Magnetic-free nonreciprocal photonic platform based on time-modulated graphene capacitors

D. Correas-Serrano, A. Alù, and J. S. Gomez-Diaz

Phys. Rev. B 98, 165428 – Published 19 October 2018

Abstract

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. 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. 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. 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 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.

Received 26 May 2018
Revised 20 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.165428

Physics Subject Headings (PhySH)

Photonics Plasmonics

Graphene Waveguides

Lorentz symmetry

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Correas-Serrano¹, A. Alù², and J. S. Gomez-Diaz^1,*

¹Department of Electrical and Computer Engineering, University of California Davis, One Shields Avenue, Kemper Hall 2039, Davis, California 95616, USA
²Photonics Initiative, Advanced Science Research Center, City University of New York, 85 St. Nicholas Terrace, New York City, New York 10031, USA; Physics Program, Graduate Center, City University of New York, New York, New York 10016, USA; and Department of Electrical Engineering, City College of the City University of New York, New York, New York 10031, USA

^*jsgomez@ucdavis.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 16 — 15 October 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Hybrid dielectric-graphene isolator based on asymmetric band gaps. (a) Dielectric waveguide loaded with a time-modulated graphene capacitor. (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 $k_{m} = 8.52 \times 10^{6} .$ Overlaid is the associated $y$ component of the guided mode (not to scale). 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. (e) Isolation and insertion loss versus graphene relaxation time for a waveguide length of 1.5 mm. (f) Poynting vector for excitation from the left (energy is transmitted to the right) and from the right (energy is frequency converted and reflected). 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.
Reuse & Permissions
Figure 2
(a) Bidirectional transmission of the isolator from Fig. 1, computed with three different approaches: (i) considering the propagation decay in the band gaps given by Eq. (3), (ii) applying coupled mode theory with the dispersion and field profiles of the unmodulated waveguide given by Eq. (5), and (iii) using harmonic-balance full-wave simulation in comsol multiphysics. (b–d) Parametric study of coupling coefficient, isolation, and insertion loss of the proposed isolator versus waveguide height and chemical potential of the graphene sheets. Parameters are the same as in Fig. 1.
Reuse & Permissions
Figure 3
Compact implementation of the hybrid dielectric/graphene isolator in Figs. 1 and 2. By using a graphene-modulated resonant ring coupled to a standard, unmodulated bus waveguide, mode coupling occurs within the resonant ring and a tenfold length reduction is achieved. Parameters are as in Figs. 1 and 2, ring radius is $39 μ m$ , and distance between bus and waveguide is 5 $μ m$ .
Reuse & Permissions
Figure 4
Hybrid graphene/dielectric isolator based on interband photonic transitions. (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. This happens only in one direction. Dashed black and solid red and blue lines denote the light cone and even and odd modes, respectively. (b) Transverse view of a multimode waveguide able to host this type of isolator. (c) Full-wave simulation of an isolator based on this principle, for the isolated direction. Shown are enlarged snapshots of the ports for better visualization. Device length is 1.36 mm; waveguide height $h$ is 6 $μ m .$ (d) Dispersion of the even and odd modes involved in the operation. (e) Transmission for both propagation directions, computed with coupled mode theory (solid lines) and full-wave simulations (markers). (f) Isolation and insertion loss versus graphene relaxation time. Graphene's chemical potential and relaxation time are 0.4 eV and 1 ps, respectively, modulation frequency is 30 GHz, $k_{m} = 1.86 \times 10^{5},$ modulation index is 0.3, and temperature is 300 K.
Reuse & Permissions
Figure 5
Hybrid graphene/dielectric isolator based on interband photonic transitions operating at $λ = 1550 nm$ . Operation is like in Fig. 4, but instead of using a single multimode wire, two coupled monomode wires supporting even and odd supermodes are used [11]. 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. (a) Transverse view of the waveguide. (b) Full-wave simulation in the isolated direction at $λ = 1550 nm$ . An enlarged view of the ports is shown for better visualization. (c) Dispersion of the quasi- even and odd supermodes. (d) Transmission for both propagation directions, computed with coupled mode theory (solid lines) and full-wave simulations (markers). (e) Isolation and insertion loss versus graphene relaxation time. 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, $k_{m} = 1.53 \times 10^{5},$ modulation index is 0.3, and temperature is 300 K.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics