Abstract

We propose stratified volume diffractive optical elements as a new type of diffractive optical element that is capable of functioning as a high-efficiency grating in applications with requirements not suited to traditional holographic or diffractive optical techniques. In this approach, diffractive optical fabrication methods are used to construct an optical structure that emulates volume grating behavior. We discuss the diffraction properties of stratified volume diffractive optical elements and compare them with those used previously in both volume holographic optical elements and stratified volume holographic optical elements. A systematic design process is then presented for deriving structure parameters. We illustrate this process by designing a prototype stratified volume diffractive optical element to meet the operational specifications for a beam-scanning element in a spaceborne coherent wind lidar. We use numerical simulation to assess the performance of the prototype element, including sensitivity to fabrication errors.

© 1999 Optical Society of America

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References

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1997 (4)

1996 (1)

1995 (5)

1993 (2)

1992 (3)

1988 (1)

1982 (1)

1981 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Amzajerdian, F.

F. Amzajerdian, M. J. Kavaya, “Development of solid state coherent lidars for global wind measurements,” presented at the Ninth Conference on Coherent Laser Radar, June 23–27, 1997, Linkoping, Sweden.

F. Amzajerdian, Center for Applied Optics, The University of Alabama in Huntsville, Huntsville, Ala. 35899 (personal communication, 1996).

Cambril, E.

Chavel, P.

Cooke, D. J.

L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).

Daschner, W.

De Beaucoudrey, N.

Drabik, T. J.

Farn, M. W.

Fleming, M. B.

Gaylord, T. K.

Granger, A.

Grann, E. B.

Gupta, M. C.

Hutley, M. C.

Johnson, R. V.

Jung, J. J.

J. J. Jung, “Stratified volume holographic optical elements: analysis of diffraction behavior and implementation using InGaAs/GaAs multiple quantum well structures,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1994).

Kavaya, M. J.

F. Amzajerdian, M. J. Kavaya, “Development of solid state coherent lidars for global wind measurements,” presented at the Ninth Conference on Coherent Laser Radar, June 23–27, 1997, Linkoping, Sweden.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Lee, S. H.

Lessard, R. A.

Li, L.

Long, P.

Magnusson, R.

Miller, J. M.

Moharam, M. G.

Nordin, G. P.

O’Shea, D. C.

Peng, S. T.

Pommet, D. A.

Rockward, W. S.

Solymar, L.

L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).

Song, L.

Stein, R.

Suleski, T. J.

Tanguay, A. R.

Tibuleac, S.

Turunen, J.

Wu, C.

Zhou, Z.

Appl. Opt. (8)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

Opt. Lett. (2)

Other (4)

J. J. Jung, “Stratified volume holographic optical elements: analysis of diffraction behavior and implementation using InGaAs/GaAs multiple quantum well structures,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1994).

F. Amzajerdian, Center for Applied Optics, The University of Alabama in Huntsville, Huntsville, Ala. 35899 (personal communication, 1996).

L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).

F. Amzajerdian, M. J. Kavaya, “Development of solid state coherent lidars for global wind measurements,” presented at the Ninth Conference on Coherent Laser Radar, June 23–27, 1997, Linkoping, Sweden.

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Figures (12)

Fig. 1
Fig. 1

Schematic illustration of the SVDOE structure.

Fig. 2
Fig. 2

Convergence of the diffraction efficiency as a function of the number of space harmonics retained in the calculation. λ0=2.06 µm, θ=9.885°, nI=1.5, nIII=1.5, nridge=2.0, ngroove=1.5, dgrating=0.638,dhomogeneous=4.6 µm.

Fig. 3
Fig. 3

Diffraction efficiency of a five-layer SVDOE as a function of total grating layer thickness (Δn=0.1). λ0=2.06 µm, θ=9.885°, nI=1.5, nIII=1.5, nridge=1.6, ngroove=1.5, dhomogeneous=2.1 µm.

Fig. 4
Fig. 4

Diffraction efficiency of a five-layer SVDOE as a function of total grating layer thickness (Δn=0.5). λ0=2.06 µm, θ=9.885°, nI=1.5, nIII=1.5, nridge=2.0, ngroove=1.5, dhomogeneous=4.6 µm.

Fig. 5
Fig. 5

Diffraction efficiency of a five-layer SVDOE as a function of the thickness of one period in the SVDOE structure (i.e., the sum of a single grating layer thickness and a single homogeneous layer thickness). λ0=2.06 µm, θ=9.885°, nI=1.5, nIII=1.5, ngroove=1.5. For Δn=0.1, nridge=1.6 and dgrating=3.139 µm; for Δn=0.5, nridge=2.0 and dgrating=0.638 µm.

Fig. 6
Fig. 6

Angular selectivity of a five-layer SVDOE with Δn=0.5. Note that, for θinc<-41°, the +1 order is evanescent and hence the diffraction efficiency is zero. λ0=2.06 µm, nI=1.5, nIII=1.5, nridge=2.0, ngroove=1.5, dgrating=0.638 µm, dhomogeneous=4.9 µm.

Fig. 7
Fig. 7

Diffraction efficiency as a function of number of grating layers. λ0=2.06 µm, θ=0°, nI=1.5, nIII=1.5, ngroove=1.5. For Δn=0.5, nridge=2.0; for Δn=0.25, nridge=1.75; for Δn=0.1, nridge=1.6.

Fig. 8
Fig. 8

Specifications for prototype design of a lidar scanner element.

Fig. 9
Fig. 9

Diffraction efficiency as a function of incidence angle for both TE and TM polarizations. Three grating layers, λ0=2.06 µm, θ=0°, nI=1.5, nIII=1.5, nridge=2.0, ngroove=1.5, dgrating=1.046 µm, dhomogeneous=4.300 µm.

Fig. 10
Fig. 10

RCWA representation of the electric field as it traverses the SVDOE prototype lidar scanner. Three grating layers, λ0=2.06 µm, θ=0°, nI=1.5, nIII=1.5, nridge=2.0, ngroove=1.5, dgrating=1.046 µm, dhomogeneous=4.300 µm.

Fig. 11
Fig. 11

Effect of statistical variation of grating layer offsets on the diffraction efficiency of the prototype lidar scanner. Three grating layers, λ0=2.06 µm, θ=0°, nI=1.5, nIII=1.5, nridge=2.0, ngroove=1.5, dgrating=1.046 µm, dhomogeneous=4.300 µm.

Fig. 12
Fig. 12

Effect of statistical variation of homogeneous layer thickness on the diffraction efficiency of the prototype lidar scanner. Three grating layers, λ0=2.06 µm, θ=0°, nI=1.5, nIII=1.5, nridge=2.0, ngroove=1.5, dgrating=1.046 µm, dhomogeneous=4.300 µm.

Equations (23)

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χ=κDgcRcS=πΔnampDgλ0cRcS,
cR=cos θ,
cS=cos θ-λ0nΛcos ϕ,
n(x)=n0+h=-h0h=Δnh expjh2πΛx,
χSVDOE=2π|Δn1|Dgλ0cRcS,
Dg,max=πλ04ΔncRcS.
cos θp=1-sin θp-λ0nΛ21/2-pλ0dbn,
El,y=i=-Sl,yi(z)exp(-jkxix),
Hl,x=-j0μ01/2i=-Ul,xi(z)exp(-jkxix),
Sl,yi(z)=m=1nwl,i,m{cl,m+ exp[-k0ql,m(z-Dl-1)]+cl,m- exp[k0ql,m(z-Dl)]},
Ul,xi(z)=m=1nvl,i,m{-cl,m+ exp[-k0ql,m(z-Dl-1)]+cl,m- exp[k0ql,m(z-Dl)]},
Sl,yi(z)=Pl,i exp[-k0γl,i(z-Dl-1)]+Ql,i exp[k0γγ,i(z-Dl)],
Ul,xi(z)=-γl,iPl,i exp[-k0γl,i(z-Dl-1)]+γl,iQl,i exp[k0γl,i(z-Dl)],
γl,i=jnl2-kxik021/2.
Sl,yUl,xZ=Dl-1=WlWlXlVl-VlXlCl+Cl-,
Sl,yUl,xZ=Dl=WlXlWlVlXl-VlCl+Cl-,
Sl,yUl,xZ=Dl-1=IIGlΓl-ΓlGlPlQl,
Sl,yUl,xZ=Dl=IGlIΓlGl-ΓlPlQl,
Sl,yUl,xZ=Dl-1=Al,1Al,1ΩlAl,2-Al,2Ωlρl,1ρl,2,
Sl,yUl,xZ=Dl=Al,1ΩlAl,1Al,2Ωl-Al,2ρl,1ρl,2.
δi,0jnI cos θδi,0+I-jYIR=l=1LAl,1Al,1ΩlAl,2-Al,2Ωl×Al,1ΩlAl,1Al,2Ωl-Al,2-1IjYIIIT,
δi,0jnI cos θδi,0+I-jYIR=A1,1(1+Ω1b1a1-1Ω1)A1,2(I-Ω1b1a1-1Ω1)T1,
T=aL-1ΩLaL-1-1ΩL-1a2-1Ω2a1-1Ω1T1,

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