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1

Di Sieno, Laura, Alberto Dalla Mora, Alessandro Torricelli, Lorenzo Spinelli, Rebecca Re, Antonio Pifferi, and Davide Contini. "A Versatile Setup for Time-Resolved Functional Near Infrared Spectroscopy Based on Fast-Gated Single-Photon Avalanche Diode and on Four-Wave Mixing Laser." Applied Sciences 9, no. 11 (June 10, 2019): 2366. http://dx.doi.org/10.3390/app9112366.

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In this paper, a time-domain fast gated near-infrared spectroscopy system is presented. The system is composed of a fiber-based laser providing two pulsed sources and two fast gated detectors. The system is characterized on phantoms and was tested in vivo, showing how the gating approach can improve the contrast and contrast-to-noise-ratio for detection of absorption perturbation inside a diffusive medium, regardless of source-detector separation.
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2

Fourkas, John T., Rick Trebino, Mark A. Dugan, and M. D. Fayer. "Extra resonances in time-domain four-wave mixing." Optics Letters 18, no. 10 (May 15, 1993): 781. http://dx.doi.org/10.1364/ol.18.000781.

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3

Wegener, M., D. S. Chemla, S. Schmitt-Rink, and W. Schäfer. "Line shape of time-resolved four-wave mixing." Physical Review A 42, no. 9 (November 1, 1990): 5675–83. http://dx.doi.org/10.1103/physreva.42.5675.

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4

Gomes, M. J. M., B. Kippelen, R. Levy, J. B. Grun, and B. Hönerlage. "Time-Resolved Four-Wave Mixing Experiments in CuCl." physica status solidi (b) 159, no. 1 (May 1, 1990): 101–6. http://dx.doi.org/10.1002/pssb.2221590111.

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5

Beach, R., D. DeBeer, and S. R. Hartmann. "Time-delayed four-wave mixing using intense incoherent light." Physical Review A 32, no. 6 (December 1, 1985): 3467–74. http://dx.doi.org/10.1103/physreva.32.3467.

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6

Shalit, Andrey, and Yehiam Prior. "Time resolved polarization dependent single shot four wave mixing." Physical Chemistry Chemical Physics 14, no. 40 (2012): 13989. http://dx.doi.org/10.1039/c2cp42112g.

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7

Belov, M. N., E. A. Manykin, and M. A. Selifanov. "Self-consistent theory of time-resolved four-wave mixing." Optics Communications 99, no. 1-2 (May 1993): 101–4. http://dx.doi.org/10.1016/0030-4018(93)90712-e.

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8

Kawanishi, S., and O. Kamatani. "All-optical time division multiplexing using four-wave mixing." Electronics Letters 30, no. 20 (September 29, 1994): 1697–98. http://dx.doi.org/10.1049/el:19941153.

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9

Strait, J., and A. M. Glass. "Time-resolved photorefractive four-wave mixing in semiconductor materials." Journal of the Optical Society of America B 3, no. 2 (February 1, 1986): 342. http://dx.doi.org/10.1364/josab.3.000342.

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10

Meyer, S., and V. Engel. "Non-perturbative wave-packet calculations of time-resolved four-wave-mixing signals." Applied Physics B 71, no. 3 (September 2000): 293–97. http://dx.doi.org/10.1007/s003400000342.

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11

Wang, Sheng, Xin Dong, Bowen Li, and Kenneth K. Y. Wong. "Polarization-independent parametric time magnifier based on four-wave mixing." Optics Letters 46, no. 22 (November 8, 2021): 5627. http://dx.doi.org/10.1364/ol.438351.

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12

Ma, H., A. S. L. Gomes, and Cid B. de Araújo. "Raman-assisted polarization beats in time-delayed four-wave mixing." Optics Letters 17, no. 15 (August 1, 1992): 1052. http://dx.doi.org/10.1364/ol.17.001052.

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13

Wasak, T., P. Szańkowski, V. V. Konotop, and M. Trippenbach. "Four-wave mixing in a parity-time (PT)-symmetric coupler." Optics Letters 40, no. 22 (November 9, 2015): 5291. http://dx.doi.org/10.1364/ol.40.005291.

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14

Ding, Thomas, Christian Ott, Andreas Kaldun, Alexander Blättermann, Kristina Meyer, Veit Stooss, Marc Rebholz, et al. "Time-resolved four-wave-mixing spectroscopy for inner-valence transitions." Optics Letters 41, no. 4 (February 5, 2016): 709. http://dx.doi.org/10.1364/ol.41.000709.

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15

Goldman, Martin V., and Edward A. Williams. "Time‐dependent phase conjugation and four‐wave mixing in plasmas." Physics of Fluids B: Plasma Physics 3, no. 3 (March 1991): 751–65. http://dx.doi.org/10.1063/1.859871.

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16

Chow, W. W., R. Indik, A. Knorr, S. W. Koch, and J. V. Moloney. "Time-resolved nondegenerate four-wave mixing in a semiconductor amplifier." Physical Review A 52, no. 3 (September 1, 1995): 2479–82. http://dx.doi.org/10.1103/physreva.52.2479.

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17

Schmitt, M., G. Knopp, A. Materny, and W. Kiefer. "Femtosecond time-resolved four-wave mixing spectroscopy in iodine vapour." Chemical Physics Letters 280, no. 3-4 (December 1997): 339–47. http://dx.doi.org/10.1016/s0009-2614(97)01139-1.

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18

Horowitz, Moshe, Daniel Kligler, and Baruch Fischer. "Time-dependent behavior of photorefractive two- and four-wave mixing." Journal of the Optical Society of America B 8, no. 10 (October 1, 1991): 2204. http://dx.doi.org/10.1364/josab.8.002204.

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19

Yu, Sungkyu, Joo In Lee, and Annamraju Kasi Viswanath. "Time-resolved four-wave mixing signal in thick bulk GaAs." Journal of Applied Physics 86, no. 6 (September 15, 1999): 3159–64. http://dx.doi.org/10.1063/1.371183.

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20

Schillak, P., and I. Balslev. "Theory of propagation effects in time-resolved four-wave mixing." Physical Review B 48, no. 13 (October 1, 1993): 9426–33. http://dx.doi.org/10.1103/physrevb.48.9426.

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21

Villaeys, A. A., and J. P. Lavoine. "Time dependent description of four wave mixing in absorbing media." Optics Communications 63, no. 5 (September 1987): 349–54. http://dx.doi.org/10.1016/0030-4018(87)90190-8.

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22

Ja, Y. H. "Real-time optical image differentiation by degenerate four-wave mixing." Applied Physics B Photophysics and Laser Chemistry 36, no. 1 (January 1985): 21–24. http://dx.doi.org/10.1007/bf00698032.

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23

Yamaguchi, K., Y. Toda, T. Ishiguro, S. Adachi, K. Hoshino, and K. Tadatomo. "Time-resolved four-wave mixing studies of excitons in GaN." physica status solidi (c) 4, no. 7 (June 2007): 2752–55. http://dx.doi.org/10.1002/pssc.200674703.

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24

MINO, HIROFUMI, AYUMU KOBAYASHI, SHOJIRO TAKEYAMA, GRZEGOSZ KARCZEWSKI, TOMASZ WOJTOWICZ, and JACEK KOSSUT. "TRIPLET BIEXCITON TRANSITION UNDER HIGH MAGNETIC FIELD IN (Cd,Mn)Te/CdTe/(Cd,Mg)Te ASYMMETRIC QUANTUM WELLS." International Journal of Modern Physics B 18, no. 27n29 (November 30, 2004): 3753–56. http://dx.doi.org/10.1142/s0217979204027402.

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Biexciton spin states in a CdMnTe / CdTe / CdMgTe single quantum well have been investigated by means of the time-integrated and the spectrally-resolved four-wave mixing measurements in magnetic fields. Applying magnetic field in a Faraday geometry, the four-wave mixing signal showed a beat like structure at an early delay-time region with a co-circular (σ+,σ+) configuration. The spectrally-resolved four-wave mixing signals indicated an additional transition appeared at 1 meV higher energy side of the exciton resonance. These results were explained well by a magnetic field induced triplet biexciton transition.
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25

SEGUR, HARVEY. "EXPLOSIVE INSTABILITY DUE TO 3-WAVE OR 4-WAVE MIXING, WITH OR WITHOUT DISSIPATION." Analysis and Applications 06, no. 04 (October 2008): 413–28. http://dx.doi.org/10.1142/s0219530508001183.

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It is known that an "explosive instability" can occur when nonlinear waves propagate in certain media that admit 3-wave mixing. In that context, three resonantly interacting wavetrains all gain energy from a background source, and all blow up together, in finite time. A recent paper [17] showed that explosive instabilities can occur even in media that admit no 3-wave mixing. Instead, the instability is caused by 4-wave mixing, and results in four resonantly interacting wavetrains all blowing up in finite time. In both cases, the instability occurs in systems with no dissipation. This paper reviews the earlier work, and shows that adding a common form of dissipation to the system, with either 3-wave or 4-wave mixing, provides an effective threshold for blow-up. Only initial data that exceed the respective thresholds blow up in finite time.
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26

Ochoa, Ellen, Lambertus Hesselink, and Joseph W. Goodman. "Real-time intensity inversion using two-wave and four-wave mixing in photorefractive Bi_12GeO_20." Applied Optics 24, no. 12 (June 15, 1985): 1826. http://dx.doi.org/10.1364/ao.24.001826.

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27

Yuan Hao, 袁浩, 武保剑 Wu Baojian, 周星宇 Zhou Xingyu, and 文峰 Wen Feng. "Equalization and Regeneration of Four-Wave Mixing for Time-Interleaved Channel." Acta Optica Sinica 34, no. 2 (2014): 0206002. http://dx.doi.org/10.3788/aos201434.0206002.

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28

Fourkas, John T., Timothy R. Brewer, Hackjin Kim, and M. D. Fayer. "Picosecond time-resolved four-wave mixing experiments in sodium-seeded flames." Optics Letters 16, no. 3 (February 1, 1991): 177. http://dx.doi.org/10.1364/ol.16.000177.

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29

Vemuri, Gautam. "Four-wave mixing with time-delayed, correlated, phase-diffusing optical fields." Physical Review A 48, no. 4 (October 1, 1993): 3256–64. http://dx.doi.org/10.1103/physreva.48.3256.

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30

Meyer, S., M. Schmitt, A. Materny, W. Kiefer, and V. Engel. "Simulation of femtosecond time-resolved four-wave mixing experiments on I2." Chemical Physics Letters 301, no. 3-4 (February 1999): 248–54. http://dx.doi.org/10.1016/s0009-2614(99)00040-8.

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31

Steffen, Thomas, John T. Fourkas, and Koos Duppen. "Time resolved four‐ and six‐wave mixing in liquids. I. Theory." Journal of Chemical Physics 105, no. 17 (November 1996): 7364–82. http://dx.doi.org/10.1063/1.472594.

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32

Khoury, Jed. "Four-wave mixing real-time intensity filtering with organic photorefractive materials." Optical Engineering 50, no. 1 (January 1, 2011): 018201. http://dx.doi.org/10.1117/1.3530048.

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33

Gelin, Maxim F., Dassia Egorova, and Wolfgang Domcke. "Efficient Calculation of Time- and Frequency-Resolved Four-Wave-Mixing Signals." Accounts of Chemical Research 42, no. 9 (September 15, 2009): 1290–98. http://dx.doi.org/10.1021/ar900045d.

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34

Klein, Avi, Shir Shahal, Gilad Masri, Hamootal Duadi, and Moti Fridman. "Four Wave Mixing-Based Time Lens for Orthogonal Polarized Input Signals." IEEE Photonics Journal 9, no. 2 (April 2017): 1–7. http://dx.doi.org/10.1109/jphot.2017.2690899.

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35

Rozouvan, Stanislav. "Commutative spatial and time symmetry of degenerate four-wave mixing measurements." Journal of the Optical Society of America B 16, no. 5 (May 1, 1999): 768. http://dx.doi.org/10.1364/josab.16.000768.

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36

Schmitt-Rink, Stefan, Shaul Mukamel, Karl Leo, Jagdeep Shah, and Daniel S. Chemla. "Stochastic theory of time-resolved four-wave mixing in interacting media." Physical Review A 44, no. 3 (August 1, 1991): 2124–29. http://dx.doi.org/10.1103/physreva.44.2124.

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37

Meyer, Kent A., John C. Wright, and David E. Thompson. "Frequency and Time-Resolved Triply Vibrationally Enhanced Four-Wave Mixing Spectroscopy." Journal of Physical Chemistry A 108, no. 52 (December 2004): 11485–93. http://dx.doi.org/10.1021/jp046137j.

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38

Grenier, P., D. Houde, S. Jandl, and L. A. Boatner. "Measurement of the soft polariton inKTa0.93Nb0.07O3by time-resolved four-wave mixing." Physical Review B 50, no. 22 (December 1, 1994): 16295–308. http://dx.doi.org/10.1103/physrevb.50.16295.

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39

Steffen, Thomas, and Koos Duppen. "Time resolved four- and six-wave mixing in liquids. II. Experiments." Journal of Chemical Physics 106, no. 10 (March 8, 1997): 3854–64. http://dx.doi.org/10.1063/1.473106.

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40

Wong, C. S., and H. K. Tsang. "Polarization-independent time-division demultiplexing using orthogonal-pumps four-wave mixing." IEEE Photonics Technology Letters 15, no. 1 (January 2003): 129–31. http://dx.doi.org/10.1109/lpt.2002.805743.

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41

Shalit, Andrey, Yuri Paskover, and Yehiam Prior. "In situ heterodyne detection in femtosecond time resolved four wave mixing." Chemical Physics Letters 450, no. 4-6 (January 2008): 408–16. http://dx.doi.org/10.1016/j.cplett.2007.11.027.

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42

Yeh, Pochi, and Arthur E. T. Chiou. "Real-time contrast reversal via four-wave mixing in nonlinear media." Optics Communications 64, no. 2 (October 1987): 160–62. http://dx.doi.org/10.1016/0030-4018(87)90044-7.

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43

Göbel, E. O., M. Koch, J. Feldmann, G. von Plessen, T. Meier, A. Schulze, P. Thomas, S. Schmitt-Rink, K. Köhler, and K. Ploog. "Time-Resolved Four-Wave Mixing in GaAs/AlAs Quantum Well Structures." physica status solidi (b) 173, no. 1 (September 1, 1992): 21–30. http://dx.doi.org/10.1002/pssb.2221730103.

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44

Borri, P., W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg. "Temperature-Dependent Time-Resolved Four-Wave Mixing in InGaAs Quantum Dots." physica status solidi (a) 190, no. 2 (April 2002): 517–21. http://dx.doi.org/10.1002/1521-396x(200204)190:2<517::aid-pssa517>3.0.co;2-k.

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45

Ivakhnik, V. V., and M. V. Savelyev. "Transient four-wave mixing in a transparent two-component medium." Computer Optics 42, no. 2 (July 24, 2018): 227–35. http://dx.doi.org/10.18287/2412-6179-2018-42-2-227-235.

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We analyze changes in the spatial structure of an object wave under four-wave mixing in a transparent two-component medium in schemes with opposing and concurrent pump waves. It is shown that in the spatial spectrum of the object wave there is a dip, whose position is determined by the propagation direction of the second pump wave. Angular rotation and frequency shift of the pump waves lead to a decrease in the conversion efficiency of high spatial frequencies. The bandwidth of the spatial frequencies cut out by the four-wave radiation converter decreases monotonically over time, whereas the bandwidth of the most efficiently converted spatial frequencies increases.
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46

Bencivenga, F., A. Calvi, F. Capotondi, R. Cucini, R. Mincigrucci, A. Simoncig, M. Manfredda, et al. "Four-wave-mixing experiments with seeded free electron lasers." Faraday Discussions 194 (2016): 283–303. http://dx.doi.org/10.1039/c6fd00089d.

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The development of free electron laser (FEL) sources has provided an unprecedented bridge between the scientific communities working with ultrafast lasers and extreme ultraviolet (XUV) and X-ray radiation. Indeed, in recent years an increasing number of FEL-based applications have exploited methods and concepts typical of advanced optical approaches. In this context, we recently used a seeded FEL to demonstrate a four-wave-mixing (FWM) process stimulated by coherent XUV radiation, namely the XUV transient grating (X-TG). We hereby report on X-TG measurements carried out on a sample of silicon nitride (Si3N4). The recorded data bears evidence for two distinct signal decay mechanisms: one occurring on a sub-ps timescale and one following slower dynamics extending throughout and beyond the probed timescale range (100 ps). The latter is compatible with a slower relaxation (time decay > ns), that may be interpreted as the signature of thermal diffusion modes. From the peak intensity of the X-TG signal we could estimate a value of the effective third-order susceptibility which is substantially larger than that found in SiO2, so far the only sample with available X-TG data. Furthermore, the intensity of the time-coincidence peak shows a linear dependence on the intensity of the three input beams, indicating that the measurements were performed in the weak field regime. However, the timescale of the ultrafast relaxation exhibits a dependence on the intensity of the XUV radiation. We interpreted the observed behaviour as the generation of a population grating of free-electrons and holes that, on the sub-ps timescale, relaxes to generate lattice excitations. The background free detection inherent to the X-TG approach allowed the determination of FEL-induced electron dynamics with a sensitivity largely exceeding that of transient reflectivity and transmissivity measurements, usually employed for this purpose.
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47

Zhu, Chang Jun, and Jun Fang He. "Study on Coherent Dynamics of Alkali Metal Atomic Wave Packets." Key Engineering Materials 538 (January 2013): 285–88. http://dx.doi.org/10.4028/www.scientific.net/kem.538.285.

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A theoretical model consisting of 5 energy levels, with the three upper states coherently excited, was proposed to analyze the coherent characteristics of atomic wave packets using perturbative theory. Pump-probe technique was implemented to detect coupled difference frequency four-wave mixing processes for studying the coherent characteristics of Rb atomic wave packets. Quantum beats were extracted the time domain signal by Fourier transform. Moreover, the variation of quantum beats was gained by time-dependent Fourier transform. The results show that the coherent characteristics of alkali metal atomic wave packets are closely related to quantum beats embedded in the time delayed four-wave mixing signal. Theoretical results are consistent with experimental observations, possessing potential applications in multi-channel information encoding and decoding.
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48

Zhu, Chang Jun, Jun Fang He, Xue Jun Zhai, Bing Xue, and Chong Hui Zhang. "Investigation of Quantum Beatings at 608 cm-1 and 70 cm-1 in Rb Vapor." Solid State Phenomena 181-182 (November 2011): 413–16. http://dx.doi.org/10.4028/www.scientific.net/ssp.181-182.413.

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Two coupled axially phase matched parametric four-wave mixings have been achieved in Rb vapor by using broad bandwidth laser pulses. Coherent radiations at 420 nm produced by difference-frequency optical wave mixing processes were detected and a pump-probe scheme was employed to record time varying characteristics of the parametric four-wave mixing signals. Quantum beatings at 608 cm-1 and 70 cm-1 were retrieved from the time varying signals by Fourier transform. Moreover, time dependent Fourier transform was utilized to analyze the dynamics of quantum beatings. The results indicate that two wave packets associated with the two quantum beating frequency components interact strongly and the quantum beating dynamics can be controlled by adjusting Rb number density.
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49

You, Jian Wei, Zhihao Lan, and Nicolae C. Panoiu. "Four-wave mixing of topological edge plasmons in graphene metasurfaces." Science Advances 6, no. 13 (March 2020): eaaz3910. http://dx.doi.org/10.1126/sciadv.aaz3910.

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We study topologically protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large life time of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states located in the topological bandgap can be achieved with a pump power of less than 10 nW. In particular, we find that the effective nonlinear edge-waveguide coefficient is about γ ≃ 1.1 × 1013 W−1 m−1, i.e., more than 10 orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultralow-power-consumption, highly integrated, and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.
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50

Kim, Dai-Sik, Jagdeep Shah, J. E. Cunningham, T. C. Damen, Wilfried Schäfer, Michael Hartmann, and Stefan Schmitt-Rink. "Giant excitonic resonance in time-resolved four-wave mixing in quantum wells." Physical Review Letters 68, no. 7 (February 17, 1992): 1006–9. http://dx.doi.org/10.1103/physrevlett.68.1006.

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