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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 15090–15097
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Towards generation of mJ-level ultrashort THz pulses by optical rectification

József András Fülöp, László Pálfalvi, Matthias C. Hoffmann, and János Hebling  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 15090-15097 (2011)
http://dx.doi.org/10.1364/OE.19.015090


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Abstract

Optical rectification of ultrashort laser pulses in LiNbO3 by tilted-pulse-front excitation is a powerful way to generate near single-cycle terahertz (THz) pulses. Calculations were carried out to optimize the output THz peak electric field strength. The results predict peak electric field strengths on the MV/cm level in the 0.3–1.5 THz frequency range by using optimal pump pulse duration of about 500 fs, optimal crystal length, and cryogenic temperatures for reducing THz absorption in LiNbO3. The THz electric field strength can be increased further to tens of MV/cm by focusing. Using optimal conditions together with the contact grating technique THz pulses with 100 MV/cm focused electric field strength and energies on the tens-of-mJ scale are feasible.

© 2011 OSA

1. Introduction

Optical rectification (OR) of femtosecond laser pulses is an efficient method to generate ultrashort THz pulses. The highest THz pulse energies and field strengths in the few-THz frequency range were achieved by using LiNbO3 (LN) as the nonlinear medium having very large effective nonlinear coefficient [1

1. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

4

4. A. G. Stepanov, S. Henin, Y. Petit, L. Bonacina, J. Kasparian, and J. P. Wolf, “Mobile source of high-energy single-cycle terahertz pulses,” Appl. Phys. B 101(1-2), 11–14 (2010). [CrossRef]

]. This requires tilting the pump pulse front relative to its wavefront in order to satisfy the phase matching condition required for efficient THz generation [5

5. J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10(21), 1161–1166 (2002). [PubMed]

]. Pumped by multi-mJ Ti:sapphire lasers this technique allowed to generate ultrashort THz pulses on the 10-µJ energy, and up to the 1-MV/cm electric field strength scale [1

1. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

,6

6. H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011). [CrossRef]

]. Such THz pulses enabled, for example, the investigation of THz-induced nonlinear optical phenomena directly in the time-domain [7

7. J. Hebling, K.-L. Yeh, M. C. Hoffmann, and K. A. Nelson, “High-power THz generation, THz nonlinear optics, and THz nonlinear spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 14(2), 345–353 (2008). [CrossRef]

] as well as time-resolved studies of ultrafast carrier dynamics in semiconductors by THz pump—THz probe measurements [8

8. J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump–terahertz probe measurements,” Phys. Rev. B 81(3), 035201 (2010). [CrossRef]

10

10. L. Razzari, F. H. Su, G. Sharma, F. Blanchard, A. Ayesheshim, H.-C. Bandulet, R. Morandotti, J.-C. Kieffer, T. Ozaki, M. Reid, and F. Hegmann, “Nonlinear ultrafast modulation of the optical absorption of intense few-cycle terahertz pulses in n-doped semiconductors,” Phys. Rev. B 79(19), 193204 (2009). [CrossRef]

]. Scaling the THz energy up to 50 µJ has been recently demonstrated by using LN and the tilted-pulse-front pumping (TPFP) technique driven by medium-scale Ti:sapphire amplifier systems with pulse energies up to 120 mJ [2

2. A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J. P. Wolf, “Generation of 30 microJ single-cycle terahertz pulses at 100 Hz repetition rate by optical rectification,” Opt. Lett. 33(21), 2497–2499 (2008). [CrossRef] [PubMed]

,4

4. A. G. Stepanov, S. Henin, Y. Petit, L. Bonacina, J. Kasparian, and J. P. Wolf, “Mobile source of high-energy single-cycle terahertz pulses,” Appl. Phys. B 101(1-2), 11–14 (2010). [CrossRef]

]. Ultrashort pulses at higher frequencies (several tens of THz, where the conversion efficiency can be higher) with electric field strengths up to 10 MV/cm and 100 MV/cm could be achieved by optical parametric amplification [11

11. F. Junginger, A. Sell, O. Schubert, B. Mayer, D. Brida, M. Marangoni, G. Cerullo, A. Leitenstorfer, and R. Huber, “Single-cycle multiterahertz transients with peak fields above 10 MV/cm,” Opt. Lett. 35(15), 2645–2647 (2010). [CrossRef] [PubMed]

] and difference-frequency generation [12

12. A. Sell, A. Leitenstorfer, and R. Huber, “Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm,” Opt. Lett. 33(23), 2767–2769 (2008). [CrossRef] [PubMed]

] in GaSe, respectively. However, due to the material properties of GaSe, this technique is not easily scalable.

Ultrashort THz pulses with energies in the millijoule range and electric field strengths at 100-MV/cm levels, exceeding by far what is presently available, are required by promising new applications. These include investigation of material properties and processes under the influence of extremely high quasi-static fields, particle acceleration by electromagnetic waves, and THz-assisted attosecond pulse generation [13

13. W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express 17(7), 5139–5146 (2009). [CrossRef] [PubMed]

,14

14. E. Balogh, J. A. Fülöp, J. Hebling, P. Dombi, G. Farkas, and K. Varjú, “Attosecond pulse generation in noble gases in the presence of extreme high intensity THz pulses,” 31st European Conf. on Laser Interaction with Matter (XXXI ECLIM), Budapest, Hungary, 6–10 Sept. 2010.

]. Some of these applications will require large-scale ultrashort-pulse laser facilities, such as ELI [15

15. The Extreme Light Infrastructure, European Project, http://www.extreme-light-infrastructure.eu.

], as the pump source.

A conventional TPFP setup consists of a femtosecond pump laser, an optical grating, an imaging lens or telescope, and the nonlinear material [1

1. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

3

3. J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25(7), B6–B19 (2008). [CrossRef]

]. The disadvantage of this setup is that beam distortions caused by imaging errors limit the useful pump spot size [16

16. L. Pálfalvi, J. A. Fülöp, G. Almási, and J. Hebling, “Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification,” Appl. Phys. Lett. 92(17), 171107 (2008). [CrossRef]

,17

17. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]

] and, consequently, the THz energy. A simpler scheme was proposed by omitting the imaging optics and bringing the grating directly in contact with the crystal [16

16. L. Pálfalvi, J. A. Fülöp, G. Almási, and J. Hebling, “Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification,” Appl. Phys. Lett. 92(17), 171107 (2008). [CrossRef]

]. The advantage of such a contact-grating setup is that, by eliminating imaging errors, larger pumped areas can be efficiently used resulting in higher THz energies and better beam quality.

In this work we show that OR of femtosecond pulses in LN by using the TPFP technique with a contact grating is a promising candidate to reach the high THz field strengths and pulse energies required by the applications mentioned above. The effect of varying the Fourier-limited (FL) pump pulse duration and the crystal temperature (to minimize its THz absorption) will be investigated in detail by numerical calculations and optimal conditions will be given. It will be shown that using FL pump pulse durations longer than the commonly used ~100 fs can allow for larger pump-to-THz energy conversion efficiencies by utilizing longer crystal lengths for THz generation. This is in contrast to simply pre-chirping a short FL pump pulse [4

4. A. G. Stepanov, S. Henin, Y. Petit, L. Bonacina, J. Kasparian, and J. P. Wolf, “Mobile source of high-energy single-cycle terahertz pulses,” Appl. Phys. B 101(1-2), 11–14 (2010). [CrossRef]

], which merely allows to achieve the shortest average pulse duration inside the nonlinear crystal.

2. Theoretical model

The applied theoretical model, described in detail in [17

17. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]

], takes into account (i) the variation of the pump pulse duration (and therefore of the pump intensity) with the propagation distance due to material and angular dispersions [17

17. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]

19

19. O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986). [CrossRef]

], (ii) the non-collinear propagation of pump and THz beams and (iii) the absorption in the THz range due to the complex dielectric function (determined by phonon resonances). All kinds of nonlinear effects but OR were neglected [20

20. K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically inverted electro-optic crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14(6), 2263–2276 (2006). [CrossRef] [PubMed]

]. The wave equation with the nonlinear polarization was solved in the spectral domain [17

17. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]

,20

20. K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically inverted electro-optic crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14(6), 2263–2276 (2006). [CrossRef] [PubMed]

]. The temporal shape of the THz field was obtained by Fourier transformation.

In order to avoid photorefraction [22

22. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005). [CrossRef]

] and reduce THz absorption [23

23. L. Pálfalvi, J. Hebling, G. Almási, Á. Péter, and K. Polgár, “Nonlinear refraction and absorption of Mg doped stoichiometric and congruent LiNbO3,” J. Appl. Phys. 95(3), 902–908 (2004). [CrossRef]

] stoichiometric LN (sLN) doped with 0.7 mol% Mg was assumed as the nonlinear medium. LN has significant absorption in the THz range at room temperature (Fig. 1
Fig. 1 Frequency dependence of the absorption coefficient of LN in the THz range for different temperatures.
). Since decreasing the temperature decreases absorption in the THz range [23

23. L. Pálfalvi, J. Hebling, G. Almási, Á. Péter, and K. Polgár, “Nonlinear refraction and absorption of Mg doped stoichiometric and congruent LiNbO3,” J. Appl. Phys. 95(3), 902–908 (2004). [CrossRef]

], low temperature cases (100 K and 10 K) were also investigated in the calculations. Since the refractive index of sLN in the THz range is large (n ≈5.0 at 1 THz), the Fresnel-loss at the output surface of the crystal is significant (about 45%). It was also taken into account in the calculations.

3. Results and discussion

3.1. Optimization for the electric field strength

The calculated THz spectra belonging to different pump pulse durations at 100 K are shown in Fig. 2(a)
Fig. 2 (a) THz spectra belonging to different FL pump pulse durations at 100 K temperature. (b) Frequency of the spectral peak of the THz pulses as function of the FL pump pulse duration at different temperatures.
. As it is obvious from Fig. 2(a), the peak spectral intensity increases and the position of the spectral intensity peak shifts towards lower frequencies with increasing pump pulse duration. This behavior can be observed for all temperatures, as it is shown for the central frequencies in Fig. 2(b). The central THz frequency varies between 1.5 and 0.27 THz for the investigated pump pulse duration range.

In order to calculate the peak electric field strength of the THz pulses their temporal shapes were calculated from the spectra by Fourier transformation. Examples are shown in Fig. 3(a)
Fig. 3 (a) Time dependence of the electric field strength of the generated THz pulses at the output of the crystal belonging to the optimal FL pump pulse durations for temperatures of 300 K and 10 K, as well as to 100 fs at 300 K. The curves belonging to 300 K were scaled up by the indicated factors. (b) Peak electric field strength of the THz pulses at the output of the crystal as function of the FL pump pulse duration at different temperatures.
. The calculated peak electric field strength of the THz pulses in air immediately after the output surface of the crystal is shown in Fig. 3(b) for different temperatures as a function of the FL pump pulse duration (τ). The encircled cross indicates the experimental conditions belonging to the values of 100 fs and 300 K. Similar parameters were used in many experiments pumped by amplified Ti:sapphire laser systems [1

1. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

,2

2. A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J. P. Wolf, “Generation of 30 microJ single-cycle terahertz pulses at 100 Hz repetition rate by optical rectification,” Opt. Lett. 33(21), 2497–2499 (2008). [CrossRef] [PubMed]

,24

24. K.-L. Yeh, J. Hebling, M. C. Hoffmann, and K. A. Nelson, “Generation of high average power 1 kHz shaped THz pulses via optical rectification,” Opt. Commun. 281(13), 3567–3570 (2008). [CrossRef]

,25

25. M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by terahertz pump—terahertz probe spectroscopy,” Phys. Rev. B 79(16), 161201 (2009). [CrossRef]

]. For such experimental conditions our calculations give 240 kV/cm for the peak of the electric field strength (Fig. 3(b)). This exceeds only by about a factor of two the value of 110 kV/cm at the output of the crystal obtained experimentally from the measured peak THz intensity and output spot size [25

25. M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by terahertz pump—terahertz probe spectroscopy,” Phys. Rev. B 79(16), 161201 (2009). [CrossRef]

]. Possible reasons for the difference are the shorter than 100 fs FL pump pulse duration in experiments and imaging errors in the pulse-front-tilting setup [17

17. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]

]. The calculated value for the peak of the THz spectrum is 1.1 THz (Fig. 2(b)), which is similar to the values observed in experiments. This approximate agreement indicates that the present calculation method gives realistic predictions for the order of magnitude of the THz output in real experiments.Increasing the pump pulse duration from the commonly used 100 fs results in significant increase in the THz peak electric field. As shown in Fig. 3(b), by choosing the optimal pump pulse duration of 600 fs for room temperature the THz peak electric field strength can be increased by a factor of more than four, resulting in the extremely high value of 1.0 MV/cm at the output of the crystal. The position of the corresponding spectral peak is reduced to 0.4 THz (Fig. 2(b)). The reason of the increase in field strength is twofold: (i) The longer pump pulse causes a shift of the THz spectrum to lower frequencies, which results in reduced absorption within the crystal (α = 5.9 cm−1 at 0.4 THz instead of α = 18 cm−1 at 1.1 THz, see Fig. 1). (ii) The longer pump pulse also allows a longer THz generation length [17

17. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]

] (Table 1).

Even higher electric field strength can be reached at lower temperatures. At temperatures of 100 and 10 K the maxima are located at 500 fs (Fig. 3(b)) with field strength values of 2.3 MV/cm and 2.8 MV/cm, respectively, corresponding to an enhancement of about one order of magnitude as compared to 300 K and 100 fs. The reason for this increase is clearly the reduced THz absorption at cryogenic temperatures (Fig. 1). In cases of optimal pump pulse duration the central THz frequency has a value of 0.40 THz at 300 K, 0.64 THz at 100 K and 0.67 THz at 10 K temperatures as it is shown in Fig. 2(b).

Figure 3(a) shows the time-dependent electric field for the optimal pump pulse durations at 300 K and 10 K temperatures. For comparison, the THz pulse shape is also shown for 100 fs and 300 K closest to recent experimental parameters, as mentioned above. It can be seen that a 12-fold increase in the peak electric field strength can be reached by cooling down the crystal to 10 K temperature and using optimal (500 fs) pump pulses, as compared to 100 fs and 300 K.

3.2. Extremely high energies and field strengths from large-area sources

The calculated optical-to-THz energy conversion efficiencies are shown in Fig. 4(a)
Fig. 4 (a) Optical-to-THz energy conversion efficiency versus the FL pump pulse duration at different temperatures. (b) THz pulse energy assuming a pump spot diameter of 5 cm versus the FL pump pulse duration at different temperatures.
versus the FL pump pulse duration. The behavior is very similar to the electric field results shown in Fig. 3(b), but the maxima are slightly shifted towards shorter pulse durations. For example, the maxima are located at 400 fs for 10 and 100 K temperatures (instead of 500 fs, as in Fig. 3(b)). As expected, the difference between the efficiency curves belonging to different temperatures are even more pronounced than between the electric field curves of Fig. 3(b). At room temperature the calculated efficiency increases from 0.31% for 100 fs to 2.0% for 500 fs. Cooling the crystal to 100 K gives 8.9% efficiency for 400 fs, while at 10 K the efficiency gets as high as almost 13% for 400 fs.

The TPFP technique is scalable to higher THz energies by increasing the pump spot size and energy. In order to fully exploit the scalability of the TPFP technique to extremely high THz pulse energies and field strengths it will be necessary to use a very large interaction area. This will be enabled by the contact-grating technique [16

16. L. Pálfalvi, J. A. Fülöp, G. Almási, and J. Hebling, “Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification,” Appl. Phys. Lett. 92(17), 171107 (2008). [CrossRef]

], which introduces no imaging errors, and can be pumped by high-energy laser pulses.

Our calculations indicate that it is feasible to scale the THz pulse energy to the tens-of-mJ level by using the contact-grating scheme with LN. Figure 4(b) shows the calculated THz pulse energies obtained by using the efficiencies given in Fig. 4(a) and a pump beam diameter of 5 cm, which is a feasible beam size for use with the contact grating. According to Fig. 4(b), an output THz energy as high as 23 mJ can be obtained by pumping a 10-mm thick LN crystal in a contact-grating setup with pulses of 500 fs duration, 40 GW/cm2 peak intensity, and 5 cm beam diameter (about 200 mJ pump pulse energy) at 10 K temperature. As compared to present experimental status [4

4. A. G. Stepanov, S. Henin, Y. Petit, L. Bonacina, J. Kasparian, and J. P. Wolf, “Mobile source of high-energy single-cycle terahertz pulses,” Appl. Phys. B 101(1-2), 11–14 (2010). [CrossRef]

] this corresponds to an increase of more than 400 times in THz pulse energy, which will open up the field for various new applications. The THz electric field strength at the output of the crystal is 2.8 MV/cm in this case, as shown in Fig. 3(b).

A way to further increase the electric field strength of the THz output is the use of optimized THz imaging optics behind the crystal. For example, by using an optical system consisting of two parabolic mirrors with focal lengths of 50 cm and 8 cm, and typical commercially available aperture sizes, the electric field strength can be scaled to the 10 MV/cm level without any significant frequency cut-off. In this case we have assumed 1 cm THz beam diameter (intensity 1/e2-value) at the output of the LN crystal, which yields a THz beam diameter of 1.6 mm in the image plane. The contact-grating setup will allow to use very large pump beam cross sections with very good output THz beam focusability. Assuming an output THz beam diameter of 5 cm, and using a single parabolic mirror with focal length of 5 cm for focusing, a spot size of 0.57 mm can be reached in the focal plane at the central frequency of 0.67 THz (Fig. 2(b)). Even though in this setup the shape of the THz signal will be distorted because of diffraction [26

26. A. E. Kaplan, “Diffraction-induced transformation of near-cycle and subcycle pulses,” J. Opt. Soc. Am. B 15(3), 951–956 (1998). [CrossRef]

], a peak electric field strength of about 100 MV/cm can be reached.

4. Conclusion

Numerical calculations were performed in order to maximize the electric field strength of THz pulses generated by tilted-pulse-front excitation in LN, motivated by various applications. It was shown that the FL pump pulse duration is a key experimental parameter in the THz generating process. According to the calculations the THz peak electric field strength can be increased by more than a factor of four to the MV/cm level directly at the crystal output by using 600 fs pump pulses instead of the commonly used 100 fs. The importance of the absorption of LN in the THz range was also discussed. The calculations predict about one order of magnitude increase in the THz peak electric field strength when the crystal is cooled to 10 K (thereby reducing its absorption) and 500 fs pump pulses are used, as compared to 100 fs pumping at room temperature. The electric field strength can easily be increased to the 10 MV/cm level by imaging. Using such optimized pump pulse duration, and cooling the LN crystal, in combination with the contact-grating technique will allow to generate THz pulses with focused peak electric field strength on the 100 MV/cm level and tens-of-mJ energy driven by efficient sub-joule class diode-pumped solid-state lasers.

The extremely high pump-to-THz energy efficiency values predicted by the calculations correspond to pump-to-THz photon conversion efficiencies exceeding 100%. We note that internal photon conversion efficiencies well above 100% are caused by cascade effects [27

27. M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. 29(17), 2046–2048 (2004). [CrossRef] [PubMed]

] and were indicated by recent experiments [1

1. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

,2

2. A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J. P. Wolf, “Generation of 30 microJ single-cycle terahertz pulses at 100 Hz repetition rate by optical rectification,” Opt. Lett. 33(21), 2497–2499 (2008). [CrossRef] [PubMed]

]. We note that the influence of the THz field on the pump pulse, which can cause an increase of the THz generation efficiency [28

28. M. Jewariya, M. Nagai, and K. Tanaka, “Enhancement of terahertz wave generation by cascaded χ(2) processes in LiNbO3,” J. Opt. Soc. Am. B 26(9), A101–A106 (2009). [CrossRef]

,29

29. M. Nagai, M. Jewariya, Y. Ichikawa, H. Ohtake, T. Sugiura, Y. Uehara, and K. Tanaka, “Broadband and high power terahertz pulse generation beyond excitation bandwidth limitation via χ(2) cascaded processes in LiNbO3,” Opt. Express 17(14), 11543–11549 (2009). [CrossRef] [PubMed]

], can be significant in case of the very large efficiency values at optimal pump pulse durations at cryogenic temperatures. A more accurate numerical study requires to take these effects into account. We also note that at very high THz fields the effective nonlinearity of LN might change (future experiments should clarify the sign and magnitude of this behavior), which can lead to a significant decrease or increase of the THz generation efficiency. In summary, three main factors are contributing to the predicted increase in the THz yield: (i) longer FL pump pulses, (ii) cooling of the LN crystal, and (iii) large pump spot size and energy, where the latter is not influenced by the uncertainties in the model.

Our preliminary experiments (with a prototype contact grating of sinusoidal profile fabricated on ZnTe by laser ablation and pumped at 1.7 μm wavelength) indicate the working of the contact-grating scheme. Further work is needed to optimize the diffraction efficiency of the grating. Very high diffraction efficiencies can be achieved by using binary gratings [30

30. T. Clausnitzer, J. Limpert, K. Zöllner, H. Zellmer, H.-J. Fuchs, E.-B. Kley, A. Tünnermann, M. Jupé, and D. Ristau, “Highly efficient transmission gratings in fused silica for chirped-pulse amplification systems,” Appl. Opt. 42(34), 6934–6938 (2003). [CrossRef] [PubMed]

,31

31. K. Nagashima and A. Kosuge, “Design of rectangular transmission gratings fabricated in LiNbO3 for high-power terahertz-wave generation,” Jpn. J. Appl. Phys. 49(12), 122504 (2010). [CrossRef]

] instead of sinusoidal gratings. Furthermore, our very recent experiments with 1.5 ps, 50 mJ pump pulses delivered about 125 μJ THz pulse energies (0.25% efficiency) at room temperature. This result supports the expectation of a significantly increased THz output for optimal pump pulse duration, as forecast by the calculations.

The predicted development of highly optimized sources for ultra-intense THz pulses will open up new applications in THz-assisted attosecond pulse generation, as well as in particle acceleration and manipulation by electromagnetic waves.

Acknowledgments

The authors acknowledge the fabrication of the grating structure on ZnTe to Cs. Vass and B. Hopp from Department of Optics and Quantum Electronics, University of Szeged. Financial support from Hungarian Scientific Research Fund (OTKA), grant numbers 76101 and 78262, and from “Science, Please! Research Team on Innovation” (SROP-4.2.2/08/1/2008-0011) is acknowledged.

References and links

1.

K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]

2.

A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J. P. Wolf, “Generation of 30 microJ single-cycle terahertz pulses at 100 Hz repetition rate by optical rectification,” Opt. Lett. 33(21), 2497–2499 (2008). [CrossRef] [PubMed]

3.

J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25(7), B6–B19 (2008). [CrossRef]

4.

A. G. Stepanov, S. Henin, Y. Petit, L. Bonacina, J. Kasparian, and J. P. Wolf, “Mobile source of high-energy single-cycle terahertz pulses,” Appl. Phys. B 101(1-2), 11–14 (2010). [CrossRef]

5.

J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10(21), 1161–1166 (2002). [PubMed]

6.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011). [CrossRef]

7.

J. Hebling, K.-L. Yeh, M. C. Hoffmann, and K. A. Nelson, “High-power THz generation, THz nonlinear optics, and THz nonlinear spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 14(2), 345–353 (2008). [CrossRef]

8.

J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump–terahertz probe measurements,” Phys. Rev. B 81(3), 035201 (2010). [CrossRef]

9.

H. Hirori, M. Nagai, and K. Tanaka, “Excitonic interactions with intense terahertz pulses in ZnSe/ZnMgSSe multiple quantum wells,” Phys. Rev. B 81(8), 081305 (2010). [CrossRef]

10.

L. Razzari, F. H. Su, G. Sharma, F. Blanchard, A. Ayesheshim, H.-C. Bandulet, R. Morandotti, J.-C. Kieffer, T. Ozaki, M. Reid, and F. Hegmann, “Nonlinear ultrafast modulation of the optical absorption of intense few-cycle terahertz pulses in n-doped semiconductors,” Phys. Rev. B 79(19), 193204 (2009). [CrossRef]

11.

F. Junginger, A. Sell, O. Schubert, B. Mayer, D. Brida, M. Marangoni, G. Cerullo, A. Leitenstorfer, and R. Huber, “Single-cycle multiterahertz transients with peak fields above 10 MV/cm,” Opt. Lett. 35(15), 2645–2647 (2010). [CrossRef] [PubMed]

12.

A. Sell, A. Leitenstorfer, and R. Huber, “Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm,” Opt. Lett. 33(23), 2767–2769 (2008). [CrossRef] [PubMed]

13.

W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express 17(7), 5139–5146 (2009). [CrossRef] [PubMed]

14.

E. Balogh, J. A. Fülöp, J. Hebling, P. Dombi, G. Farkas, and K. Varjú, “Attosecond pulse generation in noble gases in the presence of extreme high intensity THz pulses,” 31st European Conf. on Laser Interaction with Matter (XXXI ECLIM), Budapest, Hungary, 6–10 Sept. 2010.

15.

The Extreme Light Infrastructure, European Project, http://www.extreme-light-infrastructure.eu.

16.

L. Pálfalvi, J. A. Fülöp, G. Almási, and J. Hebling, “Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification,” Appl. Phys. Lett. 92(17), 171107 (2008). [CrossRef]

17.

J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]

18.

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996). [CrossRef]

19.

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986). [CrossRef]

20.

K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically inverted electro-optic crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14(6), 2263–2276 (2006). [CrossRef] [PubMed]

21.

M. C. Hoffmann, K. L. Yeh, J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15(18), 11706–11713 (2007). [CrossRef] [PubMed]

22.

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005). [CrossRef]

23.

L. Pálfalvi, J. Hebling, G. Almási, Á. Péter, and K. Polgár, “Nonlinear refraction and absorption of Mg doped stoichiometric and congruent LiNbO3,” J. Appl. Phys. 95(3), 902–908 (2004). [CrossRef]

24.

K.-L. Yeh, J. Hebling, M. C. Hoffmann, and K. A. Nelson, “Generation of high average power 1 kHz shaped THz pulses via optical rectification,” Opt. Commun. 281(13), 3567–3570 (2008). [CrossRef]

25.

M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by terahertz pump—terahertz probe spectroscopy,” Phys. Rev. B 79(16), 161201 (2009). [CrossRef]

26.

A. E. Kaplan, “Diffraction-induced transformation of near-cycle and subcycle pulses,” J. Opt. Soc. Am. B 15(3), 951–956 (1998). [CrossRef]

27.

M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. 29(17), 2046–2048 (2004). [CrossRef] [PubMed]

28.

M. Jewariya, M. Nagai, and K. Tanaka, “Enhancement of terahertz wave generation by cascaded χ(2) processes in LiNbO3,” J. Opt. Soc. Am. B 26(9), A101–A106 (2009). [CrossRef]

29.

M. Nagai, M. Jewariya, Y. Ichikawa, H. Ohtake, T. Sugiura, Y. Uehara, and K. Tanaka, “Broadband and high power terahertz pulse generation beyond excitation bandwidth limitation via χ(2) cascaded processes in LiNbO3,” Opt. Express 17(14), 11543–11549 (2009). [CrossRef] [PubMed]

30.

T. Clausnitzer, J. Limpert, K. Zöllner, H. Zellmer, H.-J. Fuchs, E.-B. Kley, A. Tünnermann, M. Jupé, and D. Ristau, “Highly efficient transmission gratings in fused silica for chirped-pulse amplification systems,” Appl. Opt. 42(34), 6934–6938 (2003). [CrossRef] [PubMed]

31.

K. Nagashima and A. Kosuge, “Design of rectangular transmission gratings fabricated in LiNbO3 for high-power terahertz-wave generation,” Jpn. J. Appl. Phys. 49(12), 122504 (2010). [CrossRef]

OCIS Codes
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 8, 2011
Revised Manuscript: June 7, 2011
Manuscript Accepted: June 9, 2011
Published: July 21, 2011

Citation
József András Fülöp, László Pálfalvi, Matthias C. Hoffmann, and János Hebling, "Towards generation of mJ-level ultrashort THz pulses by optical rectification," Opt. Express 19, 15090-15097 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15090


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References

  1. K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 µJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007). [CrossRef]
  2. A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J. P. Wolf, “Generation of 30 microJ single-cycle terahertz pulses at 100 Hz repetition rate by optical rectification,” Opt. Lett. 33(21), 2497–2499 (2008). [CrossRef] [PubMed]
  3. J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25(7), B6–B19 (2008). [CrossRef]
  4. A. G. Stepanov, S. Henin, Y. Petit, L. Bonacina, J. Kasparian, and J. P. Wolf, “Mobile source of high-energy single-cycle terahertz pulses,” Appl. Phys. B 101(1-2), 11–14 (2010). [CrossRef]
  5. J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10(21), 1161–1166 (2002). [PubMed]
  6. H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011). [CrossRef]
  7. J. Hebling, K.-L. Yeh, M. C. Hoffmann, and K. A. Nelson, “High-power THz generation, THz nonlinear optics, and THz nonlinear spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 14(2), 345–353 (2008). [CrossRef]
  8. J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier distribution in Ge, Si, and GaAs by terahertz pump–terahertz probe measurements,” Phys. Rev. B 81(3), 035201 (2010). [CrossRef]
  9. H. Hirori, M. Nagai, and K. Tanaka, “Excitonic interactions with intense terahertz pulses in ZnSe/ZnMgSSe multiple quantum wells,” Phys. Rev. B 81(8), 081305 (2010). [CrossRef]
  10. L. Razzari, F. H. Su, G. Sharma, F. Blanchard, A. Ayesheshim, H.-C. Bandulet, R. Morandotti, J.-C. Kieffer, T. Ozaki, M. Reid, and F. Hegmann, “Nonlinear ultrafast modulation of the optical absorption of intense few-cycle terahertz pulses in n-doped semiconductors,” Phys. Rev. B 79(19), 193204 (2009). [CrossRef]
  11. F. Junginger, A. Sell, O. Schubert, B. Mayer, D. Brida, M. Marangoni, G. Cerullo, A. Leitenstorfer, and R. Huber, “Single-cycle multiterahertz transients with peak fields above 10 MV/cm,” Opt. Lett. 35(15), 2645–2647 (2010). [CrossRef] [PubMed]
  12. A. Sell, A. Leitenstorfer, and R. Huber, “Phase-locked generation and field-resolved detection of widely tunable terahertz pulses with amplitudes exceeding 100 MV/cm,” Opt. Lett. 33(23), 2767–2769 (2008). [CrossRef] [PubMed]
  13. W. Hong, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field,” Opt. Express 17(7), 5139–5146 (2009). [CrossRef] [PubMed]
  14. E. Balogh, J. A. Fülöp, J. Hebling, P. Dombi, G. Farkas, and K. Varjú, “Attosecond pulse generation in noble gases in the presence of extreme high intensity THz pulses,” 31st European Conf. on Laser Interaction with Matter (XXXI ECLIM), Budapest, Hungary, 6–10 Sept. 2010.
  15. The Extreme Light Infrastructure, European Project, http://www.extreme-light-infrastructure.eu .
  16. L. Pálfalvi, J. A. Fülöp, G. Almási, and J. Hebling, “Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification,” Appl. Phys. Lett. 92(17), 171107 (2008). [CrossRef]
  17. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef] [PubMed]
  18. J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996). [CrossRef]
  19. O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986). [CrossRef]
  20. K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically inverted electro-optic crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14(6), 2263–2276 (2006). [CrossRef] [PubMed]
  21. M. C. Hoffmann, K. L. Yeh, J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15(18), 11706–11713 (2007). [CrossRef] [PubMed]
  22. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005). [CrossRef]
  23. L. Pálfalvi, J. Hebling, G. Almási, Á. Péter, and K. Polgár, “Nonlinear refraction and absorption of Mg doped stoichiometric and congruent LiNbO3,” J. Appl. Phys. 95(3), 902–908 (2004). [CrossRef]
  24. K.-L. Yeh, J. Hebling, M. C. Hoffmann, and K. A. Nelson, “Generation of high average power 1 kHz shaped THz pulses via optical rectification,” Opt. Commun. 281(13), 3567–3570 (2008). [CrossRef]
  25. M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Impact ionization in InSb probed by terahertz pump—terahertz probe spectroscopy,” Phys. Rev. B 79(16), 161201 (2009). [CrossRef]
  26. A. E. Kaplan, “Diffraction-induced transformation of near-cycle and subcycle pulses,” J. Opt. Soc. Am. B 15(3), 951–956 (1998). [CrossRef]
  27. M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. 29(17), 2046–2048 (2004). [CrossRef] [PubMed]
  28. M. Jewariya, M. Nagai, and K. Tanaka, “Enhancement of terahertz wave generation by cascaded χ(2) processes in LiNbO3,” J. Opt. Soc. Am. B 26(9), A101–A106 (2009). [CrossRef]
  29. M. Nagai, M. Jewariya, Y. Ichikawa, H. Ohtake, T. Sugiura, Y. Uehara, and K. Tanaka, “Broadband and high power terahertz pulse generation beyond excitation bandwidth limitation via χ(2) cascaded processes in LiNbO3,” Opt. Express 17(14), 11543–11549 (2009). [CrossRef] [PubMed]
  30. T. Clausnitzer, J. Limpert, K. Zöllner, H. Zellmer, H.-J. Fuchs, E.-B. Kley, A. Tünnermann, M. Jupé, and D. Ristau, “Highly efficient transmission gratings in fused silica for chirped-pulse amplification systems,” Appl. Opt. 42(34), 6934–6938 (2003). [CrossRef] [PubMed]
  31. K. Nagashima and A. Kosuge, “Design of rectangular transmission gratings fabricated in LiNbO3 for high-power terahertz-wave generation,” Jpn. J. Appl. Phys. 49(12), 122504 (2010). [CrossRef]

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