e) Time-Resolved Spectroscopy of THz Coherent Transients

In recent years experiments with ultrashort pulses were almost exclusively restricted to the visi- ble and infrared spectral range. However, the newly developed terahertz beam sources, produ- cing subpicosecond pulses of terahertz radiation, have made accessible a new frequency range for time domain spectroscopy and the studies of fast transients. These pulses essentially consist of a single cycle over the pulse duration of typically 300 fs, and are characterized by a transform-limited white spectrum extending from low frequencies up to 5 THz. This frequency range, midway between the microwave and infrared frequencies, is im- portant owing both to the samples that can be investigated and to the unusual experimental conditions encountered with these THz pulses. They allow to study gases, liquids and solids in a frequency range, which in recent years was not or only hardly accessible. The time response of TeraHertz-matter interactions can be studied by observing the pulse reshaping of femtosecond THz-pulses propagating through resonant and nonresonant media. By precisely modeling the pulse interaction with these samples the mea- surements can be analyzed directly in the time domain or parallel in the frequency domain by Fourier transforming the pulses and comparing them with theoretical spectra. This gives de- tailed insight into the material properties in the THz frequency range.

Generation and Detection of THz-Pulses

Meanwhile different techniques are known to generate and detect THz radiation, e.g., by mixing optical frequencies on an optoelectronic chip or using nonlinear crystals as sour- ces and detectors. A very successful technique for generating and detec- ting these pulses with ex- cellent signal-to-noise ratios is to use photo-conducting antenna chips irradiated with ultrashort laser pulses. When the transmitting chip is additionally supplied with a voltage, the incoming light pulses instantaneously create photo carriers which are accelerated in the supplied electric field. The rapid changes in conductivity result in short pulses of the electric current, and it is well known from classical electrodynamics that a changing current causes a radiation field which is pro- portional to the time derivative of the current. The so-called Hertzian dipole antennas are fabricated on an ion-implanted silicon-on-sapphire wafer and are located in the middle of two coplanar transmission lines separated from each other by 10 µm. The antenna gap is 5 µm wide and photoconductively shortened with 60 - 70 fs laser pulses coming at a rate of 100 MHz from a colliding pulse mode-locked (CPM) dye laser or a Ti:Sapphire laser. The emitted TeraHz radiation is collimated by a silicon lens and paraboloidal mirror into a highly directional beam with a 25 mrad divergence. After a 50 cm propagation distance this beam is fo- cused by an identical combination of mirror and lens onto the receiving antenna chip which in this case is of the same design as the transmitter. The electric field of the THz radiation induces a voltage across the gap and thus replaces the voltage source of the transmitting antenna. The actual electric field of a THz pulse is now samp- led by photoconductively shorting the antenna gap with laser pulses from a detection beam and monitoring the respective photocurrent in the antenna as a function of the time delay between the optical excitation and probe pulse.

Special Properties and Advantages of Time Resolved THz Spectroscopy

• The measured average antenna current directly represents the electric field amplitude of the pulses in contrast to the optical region, where only intensities are registered and the phase information of the field is lost. • The pulses are measured with a time resolution of 65 fs. • It's particularly noteworthy that these pulses are detected with a signal-to-noise ratio of better than 5.000:1, which for the power corresponds to a ratio of 25 Mio:1. The average power of the THz radiation is approximately 10 nW and therefore the NEP of the system only 10 -15 Watt/Hz 1/2 . • Compared with a helium cooled bolometer this setup is more than 1.000x more sensitive, although it is operated at room temperature. • The reason for this high sensitivity is mainly due to the subpicosecond gating at the detector measuring only events within this short time interval, and on the other hand the integration over more than 10 Mio pulses at a detection bandwidth of 1 Hz at the current amplifier. • This coherent detection almost completely suppresses thermal or shot noise, processes limiting the conventional techniques. • The THz pulses are unique in terms of their pulse duration and corresponding bandwidth. • They essentially consist of a single cycle and are characterized by a transform-limited white spectrum, in this case extending up to 5 THz. • In this frequency range up to now no proper radiation for time resolved measurements of fast transients is available, and • no other system with this S/N ratio, high sensitivity and broad spectral range is known.

Measurement of Gases

Almost all polar molecules have their rotational absorption lines in this spectral range and therefore can be investigated with these exceptional pulses. As an example of a measurement with symmetric top molecules is shown a plot with 10 hPa methyl fluoride in a gas cell. For the analysis of such measurement two scans are necessary, one without the vapor to determine the input pulse, and a second one with the vapor in the gas cell, to register the pulse being re- shaped and attenuated due to the pro- pagation though the sample. At this low pressure the input pulse is only slightly affected, but some signi- ficant changes in the pulse structure are already observed. The main pulse is followed by a series of coherent transients reradiated by the vapor every 20 ps after the excitation pulse. This phenomenon is best understood when switching to the frequency do- main. The spectrum of the input pulse is shown in the lower plot as the green line in direct comparison with the ab- sorption spectrum of MF. The THz pul- se which covers this full spectrum, ex- cites the molecules simultaneously on a multitude of pure rotational lines and the molecules respond to this excita- tion as a phased array of oscillators by re-radiating a free-induction decay sig- nal consisting of coherent transients. Because the MF molecule is distinguished by absorption lines with an almost constant frequen- cy separation, a periodic rephasing and dephasing of the entire ensemble of more than 50 exci- ted transitions occurs during the free induction decay, manifest as a train of subpsec THz pulses with a repetition rate equal to the frequency separation between adjacent lines. This situation is quite similar to mode-locking of lasers. Because of the rephasing of the dipoles and the commensurate frequencies involved, we term these periodic pulses "THz commensurate echoes".

What New Informations are Derived from THz-Spectroscopy?

• In the THz frequency range we observe a transition from the classical collision theory with a Lorentzian lineshape to a Van Vleck-Weisskopf line shape of collisionally broadened lines. • From this lineshape we get informations on the temporal response of the polar molecules which can align to the electric field of the THz pulses in the presence of molecular colli- sions. • The alignment characterizes the thermalization to the THz-field in the presence of colli- sions. • From this time response we derive the molecular collision time. • Also can be measured the absorption and collisional broadening at zero frequency origi- nating from molecular tunneling. • New analyses for the molecular respon- se time allow a generalized unification of the basic collision and line-shape theories of Lorentz, van Vleck-Weiss- kopf and Debye which can be described by our molecular response theory (MRT). • This shows that the applied THz experi- mental set-up allows the direct obser- vation of the ultimate time response of molecules to an external applied electric field in the presence of molecular collisions. • This response is limited by the uncertainty principle and is determined by the inverse of the spitting frequency between adjacent levels.

Doctoral Theses

J. Zhao Zeitaufgelöste Terahertz-Spektroskopie an Polymeren, Silizium und Ammoniak School of Electrical Engineering, Helmut-Schmidt-Uiversity, Hamburg 2003, Fortschr.-Ber. VDI Reihe 8 Nr. 1010, Düsseldorf, VDI-Verlag 2003, ISBN: 3-18-501008-6 B. Heinemann Weiterentwicklung und Einsatz eines Mess-Systems mit asynchroner Abtastung zur zeitaufgelösten Terahertz- Spektroskopie an Gasen School of Electrical Engineering, Helmut-Schmidt-Uiversity, Hamburg 2014

Refereed Publications in Journals and Conference Digests

H. Harde, S. Keiding, D. Grischkowsky THz Commensurate Echoes: Rephasing of Molecular Transitions in Free-Induction Decay Physical Review Letters 66, p. 1834 (1991) H. Harde, S. Keiding, D. Grischkowsky THz Coherent Transients from N 2 O Vapor in ''Quantum Electronics Laser Science'', 1991 Technical Digest Series (Optical Society of America, Washington, D.C. 1991), p. 248 (1991) H. Harde, D. Grischkowsky Coherent Transients Excited by Subpicosecond Pulses of Terahertz Radiation Journal Optical Society America B 8, p. 1642 (1991) H. Harde, D. Grischkowsky Time-Domain Spectroscopy of Molecular Vapors with Subpicosecond Pulses of THz Radiation in:''Ultrafast Processes in Spectroscopy'', Institute of Physics Conference Series No. 126, ed. by A. Laubereau and A. Seilmeier (IOP Publishing Ltd, Bristol, 1992), pp. 217-222 (1992) D. Grischkowsky, N. Katzenellenbogen, H. Harde Time-Domain Spectroscopy with Femtosecond Pulses of THz Radiation in: ''Nonlinear Optics: Materials, Fundamentals and Applications Technical Digest, 1992'' (Optical Society of America, Washington, D.C., 1992), Vol. 18, pp. 187-188 (1992) H. Harde, N. Katzenellenbogen, D. Grischkowsky THz Time-Domain Spectroscopy of Methyl Chloride Vapor in: ''Quantum Electronics and Laser Science Conference'', 1993 OSA Technical Digest Series, Vol. 3 (Optical Society of America, Washington DC), p. 89 (1993) H. Harde, N. Katzenellenbogen, D. Grischkowsky TeraHz Coherent Transients from Methyl Chloride Vapor Journal Optical Society America B 11, 1018 (1994) H. Harde, N. Katzenellenbogen, D. Grischkowsky Time-Domain Studies in Dense Molecular Vapors with Femtosecond Pulses of TeraHz Radiation in: ''5th European Quantum Electronics Conference'', Technical Digest, IEEE Catalog No. 94TH0615-5, ISBN: 0-7803-1791-2, Piscataway, p. 253 (1994) H. Harde, N. Katzenellenbogen, D. Grischkowsky Line-Shape Transition of Collision Broadened Lines Physical Review Letters 74, 1307 (1995) H. Harde, R. A. Cheville, D. Grischkowsky Collision Induced Orientation of Polar Molecules in the Field of Femtosecond Terahertz Pulses Proceedings of the 1996 European Quantum Electronics Conference, IEEE Catalog No. 96TH8162, ISBN: 0-7803-3171-0, p. 24 (1996) D. Grischkowsky, R. A. Cheville, H. Harde THz-Studies of Rotational Line-Shapes Quantum Electronics and Laser Science Conference, Vol. 12,1997 OSA Technical Digest Series (Optical Society of America), Washington DC, p. 82 (1997) H. Harde, R. A. Cheville, D. Grischkowsky Collision-Induced Tunneling in Methyl Halides Quantum Electronics and Laser Science Conference, Vol. 12, 1997 OSA Technical Digest Series (Optical Society of America), Washington DC, p. 115 (1997) H. Harde, R. A. Cheville, D. Grischkowsky Terahertz Studies of Collision-Broadened Rotational Lines Feature Article in: Journal of Physical Chemistry A, 3646-3660 (1997) H. Harde, R. A. Cheville, D. Grischkowsky Collision Induced Tunneling in Methyl Halides J. Opt. Soc. Am. B 14, 3282 (1997) H. Harde, R.A. Cheville, M. Wolff, D. Grischkowsky Line-Shape Studies of Zero-Frequency Transitions Proceedings of the 1998 European Quantum Electronics Conference, IEEE Catalog No. 98TH8326, ISBN 0-7803-4233, p. 177 (1998) H. Harde, J.-X. Zhao, M. Wolff, A. Cheville, D. Grischkowsky THz Time-Domain Spectroscopy on Ammonia 7. European Conference on Atomic and Molecular Physics (2001) H. Harde, J. Zhao, M. Wolff, R. A. Cheville, D. Grischkowsky THz Spectroscopy on Ammonia Conference on Lasers and Electrooptics (CLEO), Technical Digest Series 15, pp. 324-325 (2001) H. Harde, J. Zhao, M. Wolff, R.A. Cheville, D. Grischkowsky THz-Time-Domain-Spectroscopy on Ammonia J. Phys. Chem. A, 105 (25), pp. 6038-6047 (2001) H. Harde, J. Zhao, J. Pfuhl Ausbreitung von THz-Impulsen in resonanten und nichtresonanten Medien Symposium „Simulation in Physik, Informatik und Informationstechnik“, 66. Physikertagung, Leipzig 2002, Herausg. H. Hofman, ISSN: 0944-7121, 27-30 (2002) B. Heinemann, C. J. Fox, H. Harde Improved Fast Scanning TeraHz Pulse System Proceedings of XVIth Intern. Conference on Ultrafast Phenomena, Stresa, Italy, 09-13 June, 2008 H. Harde, D. Grischkowsky Molecular Response Theory in Terms of the Uncertainty Principle J. Phys. Chem. A 119 (34), pp 9085–9090 (2015). https://pubs.acs.org/doi/10.1021/acs.jpca.5b05909

Contributions on National Conferences and Meetings

H. Harde, D. Grischkowsky Zeitaufgelöste THz-Spektroskopie an dichten Gasen Poster Lasertag 1994, Hannover, 7. Dezember 1994 H. Harde, D. Grischkowsky, R. A. Cheville Messungen und Modellbildung zur stoßinduzierten Thermalisierung von Molekülen Poster Lasertag 1995, Hannover, 6. Dezember 1995 H. Harde Erweiterte Theorie für molekulare Stöße Lasertag 1996, Hannover, 11. Dezember 1996 H. Harde, D. Grischkowsky, R. A. Cheville Stoß-induziertes Tunneln in Methylhalogeniden Frühjahrstagung der DPG, Sektion Quantenoptik, Mainz, 6. März 1997, Verhandl. DPG (VI) 32, Q 39.5, 349 (1997) H. Harde, D. Grischkowsky, R. A. Cheville Untersuchungen mit Femtosekunden THz-Impulsen zum stoßinduzierten Tunneln in Molekülen Poster Norddeutsches Laserkolloquium 1999, Hannover, 9. Dezember 1999 H. Harde, J. Zhao, M. Wolff, A. Cheville, D. Grischkowsky THz Time Domain Spectroscopy on Ammonia Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Fachverband Molekülphysik, Berlin, 2.-4. April 2001, Verhandl. DPG (VI) 36, M-Methoden (2001) J. Zhao, H. Harde Characterization of Plastic Materials in the Terahertz Frequency Range Poster, Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Fachverband Quantenoptik, Berlin, 2.-4. April 2001, Verhandl. DPG (VI) 36, Q-Ultrakurze Pulse (2001) J. Zhao, H. Harde Untersuchungen von Polymeren im THz-Frequenzbereich Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Sektion Quantenoptik, Osnabrück, 4.-8. März 2002, Verhandl. DPG (VI), Q 434.19 (2002) H. Harde, J. Zhao, M. Wolff, R. A. Cheville, D. Grischkowsky Stoßprozesse und (NH 3 ) 2 –Dimerenbildung auf einer fs-Zeitskala Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Sektion Quantenoptik, Verhandl. (DPG) (VI) 37, Q 434.20 (2002)