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Device length is 1.26 mm, waveguide height h is 300 nm, separation d is 300 nm, graphene's chemical potential and relaxation time are 0.7 eV and 1 ps, modulation frequency is 30 GHz, k m = 1.53 × 10 5, modulation index is 0.3, and temperature is 300 K.Selena Gomez's hair is blue. (e) Isolation and insertion loss versus graphene relaxation time. (d) Transmission for both propagation directions, computed with coupled mode theory (solid lines) and full-wave simulations (markers). (c) Dispersion of the quasi- even and odd supermodes. An enlarged view of the ports is shown for better visualization. (b) Full-wave simulation in the isolated direction at λ = 1550 nm. The advantage of this approach lies in it requiring smaller k mod, since the modes have similar wave numbers, making it suitable for short wavelengths. 4, but instead of using a single multimode wire, two coupled monomode wires supporting even and odd supermodes are used. Hybrid graphene/dielectric isolator based on interband photonic transitions operating at λ = 1550 nm. Graphene's chemical potential and relaxation time are 0.4 eV and 1 ps, respectively, modulation frequency is 30 GHz, k m = 1.86 × 10 5, modulation index is 0.3, and temperature is 300 K. (f) Isolation and insertion loss versus graphene relaxation time. (e) Transmission for both propagation directions, computed with coupled mode theory (solid lines) and full-wave simulations (markers). (d) Dispersion of the even and odd modes involved in the operation. Device length is 1.36 mm waveguide height h is 6 μ m. Shown are enlarged snapshots of the ports for better visualization. (c) Full-wave simulation of an isolator based on this principle, for the isolated direction. (b) Transverse view of a multimode waveguide able to host this type of isolator. Dashed black and solid red and blue lines denote the light cone and even and odd modes, respectively. (a) Operation principle: if ω m = ω 2 − ω 1 and k m o d = k 2 − k 1, perfect phase matching occurs and total power conversion occurs between the orthogonal modes. Hybrid graphene/dielectric isolator based on interband photonic transitions.
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Graphene chemical potential and relaxation time are 0.4 eV and 1 ps, modulation frequency is 30 GHz, modulation index is 0.3, and temperature is 300 K. (f) Poynting vector for excitation from the left (energy is transmitted to the right) and from the right (energy is frequency converted and reflected). (e) Isolation and insertion loss versus graphene relaxation time for a waveguide length of 1.5 mm. Panels (c,d) show the real and imaginary parts of the wave number of the guided mode near the band gap, computed analytically for both propagation directions. Overlaid is the associated y component of the guided mode (not to scale).
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(b) Photonic isolator based on a dielectric waveguide ( y invariance is assumed) with relative permittivities ɛ 1 = ɛ 3 = 4 ( Si O 2) and ɛ 2 = 12 (Si), h = 2.75 μ m, loaded with a series of time-modulated graphene capacitors with interlayer spacing much smaller than h, resulting in an effective conductivity along z of the form shown in Eq. ( 1), with M = 0.3, ω m = 30 GHz, and k m = 8.52 × 10 6. (a) Dielectric waveguide loaded with a time-modulated graphene capacitor. Hybrid dielectric-graphene isolator based on asymmetric band gaps. We envision that this technology may pave the wave to magnetic-free, fully integrated, and CMOS–compatible nonreciprocal components with wide applications in photonic networks and thermal management. Our results, validated through harmonic-balance full-wave simulations, confirm the feasibility of the introduced low-loss ( < 3 dB) platform to realize large photonic isolation through various mechanisms, such as narrow-band asymmetric band gaps and interband photonic transitions that allow multiple isolation frequencies and large bandwidths. We introduce an analytical framework based on solving the eigenstates of the modulated structure and on spatial coupled mode theory, unveiling the physical mechanisms that enable nonreciprocity and enabling a quick analysis and design of optimal isolator geometries based on synthetic linear and angular momentum bias. The resulting hybrid graphene-dielectric platform is low loss, silicon compatible, robust against graphene imperfections, scalable from terahertz to near-infrared frequencies, and it exhibits large nonreciprocal responses using realistic biasing schemes.
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We propose a paradigm for the realization of nonreciprocal photonic devices based on time-modulated graphene capacitors coupled to photonic waveguides, without relying on magneto-optic effects.