Geometry of the polarization independent circulator. The composite device consists of two polarization splitters, each of length Lps, with two polarization converting double layer waveguides of length Lcv in-between.
The following parameters specify a device for which the simulations predict circulator functionality at wavelengths around 1.3 µm: thickness of the guiding film (= etching depth) h = 0.634 µm, width of the port waveguides w = 0.798 µm, thickness of the lower magnetooptic film in the unidirectional polarization converters t = 0.181 µm, orientation angle of the static in-plane magnetization theta = 63o, gap width g = 0.103 µm, width of the coupler segments is the polarization splitters W = 3.616 µm, length of the polarization splitters Lps = 492 µm, length of the polarization converters Lcv = 1832 µm, substrate refractive index ns = 1.95, refractive index of the guiding regions nf = 2.302, air cover nc = 1.0, offdiagonal permittivity element in the magnetooptic materials +/-xi = 0.005, corresponding to a specific Faraday rotation of +/-3000o/cm.
Simulation of the light propagation through the circulator device. The gray scale levels are related to the squareroot of the local intensity (TE and TM part) in the y-z-plane in the center of the guiding film at x=h/2. Arrows indicate the excited port, either TE or TM light is launched. The analysis of the composite device employs semivectorial WMM based coupled mode theory for the polarization splitters, and the vectorial coupled mode formalism for the magnetooptic polarization converters.
The simulation of the device serves best to explain its behaviour. Previously one has to bring to mind the function of the polarization splitters and of the unidirectional polarization converters. TM light injected in one of the polarization splitter ports leaves the splitter in the same waveguide straight ahead, while TE light changes the waveguide. This applies to both directions of light propagation. Waves propagating in the polarization converters in forward direction regain their input polarization at the output. In backward direction, TE input polarization is converted to TM output light, and vice versa. Combination of these functions leads to the light paths depicted in the figure above. Charts (a) and (b) show a straight transmission from port A to B in forward direction for both input polarizations. In backward direction, illustrated in insets (c) and (d), port B is connected to D for TE and TM polarized light. Mirrored beating patterns appear for forward transmission from D to C and for the backward connection between C and A. This is the functionality of an isolator for the two straight light paths A <-> B and D <-> C.
It depends on the definition of `ports', whether the device can be regarded as a circulator. If the ports are defined in terms of modes, thus to be specified by a spatial outlet A to D and the mode polarization TE or TM, we obtain the two separate transmission cycles ATE <-> BTE, BTE <-> DTM, DTM <-> CTM, CTM <-> ATE, and ATM <-> BTM, BTM <-> DTE, DTE <-> CTE, CTE <-> ATM. There is no circulator functionality with respect to the four waveguides if only modes of equal polarization are admitted. If one considers input and output power only, the device performs as a polarization independent four port circulator with the transmission cycle A -> B, B -> D, D -> C, C -> A.