Integrated Optical Circulator in a Silicon Ring Resonator with Two Time-Modulated Regions

Optical circulator is a three-port non-reciprocal device, which allows unidirectional light transmission between its ports and has been conventionally achieved through magneto-optical effects [1]. To overcome the limitations of the magneto-optic implementations (CMOS incompatible materials, bulky and lossy devices, high external magnetic fields), magnetic-free approaches have been proposed. The scheme of temporal modulation can be utilized to obtain an optical circulator in a CMOS compatible platform. This approach has been numerically demonstrated in the coupled photonic crystal cavities [2] and MZI modulators [3]. Here, we propose a novel magnetic-free scheme to achieve a compact and CMOS-compatible optical circulator based on a silicon ring resonator with two time-modulated regions, as we previously presented in [4], [5], coupled to two waveguides in an add-drop configuration, in which a Bragg grating is placed in one of the waveguide ports to reflect the optical signal (depicted in Fig. 1(a)). In this ring resonator, degeneracy of the clockwise (c.w.) and counter-clockwise (c.c.w.) modes is broken by the proper design of the phase difference of the modulated regions and their distance. Therefore, due to the full reflection of the designed Bragg grating, there is an acceptable transmission from port 1 to 2, port 2 to 3, and port 3 to 1 (i.e., the path <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1- &gt; 2- &gt; 3- &gt; 1)$</tex> at the resonance frequency of the c.w. mode. However, such transmission is not allowed in the reverse path, i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1- &gt; 3- &gt; 2- &gt; 1$</tex>, which corresponds to the the c.c.w. mode. The effect of the modulation frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(f_{m})$</tex> and carrier density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\Delta N)$</tex> on the forward <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(S_{21})$</tex> and reverse <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(S_{12})$</tex> transmissions and isolation is studied analytically using temporal coupled mode theory, and by investigating their effect on the two counter-acting mechanisms of frequency splitting and energy transfer to the side harmonics (Fig. 1(d)-(f)), following the simulation methodology explained in [6]. We consider the working points between the black and red curves, showing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\vert S_{21}\vert ^{2}=0.5$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\vert S_{12}\vert ^{2}=0.1$</tex>, respectively. Transmission spectrum for one of these working points is shown in Fig. 1(b), for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{m}=10$</tex> GHz and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta N=4.4\times 10^{18}\text{cm}^{-3}$</tex>. Simulated reflection spectrum for the designed Bragg grating with a period of 327 nm and 150 number of periods is depicted in Fig. 1(c), showing that it can perform as a perfect reflector.