Silicon Photonic MEMS Phase-Shifter

We present a design for an analog phase shifter based on Silicon Photonic MEMS technology. The operation principle is based on a two-step parallel plate electrostatic actuation mechanism to bring a vertically movable suspended tapered waveguide in a first step into proximity of the bus waveguide and to tune the phase of the propagating coupled mode in a second step by actuation of the suspended waveguide to tune the vertical gap. In the coupled state, the effective index of the optical supermode and the total accumulated phase delay can be varied by changing the vertical separation between the adiabatically tapered suspended and the fixed bus waveguides. Simulations predict that π phase shift can be achieved with an actuation voltage of 19 V, corresponding to a displacement of 19 nm. With an adiabatic coupler geometry, the optical signal can be coupled between the moving waveguide and the bus waveguide with low loss in a wide wavelength range from 1.5 μm to 1.6 μm keeping the average insertion loss below 0.3 dB. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

electro-absorption, MEMS-actuation is of particular interest, due to the potential of small footprint, low insertion loss and low power consumption.
So far, MEMS approaches have been exploited in compact large array switches [8,9], polarization rotators [10], phase shifters [11], and tunable fiber to chip gratings [12]. We have further proposed designs for Silicon Photonic MEMS variable optical attenuators (VOA) [13] and bistable Silicon Photonic MEMS switches [14]. Among these components phase shifters are of particular interest because of their essential role in signal processing [15,16] and their potential in free space communication application as for beam steering [17]. Experimental implementations of Silicon Photonic phase shifters include plasma dispersion effect [18] thermo-optic [19], or plasmonic phase shifters [20]. Plasma-dispersion and thermo-optical phase shifters typically require large chip area, which limits their integration in high array number with the other optical integrated circuit blocks, and plasmonic phase shifters currently present still high insertion loss, limiting scalability.
On the other hand, MEMS-based movable waveguides have been exploited recently for phase shifting in Silicon Photonics [21], implemented using the identical fabrication process as Silicon Photonic MEMS-based switches [8]. The operation principle of MEMS-based phase shifters relies on changing the effective index (n eff ) of the propagating mode via direct mechanical perturbation of the mode's evanescent field [22,23]. This approach provides compact footprint devices, as it makes accessible a high effective index modification through a short propagation length. Optical performance tuning using evanescent field perturbation by mechanical probes has previously been reported [24,25]. In [22], a silicon nitride-based waveguide-coupled opto-electro-mechanical phase shifter architecture is presented, enabling a large refractive index change (up to 0.1). Electrostatic actuation in a metal-coated bridge is used to modify the waveguide-bridge separation and to dynamically perturb the effective index and control the phase shift. In [23] an electrostatically actuated silicon nitride-based phase shifter is demonstrated. The effective index of the waveguide is perturbed by an actuated rod, which interacts with the side evanescent field. These MEMS phase shifters are mainly silicon nitride-based, and they require footprint optimization as well as low power performance to fit as a building block for a universal photonic chip block. Here, we elaborate the discussion on our recently proposed design based on the same technology [26]. We present a compact design for an analog Silicon Photonic MEMS phase-shifter with a lowpower double-step electrostatic actuation. With such an actuation, analog tuning of the vertical gap between bus and coupler waveguides can be achieved. A broadband low-loss full period phase shift of π is accessible with a low actuation voltage.

Design and principle of operation
A sketch representing the general idea of phase shifting using electrostatic actuation is presented in Fig. 1(a). The bus waveguide is fixed while the movable waveguide can approach the bus waveguide and interrupt its evanescent field tail and form a coupledwaveguide system. In the coupled-waveguide system, a substantial portion of the carrier signal power is guided by the coupled optical supermode [27]. This portion can be maximized for an optimum coupling efficiency, which is mainly dependent on physical gap between the coupled waveguides. Since the other parameters (such as the waveguide(s) material and dimensions) that influence the propagation vector are fixed by design, the accumulated phase for the propagating signal along the coupled system is disciplined by the effective index of the supermode which is strictly dependent on the gap between two waveguides. Therefore, the total phase of the propagating optical signal through a coupled-waveguide system can be tuned by tuning the gap between the coupled waveguides.
In our design the bus waveguide and the moving waveguide are aligned vertically, and the suspended waveguide follows an adiabatic taper profile enabling a broadband efficient light power transmission. The width of the bus waveguide is fixed to 600 nm while the tapered waveguide is symmetrically narrow in the two ends (input and output), and it is wide in the This design is resilient against pull-in instability, electric breakdown, and buckling [29]: In the ON state, the applied voltage remains below and far from the pull-in voltage for the inner parallel plate actuator to provide a secure vertical gap tuning, since the stiff straight connection part has a large spring constant. The vertical gap does not reach the critical gap for electrical breakdown, as a series of mechanical stoppers are implemented in the platform design to securely control the initial gap between the electrodes. The mechanical stoppers are based on the same design of [8], where stiction tests show reliable operation for up to 48 h of contact time. Performance of the design is simulated under various stress conditions to verify its robustness against buckling failure.

Optical
The initial gap between the moving waveguide and the bus waveguide is set to 1 μm (defined by the platform fabrication process) to guarantee zero power coupling in the OFF state. In ON state the waveguides will be in the coupled regime with initial vertical gap of g = 185 nm defined by the mechanical stoppers [8]. By tapering the movable waveguide adiabatically, a minimized power beating between the coupled waveguides and a broadband power transmission is achieved for any given vertical gap. For such a coupled waveguide system the optical power is carried by the coupled supermode with position-dependent effective index which is higher than that of the uncoupled bus waveguide (n eff = 2.705 at λ = 1.55 μm) [8]. To evaluate the phase shift introduced by the moving waveguide displacement in the ON state the total accumulated phase of the propagating signal for two desired vertical gap states is calculated. The total accumulated phase for a signal propagating through the coupled waveguides with length of L and vertical gap of g is defined as In this way, the phase shift at the various gap states in ON state can be calculated with a high precision. The supermode profile for four different cross-sections along the propagation direction (x) is shown in Fig. 3 (a), for g = 185 nm and λ = 1.55 μm. The supermode dispersion along the adiabatic coupler is shown in Fig. 3 (b), and the normalized electric field distribution along the propagation direction is plotted in Fig. 3 (c), which shows efficient field transfer between the waveguides.
In ON state, in the two narrow sides of the coupler, the supermode index is dominated by the bus waveguide mode index, while in the central part of the coupler (where the moving waveguide is wider than the bus waveguide), the effective index is dominated by the suspended waveguide mode index. As a consequence of the symmetric adiabatic coupler design, the optical power is first coupled to the moving waveguide and then coupled back to the bus waveguide through the coupling length of L = 60 µm. In our design, which is optimized for telecommunication C-band (1530 nm-1565 nm), implementation of the adiabatically tapered waveguide promises a low loss and broadband power transfer between two waveguides. However, during the power transfer, a slight beating of the electric field appears because of the multimode behavior of the adiabatic coupler as it supports two propagating supermodes for the taper widths wider than w(x = 24 µm). In addition, the fringes in electric field distribution which are mainly apparent in the second half of the coupler are originating from interference between the propagating wave and the reflected portion of the light from the waveguide-air facet at the end of the coupler.
The evolution of the averaged supermode effective index (n ave ) and the phase shift by the vertical gap for λ = 1.55 μm is shown in Fig. 4 (a). Based on this figure a full π phase shift is applicable by a vertical gap change of Δg = 19 nm which corresponds to 0.165 rad/nm phase shift related to a vertical gap decreasing from g 1 = 185 nm to g 2 = 166 nm (Δg = 19 nm). This amount of phase shift corresponds to the averaged effective index change of Δn eff ≈ 0.026 for λ = 1.55 μm. Transmission spectrum of the adiabatic vertical coupler for two vertical gap states g 1 = 185 nm and g 2 = 166 nm are plotted in Fig. 4 (b) which show a low loss performance over a wide wavelength range with minimum transmission of 95% for λ = 1.55 μm. For a wideband operation, both low loss transmission and minimized phase shift dispersion is desired. For our design the calculated phase shift difference between λ 1 = 1.5 μm and λ 2 = 1.6 μm is ≈ 0.11π which corresponds to a relatively low phase shift dispersion of 11 × 10 −4 π rad/nm. This low dispersion leads to only maximum of ≈ 0.035π phase shift difference in the telecommunication C-band (1530 nm-1565 nm). When the device is in the OFF state (g = 1 µm) no coupling to the top waveguide is recorded, since simulations show that less than −60 dB is measured in the top waveguide after the first adiabatic taper. The value stays less than −50 dB when the gap is reduced within the stable regime of the first electrostatic actuation (1 µm -666 nm). The variation of n eff is also negligible for this gap range, producing no phase shift. When the gap is ~500 nm the coupling to the top waveguide and n eff change start to be detectable, however these positions are not accessible due to the instability of the parallel plate actuator. This behavior highlights also one advantage of the two-step actuator: precise control of the position is achievable in the ON state while allowing sufficiently big displacement between the ON and OFF positions to have no perturbation in the latter state.

Mechani
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Conclusion
We propose a design for an analog Silicon Photonic MEMS-based phase shifter with a low loss and broadband performance over the telecommunication C-band. The phase shifter includes a vertical adiabatic coupler composed of fixed and vertically movable waveguides. The symmetrically tapered 60 µm long vertically moving waveguide is actuated in two steps using two pairs of electrodes following the parallel plate electrostatic actuation mechanism to approach the fixed bus waveguide and consequently modify the signal phase. Numerical simulations are used for performance evaluation. The phase shifter turns ON by applying 4 V to the first pair of the electrodes leading to their pull-in and bringing the waveguides to a well-controlled 185 nm of vertical gap. In the ON state a full π phase can be achieved by decreasing the gap by 19 nm, by applying 19 V to the inner set of the electrodes. The two sets of soft and stiff springs lead to a robust design against stress related failure mechanisms as well as the pull-in instability in ON state. FDTD simulations predict an average insertion loss at a full period phase shift in the C-band below 0.3 dB. The design is entirely compatible with previously demonstrated surface micromachined Silicon Photonic MEMS manufacturing process, occupies a total footprint of merely 60 μm × 40 μm and can serve as an efficient building block for MEMS-based reconfigurable Silicon Photonic integrated circuits.