Formation of gigahertz pulse train by chirped terahertz pulses interference
Xinrui Liu, Maksim Melnik, Egor Oparin, Maria Zhukova, Joel J.P.C. Rodrigues, Anton Tcypkin, Sergei Kozlov
DDraft 1
Formation of gigahertz pulse train by chirped terahertzpulses interference X INRUI L IU , M AKSIM M ELNIK , E
GOR O PARIN , M ARIA Z HUKOVA , J OEL
J. P. C. R
ODRIGUES ,A NTON T CYPKIN , AND S ERGEI K OZLOV International Laboratory of Femtosecond Optics and Femtotechnologies, ITMO University, St. Petersburg, Russia Federal University of Piauí, Teresina, PI, Brazil Instituto de Telecomunicações, Portugal * Corresponding author: [email protected] October 17, 2019
The development of multiplexing information trans-mission technology in the THz band may accelerate thearrival of the 6G era. In this paper, has demonstratedthe feasibility of forming a sequence of subpulses inthe temporal domain and the corresponding quasidis-crete spectrum in the THz frequency range. It is shownthat despite the fact that the THz pulse has an exponen-tial chirp, there is a "linkage relation" between spec-trum and temporal structures of the THz pulse train.This fact can be used for encoding information in THzpulses for implementation in 6G communication sys-tems in the future.
The maturity and commercialization of the fifth generation(5G) communications has already arrived. 6G – a technologythat is considered 100 to 1000 times [1] faster than 5G, is con-sidered to come to our lives in the next ten years [2]. Freshspectral bands as well as advanced physical layer solutions arerequired for future wireless communications [3]. A lot of dif-ferent R&D projects for the 6G network technology have beenlaunched all over the world in the past two years [4, 5]. Dueto the unique characteristics of the terahertz (THz) band, THztechnology meets and satisfies the 6G requirements [6, 7]: ultra-wide band (0.06-10 THz for THz range) [8], ultra-high data rate(up to 1 Tbps) [9], and low-latency communications (less than0.1 ms) [10]. Now terahertz technology is considered to be apowerful supporter of the 6G network in physical layer, notonly just a candidate. Terahertz massive multiple input multipleoutput (MIMO) antenna plays an important role in “beyond5G” [11–13]. The implementation of these “ultra-techniques”relies on ultra-fast coding and decoding methods on terahertzwave. Moreover, pulsed broadband THz technologies can alsocontribute to this area. For instance, quasi-discrete THz super-continuum, obtained via interference of two THz pulses, canbe used to achieve data transfer rate of 34.1 Gb/s with 31 THzspectral lines [14]. One of the promising techniques for dataencoding is implemented by cutting out the spectral lines in quasi-discrete spectrum which correspond to the separate sub-pulses in temporal pulse train. Perspectives of this method wasboth experimentally [15, 16] and theoretically [17] demonstrated.However, method mentioned in these works was implementedonly in NIR range. In this paper, we improved the method towork in the terahertz range by utilizing two chirped THz pulses.The corresponding relationship between the temporal and spec-tral pulses of sequence is demonstrated. In spite of a not linear,but an exponential chirp, there is a "linkage relation" betweenthe emerging temporal and spectral structures - changes in spec-trum will lead to similar changes in temporal domain. Thistechnique allows to create communication network and deviceswhich can operate at room temperature.
Fig. 1.
Experimental setup for THz pulse train generationfrom interference of two chirped THz pulses based on the con-ventional THz time-domain spectrometer. BS – beamsplitter,M1–M2 – Michelson interferometer mirrors, NL – nonlinearcrystal for optics–to–THz conversion, HMW – hollow metalwaveguide, EO – electro-optical detection system.Figure 1 illustrates the experimental setup for THz pulse traingeneration from interference of two chirped THz pulses basedon the conventional THz time-domain spectrometer [18]. In thissystem, the THz radiation is generated by the optical rectificationof femtosecond pulses in an InAs crystal located in 2.4 T mag-netic field [19]. The Yb-doped solid-state fs oscillator (centralwavelength 1050 nm, duration 100 fs, pulse energy 70 nJ, repe-tition rate 70 MHz) is used as a pump. The THz radiation hasestimated average power 30 µ W, FWHM ∼ a r X i v : . [ phy s i c s . op ti c s ] O c t raft 2 CdTe crystal is used for electro-optical detection.It is known that two-beam interference leads to quasi-discretespectrum spectrum [14]. In this work Michelson interferometerin front of a THz generator is used to create two consecutive THzpulses. One of the mirror is fixed while the other is located on thelinear stage which allow to ajust the time delay between fs pulses.Then these pulses pass through the hollow metal waveguide,where two consecutive phase-modulated pulses are formed [20].Figure 2(a) and (b) show example of generated single Thz pulseand its spectrum and figure 2(c) and (d) illustrate the chirpedTHz pulse obtained from hollow stainless steel metal waveguidewith 23 mm length, 0.89 mm tip inner diameter, and 1.43 mmouter diameter.
Fig. 2. (a) Single THz pulse generated in InAs and (b) its spec-trum. (c) The chirped pulse from hollow metal waveguide and(d) its spectrum.As can be seen from the figure 2, chirping in a metal waveg-uide leads to an increase in the THz pulse duration from 2 ps to7 ps, while the corresponding spectrum undergoes only minorchanges. For example, the water absorption line at a frequencyof 0.55 THz remains unchanged. However, at low frequenciesthere is a drop due to the fact that at these frequencies the signaldoes not propagate in the waveguide with such parameters. The0.3 THz dip is also caused by the propagation features of THzradiation in the waveguide [20–22].The presence of the chirp makes it possible to observe notonly the formation of a quasi-discrete spectrum [14], but alsothe formation of a train of pulses during the interference [16, 17].The chirp of experimentally obtained THz pulses is shown infigure 3(a) (red curve). As can be seen, it is well approximatedby an exponential function (blue curve). Figure 3(b) and (c)illustrates the experimental quasi-discrete spectrum and thetemporal structure of the formed pulse train.It was previously shown [16, 17] that for the case of linearlychirped pulse with itself shifted by a time delay shorter than itsduration interference quasi-discrete spectrum and pulse trainformed have strict correspondence. This means that each sub-pulse in the temporal structure has its own spectral line in thequasi-discrete spectrum. However, such a correspondence wasproved [17] only in the case of quasi-linear chirp. In this paper,the chirp is exponential, so the presence of a correspondence
Fig. 3. (a) Experimental chirp of Thz pulse and its exponentialapproximation, (b) quasi-discrete spectrum (c) and temporalstructure of the pulse train.between the temporal and spectral structures is not obvious.Despite this, it can be seen in figure 3 that the same numberof substructures can be distinguished in the structures formed,which may indicate such a correlation. In the THz spectrumin figure 3(b) three discernable pulse spikes can be seen; in thetemporal structure 3(c) these spikes correspond to three pulsesof different frequencies. The time interval between the maximaof the first two pulses of a higher frequency is 10 ps, that meanstheir repetition rate is 100 GHz.To verify the assumptions made during the analysis of ex-perimental data, a numerical simulation was carried out withparameters close to experimental ones. THz pulse with expo-nential chirp can be represented as: E = E · exp ( − t τ ) · sin ( πν ( + exp ( − α t )) t ) (1) where E is the pulse amplitude, ω is the pulse central fre-quency, τ is the pulse duration, α is the inverse steepness ofexponential chirp. To match the experiment, these parameterswere chosen as follows: ν = 0.45 THz, τ = 7 ps and α = 1/22ps − .Figure 4(a,b) illustrates the THz pulse with exponential chirpspectrum and temporal structure obtained from numerical simu-lation respectively. The interference of two such chirped pulsescan be represented as [16, 17]: E sum = E ( t ) + E ( t + ∆ t ) (2) where ∆ t is the time delay between pulses.Figure 4(c,d) represents such pulse interference with itselfshifted on the time delay ∆ t = 4 ps and the corresponding quasi-discrete spectrum. It can be seen that simulation results arepretty similar to the experimental one. The existing discrepancyis due to the fact that the experimental pulse has a non-Gaussianprofile. To confirm the correspondence between the temporaland spectral structures formed during the interference, a nu-merical simulation of the cutting out one of the lines of thequasi-discrete spectrum was performed. The results are shownin Figure 5. raft 3 Fig. 4. (a) Spectrum, (b) temporal structure and chirp of simu-lated chirped THz pulse. (c) quasi-discrete spectrum and (d)pulse train formed from interference of two chirped pulses.It can be seen that cutting out one of the spectral peaks leadsto the vanishing of the subpulse in temporal structure. How-ever, there is some ambiguity in temporal domain which can beexplained by the presence of a residual interference term. Thisterm can be eliminated by the proper selection of experimentalparameters [17]. Thus, changes in spectrum will lead to similarchanges in temporal domain. In other words there is "linking re-lation" between spectrum and temporal structures of THz pulsetrain. Since this special "linkage relation" between spectrum andtemporal domain of chirped THz pulse train, some narrow bandspectral filters can be used in the future work take an importantpart of terahertz information encoding and information transfersystem.
Fig. 5.
One of comparison example of uncoded (blue solidline) and coded (red dashed line) pulse train with cutting outone of the lines (a) in quasi-discrete spectrum and (b) corre-sponding pulse train changes.In conclusion, this paper has shown the feasibility of form-ing a sequence of subpulses with a 100 GHz frequency in thetemporal domain and the corresponding quasidiscrete spectrumin the THz frequency range. It is shown that despite the factthat the THz pulse has an exponential chirp, there is a "linkagerelation" between the temporal and spectral structures. This factcan be used in the future for encoding information using suchTHz pulses for implementation in 6G communication systems.
FUNDING
Government of the Russian Federation (08-08).
ACKNOWLEDGMENT
This work was partially supported by the National Fundingfrom the FCT - Fundação para a Ciência e a Tecnologia throughthe UID/EEA/50008/2019 Project; by the Government of theRussian Federation, Grant 08-08; and by Brazilian NationalCouncil for Research and Development (CNPq) via Grants No.431726/2018 − REFERENCES
1. J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong,and J. C. Zhang, “What will 5g be?” IEEE J. on selected areas commu-nications , 1065–1082 (2014).2. A. Yastrebova, R. Kirichek, Y. Koucheryavy, A. Borodin, and A. Kouch-eryavy, “Future networks 2030: Architecture & requirements,” in (IEEE, 2018), pp. 1–8.3. Z. Zhang, Y. Xiao, Z. Ma, M. Xiao, Z. Ding, X. Lei, G. K. Karagiannidis,and P. Fan, “6g wireless networks: Vision, requirements, architecture,and key technologies,” IEEE Veh. Technol. Mag. , 28–41 (2019).4. B. Zong, C. Fan, X. Wang, X. Duan, B. Wang, and J. Wang, “6gtechnologies: Key drivers, core requirements, system architectures,and enabling technologies,” IEEE Veh. Technol. Mag. , 18–27 (2019).5. P. Yang, Y. Xiao, M. Xiao, and S. Li, “6g wireless communications:Vision and potential techniques,” IEEE Netw. , 70–75 (2019).6. T. S. Rappaport, Y. Xing, O. Kanhere, S. Ju, A. Madanayake, S. Mandal,A. Alkhateeb, and G. C. Trichopoulos, “Wireless communications andapplications above 100 ghz: Opportunities and challenges for 6g andbeyond,” IEEE Access , 78729–78757 (2019).7. Y. Xing and T. S. Rappaport, “Propagation measurement system andapproach at 140 ghz-moving to 6g and above 100 ghz,” in (IEEE, 2018), pp.1–6.8. A. S. Cacciapuoti, K. Sankhe, M. Caleffi, and K. R. Chowdhury, “Beyond5g: Thz-based medium access protocol for mobile heterogeneousnetworks,” IEEE Commun. Mag. , 110–115 (2018).9. K. B. Letaief, W. Chen, Y. Shi, J. Zhang, and Y.-J. A. Zhang, “Theroadmap to 6g–ai empowered wireless networks,” arXiv preprintarXiv:1904.11686 (2019).10. E. C. Strinati, S. Barbarossa, J. L. Gonzalez-Jimenez, D. Ktenas,N. Cassiau, L. Maret, and C. Dehos, “6g: The next frontier: From holo-graphic messaging to artificial intelligence using subterahertz and visi-ble light communication,” IEEE Veh. Technol. Mag. , 42–50 (2019).11. S. A. Busari, K. M. S. Huq, S. Mumtaz, and J. Rodriguez, “Terahertzmassive mimo for beyond-5g wireless communication,” in ICC 2019-2019 IEEE International Conference on Communications (ICC), (IEEE,2019), pp. 1–6.12. K. M. S. Huq, S. A. Busari, J. Rodriguez, V. Frascolla, W. Bazzi, andD. C. Sicker, “Terahertz-enabled wireless system for beyond-5g ultra-fast networks: A brief survey,” IEEE Netw. , 89–95 (2019).13. A.-A. A. Boulogeorgos, A. Alexiou, T. Merkle, C. Schubert, R. Elschner,A. Katsiotis, P. Stavrianos, D. Kritharidis, P.-K. Chartsias, J. Kokkoniemi et al. , “Terahertz technologies to deliver optical network quality ofexperience in wireless systems beyond 5g,” IEEE Commun. Mag. ,144–151 (2018).14. Y. V. Grachev, X. Liu, S. E. Putilin, A. N. Tsypkin, V. G. Bespalov, S. A.Kozlov, and X.-C. Zhang, “Wireless data transmission method usingpulsed thz sliced spectral supercontinuum,” IEEE Photonics Technol.Lett. , 103–106 (2017). raft 4
15. A. N. Tsypkin, S. E. Putilin, A. V. Okishev, and S. A. Kozlov, “Ultrafastinformation transfer through optical fiber by means of quasidiscretespectral supercontinuums,” Opt. Eng. , 1 – 3 (2015).16. A. Tcypkin and S. Putilin, “Spectral-temporal encoding and decodingof the femtosecond pulses sequences with a thz repetition rate,” Appl.Phys. B , 44 (2017).17. M. Melnik, A. Tcypkin, S. Putilin, S. Kozlov, and J. J. Rodrigues, “Anal-ysis of controlling methods for femtosecond pulse sequence with tera-hertz repetition rate,” Appl. Phys. B , 98 (2019).18. Y. V. Grachev, M. O. Osipova, and V. G. Bespalov, “Comparison ofan electro-optical system and photo-conducting antenna employed asdetectors of pulsed terahertz radiation by means of a new method formeasuring spectral width,” Quantum Electron. , 1170–1172 (2014).19. V. Bespalov, A. Gorodetskiy, I. Y. Denisyuk, S. Kozlov, V. Krylov,G. Lukomskiy, N. Petrov, and S. Putilin, “Methods of generating super-broadband terahertz pulses with femtosecond lasers,” J. Opt. Technol. , 636–642 (2008).20. R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation ofultrawideband short pulses of terahertz radiation through submillimeter-diameter circular waveguides,” Opt. Lett. , 1431–1433 (1999).21. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Tera-hertz waveguides,” J. Opt. Soc. Am. B , 851–863 (2000).22. M. M. Nazarov, A. V. Shilov, K. A. Bzheumikhov, Z. C. Margushev, V. I.Sokolov, A. B. Sotsky, and A. P. Shkurinov, “Eight-capillary claddingthz waveguide with low propagation losses and dispersion,” IEEETransactions on Terahertz Sci. Technol.8