Abstract

We present a detailed experimental and theoretical study of terahertz (THz) generation and beam propagation in an optoelectronic THz system consisting of a large-area (ZnTe) electro-optic emitter and a standard electro-optic detector, and provide a comparison to typical biased GaAs emitters. As predicted by theory, in the absence of saturation the generated THz pulse energy is inversely proportional to the area of the optical pump beam incident on the emitter, although the detected on-axis electric field amplitude of the subsequently focused THz beam is practically independent of this area. This latter result promotes the use of larger emitter crystals in amplifier-laser-based THz systems in order to minimize saturation effects. Moreover, the generation of an initially larger THz beam also provides improved spatial resolution at intermediate foci between emitter and detector.

©2005 Optical Society of America

1. Introduction

Broadband optoelectronic terahertz (THz) generation and detection with femtosecond (fs) optical pulses is a powerful and well-studied method for performing far-infrared spectroscopy, imaging and sensing [1]. Among the various approaches developed to date, those employing low-repetition-rate high-pulse-energy amplifier lasers as the optical pulse source offer distinct advantages due to (i) the comparatively high THz pulse energies achieved, and (ii) the ability to efficiently generate synchronous pulses in other regions of the electromagnetic spectrum. This opens the way for important THz applications such as nonlinear spectroscopy [2,3] and single-shot imaging [4].

An overview of amplifier-laser-based THz systems is provided in Ref. [5,6], including a discussion of large-area GaAs antennae emitters [78], THz beam propagation [6,9] and applications of such systems [10]. For the case of THz generation in electro-optic crystals, detailed analyses exist on the influence of the crystal orientation and thickness [11,12]. However, despite the fact that large-area electro-optic crystals (i.e. with illuminated dimensions much greater than the THz-wavelength) have already been used in conjunction with amplifier lasers in applications [10,13] and for the testing of organic electro-optic materials [14], there is still a lack of analysis in the literature in terms of the optimum optical pump beam geometry. In this paper we examine the performance of amplifier-laser-based THz systems with respect to the optical pump beam size, both theoretically and experimentally, and provide a comparison with the performance of standard large-area biased GaAs emitters.

For high-repetition-rate (and therefore, low pulse-energy) THz systems, it is common experimental practice to tightly focus the optical pump beam into the emitter crystal in order to maximize conversion efficiency. This is a rational strategy because the energy conversion efficiency of the second-order non-linear generation process is proportional to the optical pump fluence (in the absence of saturation effects) [15]. In addition, the effective size of the emitter (i.e. that of the pump beam inside the crystal) is significantly smaller than the THz-wavelength, hence the emitter is effectively a point source and no significant influence on the subsequent THz beam propagation is expected by further focusing of the pump beam.

The situation changes drastically when an amplifier laser system with high pump pulse energies in the µJ-mJ range is employed. In this case, the spot size of the pump beam must be significantly increased to avoid damaging the emitter crystal due to dielectric breakdown. In addition, saturation effects in the generation process become important for such high pulse energies. In order to overcome such problems, electro-optic emitter crystals are usually employed with an unfocused pump beam with a diameter in the mm-cm range. As demonstrated both theoretically and experimentally in this paper, increasing the size of the optical pump beam does not actually reduce the detected (on-axis) THz electric field, due to the improved focusing properties of larger beams, with the resulting optimal strategy being to defocus the optical pump beam on the emitter insofar as practicable whilst minimizing saturation effects.

2. Modeling

The starting point for our analysis of the non-linear THz generation process is by considering a small area element of the emitter crystal. We assume a thin crystal and smoothly-varying spatial profiles and treat the incoming optical and generated THz fields as plane waves within each area element. In a general form, the generated THz pulse emerging from such a unit area of the emitter crystal can be written as:

ETHz(t)=KeffWoptT(t).

Here E THz(t) is the generated THz electric field directly after the emitter crystal, K eff is a factor which describes the overall efficiency of the second-order non-linear THz generation process, T(t) is a normalized function (∫T 2 (t)dt=1) which describes the temporal form of the generated THz-pulse, and opt W is the optical fluence of the incident pump pulse. In the absence of saturation, both K eff and T(t) are independent of W opt but depend on various other experimental parameters (e.g. the crystal type, its thickness and orientation, the temporal form and wavelength of the optical pump pulse). In the modeling section of this paper we will not explicitly treat saturation effects. In the experimental results sections, the effects of saturation are discussed on a phenomenological basis, in terms of the deviation of the data for higher optical pulse energies from the behavior predicted by Eq. (1).

We now integrate over the emitter surface, assuming a Gaussian optical pump profile, i.e.,

Wopt(r)=2JoptAoptexp(2r2ropt2),

where J opt is the pulse energy and A opt=πropt2 is the 1/e 2-area of the optical pump beam. The total energy of the generated THz pulse is then given by:

JTHz=cε0[ETHz(r,t)]2rdrdφdt=cε0Keff2Jopt2Aopt.

Thus the energy of the generated THz pulse is proportional to the square of the optical pump pulse energy and inversely proportional to the illuminated emitter area. For single pixel detection, the THz beam is usually focused onto the detector crystal. Here we will assume a ‘2-f’ geometry (i.e. the distances between emitter and the subsequent focusing element and between the focusing element and the detector are both equal to the focal length f of the focusing element). Only in this configuration one does maintain a common focal plane for all THz frequency components [6]. It should be noted that the presence of an additional intermediate focus (achieved with two additional focusing elements) e.g. for the placement of a spectroscopic sample, does not affect the following results so long as the 2-f geometry is maintained throughout the system. The resulting 1/e 2-radius of the THz beam at the focal plane (using paraxial Gaussian beam theory) is given by [9]:

rdet=rTHz2πcfdetωTHzATHz=2cfdetωTHzrTHz

Here r THz=r opt/√2 is the 1/e 2-radius of the THz beam directly at the emitter and f det is the effective focusing length of the focusing element. The expression in Eq. (4) shows that the focal diameter of a THz-beam generated at a subsequent focus (i.e. a sample measurement plane or at the detector) is inversely proportional to the diameter of the optical pump beam. We note that tighter focusing of the THz beam not only increases the on-axis THz electric field strength, but is also important for the spatial resolution in applications such as single-pixel THz-imaging.

Applying Gaussian beam theory to each Fourier component of E THz(t) in Eq. (1), one can derive an expression for the on-axis THz field at the detector as,

Edet(r=0,t)=Edet0ddtT(t)
withEdet0=KeffJopt2πcfdet

This expression shows that the on-axis THz field Edet0 at the detector is independent of the illuminated area of the emitter (A opt). This is an important result, because in typical electro-optic detection set-ups the diameter of the optical probe beam is small compared to that of the THz beam and thus only the THz electric field about the beam axis is detected. Hence the electro-optically-detected THz signal amplitude is predicted to be independent of the illuminated area of the emitter within this model.

 figure: Fig. 1.

Fig. 1. Schematic of experimental setup with two possible terahertz emitters.

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3. Experimental results

In the following we present experimental data, which confirm the predictions of the foregoing model. The experimental THz system (see Fig. 1) has been reported elsewhere [5,13]. The system employs a Clark-MXR CPA-2001 amplifier laser, which provides optical pulses of ~150-fs duration (FWHM) with a pulse energy of up to 850 µJ at a repetition rate of 1 kHz. We performed the experiments using two different optical pump beam diameters incident on the emitter, corresponding to r opt=4 mm (“small beam”) and 12 mm (“large beam”, achieved by expanding the pump beam with a telescope). A large-area <110>-cut ZnTe crystal with 25-mm diameter and 2-mm thickness was used for the electro-optic emitter. We also performed comparative measurements by replacing the ZnTe emitter with a 3×3 cm2 large-area GaAs antenna with a DC external bias field of 1 kV/cm. The generated THz beam was focused and recollimated by two paraboloidal mirrors both with an effective focal length (off-axis distance) of f=50.4mm. The collimated beam was then focused onto a 1-mm-thick <110>-cut ZnTe crystal for electro-optic detection with a third paraboloidal mirror with f det=50.4 mm. A strict 2-f geometry was maintained along the whole beam path. The optical probe beam for the electro-optic detection was introduced collinearly with the THz beam using a pellicle beamsplitter before the last focusing mirror. Due to the shorter relative wavelength, the optical probe beam focuses much more tightly in the detector crystal than the THz beam. Thus only the on-axis THz electric field is effectively sampled in the detector crystal. In order to provide complementary THz pulse energy measurements, we could redirect the THz beam to either a magnetic-field-enhanced InSb-bolometer or a calibrated room temperature optoacoustic detector (Golay cell).

In Fig. 2(a), the detected (on-axis) temporal THz electric field using the ZnTe emitter is shown, for the case of ropt =12 mm (large beam) and a pump pulse energy of 360 µJ. For comparison, in Fig. 2(b) the corresponding signal measured using the large-area GaAs emitter (1-kV/cm DC bias field) is shown. In Fig. 2(c) the THz power spectra obtained by numerical Fourier transformation of the two signals in Fig. 2(a,b) are shown. The spectral data illustrate that high dynamic range of 3.5 orders of magnitude can be achieved with the ZnTe emitter up to frequencies as high as ~2.8 THz.. The strong oscillations in the time domain and the absorption lines in the frequency domain (e.g. at 1.1 THz and 1.6 THz) are due to water vapor absorption in the ambient air of the THz beam path. (The stronger relative time-domain oscillations observed for the ZnTe emitter is a result of the higher THz bandwidth compared to the GaAs emitter.) It is clear that the ZnTe emitter outperforms the GaAs emitter, in terms of the maximum detected temporal amplitude, bandwidth and THz pulse energy, for the experimental parameters used here.

 figure: Fig. 2.

Fig. 2. Time-domain THz pulse signals emitted from (a) a large-area ZnTe crystal and (b) a large-area GaAs antenna with 1-kV/cm external DC bias, and (c) corresponding power spectra. Both emitters were illuminated with 360-µJ, 150-fs optical pump pulses.

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At this point it should be stated that the highest reported external bias fields that have been applied to such GaAs emitters range up to 10.7 kV/cm [7]. For such a bias field one obtains a temporal THz signal with an amplitude of up to 150 kV/cm [7]. However, the use of such high external bias fields requires a pulsed high-voltage source with µs-duration voltage-pulses in order to avoid electrical breakdown across the GaAs emitter. This technique leads to a very large amount of background electrical noise, leading to a higher noise level in the measured signals which is difficult to suppress. In practice, the dynamic range achieved cannot be improved significantly with these higher bias voltages because of the increased background noise. Thus, for most THz applications, the ZnTe emitter still provides superior performance.

 figure: Fig. 3.

Fig. 3. (a) Electro-optically measured peak amplitude of THz pulses generated using ZnTe and GaAs emitters vs optical pump pulse energy, with two optical pump beam diameters corresponding to ropt=4 mm (“small beam”) and 12 mm (“large beam”). Inset shows magnified views of low pulse-energy region. (b) Corresponding data with both optical pump pulse energy and THz peak amplitudes normalized to respective pump beam 1/e2-area Aopt (Common x-axis range only).

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In Fig. 3(a), the electro-optically measured peak amplitude of the THz electric field is plotted as a function of the optical pump pulse energy for both types of emitter and the two different pump beam diameters. In order to compare the effects of saturation, in Fig. 3(b) the same data are plotted after normalizing both the optical pump energy and THz amplitude to the 1/e2-area of the optical pump beam. The data show a variety of interesting features, which we address for each emitter in turn.

For the ZnTe emitter, the unnormalized data in Fig. 3(a) for the two different pump beam diameters are almost indistinguishable at low optical pulse energies <5 µJ (see inset of Fig. 3). This confirms the prediction of Eq. (6), i.e. that the on-axis THz electric field at the detector is essentially independent of the pump beam diameter below saturation. For higher laser pulse energies one observes the influence of saturation for both pump beam diameters, with a more pronounced effect observed for the case of the small pump beam diameter (higher optical pump fluence). However, the normalized ZnTe emitter data in Fig. 3(b) show a close agreement of the two curves for each pump beam diameter over the whole available range of comparison (i.e. <50 µJ/cm2). This demonstrates that the degree of saturation or the ZnTe emitter is a function of the optical pump fluence alone. Hence we can conclude that any saturation effects in the electro-optic emitter can be overcome by simply enlarging the pump beam diameter, with the reduction in total THz pulse energy compensated by the improved focusing of the THz beam at the detector.

One can clearly see that this works in practice from inspection of the data in Fig. 3(a). At higher pulse energies a significantly higher THz field signal is detected for the ZnTe emitter if the large pump beam is used, because saturation effects have been reduced due to the reduced pump fluence at the emitter crystal. For a pulse energy of 360 µJ, this leads to an improvement by a factor of ~2.5 for the field amplitude. In order to indicate how far expanding the optical pump beam could in principle improve the measured THz field for a ZnTe emitter, we include a linear extrapolation of the data at low pulse energies in Fig. 3(a,b).

From an analysis of the saturation factors for the ZnTe data in Fig. 3(b), we can also estimate the performance for the specific case of r opt=20 mm and an optical pulse energy of 360 µJ, which is included as a single point in Fig. 3(a). This indicates that an additional factor of ~1.3 in the peak THz amplitude could be achieved under such conditions. Unfortunately our crystal size was limited to 25 mm, so we could not test this prediction experimentally.

The situation is more complicated for the GaAs emitter. Theoretical models for the emitted THz field from (large-area) biased-semiconductor antennae have been given in the literature [6,8]. Assuming a uniform applied bias field across the emitter and that the near-field emitted THz field amplitude is small compared to this bias field, these models predict a dependence of the emitted THz pulse on the optical-pump-pulse energy with the same form as that for the second-order non-linear generation mechanism given in Section 2. The first deviation from this ideal model arises due to field enhancement near the bias electrodes, such that the applied bias is not equally distributed across the antenna. This leads to a spatial variation of the nominal conversion efficiency across the antenna and a corresponding distortion of the emitted THz beam profile. Upon reaching emitted THz amplitudes comparable with the bias field, a complex saturation behavior sets in due to near-field radiation screening of the bias field by the THz field itself [8,16] (and to a lesser degree, dynamic screening by the photoinduced space charge across the antenna). These screening effects strongly reduce the conversion efficiency of the THz generation process, as well as resulting in a severe distortion of the emitted THz beam (which deviates strongly from a Gaussian shape, resulting in reduced on-axis THz fields at the detector focus).

Although a quantitative analysis of these effects falls outside the scope of this paper, one can still observe their qualitative impact in the experimental data for the GaAs emitter. In Fig. 3(a,b) it can be seen that the saturation behavior is much more drastic for the GaAs emitter than for the ZnTe emitter. Above a certain laser pulse energy no further increase in the detected THz signal can be achieved by increasing the pump pulse energy, whereby even a slow roll-off in the detected THz is observed. In addition, from comparison of the small and large beam data for the GaAs emitter in Fig. 3, is seen that the THz signal amplitude reached in this regime of “complete” saturation scales with the optical pump beam area. These observations are consistent with the foregoing discussion of the saturation mechanisms.

In the following we switch to complementary measurements of the total emitted THz pulse energy. (Measurements for THz pulse energies of up to 30 pJ were performed with a magnetic-field-enhanced InSb-bolometer, whilst higher pulse energies were measured with a calibrated room temperature optoacoustic detector (Golay cell) which has a higher saturation threshold.) In Fig. 4(a) the measured total THz pulse energy (within the detection bandwidth) is plotted for the two different emitter types and the two optical pump beam sizes. For the ZnTe emitter the detected THz pulse energy scales quadratically with the pump pulse energy for low pump pulse energies as expected from Eq. (3), with the onset of saturation becoming significant for pump pulse energies ~50 µJ. In addition the THz pulse energy generated by the ZnTe emitter (below saturation) is inversely proportional to the optical pump beam diameter (in comparing the two curves shown here), which is also consistent with Eq. (3). A comparison with the ZnTe data in Fig. 3 illustrates one of the key messages of this paper: Although the THz pulse energy can be increased by reducing the pump beam diameter, one cannot take advantage of the higher generated THz pulse energies in a electro-optic detection setup, because the THz beam diameter at the detector is correspondingly larger. In order to illustrate the potential of the ZnTe emitter, the pulse energy data are extrapolated to a pump pulse energy of 360 µJ (using the saturation characteristics determined from the electro-optic detection data in Fig. 3 and Eq. (3)), which predicts that THz pulse energies of up to 250 pJ are achievable with the ZnTe emitter. For the GaAs emitter, a similar saturation behavior in the THz pulse energy is observed as that for the on-axis detected THz field measured electro-optically (taking into consideration the quadratic relation between THz field and pulse energy). It is interesting to note that the pulse energy data for the GaAs emitter do not display the weak roll-off observed for the corresponding on-axis THz field data. This is most likely related to the distortion of the initial THz beam profile that occurs in saturation which degrades the on-axis THz field at subsequent foci but has only a weak effect on the total emitter THz pulse energy.

 figure: Fig. 4.

Fig. 4. (a) Measured THz pulse energies for both ZnTe and GaAs emitters and each optical pump beam size ropt=4 mm (“small beam”) and 12 mm (“large beam”), using bolometric detection. (b) Graph of the corresponding THz energy conversion efficiency (within the detection bandwidth) vs the effective fluence (optical pump pulse energy normalized to the respective pump beam 1/e2-area, Aopt). Inset: Magnified view for low pump fluence (note the different vertical scaling).

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The measured THz pulse energies allow us to estimate the THz-generation conversion efficiencies (J THz/J opt), which are plotted in Fig. 4(b) for each emitter/pump beam size as a function of the effective pump pulse fluence (J opt/A opt). According to Eq. (3), for the ZnTe emitter the energy conversion efficiency below saturation should be a linear function of the effective pump fluence, where the slope is given by ( 0 Keff2). As discussed in Section 2, this relation can be generalized in the case where saturation effects are significant by taking K eff=K eff(J opt/A opt), i.e. the saturation factor should be a function of the effective pump fluence. These predictions are confirmed for the ZnTe emitter in Fig. 4(b) (see inset), where the data for the two pump beam sizes are indistinguishable within experimental error, including the range where saturation effects are significant (i.e. above J opt/A opt~20µJ/cm2). The data indicate that the maximal pulse energy conversion efficiency which can be achieved is ~1.5×10-6. The dominant mechanism for this saturation effect has been attributed to two-photon absorption of the pump beam and related free-carrier absorption in the ZnTe emitter crystal [17].

Inspection of the corresponding data for the GaAs emitter in Fig. 4(b) demonstrates the strong contrast in conversion efficiency and saturation behavior for the two different emitters. As can be seen, the THz energy conversion efficiency for the GaAs emitter (and the large optical pump beam) reaches a maximum value of ~12×10-6 for a relatively low effective pulse fluence of 2 J opt/A opt~10µJ/cm2, from where it rapidly degrades to below that of the ZnTe emitter at ~80 µJ/cm2. Note that the GaAs-emitter data for the two pump beam sizes differ significantly due to the bias-field non-uniformity and more complex saturation behavior (as already discussed above).

 figure: Fig. 5.

Fig. 5. Measured THz beam intensity profiles measured (a) directly after the ZnTe emitter and (b) at a subsequent focal plane, for three characteristic frequency components (0.62, 1.25 and 2.19 THz), for the two optical pump beam sizes, ropt=4 mm (“small beam”) and 12 mm (“large beam”), as indicated. Red solid line 1/e2-beam region. Yellow dashed line: Expected 1/e2-beam region according to Eq. (4).

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We conclude this experimental section by addressing the THz-focal-diameter dependence on the optical-pump-beam diameter. In Fig. 5 we present the measurements of the THz beam intensity profile directly after the emitter (Fig. 5(a)) and at a focus generated by a parabolic mirror with an off-axis distance f=50.4 mm placed at a distance f following the emitter (Fig. 5(b)). The measurements were carried out by passing circular metallic apertures with diameters of 5 mm (emitter) and 0.5 mm (focus), respectively, across the beam profile, and measuring the detected THz field electro-optically at a subsequent focal plane. The detected temporal electric field data was then Fourier-transformed, yielding spectrally resolved intensity profiles, as shown here for three characteristic frequencies (0.62, 1.25 and 2.19 THz). These frequencies represent the lower end, the maximum, and the higher end of the accessible spectrum. The beam profile is plotted normalized to the maximum value for each set of data. One can clearly observe that the size of the THz beam directly after the emitter scales with the optical pump beam size, with only a weak dependence on THz frequency. In contrast, the beam diameter at the subsequent focal plane reflects the reciprocal relation to the beam exiting the emitter, as predicted by Eq. (4). The focused THz intensity profiles in Fig. 5(b) coincide well in most cases with the theoretical prediction, which is plotted as a yellow line. Note that the deviation observed for the small-beam/0.62-THz profile in Fig. 5(b) is most likely due to imaging aberrations occurring after the aperture, whose diameter is comparable with the THz wavelength (0.48 mm) for this frequency.

We note that the significantly reduced THz focal diameter when using the large optical pump beam is a critical issue for the resolution of THz imaging systems which employ a single-pixel raster-scan technique. For instance, for a frequency of 2.19 THz, the resultant 1/e2-diameter is 0.8 mm for the large pump beam, compared 1.5 mm for the small pump beam).

4. Summary

In summary we have presented a combined theoretical and experimental analysis of the THz pulse characteristics and beam propagation in systems employing large-area THz emitters and optical pump-pulse energies in the range ~1–350 µJ. We have investigated a large-area electro-optic (ZnTe) emitter, which exhibits a considerably higher saturation level than a standard large-area GaAs emitter. Furthermore, the saturation effects in the electro-optic THz generation process can be overcome by increasing the pump beam diameter, without any significant penalty in the detected electro-optic signal, despite the fact that the total THz pulse energy is reduced. This is due to the tighter focusing of the initially larger THz beam, which also results in improved spatial resolution in imaging applications. The study also shows for pulse energies greater than ~150 µJ that a large-area ZnTe electro-optic emitter outperforms a large-area GaAs emitter (with 1 kV/cm external bias) in terms of peak amplitude, pulse energy and bandwidth.

Acknowledgments

This work was supported by the DFG-Project RO 770/21-1 (Deutsche Forschungsgemeinschaft).

References and links

1. B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002). [CrossRef]  

2. G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002). [CrossRef]  

3. C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004). [CrossRef]  

4. Z. Jiang and X.-C. Zhang, “Single-shot spatiotemporal terahertz field imaging,” Opt. Lett. 23, 1114–1116 (1998). [CrossRef]  

5. T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

6. T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002). [CrossRef]  

7. D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, “Generation of high-power sub-single-cycle 500-fs electromagnetic pulses,” Opt. Lett. 18, 290–292 (1993). [CrossRef]   [PubMed]  

8. J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991). [CrossRef]  

9. A. Gürtler, C. Winnewisser, H. Helm, and P. U. Jepsen, “Terahertz pulse propagation in the near field and in the far field,” J. Opt. Soc. Am. A 17, 74–83 (2000). [CrossRef]  

10. T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001). [CrossRef]   [PubMed]  

11. Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001). [CrossRef]  

12. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001) [CrossRef]  

13. N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003). [CrossRef]  

14. T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995). [CrossRef]  

15. A. Yariv, Quantum Electronics (John Wiley, New York, 1998).

16. N. Hasegawa, “A fundamental work on THz measurement techniques for application to steel manufacturing processes.” (Dissertation, University of Frankfurt, 2004), http://deposit.ddb.de/cgi-bin/dokserv?idn=975373056.

17. F.G. Sun, W. Ji, and X.-C. Zhang, “Two-photon absorption induced saturation of THz radiation in ZeTe,” in Conference on Lasers and Electro-Optics, OSA Technichal Digest (Optical Society of America, Wasgington DC, 2000), 479–480.

References

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  1. B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
    [Crossref]
  2. G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
    [Crossref]
  3. C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004).
    [Crossref]
  4. Z. Jiang and X.-C. Zhang, “Single-shot spatiotemporal terahertz field imaging,” Opt. Lett. 23, 1114–1116 (1998).
    [Crossref]
  5. T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).
  6. T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002).
    [Crossref]
  7. D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, “Generation of high-power sub-single-cycle 500-fs electromagnetic pulses,” Opt. Lett. 18, 290–292 (1993).
    [Crossref] [PubMed]
  8. J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
    [Crossref]
  9. A. Gürtler, C. Winnewisser, H. Helm, and P. U. Jepsen, “Terahertz pulse propagation in the near field and in the far field,” J. Opt. Soc. Am. A 17, 74–83 (2000).
    [Crossref]
  10. T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
    [Crossref] [PubMed]
  11. Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
    [Crossref]
  12. P. C. M. Planken, H.-K. Nienhuys, H. J. Bakker, and T. Wenckebach, “Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe,” J. Opt. Soc. Am. B 18, 313–317 (2001)
    [Crossref]
  13. N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003).
    [Crossref]
  14. T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
    [Crossref]
  15. A. Yariv, Quantum Electronics (John Wiley, New York, 1998).
  16. N. Hasegawa, “A fundamental work on THz measurement techniques for application to steel manufacturing processes.” (Dissertation, University of Frankfurt, 2004), http://deposit.ddb.de/cgi-bin/dokserv?idn=975373056.
  17. F.G. Sun, W. Ji, and X.-C. Zhang, “Two-photon absorption induced saturation of THz radiation in ZeTe,” in Conference on Lasers and Electro-Optics, OSA Technichal Digest (Optical Society of America, Wasgington DC, 2000), 479–480.

2004 (1)

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004).
[Crossref]

2003 (1)

N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003).
[Crossref]

2002 (3)

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002).
[Crossref]

2001 (3)

2000 (1)

1998 (1)

1995 (1)

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
[Crossref]

1993 (1)

1991 (1)

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[Crossref]

Auston, D. H.

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[Crossref]

Bakker, H. J.

Bauer, T.

T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
[Crossref] [PubMed]

Bucksbaum, P. H.

Carrig, T. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
[Crossref]

Chen, Q.

Clement, T. S.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
[Crossref]

Czasch, S.

T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
[Crossref] [PubMed]

Darrow, J. T.

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[Crossref]

Döhler, G.

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

Dykaar, D. R.

Elsaesser, T.

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004).
[Crossref]

Ferguson, B.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

Fitzgerald, A.

T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
[Crossref] [PubMed]

Gürtler, A.

Hahn, T.

T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

Hasegawa, N.

N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003).
[Crossref]

N. Hasegawa, “A fundamental work on THz measurement techniques for application to steel manufacturing processes.” (Dissertation, University of Frankfurt, 2004), http://deposit.ddb.de/cgi-bin/dokserv?idn=975373056.

T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

Hattori, T.

T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002).
[Crossref]

Helm, H.

Jacob, F.

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

Jepsen, P. U.

Ji, W.

F.G. Sun, W. Ji, and X.-C. Zhang, “Two-photon absorption induced saturation of THz radiation in ZeTe,” in Conference on Lasers and Electro-Optics, OSA Technichal Digest (Optical Society of America, Wasgington DC, 2000), 479–480.

Jiang, Z.

Jones, R. R.

Kiesel, P.

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

Kress, M.

T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

Löffler, T.

N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003).
[Crossref]

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
[Crossref] [PubMed]

T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

Luo, C.

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004).
[Crossref]

Nienhuys, H.-K.

Ohta, K.

T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002).
[Crossref]

Planken, P. C. M.

Reimann, K.

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004).
[Crossref]

Rodriguez, G.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
[Crossref]

Roskos, H.

T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

Roskos, H. G.

N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003).
[Crossref]

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
[Crossref] [PubMed]

Rungsawang, R.

T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002).
[Crossref]

Segschneider, G.

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

Siebert, K. J.

T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
[Crossref] [PubMed]

Stewart, K. R.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
[Crossref]

Sun, F.G.

F.G. Sun, W. Ji, and X.-C. Zhang, “Two-photon absorption induced saturation of THz radiation in ZeTe,” in Conference on Lasers and Electro-Optics, OSA Technichal Digest (Optical Society of America, Wasgington DC, 2000), 479–480.

Tani, M.

Tautz, S.

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

Taylor, A. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
[Crossref]

Thomson, M.

N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003).
[Crossref]

T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

Tukamoto, K.

T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002).
[Crossref]

Wenckebach, T.

Winnewisser, C.

Woerner, M.

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (John Wiley, New York, 1998).

You, D.

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

Q. Chen, M. Tani, Z. Jiang, and X.-C. Zhang, “Electro-optic transceivers for terahertz-wave applications,” J. Opt. Soc. Am. B 18, 823–831 (2001).
[Crossref]

Z. Jiang and X.-C. Zhang, “Single-shot spatiotemporal terahertz field imaging,” Opt. Lett. 23, 1114–1116 (1998).
[Crossref]

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[Crossref]

F.G. Sun, W. Ji, and X.-C. Zhang, “Two-photon absorption induced saturation of THz radiation in ZeTe,” in Conference on Lasers and Electro-Optics, OSA Technichal Digest (Optical Society of America, Wasgington DC, 2000), 479–480.

Appl. Phys. A (1)

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, “Nonlinear terahertz spectroscopy of semiconductor nanostructures,” Appl. Phys. A 78, 435–440 (2004).
[Crossref]

Appl. Phys. Lett. (3)

J. T. Darrow, X.-C. Zhang, and D. H. Auston, “Power scaling of large-aperture photoconducting antennas,” Appl. Phys. Lett. 58, 25–27 (1991).
[Crossref]

N. Hasegawa, T. Löffler, M. Thomson, and H. G. Roskos, “Remote identification of protrusions and dents on surfaces by THz reflectometry with spatial beam filtering and out-of-focus detection,” Appl. Phys. Lett. 83, 3996–3998 (2003).
[Crossref]

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro-optic crystal mosaics,” Appl. Phys. Lett. 66, 10–12 (1995).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (1)

T. Hattori, R. Rungsawang, K. Ohta, and K. Tukamoto, “Gaussian beam analysis of temporal waveform of focused terahertz pulses,” Jpn. J. Appl. Phys. 41, 5198–5204 (2002).
[Crossref]

Nature Materials (1)

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials 1, 26–33 (2002).
[Crossref]

Opt. Lett. (2)

Optics Express (1)

T. Löffler, T. Bauer, K. J. Siebert, H. G. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Optics Express 9, 616–621 (2001).
[Crossref] [PubMed]

Phys. Rev. B (1)

G. Segschneider, F. Jacob, T. Löffler, H. G. Roskos, S. Tautz, P. Kiesel, and G. Döhler, “Free-carrier dynamics in low-temperature-grown GaAs at high excitation densities investigated by time-domain terahertz spectroscopy,” Phys. Rev. B 65, 125205-1 (2002).
[Crossref]

Other (4)

T. Löffler, M. Kress, M. Thomson, T. Hahn, N. Hasegawa, and H. Roskos, “Comparative performance of terahertz emitters in amplifier-laser-based systems,” Semiconductor Science and technology, (in press).

A. Yariv, Quantum Electronics (John Wiley, New York, 1998).

N. Hasegawa, “A fundamental work on THz measurement techniques for application to steel manufacturing processes.” (Dissertation, University of Frankfurt, 2004), http://deposit.ddb.de/cgi-bin/dokserv?idn=975373056.

F.G. Sun, W. Ji, and X.-C. Zhang, “Two-photon absorption induced saturation of THz radiation in ZeTe,” in Conference on Lasers and Electro-Optics, OSA Technichal Digest (Optical Society of America, Wasgington DC, 2000), 479–480.

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Figures (5)

Fig. 1.
Fig. 1. Schematic of experimental setup with two possible terahertz emitters.
Fig. 2.
Fig. 2. Time-domain THz pulse signals emitted from (a) a large-area ZnTe crystal and (b) a large-area GaAs antenna with 1-kV/cm external DC bias, and (c) corresponding power spectra. Both emitters were illuminated with 360-µJ, 150-fs optical pump pulses.
Fig. 3.
Fig. 3. (a) Electro-optically measured peak amplitude of THz pulses generated using ZnTe and GaAs emitters vs optical pump pulse energy, with two optical pump beam diameters corresponding to ropt=4 mm (“small beam”) and 12 mm (“large beam”). Inset shows magnified views of low pulse-energy region. (b) Corresponding data with both optical pump pulse energy and THz peak amplitudes normalized to respective pump beam 1/e2-area Aopt (Common x-axis range only).
Fig. 4.
Fig. 4. (a) Measured THz pulse energies for both ZnTe and GaAs emitters and each optical pump beam size ropt=4 mm (“small beam”) and 12 mm (“large beam”), using bolometric detection. (b) Graph of the corresponding THz energy conversion efficiency (within the detection bandwidth) vs the effective fluence (optical pump pulse energy normalized to the respective pump beam 1/e2-area, Aopt). Inset: Magnified view for low pump fluence (note the different vertical scaling).
Fig. 5.
Fig. 5. Measured THz beam intensity profiles measured (a) directly after the ZnTe emitter and (b) at a subsequent focal plane, for three characteristic frequency components (0.62, 1.25 and 2.19 THz), for the two optical pump beam sizes, ropt=4 mm (“small beam”) and 12 mm (“large beam”), as indicated. Red solid line 1/e2-beam region. Yellow dashed line: Expected 1/e2-beam region according to Eq. (4).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

E THz ( t ) = K eff W opt T ( t ) .
W opt ( r ) = 2 J opt A opt exp ( 2 r 2 r opt 2 ) ,
J THz = c ε 0 [ E THz ( r , t ) ] 2 r d r d φ d t = c ε 0 K eff 2 J opt 2 A opt .
r det = r THz 2 π c f det ω THz A THz = 2 c f det ω THz r THz
E det ( r = 0 , t ) = E det 0 d d t T ( t )
with E det 0 = K eff J opt 2 π c f det

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