NANO-OPTO-ELECTRO-MECHANICAL (NOEM) OSCILLATOR WITH CONTROLLABLE NON-LINEAR DYNAMICS

B. Dong1, 2, J. G. Huang3, H. Cai2, P. Kropelnicki2, A. B. Randles2, Y. D. Gu2 and A. Q. Liu1† 1School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798

2Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), Singapore 117685

3School of Mechanical Engineering, Xi'an Jiaotong University, Xi’an 710049, China ABSTRACT

In this paper, a nano-opto-electro-mechanical (NOEM) oscillator with controllable non-linear dynamics is demonstrated. An optical gradient force driven cantilever shows high non-linearity due to non-linear behavior of the optical force. The non-linear dynamics of the oscillator which utilizes opto-mechanical interaction is well studied and controlled by varying the optical signal, including the power and wavelength. The resonance frequency of the oscillator can be tuned by up to 50 KHz by changing the detuning condition of the opto-mechanical system. It has potential applications such as optical navigation sensors, actuators and optical switches.

INTRODUCTION

Microelectromechanical Systems (MEMS) based oscillator has been intensively developed over the past decade as a promising alternative for various applications like timing and frequency control. [1-2] However, micro-scale dimension of MEMS oscillators restrict its applications in high frequency field. Therefore, Nanoelectromechanical Systems (NEMS) based oscillator provides an alternative of current MEMS oscillator to achieve high frequency and high Q-factor.

Opto-mechanics has been developed recently which utilize near-field cavity optomechanics to achieve effective actuation of nano-scale devices [3]. Optomechanical phenomena in photonics devices provide a new means of light-light interaction medicated by optical force actuated mechanical motion, enabling all-optical signal processing without resorting to electro-optical conversion or non-linear materials [4-6]. In this paper, a nano-opto-electro-mechanical (NOEM) oscillator with controllable non-linear dynamics is demonstrated. The non-linear dynamics of the oscillator which utilizes opto-mechanical interaction is well studied and controlled by varying the optical signal, such as power and wavelength. It has potential applications such as optical navigation sensors, actuators and optical switches.

DESIGN AND THEORY

The oscillator consists of a cantilever beam, a tunable ring resonator, two bus waveguides and electrical pads, as shown in Figure 1(a). High power control light is pumped into the bus waveguide through control input port, and coupled into the tunable ring resonator. The tunable ring resonator has a diameter of 40 μm, and it can generate an attractive optical gradient force over the cantilever beam due to evanescent wave interaction. Signal light is pumped

from the input port of the signal waveguide, and transmit through the slit to the output port. Part of the signal waveguide is cantilever beam, which has a width of 450 nm and length of 15 μm. There is also an electrical pad close to the cantilever, which provides an attractive electrostatic force over the cantilever beam. The cantilever beam is “pulled” by optical force generated from the ring resonator, and balanced by the mechanical spring force and electrostatic force, as shown in Figure 1(b). When the optical gradient force is modulated with frequency close to the resonance frequency of the cantilever beam, the cantilever behaves as an oscillator. The waveguide of ring resonator is sandwiched by two silicon pads, which is P-doped and N-doped respectively. The resonance wavelength of the ring resonator can be controlled by varying the injection current through the p-i-n junction. The control light can therefore be modulated by modulating the injection current. The motion of the cantilever can be monitored by monitoring the transmitted signal light’s power.

(a)

(b)

Figure 1: (a) Schematic of opto-mechanical oscillator and (b) force analysis of the cantilever beam.

The optical force applied on the cantilever can be expressed as [7]

978-1-4799-3509-3/14/$31.00 ©2014 IEEE 1261 MEMS 2014, San Francisco, CA, USA, January 26 - 30, 2014

2 2

2 ( )( )

( )e optical om

opticalc

P g xF x

xγ

ω γ= −

Δ + (1)

where eγ is the external damping due to waveguide-ring

coupling, cω is the control light frequency, ( )omg x is the

optomechanical coupling coefficient, γ is the total optical

damping coefficient and (x) is the light detuning which is defined as ( ) ( )c rx xω ωΔ = − , and rω is the resonance

frequency of the ring resonator., The optical force can be controlled by the light detuning and optical power as shown in Eq. (1). Due to non-linearly of the optical gradient force, it can cause non-linear dynamic behavior of the cantilever, which typically happen at large deformation. To investigate the optical force induced nonlinear behavior of the oscillator, the optical force is expended at the equilibrium point to third order as [6]

2 3 40 1 2 3( ) ( ) ( )opticalF x F x k x k x k x o xδ δ δ δ= + + + + (2)

where the coefficient 1k is the force constant corresponding

to the optical spring effect, 2k and 3k are the quadratic and

cubic nonlinear coefficients, respectively. In fact, the quadratic term can be ignored for the primary resonance. Therefore, the cubic factor has dominant effects on the resonance of cantilever beam.

Due to existence of nonlinear coefficients, the cantilever waveguide can be modeled as a nonlinear oscillator driven by the optical force with quadratic and cubic nonlinearities, which can be expressed as a typical Duffing oscillator [8]

32 cosx x x x F tξ η+ + + = Ω (3)

where ξ is the damping ratio, η is cubic stiffness parameter, F is the excitation amplitude and Ω is the excitation frequency. The solution to the above equation is given by [8]

2 22 2 23

34 ( ( ) )8

F a aξ σ α= + − (4)

where 2

1

m

F Fω

= , 2

1

m

ξ ξω

= , a is the resonance amplitude

and σ is the detuning of driving force frequency defined as

mω ω− and 3α is the cubic coefficient defined as

3 3 /k mα = − . The cubic factor 3α as a function of laser

detuning is shown in Figure 2. It shows that the cubic term can either be positive or negative, which is depend on the later detuning. Therefore, by changing the laser detuning condition, the cubic factor can be modified.

When the driven force is fixed, the different cubic coefficient will result different behavior, as shown in Figure 3. Unlike the amplitude response in the linear case, the amplitude response in the nonlinear case can be multiple-valued. The response curves lean toward the lower frequencies for negative values, resulting in a softening response; the resonance curves lean toward the high frequencies for positive values, resulting in a hardening response. The absolute value of 3α determines the

frequency shift for both softening and hardening response.

Figure 2: Duffing coefficients at different wavelength detuning condition.

Figure 3: Mechanical response of oscillator at different cubic factor.

The cubic coefficient can be easily tuned by the input power, wavelength detuning and the equilibrium point. It can be seen that the cubic coefficient is different at different deformation. When the input light is red detuned, the cubic coefficient is positive, which means the oscillator shows the hardening nonlinearity. When the input light is blue detuned, the cubic coefficient is negative, which means the oscillator shows the hardening nonlinearity.

To effectively control the cubic factor via light detuning, a p-i-n junction is used to modulate the resonance wavelength of the ring resonator, which is shown in Figure 4. When applying a forward bias current, the free electrons is injected into the waveguide, changing the refractive index of the waveguide. Therefore, the resonance wavelength can be well tuned by controlling the injection current across the p-i-n junction. At fixed-wavelength pumping light, the resonance wavelength of the ring resonator can be controlled to be either blue or red detuned. Furthermore, due to the fast modulation speed, which is in nano second level, the resonance behavior of the cantilever beam can be rapidly

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changed to realize in-time control by changing the detuning properties.

(a)

(b)

Figure 4: (a) Schematic of the p-i-n tunable ring resonator and (b) spectrum demonstration of control light. FABRICATION AND DISCUSSIONS

The nonlinear oscillator is fabricated by nano-photonic fabrication processes using standard silicon-on-insulator wafer, with a 220 nm thick silicon structure layer and a 2 μm buried oxide layer. The waveguide structures have a width of 450 nm and a height of 220 nm for a single mode transmission. The silicon bean is designed to have a width of 200 nm while the coupling gap between the ring resonator and the silicon beam is 150 nm. The waveguides and ring resonators are patterned by deep UV lithography, followed by plasma dry etching to transfer the photo resist pattern into the structure layer. The p-i-n junction of the ring resonator has a 70-nm silicon slab layer for doping and supporting. After etching, a 2-μm SiO2 layer is deposited on the structure layers to ensure a low optical loss. A 40-nm Al2O3 is deposited and patterned, which is used as the protection film to protect those fixed structures and leave the window area for suspended structures open. Finally, the cantilever beam is released from the substrate via HF vapor release processes. Figure 5 shows the scan electron microscopy (SEM) image of silicon cantilever beam and signal waveguide.

Figure 5: SEM images of the silicon cantilever beam and signal waveguide.

The oscillator is tested at static control light. Figure 6 shows the transmission spectra of the oscillator at red detuned pumping light. By change the detuning of the control light, the resonance wavelength shifts about 0.48 nm, which correspond a 16-nm displacement of the cantilever.

Figure 6: Transmission spectra of the tunable oscillator at red detuned control light. CONCLUSIONS

In conclusion, an opto-mechanical oscillator with controllable non-linear dynamics is designed, fabricated and experimentally demonstrated. The non-linear behavior of optical force driven oscillator shows great potential for tunable all optical oscillator. Fabricated with CMOS compatible process, this opto-mechanical oscillator can be easily packaged and integrated with other photonic devices. It has potential applications such as optical resonator type gyroscope, accelerometer and optical communication devices.

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ACKNOWLEDGMENS The authors would like to acknowledge the support from the Science and Engineering Research Council of A*STAR, Singapore, under SERC Grant 1021650084. REFERENCES [1] D. K. Agrawal, J. Woodhouse, and A. A. Seshia,

"Modeling nonlinearities in MEMS oscillators," Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol. 60, pp. 1646-1659, 2013.

[2] W. M. Zhu, T. Zhong, A. Q. Liu, X. M. Zhang and M. Yu, “Micromachined optical well structure for thermo-optic switching”, Appl. Phys. Lett., vol. 91, 261106, 2007.

[3] G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, et al., "Near-field cavity optomechanics with nanomechanical oscillators," Nat Phys, vol. 5, pp. 909-914, 2009.

[4] B. Dong, H. Cai, G. I. Ng, P. Kropelnicki, J. M. Tsai, A. B. Randles, M. Tang, Y. D. Gu, Z. G. Suo and A. Q. Liu, "A nanoelectromechanical systems actuator driven and controlled by Q-factor attenuation of ring

resonator," Applied Physics Letters, Vol 103, 181105, 2013.

[5] H. Cai, B. Dong, J. F. Tao, L. Ding, J. M. Tsai, G. Q. Lo, A. Q. Liu and D. L. Kwong, "A nanoelectromechanical systems optical switch driven by optical gradient force," Applied Physics Letters, Vol 102, 023103, 2013.

[6] H. Li, Y. Chen, J. Noh, S. Tadesse, and M. Li, "Multichannel cavity optomechanics for all-optical amplification of radio frequency signals," Nat Commun, vol. 3, p. 1091, 10/02/online 2012.

[7] M. Ren, J. Huang, H. Cai, J. M. Tsai, J. Zhou, Z. Liu, Z. Suo, and A. Q. Liu, "Nano-optomechanical actuator and pull-back instability," ACS Nano, Vol 7, pp.1676–1681, 2013.

[8] I. Kovacic, M. J. Brennan, The Duffing Equation: Nonlinear Oscillators and their Behaviour, Wiley, 2011.

CONTACT

*A. Q. Liu, +65-67904336; eaqliu@ntu.edu.sg

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