BIPOLAR OPTICAL FORCES IN COUPLED PHOTONIC CRYSTAL CAVITIES

Feng Tian, Guangya Zhou*, Yu Du, and Fook Siong Chau National University of Singapore, Singapore

E-mail: mpezgy@nus.edu.sg

ABSTRACT

Due to their high quality (Q) factors, resonance modes of cavities are capable of generating much larger optical gradient forces than waveguide modes. Here we experimentally demonstrate the use of resonance modes of double-coupled one-dimensional photonic crystal cavities to generate bipolar optical forces. Mechanical and thermal detunings of the probe resonance modes of the device are calibrated respectively with a nanoelectromechanical system (NEMS) actuator and a temperature-controlled testing platform. Detuning due to the optomechanical effect is hence decoupled from that of the thermo-optic effect. Pumped by third-order even (odd) mode, one cavity is pulled to (pushed away from) the other cavity by 37.1 nm (11.4 nm).

INTRODUCTION

Optical gradient forces produced in nano-optomechanical devices can mechanically reconfigure nanophotonic circuits. And the force can be switched between attraction and repulsion by adjusting the optical mode. Bipolar tunings of coupled waveguides [1, 2] and coupled ring resonators [3] have been experimentally demonstrated, but bipolar optical forces based on coupled one-dimensional photonic crystal cavities (1D PCCs) has not been reported. 1D PCCs have properties of small footprint, high Q-factor, small mass, and design flexibility. Filters of double-coupled 1D PCCs actuated by optical forces of propagating waveguide modes have been demonstrated and theoretical analysis shows that cavity resonance modes can generate significantly larger optical forces due to their high Q-factors [4]. Here, we realize the bipolar optical forces in double-coupled 1D PCCs utilizing their resonance modes with high energy efficiency.

DEVICE DESIGN

An SEM image of the proposed device is shown in Fig. 1. One of the double-coupled 1D PCCs is integrated with the suspended silicon nanowire waveguides for light input and output, while the other movable 1D PCC is supported by the folded free-standing beams k3. The force of the NEMS comb drive (F) is applied to the mass m1 suspended by spring k1. They are connected with the spring k2 forming a displacement shrinkage mechanism for accurate cavity gap control. The cavities’ gap change (Δg) is represented as 1 3 1 3 2( )∆ = + +g F k k k k k . The beams of spring k1 has a length of 15 µm and

width of 374 nm while springs k2 and k3 have identical beam dimensions of 15 µm length and 165 nm width. In the comb drive region, there are 84 movable fingers with an initial finger overlap of 480 nm, finger width of 180 nm and finger gap spacing of 230 nm. The design of the 1D PCC complies with the principles of high Q and high transmission cavities [5]. Cavity beams of 670 nm width are fabricated. The two cavities separated at an initial gap of 144.2 nm. All the periods of the photonic crystal lattices are the same (300 nm). The diameter of the hole in the center of cavity is 190 nm and on either side, their diameters are gradually tapered to 40 nm after 39 lattices.

Figure 1 SEM image of the fabricated device.

CHARACTERIZATION

Figure 2 Measured spectrum of the double-coupled cavities, in which various resonance peaks are marked and respective FDTD-simulated mode profiles are displayed.

Figure 2 shows a measured transmission spectrum of the device, where the resonance peaks of the second-order even (TEe,2), the third-order odd (TEo,3), the third-order even (TEe,3), the fourth-order odd (TEo,4), and the fourth-order even (TEe,4) are marked.

Optical MEMS and Nanophotonics 2013, Kanazawa, Japan, 18-22 August 2013

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Here, we choose the first four resonances to carry out the experiments. TEe,2 and TEo,3 are used as probe signals, while TEe,3 and TEo,4 are used as pumps. Based on SEM-measured cavity geometries, the FDTD-simulated electric field profiles of these four resonance modes are shown in Fig. 2. The measured resonant wavelengths are determined to be 1554.052 nm, 1563.003 nm, 1567.936 nm and 1574.423 nm respectively. The measured Q-factors of these resonances are 61500, 61900, 16300 and 14800 respectively. The narrower peaks of TEe,2 and TEo,3 make them more suitable as probe signals for precise measurement of resonance detuning.

RESULTS

Figure 3 Pumped by TEe,3 and TEo,4 with various input powers, the cavity gap is diminished and enlarged respectively, and the corresponding attractive and repulsive optical forces are calculated.

The device is pumped by modes of TEe,3 (for attractive force) and TEo,4 (for repulsive force) with various pump powers (power values in the waveguide estimated just before the cavities) with corresponding tracked wavelengths. A bias voltage of 3 V is applied to the NEMS actuator and the initial gap width between the cavities is set at 139.4 nm. The detunings of the probe resonances that are directly measured in the experiment comprises both thermal detuning and optomechanical detuning. We decouple the optomechanical detuning and thermal detuning by [6]:

T Th OMo o oλ λ λ∆ = ∆ + ∆ (1)

T Th OM Th OM OMe e e o o o( )λ λ λ α λ β λ λ∆ = ∆ + ∆ = ×∆ + ∆ ×∆ (2)

where ΔλoT and Δλe

T are respectively the total detuning of odd and even modes; Δλo

Th and ΔλeTh are

the components of thermal detuning; ΔλoOM and

ΔλeOM are the components of optomechanical

detuning; α is the ratio of the temperature detuning of the even and odd modes, which has been measured to be 0.96 by heating the device; and β(Δλo

OM), a function of Δλo

OM, represents the ratio of the optomechanical detuning of the even and odd modes, which is precisely calibrated by means of NEMS actuation of the device under a SEM. Based on the

obtained ΔλoOM and Δλe

OM from Eq. (1) and (2) and their relations with gap width, the variations of the gap width attracted (repulsed) by the force of TEe,3 (TEo,4) mode are derived and plotted in Fig. 3. It is observed that the gap is decreased by a maximum of 37.1 nm (for pump mode of TEe,3) and increased by a maximum of 11.4 nm (for pump mode of TEo,4). A spring constant, kopt=0.166 N/m, simulated by finite element method (FEM), is used to estimate the optical force Fopt by Fopt=kopt×Δg. The maximum optical forces generated by the selected resonant modes are found to be around -6.2 nN (attractive) and 1.9 nN (repulsive), respectively.

CONCLUSIONS

In summary, we have experimentally demonstrated the bipolar optical forces that exist in resonance modes of double-coupled 1D PCCs. TEe,2 and TEo,3 are taken to be the probe modes while TEe,3 and TEo,4 act as pump modes. Optomechanical detuning is decoupled from thermal detuning. Results show a highly efficient conversion of light energy to mechanical energy. The maximum attractive and repulsive forces produced by TEe,3 at 0.81 mW and TEo,4 at 0.87 mW (power values in the waveguide just before the cavities) are -6.2 nN and 1.9 nN respectively with corresponding gap changes of -37.1 nm and 11.4 nm.

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