Abstract

A deep-etched polarization-independent binary fused-silica phase grating as a three-port beam splitter is designed and manufactured. The grating profile is optimized by use of the rigorous coupled-wave analysis around the 785nm wavelength. The physical explanation of the grating is illustrated by the modal method. Simple analytical expressions of the diffraction efficiencies and modal guidelines for the three-port beam splitter grating design are given. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results are in good agreement with the theoretical values.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Schnabel, A. Bunkowski, O. Burmeister, and K. Danzmann, “Three-port beam splitters-combiners for interferometer applications,” Opt. Lett. 31, 658-660 (2006).
    [CrossRef] [PubMed]
  2. Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006). ,
    [CrossRef]
  3. Y. Lin, D. Rivera, and K. P. Chen, “Woodpile-type photonic crystals with orthorhombic or tetragonal symmetry formed through phase mask techniques,” Opt. Express 14, 887-892(2006).
    [CrossRef] [PubMed]
  4. C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961-5969 (1995).
    [CrossRef] [PubMed]
  5. http://www.optometrics.com.
  6. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068-1076 (1995).
    [CrossRef]
  7. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779-784 (1996).
    [CrossRef]
  8. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
    [CrossRef]
  9. A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309-330 (2005).
    [CrossRef]
  10. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, A. Tishchenko, and O. Parriaux, “Investigation of the polarization-dependent diffraction of deep dielectric rectangular transmission gratings illuminated in Littrow mounting,” Appl. Opt. 46, 819-826 (2007).
    [CrossRef] [PubMed]
  11. J. Feng, C. Zhou, J. Zheng, and B. Wang, “Modal analysis of deep-etched low-contrast two-port beam splitter grating,” Opt. Commun. 281, 5298-5301 (2008).
    [CrossRef]
  12. E. Gamet, A. V. Tishchenko, and O. Parriaux, “Cancellation of the zeroth order in a phase mask by mode interplay in a high index contrast binary grating,” Appl. Opt. 46, 6719-6726(2007).
    [CrossRef] [PubMed]
  13. J. Zheng, C. Zhou, B. Wang, and J. Feng, “Beam Splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075-1083 (2008).
    [CrossRef]
  14. J. Zheng, C. Zhou, J. Feng, and B. Wang, “Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings,” Opt. Lett. 33, 1554-1556 (2008).
    [CrossRef] [PubMed]
  15. S. Wang, C. Zhou, H. Ru, and Y. Zhang, “Optimized condition for etching fused-silica phase gratings with inductively coupled plasma technology,” Appl. Opt. 44, 4429-4434(2005).
    [CrossRef] [PubMed]
  16. S. Wang, C. Zhou, Y. Zhang, and H. Ru, “Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm,” Appl. Opt. 45, 2567-2571 (2006).
    [CrossRef] [PubMed]
  17. B. Wang, C. Zhou, S. Wang, and J. Feng, “Polarizing beam splitter of a deep-etched fused-silica grating,” Opt. Lett. 32, 1299-1301 (2007).
    [CrossRef] [PubMed]
  18. B. Wang, C. Zhou, J. Feng, H. Ru, and J. Zheng, “Wideband two-port beam splitter of a binary fused-silica phase grating,” Appl. Opt. 47, 4004-4008 (2008).
    [CrossRef] [PubMed]

2008 (4)

2007 (3)

2006 (4)

2005 (2)

S. Wang, C. Zhou, H. Ru, and Y. Zhang, “Optimized condition for etching fused-silica phase gratings with inductively coupled plasma technology,” Appl. Opt. 44, 4429-4434(2005).
[CrossRef] [PubMed]

A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309-330 (2005).
[CrossRef]

1996 (1)

1995 (2)

1981 (1)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
[CrossRef]

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
[CrossRef]

Bunkowski, A.

Burmeister, O.

Chen, K. P.

Clausnitzer, T.

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
[CrossRef]

Danzmann, K.

Feng, J.

Gamet, E.

Gaylord, T. K.

Grann, E. B.

Kämpfe, T.

Kley, E.-B.

Lalanne, P.

Lin, Y.

Liu, L.

Liu, Y. J.

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006). ,
[CrossRef]

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Parriaux, O.

Pommet, D. A.

Rivera, D.

Ru, H.

Schnabel, R.

Sun, X. W.

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006). ,
[CrossRef]

Tishchenko, A.

Tishchenko, A. V.

E. Gamet, A. V. Tishchenko, and O. Parriaux, “Cancellation of the zeroth order in a phase mask by mode interplay in a high index contrast binary grating,” Appl. Opt. 46, 6719-6726(2007).
[CrossRef] [PubMed]

A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309-330 (2005).
[CrossRef]

Tünnermann, A.

Wang, B.

Wang, S.

Zhang, Y.

Zheng, J.

Zhou, C.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

Y. J. Liu and X. W. Sun, “Electrically tunable two-dimensional holographic photonic crystal fabricated by a single diffractive element,” Appl. Phys. Lett. 89, 171101 (2006). ,
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Acta (1)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413-428 (1981).
[CrossRef]

Opt. Commun. (1)

J. Feng, C. Zhou, J. Zheng, and B. Wang, “Modal analysis of deep-etched low-contrast two-port beam splitter grating,” Opt. Commun. 281, 5298-5301 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

A. V. Tishchenko, “Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309-330 (2005).
[CrossRef]

Other (1)

http://www.optometrics.com.

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 illustration of a fused-silica beam splitter grating: n 1 and n 2 , refractive indices of air and fused-silica, respectively; Λ, grating period; b, ridge width; h, groove depth; φ 1 and φ 1 , diffraction angles of the 1st and 1 st diffractive orders, respectively.

Fig. 2
Fig. 2

Contour of the efficiency ratio between the 1st and the 0th diffractive orders versus grating period and groove depth for (a) TM polarization and (b) TE polarization, respectively.

Fig. 3
Fig. 3

Fabrication tolerance of the three-port binary-phase beam splitter. Contour of the efficiency ratio between the 1st and the 0th diffractive orders versus duty cycle and groove depth for (a) TM polarization and (b) TE polarization, respectively.

Fig. 4
Fig. 4

Diffraction efficiencies of the 0th and 1st diffractive orders of the grating versus groove depth for a TE-polarized wave calculated by RCWA ( solid curves) and a simplified modal method (dashed curves), respectively ( Λ = 1068 nm and f = 0.5 ).

Fig. 5
Fig. 5

Scanning electron micrograph of the three-port beam splitter grating.

Fig. 6
Fig. 6

Theoretical (solid curves) and experimental (dashed curves) diffraction efficiency of the three-port beam splitter grating at different incident angles for (a) TM polarization and (b) TE polarization.

Equations (15)

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

n out sin ( φ m ) = n in sin ( φ in ) + m λ / Λ ,
cos [ k 1 ( Λ b ) ] cos ( k 2 b ) k 1 2 + k 2 2 2 k 1 k 2 sin [ k 1 ( Λ b ) ] sin ( k 2 b ) = cos ( α Λ ) ,
E y m ( x ) u q ( x ) = | 0 Λ E y m ( x ) u q ( x ) d x | 2 0 Λ | E y m ( x ) | 2 d x 0 Λ | u q ( x ) | 2 d x ,
E y in = t in 0 u 0 ( x ) + t in 2 u 2 ( x ) ,
t in q = 0 Λ E y in ( x ) u q ( x ) d x 0 Λ | E y in ( x ) | 2 d x 0 Λ | u q ( x ) | 2 d x .
E y out ( x , h ) = E 1 e i k x x + E 0 + E 1 e i k x x = t in 0 u 0 ( x ) e i k z n 0 eff h + t in 2 u 2 ( x ) e i k z n 2 eff h .
1 Λ 0 Λ [ t in 0 u 0 ( x ) + t in 2 u 2 ( x ) ] d x = 1 ,
E 0 = 1 Λ 0 Λ [ t in 0 u 0 ( x ) e i k z n 0 eff h + t in 2 u 2 ( x ) e i k z n 2 eff h ] d x .
1 Λ 0 Λ [ t in 0 u 0 ( x ) + t in 2 u 2 ( x ) ] cos ( k x x ) d x = 0 ,
E 1 = E 1 = 1 Λ 0 Λ [ t in 0 u 0 ( x ) e i k z n 0 eff h + t in 2 u 2 ( x ) e i k z n 2 eff h ] cos ( k x x ) d x .
η 0 TE = | E 0 | 2 = | A e i k z n 0 eff h + ( 1 A ) e i k z n 2 eff h | 2 ,
η 1 TE = η 1 TE = | E 1 | 2 = 4 B 2 sin 2 Δ φ 2 ,
A = 1 Λ 0 Λ t in 0 u 0 ( x ) d x ,
B = | 1 Λ 0 Λ ( t in 0 u 0 ( x ) cos k x x ) d x | ,
4 [ B 2 + A ( 1 A ) ] sin 2 Δ φ 2 = 1 .

Metrics