Page 168 - Principles and Applications of NanoMEMS Physics

156 Chapter 4

/ 1 2
τ Q ª cos θ sin θ º
2
2
ϕ = 0 « + » , (2)
κ « ( 1+ V AC _ 2ω V ) ′ ( 1−V AC _ 2ω V ′ ) »
0 2 2
¬
¼
where V ′ is a structure-dependent parameter, showing that the gain increases
with the pump signal amplitude. The device has the potential to exploit the
Casimir effect.

4.2.2.2.4 Casimir Effect Oscillator

This device, which was proposed and analyzed by Serry, Walliser, and
Maclay [180] in 1995, Figure 4-6, and experimentally realized by Chan,
Aksyuk, Kleiman, Bishop and Capasso [181] in 2001, represents the first
clear demonstration of the impact of the Casimir force in the performance of
NEMX.

π π π 3 3 3 c =c =c = R R R
F F F Spring = = = kz kz kz F F F = = = 0. 0.2 2
Spring
Spring
Casimir
Casimir
Casimir
120 z z z
120
120 4 4 4
0.
0.1 1
V V V ( ( ( ) z) z) z
0 0
Spring
Spring
Spring
0.1
0.1
Spring+Casim
Spring+Casim
Spring+Casimir ir ir
0.2
0.2 1 1 0.5 0 0 0.5 1 1
0.5
z z z
z z z
0.5
0 z’ z’ z’ max
0 0
max
max
z z z
z z z max
max
max
2 2 2
·
1 1
¨ ¨ ¨
V V V Spring (z)(z)(z ) = = = 1 § z ·§ z ·§ z ¸ ¸ ¸ ¸ ¸ ¸ V V V (z)(z)(z ) = = = C C C
¨ ¨ ¨
Spring
Spring
Casim
Casimir ir ir
2 z z z max ¹ ¹ ¹ Casim § § § z z z · · · 3 3 3
2 2
© © ©
max
max
1 ¨1 ¨
¨ ¨ ¨ 1 ¨ − − − ¸ ¸ ¸ ¸ ¸ ¸
© © © z z z max ¹ ¹ ¹
max
max
Figure 4-6. Summary of nonlinear Casimir effect MEM resonator physics [22].
The experiment entailed changing the proximity of a vibrating rotational
resonator to a metallic sphere, Figure 4-7(a), to measure its behavior in the
absence/presence of the Casimir force. After determining the drive for linear
response, the proximity of the oscillator to a metallic sphere was varied and
the resonance frequency measured exhibited a behavior as depicted in Figure
4-7(b). For sphere-oscillator distances greater than .3 3 µ m , the oscillator
resonance frequency was equal to the drive frequency, 2748Hz, and the
angular amplitude frequency response was symmetric and centered around
the drive frequency, ω = k I , where k is the spring constant and I the
0
moment of inertia, consistent with mass-spring force oscillator behavior.