Impact of non-linearity and non-integer dimension on the reflection and transmission coefficients

References

• Franken PA, Hill AE, Peters CW, et al. Generation of optical harmonics. Phys Rev Lett. 1961;7:118–119.
   Web of Science ®Google Scholar
• Fejer MM. Nonlinear optical frequency conversion. Phys Today. 1994;47:25–32.
   Web of Science ®Google Scholar
• Pan JW, Chen ZB, Lu CY, et al. Multiphoton entanglement and interferometry. Rev Mod Phys. 2012;84:777–838.
   Web of Science ®Google Scholar
• Petrich W. Mid-infrared and Raman spectroscopy for medical diagnostics. Appl Spectrosc Rev. 2001;36:181–237.
   Web of Science ®Google Scholar
• Shi J, Li Y, Kang M, et al. Efficient second harmonic generation in a hybrid plasmonic waveguide by mode interactions. Nano Letters. 2019;19:3838–3845.
   PubMed Web of Science ®Google Scholar
• Vyunishev AM, Arkhipkin VG. Quasi-phase-matched second-harmonic generation in nonlinear crystals with harmonic modulation of nonlinearity. Laser Phys. 2020;30:045401.
   Google Scholar
• Valagiannopoulos C, Sarsen AK, Alù A. Angular memory of photonic metasurfaces. IEEE Trans Antennas Propag. 2021;69:7720–7728.
   Web of Science ®Google Scholar
• Li G, Zhang S, Zentgraf T. Nonlinear photonic metasurfaces. Nat Rev Mater. 2017;2:1–14.
   Web of Science ®Google Scholar
• Valagiannopoulos C. Multistability in coupled nonlinear metasurfaces. IEEE Trans Antennas Propag. 2022;70:
   Web of Science ®Google Scholar
• Krasnok A, Tymchenko M, Alù A. Nonlinear metasurfaces: a paradigm shift in nonlinear optics. Mater Today. 2018;21:8–21.
   Web of Science ®Google Scholar
• Rodriguez SL, Scalora M, Johnson AS, et al. Study of second and third harmonic generation from an indium tin oxide nanolayer: influence of nonlocal effects and hot electrons. Appl Photonics. 2020;5:010801.
   Google Scholar
• Lim E, Taguchi D, Iwamoto M. Study of rectifying property of ITO/PI/TIPS-pentacene/Au diodes by electric field induced optical second harmonic generation. Org Electron. 2013;14:1903–1908.
   Web of Science ®Google Scholar
• Arie A, Voloch N. Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals. Laser Photon Rev. 2010;4:355–373.
   Web of Science ®Google Scholar
• Shen YR. The principles of nonlinear optics. New York: John Wiley & Sons; 1984.
   Google Scholar
• Lembrikov BI. Nonlinear optics-novel results in theory and applications. IntechOpen; 2019.
   Google Scholar
• Kuo PS, Fang W, Solomon GS. 4-quasi-phase-matched interactions in GaAs microdisk cavities. Opt Lett. 2009;34:3580–3582.
   PubMed Web of Science ®Google Scholar
• Lin G, Coillet A, Chembo YK. Nonlinear photonics with high-Q whispering-gallery-mode resonators. Adv Opt Photonics. 2017;9:828–890.
   Web of Science ®Google Scholar
• Myers LE, Bosenberg WR. Periodically poled lithium niobate and quasiphase-matched optical parametric oscillators. IEEE J Quantum Electron. 1997;33:1663–1672.
   Web of Science ®Google Scholar
• Traynor NJ, Lefort L, Alam S, et al. Strong self-phase modulation in periodically poled lithium niobate under subpicosecond pump pulses. IEEE J Quantum Electron. 2001;37:1292–1300.
   Google Scholar
• Armstrong JA, Bloembergen N, Ducuing J, et al. Interactions between light waves in a nonlinear dielectric. Physical Review. 1962;127:1918–1939.
   Web of Science ®Google Scholar
• Boyd RW. Nonlinear optics. San Diego (CA): Academic Press; 1992.
   Google Scholar
• Liu J, Ouyang C, Huo F, et al. Progress in the enhancement of electro-optic coefficients and orientation stability for organic second-order nonlinear optical materials. Dyes Pigm. 2020;181:108509.
   Google Scholar
• Qayyum A, Abbas M. Study of reflection/transmission behavior of a planar nonlinear dielectric–NID interface. Results in Optics. 2021;5:100119.
   Google Scholar
• Qayyum A, Abbas M. Study of reflection and transmission coefficients of a linear dielectric–nonlinear NID planar interface. Phys B Condensed Matter. 2022;644:414217.
   Google Scholar
• De L, Vitorio A. Aspects of wave propagation in a nonlinear medium: Birefringence and the second-order magnetoelectric coefficients. Phys Rev A. 2022;105:023530.
   Google Scholar
• Mandelbrot BB. The fractal geometry of nature. New York: WH Freeman; 1983.
   Google Scholar
• Brouers F, Al-Musawi TJ. Brouers–Sotolongo fractal kinetics versus fractional derivative kinetics: a new strategy to analyze the pollutants sorption kinetics in porous materials. J Hazard Mater. 2018;350:162–168.
   PubMed Web of Science ®Google Scholar
• He JH. Fractal calculus and its geometrical explanation. Results Phys. 2018;10:272–276.
   Web of Science ®Google Scholar
• Maraghechi P, Elezzabi AY. Enhanced THz radiation emission from plasmonic complementary Sierpinski fractal emitters. Opt Express. 2010;18:27336–27345.
   PubMed Web of Science ®Google Scholar
• Werner DH, Ganguly S. An overview of fractal antenna engineering research. IEEE Antenn Propag Mag. 2003;45:38–57.
   Web of Science ®Google Scholar
• Wen W, Zhou L, Hou B, et al. Resonant transmission of microwaves through sub wavelength fractal slits in a metallic plate. Phys Rev B Condens Matter Mater. 2005;72:1534061–1534064.
   Google Scholar
• Mahler L, Tredicucci A, Beltram F, et al. Quasi-Periodic distributed feedback laser. Nat Photonics. 2010;4:165–169.
   Web of Science ®Google Scholar
• Feder J. Fractals. New York, London: Plenum Press; 1988.
   Google Scholar
• Tarasov VE. Electromagnetic waves in non-integer dimensional spaces and fractals. Chaos Solitons Fractals. 2015;81:38–42.
   Web of Science ®Google Scholar
• Tarasov VE. Electrodynamics of fractal distributions of charges and fields. Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. New York: Springer; 2011.
   Google Scholar
• Zubair M, Mughal MJ, Naqvi QA. Fractional fields and waves in fractional dimensional space, New York (NY): Springer-verlag; 2012. (Springer Science & Business Media).
   Google Scholar
• Abbas M, Rizvi AA, Naqvi QA. Two dimensional Green's function non-integer dimensional dielectric half-space geometry. Optik. 2016;127:8530–8535.
   Web of Science ®Google Scholar
• Abbas M, Rizvi AA, Naqvi QA. Fractional dual fields to the Maxwell equations for a line source buried in dielectric half space. Optik. 2017;129:225–230.
   Web of Science ®Google Scholar
• Abbas M, Rizvi AA, Fiaz MA, et al. Scattering of electromagnetic plane wave from a low contrast circular cylinder buried in non-integer dimensional half space. J Electromagn Waves Appl. 2017;31:263–283.
   Web of Science ®Google Scholar
• Stillinger FH. Axiomatic basis for spaces with non-integer dimension. J Math Phys. 1977181224–1234.
   Web of Science ®Google Scholar