**2.2 Color design and simulation**

380 Microelectromechanical Systems and Devices

<sup>1</sup> <sup>2</sup> <sup>2</sup> cos <sup>2</sup> *n*

2 2 cos sin 1 2 2 

and take atmospheric air as Intermediate 1 with *n1*=1, the optical path length difference

A constructive interference takes place when the two reflective lights are in-phase and a destructive interference takes place when the two reflective lights are out-of-phase. A maximum constructive interference happens when the two lights are with 0° phase

Similarly, a minimum destructive interference happens when the two light are with 180°

<sup>1</sup> 2 cos ( ) 2 2 <sup>2</sup> *nd m* 

Here *m* is an integer and λ is the wavelength for both cases. The interference from the

Since the system is designed for information display, a maximum constructive interference is expected. According to Equation 12, one can easily design specific output light (wavelength) with specific intermediate (*n2, d*) under fixed angle of incidence *θ2*. It is also possible to calculate a multilayer system according to Equation 8 when the intermediate material is not air. Based on Figure 10, a multilayer structure shown in Figure 11 was chosen for color filtering. A premise is also made here: The color (color 1) filtered by the structure in Figure 11(a) is different from the color (color 2) filtered by the structure in Figure 11(b). The change of the multilayer structure hence lies on the mechanical control by MEMS. Here a special note should be put that a color of either color 1 or color 2 is not necessary to be both destructive interferences, rather, a color will be good enough to distinguish from another even though it is not formed by interference. The multilayer system in Figure 11 is switching between six layers and five layers (excluding ambient air layers: Intermediate 1). Thus, when talking about a multilayer system with more than three intermediates (four interfaces), the optical path length difference becomes relatively complicated which will be

 

*n d*

cos tan sin 22 2

2 cos 2 2 *n d*

2 cos 2 2 *nd m*

transmissive side can be also evaluated from the Interface 2.

discussed and simulated by commercial software later.

difference or zero (or 2π) phase change:

phase difference or π phase change:

**2.1.2 Multiple layer model** 

With trigonometric function:

becomes

<sup>1</sup> <sup>2</sup> 1 sin <sup>2</sup>

  (8)

(9)

(11)

(12)

(13)

(10)
