Abstract

We propose and analyze a new mode of operation for an optically addressed deformable mirror device. The device consists of an array of metallized membrane mirrors supported above an optically addressed photoconductive substrate. A conductive transparent electrode is deposited on the backside of the substrate. A variable polarity voltage is applied between the membrane and the back electrode of the device accompanied with high-frequency modulated light. The membrane is deformed when a modulated light illuminates the backside of the device. This occurs due to impedance and bias redistribution between the two cascaded impedances. This operating mechanism of a microelectromechanical systems device is suitable for detecting moving targets.

© 2007 Optical Society of America

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References

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  1. B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, "Photoconductive optically driven deformable membrane for spatial light modulator applications that use GaAs substrates," Appl. Opt. 45, 2615-2622 (2006).
    [CrossRef] [PubMed]
  2. B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, "Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," Appl. Opt. 45, 3226-3236 (2006).
    [CrossRef] [PubMed]
  3. J. Khoury, C. L. Woods, B. Haji-saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, "Optically driven micro-electro-mechanical-systems deformable mirror under high frequency ac bias," Opt. Lett. 31, 808-810 (2006).
    [CrossRef] [PubMed]
  4. F. Vachss and L. Hesselink, "Synthesis of a holographic image velocity filter using the nonlinear photorefractive effect," Appl. Opt. 27, 2887-2894 (1988).
    [CrossRef] [PubMed]

2006 (3)

1988 (1)

Drehman, A.

Goodhue, W.

Haji-saeed, B.

Hesselink, L.

Khoury, J.

Kierstead, J.

Kolluru, R.

Leon, R.

Pyburn, D.

Sengupta, S. K.

Testorf, M.

Vachss, F.

Woods, C. L.

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Figures (6)

Fig. 1
Fig. 1

One pixel architecture of the device.

Fig. 2
Fig. 2

(Color online) Schematic illustrating a deformable membrane that is driven via very-high-frequency-modulated light, with dc bias.

Fig. 3
Fig. 3

(Color online) Equivalent circuit of this device, which consists of a cascade of a photoconductive resistor and a capacitor.

Fig. 4
Fig. 4

(Color online) Proposed scheme for operating the device with a variable polarity voltage that changes between V0 and V0 and the high-frequency ac light modulation.

Fig. 5
Fig. 5

(Color online) Voltage across the capacitor for two cycles: one goes from negative to positive voltage, and the second cycle goes from positive to negative. In these plots it was assumed that b/ac=1 , g/aωc=1 , and ω=50 .

Fig. 6
Fig. 6

(Color online) Membrane deflection as a function of light intensity for different γ values (modulation contrast).

Equations (41)

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R=ρLA=L/Aqμnn,
I=I0+I1  sin  ωt,
n=nd+n0+n1  sin  ωt,
R(t)=ρLA=L/Aqμnn(t)
=L/Aqμn(nd+n0+n1  sin  ωt)
=L/Aqμnnd+qμnn0+qμnn1  sin  ωt,
R(t)=ab+g  sin  ωt.
VC=V0(1exp[1ωτ0(1cos(ωt))]et/τd)=V0(1exp[2sin2(ωt)ωτ0]et/τd)
VC=V0  exp[1ωτ0(1cos(ωt))]et/τd=V0  exp[2sin2(ωt)ωτ0]et/τd,
τd=aCb,
τ0=aCg.
VC=V0(12  exp[1ωτ0(1cos(ωt))]et/τd)=V0(12  exp[gaωC(1cos(ωt))]ebt/aC),
ΔV2¯=1τp0τp(VC02VC2)dt=4V02τdωτpτ0{1e2τp/τd1eτp/τd+24+ω2τd2×[τde2τp/τd(ω  sin(ωτp)2τd  cos(ωτp))+2]11+ω2τd2[τdeτp/τd(ω  sin(ωτp)1τd  cos(ωτp))+1]},
Δh=ε0r12ΔV2¯8Ts2ε0r128Ts2×4V02τdωτpτ0{1e2τp/τd1eτp/τd+24+ω2τd2×[τde2τp/τd(ω  sin(ωτp)2τd  cos(ωτp))+2]11+ω2τd2[τdeτp/τd(ω  sin(ωτp)1τd  cos(ωτp))+1]},
γ=I1I0.
V0=Ri+qC.
dV0dt=idRdt+Rdidt+1Cdqdt.
0=idRdt+Rdidt+iC.
1ididt=1RC1RdRdt.
ln  i=b+g  sin  ωtaCdtln(ab+g  sin  ωt)
=(bt+g/ω  cos  ωtaC)ln(ab+g  sin  ωt)+C0,
i=exp[ln(ab+g  sin  ωt)bt+g/ω  cos  ωtaC+C0]
=A1(b+g  sin  ωt)a  exp  [(bt+g/ω  cos  ωtaC)],
VC(t)=q(t)C={0,V0,when  t=0when  t.
q(t)=0tIdt=0tA1(b+g  sin  ωt)a×exp[1aC(bt+g/ω cos  ωt)]dt.
q(t)=g/ωbt+g/ω  cos  ωtA1ae(1/aC)udu=A1aaCe(1/aC)u|g/ωbt+g/ω cos  ωt)
=A1C  exp[1aC(bt+g/ω  cos  ωt)]+A1Ceg/aωC.
limtVC=limtq(t)CorV0=A1eg/aωC;
A1=V0eg/aωC.
VC=qC=V0(1eg/aωC  exp[1ac(bt+g/ω cos  ωt)])
=V0(1exp[1ωτ0(1cos(ωt))]et/τd)
=V0(1exp[2sin2(ωt)ωτ0]et/τd),
VC=V0eg/aωC  exp[1aC(bt+gω  cos  ωt)]
=V0  exp[1ωτ0(1cos(ωt))]et/τd
=V0  exp[2sin2(ωt)ωτ0]et/τd,
h=ε0r12ΔV28Ts2.
VC=V0(12  exp[gaωC(1cos(ωt))]ebt/aC)=V0(12  exp[1ωτ0(1cos(ωt))]et/τd),
VC0=V0(12ebt/aC)=V0(12et/τd).
ΔV2¯=1τp0τp(VC02VC2)dt=1τp0τpV02[4e2t/τd4et/τd4exp[2/ωτ0(1cos  ωt)]e2t/τd+4  exp[1/τd(1cos  ωt)]et/ωτ0]=1τp0τp4V02[e2t/τd(1exp[2/ωτ0(1cos  ωt)])et/τd(1exp[1/ωτ0(1cos  ωt)])].
ΔV21τp0τp4V02[e2t/τd(1(1  +  2ωτ0(1cos  ωt)))et/τ0(1(1+1ωτ0(1cos  ωt)))]=1τp0τp4V02[2ωτ0e2t/τd+2ωτ0  cos  ωte2t/τd+1ωτ0et/τd1ωτ0et/τd  cos  ωtet/τd]=4V02ωτpτ0×[τd(e2τp/τd1)+2τd4+ω2τd2[τde2τp/τd(ω  sin  ωτp2τd  cos  ωτp)+2]+τd(eτp/τd1)+τd1+ω2τd2[τdeτp/τd(ω  sin  ωτp1τd  cos  ωτp)+1]]=4V02τdωτpτ0×{1e2τp/τd1eτp/τd+24+ω2τd2[τde2τp/τd(ω  sin(ωτp)2τd  cos(ωτp))+2]11+ω2τd2[τdeτp/τd(ω  sin(ωτp)1τd  cos(ωτp))+1]}.
Δh=ε0r12ΔV28Ts2ε0r128Ts2×4V02τdωτpτ0×{1e2τp/τd1eτp/τd+24+ω2τd2×[τde2τp/τd(ω  sin(ωτp)2τd  cos  (ωτp))+2]11+ω2τd2[τdeτp/τd(ω  sin(ωτp)1τd  cos  (ωτp))+1]}.

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