siph_ringres_var :
An optical ring modulator.

The siph_ringres_var primitive represents an optical ring modulator, i.e., an optical ring resonator of which resonance wavelengths can be controlled by an xreal-typed input ctrl. A typical silicon microring modulator is made of a main waveguide that connects between the ports, a ring waveguide whose round-trip delay is modulated by the input ctrl, and a directional coupler that couples these two waveguides. This siph_ringres_var primitive models the optical ring modulator as a reciprocal element that can receive incident waves from any port and propagate waves with the symmetrical transfer characteristics.


                 in  --------------------- thru
                              ---
                             /   \
                            |  O--|------- ctrl
                             \   /
                              ---

The parameter oplength_cpl specifies the optical path length of the directional coupler in meters, which is equal to the shortest delay between the ports in and thru multiplied by the speed of light in free space (c0=2.99792458e8 meters/sec). The parameters gain_thru and gain_cpl specify the transmission and coupling gains of the directional coupler, respectively. The wave being coupled to an opposite-side waveguide experiences a -pi/2 phase shift. Note that this primitive does not model the dependencies of the gains gain_thru and gain_cpl on the light’s wavelength or waveguide’s length.

The parameter oplength_ring specifies the nominal optical path length of the ring when the input ctrl is equal to 0, including the optical path length of the directional coupler. When the input ctrl is not zero, the optical path length of the ring is determined by oplength_ring * (1 + gain_mod*ctrl), where the parameter gain_mod is the modulation gain that defines the relative change in the optical path length per unit change in the input ctrl. The ring modulator’s resonance occurs when this optical path length of the ring is equal to an integer-multiple of the wavelength of the incident wave. The parameter gain_ring specifies the additional gain through a round trip of the ring waveguide excluding the transmission gain of the directional coupler.

The parameter dispersion specifies the total group delay dispersion (GDD) of the ring waveguide at the center wavelength specified by the parameter wavelength. The GDD is defined as the change in the group delay (tg) with respect to the angular frequency (w), which can be measured directly or derived from the dispersion coefficient (D) (in second/meter^2) as:


         dtg       (wavelength)^2               (wavelength)^2         (oplength)
  GDD = ----- = - ---------------- * D * l = - ---------------- * D * ------------.
         dw            2*PI                         2*PI                   ng

Note that such dispersion in the group delay can cause shifts in the periodic patterns of the ring modulator’s frequency response.

The parameter Zrel specifies the main waveguide’s characteristic impedance relative to a reference impedance (Z0) of your choice. Note that the use of this relative impedance allows one to determine the amount of reflections at impedance discontinuities without having to know the absolute values of the characteristic impedances. While the choice of the reference impedance (Z0) can be arbitrary, it must be consistent across all the silicon-photonic components used in a system. In other words, all the equivalent circuit elements describing the impedance relationships at the optical ports must use the impedance values relative to the same Z0.

Input/Output Terminals

Name	I/O	Type	Description
in	input	xreal	input port
thru	input	xreal	thru port
ctrl	input	xreal	control port

Parameters

Name	Type	Default	Unit	Description
Zrel	real	1.0	None	relative characteristic impedance
oplength_cpl	real	38.75u	meters	optical path length of coupler
oplength_ring	real	155u	meters	optical path length of ring
gain_thru	real	0.99	None	transmission gain of coupler
gain_cpl	real	0.14	None	coupling gain of coupler
gain_ring	real	0.99	None	additional gain of ring
gain_mod	real	2e-4	None	modulation gain
dispersion	real	0.0	second^2	group delay dispersion
wavelength	real	1550n	meters	center wavelength

siph_ringres_var :An optical ring modulator.

siph_ringres_var :
An optical ring modulator.