150 fs (FWHM) pulses drops to 10% at 5.3 THz and to 2% at 7 THz.


r

∆n(r)

THz

ETHz = 0 Intensity I

Probe ETHz > 0 ETHz < 0 EO crystal

Pockels Effect: ∆n(ρ,τ) = -n3r/2 ETHz (ρ,τ)

Radius ρ

Figure 1. Principle of terahertz-induced lensing

In the standard configuration of EO sampling, a time-varying birefringence is induced by the THz electric field in an electro-optic crystal that has no intrinsic birefringence. Since most crystals with high Pockels coefficients are strongly birefringent, it is favourable to find a variation of electro-optic sampling that is independent of birefringence. Let us consider a THz pulse that is focused onto an electro-optic crystal. The distribution of the THz field within the crystal is assumed to be radially symmetric. The Pockels effect leads to a refractive index profile with r the Pockels coefficient and n the refractive index of the crystal without applied field. This profile distorts the phase fronts of a copropagating optical probe pulse in the same way as a lens, thus leading to a modification of the probe beam profile in the far field (see Figure 1). By monitoring the probe beam while delaying the probe pulse relatively to the THz pulse, it is possible to extract the information about ET Hz (t). This method is called terahertz-induced lensing (TIL) and is reported in Ref. 15. It is important to note the difference between terahertz-induced lensing (TIL) and the well-known Kerr-lens effect or z-scan measurements. In the latter, the third-order nonlinear susceptibility χ(3) causes an index change proportional to the intensity of the pump beam; therefore the sign of ∆n depends solely on the sign of χ(3) . In TIL however it is the THz field that is proportional to ∆n. Thus the index change can have either sign, and the TIL can lead to focusing and defocusing in the same material, depending on the sign of ET Hz (t). The intensity in the center of the probe beam can be measured e.g. by placing the end face of an optical fiber that is connected to a photo detector. It can be shown that the change of this center intensity is proportional to the applied THz field which can thus be easily detected.15 In addition, the sensitivity in DAST is reported to be more than three times better than that of conventional electro-optic sampling with the most used material ZnTe. TIL is fast and easy to adjust and is therefore an attractive method for applications in THz sensing.

4. EXPERIMENTAL For the experiments, we have used the tunable output of an optical parametric amplifier (Light Conversion Ltd., TOPAS), pumped with an amplified Ti:Sapphire laser (Clark-MXR, CPA 2001). Typical pulse energies are 50 µJ at a pulse length of 150 fs FWHM. The experimental setup is shown in Figure 2. The incoming infrared laser pulse is split into a pump beam and a probe beam. The pump beam is used to generate a THz pulse in a DAST crystal and is then blocked by a tissue that is transparent to THz radiation. The THz pulse is focused by an ellipsoidal mirror onto a second DAST crystal where it induces a temporally and spatially varying change in the refractive index through the linear electro-optic effect (Pockels effect). This refractive index profile can be read out with the coninciding probe beam by the newly developed technique of terahertz-induced lensing (See Sect. 3.2). Time-resolution – and therefore coherent detection – is achieved by varying the path length of the probe beam with a computer controlled delay line.


Pump beam

Probe beam

Varibale delay

DAST

IRB Mirror

Detection Pellicle Detection Crystal

Figure 2. Figure 1: Scheme of the setup for generation and detection of THz pulses. Detection part includes either TIL or EO. The pump beam is blocked by means of a tissue, which is transparent for the THz pulse (IRB).

Frequency [THz]

3.0

χ(2) 111

B

2.0 1.0 0.0

A 800 1200 1600 Wavelength [nm]

Figure 3. Calculation of velocity-matching condition n(ωT Hz ) = ng,opt (λ) using the data from Walther et al.11

5. RESULTS AND DISCUSSION (2)

Due to the highly polar nature of DAST, the largest element of the nonlinear susceptibility tensor is χ111 , with the 1-direction being along the polar axis. Since the THz generation efficiency is proportional to χ(2) , all the results presented in the following are measured with the polarisation of all waves in the 1-direction. The dispersion n1 (ω) of DAST in the THz range is mainly governed by a strong absorption line at 1.1 THz which is attributed to a TO phonon resonance (the simple vibration of the anion–cation pair).16 Together with refractive index data for optical wavelengths17 one can determine the pairs of THz frequency/optical wavelength for which velocity-matching (n(ω) = ng (λopt )) is given. There are two distinct branches where this condition is valid. The first comprises frequencies below 1 THz that match wavelengths between 950 and 1150 nm. Experimental results for this branch are presented in Section 5.1. The second branch connects the frequency range from 1.8 THz to 4 THz with wavelengths 1300 nm to 1700 nm. Since the dispersion in this range is significantly smaller than in the first branch, the tunability is less than in the first branch below 1 THz. Detailed results are found in Section 5.2.


Spectral Amplitude

THz induced modulation

1.5 1.0 0.5 0.0

–0.5 –1.0 –5

0

5 Time [ps]

10

15

0.4

0.2

0.0 0

1

2 3 4 Frequency [THz]

5

Figure 4. Left panel: Typical THz pulse, generated in a 0.6 mm DAST single crystal at λ = 1500 nm (pulse width=150 fs), measured with TIL. Right panel: The corresponding spectrum.

5.1. 950-1150 nm The THz pulses have been measured at pump wavelengths between 850 and 1400 nm for two different DAST plates having polished faces normal to the crystal c-axis with thicknesses of 0.69 and 2.11 mm, respectively. A 0.5 mm ZnTe < 110 > plate18 has been used as a detector in the electro-optic (EO) sampling setup. We have found that the THz signal emitted by a 2 mm thick crystal of the standard source ZnTe is smaller by more than an order of magnitude than that from DAST. Even near the velocity matching wavelength in ZnTe at 820 nm,19 the amplitude from the DAST crystal is larger by a factor of 1.5. This shows the superiority of DAST as a source of THz pulses. The most efficient generation in DAST has been measured for a pump wavelength of 1050 nm. When using other wavelengths, one does either not make use of the whole crystal length of DAST due to velocity-mismatch, or most of the THz power is absorbed by the crystal itself, as is described in Section 3.1.

5.2. 1300-1700 nm Figure 4 shows a typical THz transient generated and detected in DAST crystals by optical pulses at a wavelength of 1500 nm. The maximum modulation of the probe’s center intensity was 140% at t = 0 ps. The spectrum that corresponds to the ET Hz (ω) function in Eq. 7 is composed on the one hand of the locally emitted spectrum a(ω) which limits the spectrum for frequencies below 0.3 THz as well as for above 4 THz. On the other hand, the fraction f (ω, l) in Eq. 7 leads to dips at 1.1 THz and 3.0 THz due to absorption and to a distinct maximum at 2.05 THz due to velocity-matching. Since the influence of propagation effects – velocity-mismatch and THz absorption – increases with crystal length, it is expected that the spectrum generated and detected with thin crystals mostly resembles the locally emitted spectrum (see Eq. (5)). Figure 5 presents a measured spectrum obtained with the thinnest crystals available (d=250 µm). The result is compared to the theoretical function (Eq. 5) with the filtering effect of the finite probe pulse length accounted for. The comparison between the two curves shows that the achieved bandwidth is 0.5 to 6.7 THz and is limited only by the pulse length. Some additional absorption lines between 3 and 6 THz are visible. Except for the line at 5.0 THz, which has already been observed earlier,13 these lines are significantly weaker than the one at 1.1 THz, so that the THz amplitude at these frequencies is still well above the noise level.

6. CONCLUSIONS In conclusion, we have presented the spectra of broadband THz pulses generated and detected in crystals of the polar organic salt DAST. We have shown that nearly velocity-matched generation of frequencies above 2 THz is possible with optical pulses with a wavelength between 1300 nm and 1600 nm. The THz bandwidth is limited to 6.7 THz only due to optical pulse length of 150 fs (FWHM). From this it is clear that the use of DAST crystals is highly attractive for applications such as imaging or spectroscopy in the range between 2 to 7 THz (67 to 233 cm−1 ).


Log(Amplitude) 0

2

4 6 8 10 Frequency [THz]

12

Figure 5. Solid line: Spectrum of a THz pulse, generated in a 0.25 mm DAST crystal at a wavelength of 1350 nm and detected in 0.44 mm of DAST (TIL). Dotted line: Theoretical spectrum without any propagation effects, but accounting for finite probe pulse lengt; τF W HM =150 fs for both bump and probe pulse. The signal is above noise level up to a frequency of 6.7 THz, corresponding to the upper resolution limit.

ACKNOWLEDGMENTS The authors would like to thank Blanca Ruiz and Jaroslav Haifler for the growth and the preparation of the DAST crystals. This work was supported by the Swiss National Science Foundation.

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