Abstract

We study the rigorous design and analysis of stacked rotated gratings (SRGs) for novel photonic devices. A concept of sampling frequency is proposed to systematically design SRGs. With the help of a rectangular sampling lattice, we extend the standard 3D rigorous coupled-wave analysis (RCWA) algorithm to the analysis of SRGs. The resultant SRG-RCWA algorithm can be used to exactly analyze SRGs that have grating parameters that match the Fourier expansion represented by the sampling lattice. SRGs that do not fall in this category can often still be closely approximated with our approach. The SRG-RCWA algorithm has been successfully applied to the characterization of two fabricated SRGs that are designed to function as circular polarization filters for an IR imaging polarimetry system. The agreement between numerical SRG-RCWA results and experimental measurements demonstrates its validity and usefulness.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).
  2. E. G. Johnson, "Design and analysis of single and cascaded diffractive optical elements," Ph.D. dissertation (The University of Alabama in Huntsville, 1996).
  3. D. Chambers, "Stratified volume diffractive optical elements," Ph.D. dissertation (The University of Alabama in Huntsville, 2000).
  4. D. Chambers, G. P. Nordin, and S. Kim, "Fabrication and analysis of a three-layer stratified volume diffractive optical element high-efficiency grating," Opt. Express 11, 27-38 (2003).
    [CrossRef] [PubMed]
  5. R. B. Hwang and S. T. Peng, "Performance evaluation of a bigrating as a beam splitter," Appl. Opt. 36, 2011-2018 (1997).
    [CrossRef] [PubMed]
  6. S. Lin and J. G. Fleming, "Creation of a 3D silicon photonic crystal," Opt. Photon. News 9(12), 35-37 (1998).
  7. P. C. Deguzman and G. Nordin, "Stacked subwavelength gratings as circular polarization filters," Appl. Opt. 40, 5731-5737 (2001).
    [CrossRef]
  8. M. G. Moharam and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 73, 1105-1112 (1983).
    [CrossRef]
  9. R. Brauer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings," Opt. Commun. 100, 1-5 (1993).
    [CrossRef]
  10. M. G. Moharam, D. A. Pommet, and E. B. Grann, "Stable implementation of the rigorous coupled-wave analysis for surface relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995).
    [CrossRef]
  11. J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).
  12. P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997).
    [CrossRef]
  13. P. C. Deguzman, "Stacked subwavelength gratings for imaging polarimetry," Ph.D. dissertation (The University of Alabama in Huntsville, 2000).

2003 (1)

2001 (1)

1998 (1)

S. Lin and J. G. Fleming, "Creation of a 3D silicon photonic crystal," Opt. Photon. News 9(12), 35-37 (1998).

1997 (2)

1995 (1)

1993 (1)

R. Brauer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings," Opt. Commun. 100, 1-5 (1993).
[CrossRef]

1983 (1)

Brauer, R.

R. Brauer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings," Opt. Commun. 100, 1-5 (1993).
[CrossRef]

Bryngdahl, O.

R. Brauer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings," Opt. Commun. 100, 1-5 (1993).
[CrossRef]

Chambers, D.

Deguzman, P. C.

P. C. Deguzman and G. Nordin, "Stacked subwavelength gratings as circular polarization filters," Appl. Opt. 40, 5731-5737 (2001).
[CrossRef]

P. C. Deguzman, "Stacked subwavelength gratings for imaging polarimetry," Ph.D. dissertation (The University of Alabama in Huntsville, 2000).

Fleming, J. G.

S. Lin and J. G. Fleming, "Creation of a 3D silicon photonic crystal," Opt. Photon. News 9(12), 35-37 (1998).

Gaylord, T. K.

Grann, E. B.

Hwang, R. B.

Johnson, E. G.

E. G. Johnson, "Design and analysis of single and cascaded diffractive optical elements," Ph.D. dissertation (The University of Alabama in Huntsville, 1996).

Kim, S.

Lalanne, P.

Lin, S.

S. Lin and J. G. Fleming, "Creation of a 3D silicon photonic crystal," Opt. Photon. News 9(12), 35-37 (1998).

Loewen, E.

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

Moharam, M. G.

Nordin, G.

Nordin, G. P.

Peng, S. T.

Pommet, D. A.

Popov, E.

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

Turunen, J.

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

Wyrowski, F.

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

R. Brauer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings," Opt. Commun. 100, 1-5 (1993).
[CrossRef]

Opt. Express (1)

Opt. Photon. News (1)

S. Lin and J. G. Fleming, "Creation of a 3D silicon photonic crystal," Opt. Photon. News 9(12), 35-37 (1998).

Other (5)

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

E. G. Johnson, "Design and analysis of single and cascaded diffractive optical elements," Ph.D. dissertation (The University of Alabama in Huntsville, 1996).

D. Chambers, "Stratified volume diffractive optical elements," Ph.D. dissertation (The University of Alabama in Huntsville, 2000).

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

P. C. Deguzman, "Stacked subwavelength gratings for imaging polarimetry," Ph.D. dissertation (The University of Alabama in Huntsville, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic of the stacked rotated grating structure.

Fig. 2
Fig. 2

Frequency sampling lattice of SRG-RCWA and three sample grating K¯ -vectors.

Fig. 3
Fig. 3

Coordinate system of the sandwich grating stack.

Fig. 4
Fig. 4

Comparison of three algorithms on the sandwich grating stack.

Fig. 5
Fig. 5

(a) Transmittance and (b) extinction ratio of SRG sample Stack 1.

Fig. 6
Fig. 6

(a) Transmittance and (b) extinction ratio of SRG sample Stack 2.

Tables (3)

Tables Icon

Table 1 Detail Structural Parameters of Two SRG Sample Devices as Circular Polarization Detectors

Tables Icon

Table 2 SRG-RCWA Sampling Frequencies and Sampling Numbers for the Simulation of Two SRG Sample Devices

Tables Icon

Table 3 Input Elliptical Polarization Parameters to SRG-RCWA Simulation

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Λ=1[(nxfsx)2+(nyfsy)2]1/2,
sinβ=nyfsy[(nxfsx)2+(nyfsy)2]1/2=nyfsyΛ.
Grating1:nx=1,ny=1;Λ=12=0.707μm,β=45°,
Grating2:nx=4,ny=3;Λ=125=0.2μm,β=36.87°,
Grating  3:nx=3,ny=4;Λ=125=0.2  μm ,β=53.13°.
ε(x,y)=g,hε,ghexp[j(2πgfsxx+2πhfsyy)],
ε1(x,y)=g,hA,ghexp[j(2πgfsxx+2πhfsyy)],
ε,gh=1Λsx1Λsy0Λsx0Λsyε(x,y)×exp[j(2πgfsxx+2πhfsyy)]dxdy,
A,gh=1Λsx1Λsy0Λsx0Λsyε1(x,y)×exp[j(2πgfsxx+2πhfsyy)]dxdy,
kxm=k0[n1sinθcosφm(λ0fsx)],
kyn=k0[n1sinθsinφn(λ0fsy)],
ε,g=1Λ0Λε(x)exp(j2πΛgx)dx,
A,g=1Λ0Λε1(x)exp(j2πΛgx)dx,
CERTRCP/TLCP,

Metrics