Lecture 23 Optical MEMS (5)

Transcription

1 EEL6935 Advanced MEMS (Spring 2005) Instructor: Dr. Huikai Xie Lecture 23 Optical MEMS (5) Agenda: Microlenses Diffractive Microgratings Example Devices Reference: S. Sinzinger and J. Jahns, Chapter 6 in Microoptics, Wiley-VCH, 2003 EEL6935 Advanced MEMS 2005 H. Xie 4/6/ Limitation of Refractive Optical Elements Refractive optical elements require considerable thickness. For example, microlenses need 10~100µm-thick microstructures. Even more challenging if aspherical lenses or complex phase profiles are needed. EEL6935 Advanced MEMS 2005 H. Xie 2

2 Reduced Phase Thickness But we know that a light wave repeats itself after any multiple wavelengths or a phase lag of multiple 2 π. iφ 0 0 ( + 2 ) U( x, φ) = U ( x) e = U ( x) e i φ Nπ Thus, only a maximum phase lag of 2 π is necessary. The phase difference between path 1 and path 2 is given by Path 1 Path 2 ( nt t) φ = t max = λ 0 ( n 1) 2π λ 0 For example, for λ 0 =633nm and n=1.5, the thickness needed is only 1.27µm. n t EEL6935 Advanced MEMS 2005 H. Xie 3 Blazing Therefore, the thickness of a prism or lens can be significantly reduced. High lateral resolution is required, which is in fact photolithography can provide. EEL6935 Advanced MEMS 2005 H. Xie 4

3 Phase Quantization Step 1 Continuous phase mapping of the phase into [0,2π] periodically Step 2 Continuous phase in each interval [0,2π] an integer number of discrete values e iφ Q ( x) ( x) 2π φ q=+ iq rect q N 2 π / N (1) = e q= EEL6935 Advanced MEMS 2005 H. Xie 5 Phase Quantization The rect function can be expanded into a Fourier series ( x + ) sinc ( J / N) 2 πi( J / N) q ijφ( x) φ rect q = e e 2 π / N J = N (2) Substituting (2) into (1) yields φ 1 Q e = sinc m+ e m N ( ) ( + 1) φ ( ) i x i Nm x 1 =sinc N + m= ( 1) ( + 1) φ ( ) m i Nm x e Nm+ 1 EEL6935 Advanced MEMS 2005 H. Xie 6

4 Phase Quantization If φ(x) is the phase of g(x) and φ Q (x) is the quantized phase of φ(x), then he reconstructed signal G Q (ν) ( 1) m 1 G Q ( v) = sinc G m v N m Nm + 1 where ( ) i2 π mvx i( Nm + 1) φ ( x) G m v = e e dx The m=0 term recovers the undistorted signal. ( ) The m 0 terms generate ghost images which contribute to background noise if not separated. Diffraction Efficiency η = sinc N 2 1 (2) Superposition of a number of ghost signals EEL6935 Advanced MEMS 2005 H. Xie 7 Alternative Quantization Schemes for Microlenses Fresnel zones Concentric rings decrease with increasing radii Superzones Phase depth increases toward edges Constant pixel size quantization EEL6935 Advanced MEMS 2005 H. Xie 8

5 Diffractive Optical Components 1x2 Beamsplitter 1xN Beamsplitter (e.g., Dammann Grating) Beam Deflector Diffractive Lens EEL6935 Advanced MEMS 2005 H. Xie 9 Multi-mask Processing Fabrication of Diffractive Optics Linear Mask Sequence N-1 processing steps Arbitrary step heights Logarithmic Mask Sequence (log 2 N) processing steps Dependent etching depths EEL6935 Advanced MEMS 2005 H. Xie 10

6 Fabrication Errors Fabrication of Diffractive Optics Ideal Process Lateral misalignment of two masks Error in etching depth EEL6935 Advanced MEMS 2005 H. Xie 11 Fabrication Errors Fabrication of Diffractive Optics Resulting profile Phase error Over-etching Under-etching Partially isotropic etching EEL6935 Advanced MEMS 2005 H. Xie 12

7 Diffractive Lenses Fresnel zone plates (FZPs) 2 2 j ( ) 2 r + f = f + jλ r = 2 jλ f + j j ( λ ) 2 Binary phase or amplitude rings Optical path difference from adjacent zones is Nλ, where N is an integer and λ is the wavelength. Size is comparable to the optical fiber, good for integration Flat and thin, ideal for microfabrication Easily designed to different wavelengths For paraxial approximation, i.e., f>>j max λ, and r 2 jλ f j r1 λ r1 f = 2λ 2λ EEL6935 Advanced MEMS 2005 H. Xie 13 Microgratings 1st order (m = -1) a θ φ 0th order (m = 0) 1st order (m = 1) α a Two types of reflective grating Grating Equation: a(sin θ sinφ) = mλ ( m = 0, ± 1, ± 2, ) Resolution Power: R = λ /( λ) min = mn ( m = 1) EEL6935 Advanced MEMS 2005 H. Xie 14

8 DOE Example Devices -1 Polysilicon microstructure Latched up vertically 280µm in lens diameter Lin et al, IEEE Photonics Technology Letters, 1994 EEL6935 Advanced MEMS 2005 H. Xie 15 DOE Example Devices -2 XYZ-Adjustable Microlens Fan et al. (UCLA), Transducers 97 EEL6935 Advanced MEMS 2005 H. Xie 16

9 DOE Example Devices level Fresnel Zone Plate Pawlowski, 1993 EEL6935 Advanced MEMS 2005 H. Xie 17 DOE Example Devices -4 Kinoform Microlens Array (Fused Silica) Eight levels Fused silica 0.2mm by 0.2mm Diffraction efficiency: 85% Soldatenkov et al, LFNM 2003 EEL6935 Advanced MEMS 2005 H. Xie 18

10 DOE Example Devices -5 Diffraction Grating for Spectroscopic Applications Kiang et al. (UC-Berkeley), Transducers 97 EEL6935 Advanced MEMS 2005 H. Xie 19 DOE Example Devices -6 Force Sensor Based on Diffractive Gratings Zhang et al (Stanford), Sensors & Actuators, 2004 EEL6935 Advanced MEMS 2005 H. Xie 20