Terahertz-induced cascaded interactions between spectra offset by large frequencies
Koustuban Ravi and Franz X. Kärtner
Koustuban Ravi1,2,* and Franz X. Kärtner1,2,3
1Center for Free-Electron Laser Science, DESY, Notkestraβe 85, Hamburg 22607, Germany
2Research Laboratory of Electronics, Massachusetts Institute of Technology, USA
3Department of Physics, University of Hamburg, Hamburg 22761, Germany
*Corresponding author: koustuban.ravi@cfel.de
Franz X. Kärtner https://orcid.org/0000-0001-8829-5461
K Ravi
F Kärtner
Koustuban Ravi and Franz X. Kärtner, "Terahertz-induced cascaded interactions between spectra offset by large frequencies," Opt. Express 27, 19254-19269 (2019)
Terahertz and X-ray Optics
High power lasers
Laser damage
Phase matching
Terahertz generation
Original Manuscript: March 11, 2019
Revised Manuscript: May 12, 2019
Manuscript Accepted: May 12, 2019
We explore the dynamics of a system where input spectra in the optical domain with very disparate center frequencies are strongly coupled via highly phase-matched, cascaded second-order nonlinear processes driven by terahertz radiation. The only requirement is that one of the input spectra contain sufficient bandwidth to generate the phase-matched terahertz-frequency driver. The frequency separation between the input spectra (or pump and seed spectra) can be more than ten times larger than the phase-matched terahertz frequency. This is in contrast to our previous work on cascaded parametric amplification, where the frequency separation between the pump and seed is required to be equal to the phase-matched terahertz frequency. A practical application of such a system where the cascading of a narrowband pump line centered at 1064 nm induced by a group of weaker seed lines centered about 1030 nm and separated by the phase-matched terahertz frequency is introduced. This approach is predicted to generate terahertz radiation with percent-level conversion efficiencies and millijoule-level pulse energies in cryogenically-cooled periodically poled lithium niobate. A model that solves for the nonlinear coupled interaction of terahertz and optical waves is employed. The calculations account for second and third-order nonlinearities, dispersion in the optical and terahertz domains as well as terahertz absorption. Ramifications of pulse formats on laser-induced damage are estimated by tracking the generated free-electron density. Strategies to mitigate laser-induced damage are outlined.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Cascaded interactions mediated by terahertz radiation
M. Hemmer, G. Cirmi, K. Ravi, F. Reichert, F. Ahr, L. Zapata, O. D. Mücke, A.-L. Calendron, H. Çankaya, D. Schimpf, N. H. Matlis, and F. X. Kärtner
Cascaded DFG via quasi-phase matching with Cherenkov-type PPLN for highly efficient terahertz generation
Juntao Huang, Zhiming Rao, and Fangsen Xie
Pulse sequences for efficient multi-cycle terahertz generation in periodically poled lithium niobate
Koustuban Ravi, Damian N. Schimpf, and Franz X. Kärtner
Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production
Mark Cronin-Golomb
Cascaded parametric amplification for highly efficient terahertz generation
Koustuban Ravi, Michael Hemmer, Giovanni Cirmi, Fabian Reichert, Damian N. Schimpf, Oliver D. Mücke, and Franz X. Kärtner
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Ahr, F.
Aßmann, R.
Assmann, R.
Bache, M.
Baek, Y.
Beigang, R.
Berggren, K.
Beržanskis, A.
Boyd, R. W.
Browne, P. G.
Calendron, A.
Calendron, A.-L.
Cankaya, H.
Çankaya, H.
Carbajo, S.
Chang, G.
Chapman, H.
Cirmi, G.
Cronin-Golomb, M.
Danielius, R.
Dorda, U.
Dörner, K.
Dubietis, A.
Dunn, M. H.
Dwayne Miller, R. J.
Fakhari, M.
Fallahi, A.
Floettmann, K.
Fromme, P.
Fülöp, J. A.
Graafsma, H.
Granados, E.
Hartin, A.
Hayashi, S.
Hebling, J.
Hemmer, M.
Hobbs, R.
Hoffmann, M. C.
Hong, K.-H.
Hong, Y.
Hua, Y.
Huang, W.
Huang, W. R.
Ishizuki, H.
Jewariya, M.
Jundt, D. H.
Kalaydzhyan, A.
Kärtner, F.
Kärtner, F. X.
Kawase, K.
Kuhl, J.
Lemery, F.
Letrun, R.
Lin, H.
Matlis, N.
Matlis, N. H.
Mazalova, V.
Meents, A.
Meng, Q.
Miller, R.
Minamide, H.
Molter, D.
Moriena, G.
Moses, J.
Mücke, O.
Mücke, O. D.
Murate, K.
Nagai, M.
Nanni, E.
Nanni, E. A.
Nawata, K.
Nelson, K. A.
Olgun, H. T.
Pálfalvi, L.
Peter, A.
Piot, P.
Piskarskas, A.
Polgár, K.
Putnam, W.
Rae, C. F.
Ravi, J.
Ravi, K.
Reichert, F.
Sarrou, I.
Schiek, R.
Schimpf, D.
Schimpf, D. N.
Stegeman, G. I.
Su, Z.
Taira, T.
Taira, Y.
Tanaka, K.
Theuer, M.
Tripathi, S. R.
Varanavicius, A.
Vodopyanov, K.
Vodopyanov, K. L.
Walsh, D. A.
Wang, L.
Wise, F. W.
Wu, X.
Yahaghi, A.
Yeh, K.-L.
Yu, J.
Zapata, L.
Zapata, L. E.
Zhang, B.
Zhang, D.
Zhou, C.
J. Opt. Soc. Am. B (1)
J. Phys. B: At. Mol. Opt. Phys. (1)
JOSA B (1)
Laser & Photonics Rev. (1)
Nat. Commun. (1)
Nat. Photonics (1)
Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers. Detect. Assoc. Equip. (1)
Opt. letters (3)
Phys. Rev. Accel. Beams (1)
Fig. 1 Example of a previously studied terahertz generation system where it is necessary to consider the simultaneous evolution of many phase-matched second-order processes even if optical-to-terahertz energy conversion efficiencies are low. (a) Initial interactions in a cascaded terahertz parametric amplifier. An OPA-like input of a strong optical pump at ω0 and weaker optical seed at ω−1 is used. The frequency separation between pump and seed is required to be equal to the phase-matched terahertz frequency, i.e. ω0 − ω−1 = ΩTHz. The double arrows delineate the pair of waves involved in the interaction and the dotted arrows indicate the product of those interactions. For an input comprised of a strong pump at ω0 and weak seed at ω−1 in the optical domain, a terahertz wave at ΩTHz corresponding to the beat frequency is first generated which then drives via sum frequency generation, the component at ω+1. (b) In subsequent steps, the generated terahertz radiation drives generation of red-shifted components ω−2,−3 and further blue-shifted components, e.g. ω+2. SFG consumes a terahertz photon while DFG generates one. Therefore, absolute conversion efficiencies are low in the absence of a mechanism which prefers DFG.
Fig. 2 Schematic describing the spectral dynamics of the present system. (a) A pump (higher intensity) and seed (lower intensity) with very disparate center frequencies. The frequency separation between pump and seed is very different fromthe phase-matched terahertz frequency. The angular frequency of the pump ωp may be larger or smaller than ωs. However, a few lines separated by the phase-matched terahertz angular frequency ΩTHz are centered about the seed at ωs, which beat to generate terahertz radiation. This subsequently mediates the cascaded processes. (b) The generated terahertz radiation first modulates both the pump and seed lines, producing a series of side-bands ωs±m and ωppmm (m = 1, 2, …), about the seed and pump respectively by DFG and SFG processes. (c) Eventually, the spectral gap between the pump and seed reduces and the process produces a net red-shift if phase matching conditions are favorable. This is accompanied with an increase in terahertz generation.
Fig. 3 Variations in input spectral formats producing similar dynamics. (a) Seed is located at a smaller angular frequency, i.e. ωs < ωp. (b) Additional lines to generate terahertz radiation are distributed about the pump rather than the seed, i.e. ωp±1 = ωp ± ΩTHz and ωp < ωs. (c) Additional lines are provided adjacent to the pump and ωp > ωs. In all cases, the cascading dynamics will be similar if phase-matching towards red-shifted frequencies is superior.
Fig. 4 (a) The total optical spectrum (i.e. pump and seed) is plotted for various locations along the crystal z in panels (i)-(iv). Initially, the pump and seed spectra are very disparate in panel (i). After initial modulation bythe generated terahertz radiation, they begin to merge as seen at location (ii). Subsequently, they completely merge in (iii), followed by significant preferential red-shift in panel (iv). The merging of the spectra, i.e. at z=4 cm is seen to be the point at which conversion efficiency begins to grow rapidly. (b) Terahertz efficiency growth as a function of propagation length z for fc = 10 THz, Is = 0.01Ip and Nw = 2 in cryogenically-cooled PPLN crystals. An exponential growth of terahertz conversion efficiency, followed by a drop due to phase mismatch is observed. (c) The phase-mismatch as a function of detuning from the signal frequency is plotted. Phase-matching for red shifting with respect to ωp is preferred.
Fig. 5 Dispersion curves and their influence on cascading dynamics. Absorption is switched off to not obfuscate the overarching physics without loss of generality. (a) Plot showing evolution of the total optical spectrum along crystal length for conventional phase-matching conditions in PPLN. This represents the experimentally relevant case. Initial modulation of pump and seed spectra around ωp, ωs respectively is evident. Effective red-shift occurs only when the two spectra merge at ≈4 cm. This is followed by preferential red-shift and then subsequently back-conversion due to phase-mismatch. (b) Cascading dynamics for a fictitious dispersion curve where ωp < ω < ωs and ω > ωs are very highly phase mismatched. In this situation, the initially generated terahertz radiation by beating between lines distributed about ωs, drives the continuous red-shift of the spectrum about ωp. Since the need for modulation is greatly reduced, significant red-shift occurs at much shorter distances of z = 2 cm. (c) A dispersion curve, where only ω > ωs is phase-mismatched. In this case, the spectrum about ωp will blue shift to a much larger extent till it reaches ωs before commencing a red shift. Thus, the threshold point occurs at distances z = 6 cm, i.e. larger than that in (a). (d) Conversion efficiencies for various cases (a)-(c). (e) Dispersion in phase matching corresponding to the cases in (a)-(c).
Fig. 6 (a) Spectral dynamics for Nw = 5 lines about ωs separated by fc = 10 THz from ωp. (b) The threshold point at which terahertz efficiency experiences growth is reduced compared to the case of Nw = 2, fc = 10 THz.
Fig. 7 (a) Terahertz conversion efficiency as function of terahertz frequency shows initial increase and subsequent saturation due to increased absorption. (b) Requisite crystal lengths for maximizing efficiency show inverse dependence with terahertz frequency and peak seed intensity.
Fig. 8 Spectral (left hand side panels) and temporal evolution (right hand side panels) along crystal length z for various input pulse formats in (a)-(c). A larger initial bandwidth of seed (i.e. larger Nw) and larger ratio of Is/Ip enables keeping the peak intensity stable during the cascading process. However, while intensity growth is reduced in such cases, absolute intensity may still be higher as seen in (b). To circumvent this, the total input fluence can be reduced as in (c). The maximum permissible intensity within the crystal is ascertained by tracking the generated free-electron density in the subsequent section.
Fig. 9 (a)Terahertz efficiency versus length for various values of Is/Ip, number of seed lines Nw and total fluence levels. (b) Corresponding carrier density generated for each case as a function of length. The green horizontal line represents the laser-induced damage threshold free-electron density calculated by using the laser-induced damage threshold fluence levels from Table 1.
Fig. 10 (a)Terahertz efficiency versus length in PPLN crystals phase matched for 0.3 THz for various values of I s / I p , N w. The pump is located at 1064 nm and seed at 1030 nm. (b) Spectral broadening and red-shift accompanying the percent-level conversion efficiencies.