Abstract

A binary diffractive optical element, acting as a polarizing beam splitter, is proposed and analyzed. It behaves like a transmissive blazed grating, working on the first or the second diffraction order, depending on the polarization state of the incident radiation. The grating-phase profile required for both polarization states is obtained by means of suitably sized subwavelength groups etched in an isotropic dielectric medium. A rigorous electromagnetic analysis of the grating is presented, and numerical results concerning its performances in terms of diffraction efficiency as well as frequency and angular bandwidths are provided.

© 2001 Optical Society of America

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  17. J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in OpticsE. Wolf, ed. (North Holland, Amsterdam, 2000), Vol. XL, pp. 327–341.
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2000 (2)

1999 (2)

F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “On anisotropic gratings,” Atti Fond. Giorgio Ronchi LIV, 59–67 (1999).

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A: Pure Appl. Opt. 1, 215–219 (1999).

1997 (1)

1996 (6)

1995 (2)

1994 (1)

1992 (2)

1990 (1)

1988 (1)

1986 (2)

1978 (1)

1971 (1)

P. Kunstmann, H. J. Spitschan, “General complex amplitude addition in a polarization interferometer in the detection of pattern differences,” Opt. Commun. 4, 166–168 (1971).
[CrossRef]

Azzam, R. M. A.

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “On anisotropic gratings,” Atti Fond. Giorgio Ronchi LIV, 59–67 (1999).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (extended) (Cambridge U. Press, Cambridge, UK, 1999).

Bräuer, R.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).

Bryngdahl, O.

Cambril, E.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A: Pure Appl. Opt. 1, 215–219 (1999).

Carey, C. D.

Chavel, P.

M. L. Lee, T. Lalanne, P. Chavel, “Blazed-binary diffractive elements with period much larger than the wavelength,” J. Opt. Soc. Am. A 17, 1250–1255 (2000).
[CrossRef]

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A: Pure Appl. Opt. 1, 215–219 (1999).

Chipman, R. A.

De Biase, G. A.

Doumuki, T.

Gaylord, T. K.

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “On anisotropic gratings,” Atti Fond. Giorgio Ronchi LIV, 59–67 (1999).

Granet, G.

Grann, E. B.

Guattari, G.

F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “On anisotropic gratings,” Atti Fond. Giorgio Ronchi LIV, 59–67 (1999).

Guizal, B.

Hazart, J.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A: Pure Appl. Opt. 1, 215–219 (1999).

Ito, M.

Kaku, T.

Kawakami, S.

Knop, K.

Kuittinen, M.

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in OpticsE. Wolf, ed. (North Holland, Amsterdam, 2000), Vol. XL, pp. 327–341.

Kunstmann, P.

P. Kunstmann, H. J. Spitschan, “General complex amplitude addition in a polarization interferometer in the detection of pattern differences,” Opt. Commun. 4, 166–168 (1971).
[CrossRef]

Lalanne, P.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A: Pure Appl. Opt. 1, 215–219 (1999).

P. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Lalanne, T.

Launois, H.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A: Pure Appl. Opt. 1, 215–219 (1999).

Lee, E. H.

Lee, M. L.

Lemercier-Lalanne, D.

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Li, L.

Marom, D. M.

Matsumoto, S.

Maystre, D.

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1984), Vol. XXI, pp. 1–68.
[CrossRef]

Mendlovic, D.

Midwinter, J. E.

Miller, J. M.

Moharam, M. G.

Morris, G. M.

Noponen, E.

Ojima, M.

Pezzaniti, J. L.

Pommet, D. A.

Saito, A.

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “On anisotropic gratings,” Atti Fond. Giorgio Ronchi LIV, 59–67 (1999).

Schmitz, M.

Selviah, D. R.

Shiraishi, K.

Song, S. H.

Spitschan, H. J.

P. Kunstmann, H. J. Spitschan, “General complex amplitude addition in a polarization interferometer in the detection of pattern differences,” Opt. Commun. 4, 166–168 (1971).
[CrossRef]

Sugita, Y.

Taghizadeh, M. R.

Takayama, S.

Tamada, H.

Tervo, J.

Tsunoda, Y.

Turunen, J.

Vasara, A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (extended) (Cambridge U. Press, Cambridge, UK, 1999).

Wyrowski, F.

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in OpticsE. Wolf, ed. (North Holland, Amsterdam, 2000), Vol. XL, pp. 327–341.

Yamaguchi, T.

Appl. Opt. (5)

Atti Fond. Giorgio Ronchi (1)

F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “On anisotropic gratings,” Atti Fond. Giorgio Ronchi LIV, 59–67 (1999).

J. Mod. Opt. (1)

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, H. Launois, “A transmission polarizing beam splitter grating,” J. Opt. A: Pure Appl. Opt. 1, 215–219 (1999).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Opt. Commun. (1)

P. Kunstmann, H. J. Spitschan, “General complex amplitude addition in a polarization interferometer in the detection of pattern differences,” Opt. Commun. 4, 166–168 (1971).
[CrossRef]

Opt. Lett. (5)

Other (5)

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1984), Vol. XXI, pp. 1–68.
[CrossRef]

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in OpticsE. Wolf, ed. (North Holland, Amsterdam, 2000), Vol. XL, pp. 327–341.

M. Born, E. Wolf, Principles of Optics, 7th ed. (extended) (Cambridge U. Press, Cambridge, UK, 1999).

C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).

M. Bass, ed., Handbook of Optics, Devices, Measurements, and Properties, 2nd ed. (McGraw-Hill, New York, 1995), Vol. 2.

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Figures (12)

Fig. 1
Fig. 1

Geometry of the grating and the polarization states of the incident wave. See text for details.

Fig. 2
Fig. 2

From the birefringent blazed grating to the equivalent subwavelength binary grating.

Fig. 3
Fig. 3

Diffraction efficiencies of the transmitted orders TE2 (filled circles) and TM1 (open circles) plotted as functions of the period normalized to the incident wavelength d0 for the binary grating shown in Fig. 1 with a subperiod of d s = 0.01d (M = 100).

Fig. 4
Fig. 4

Diffraction efficiencies of the transmitted orders TE2 (filled circles) and TM1 (open circles) plotted as functions of d0 for a blazed grating made with the uniaxial birefringent material predicted by form-birefringence theory (n TE = 1.4893, n TM = 1.2446, a 0 = 4.0866λ0).

Fig. 5
Fig. 5

Diffraction efficiencies of the transmitted orders TE1 (crosses) and TM1 (circles) plotted as functions of d0 for the case of Fig. 3.

Fig. 6
Fig. 6

Diffraction efficiencies of the transmitted orders TE2 (filled circles) and TM2 (crosses) plotted as functions of d0 for the case of Fig. 3.

Fig. 7
Fig. 7

Diffraction efficiencies of the transmitted orders TE2 (filled circles) and TM1 (open circles) plotted as functions of the incidence angle ϑ for the binary grating of Fig. 3 when d = 19λ0.

Fig. 8
Fig. 8

Same as for Fig. 7 [TE2 (filled circles), TM1 (open circles)] plotted versus the incidence wavelength normalized to the operation wavelength λ i 0.

Fig. 9
Fig. 9

Same as for Fig. 3 [TE2 (filled circles), TM1 (open circles)] but for a binary grating with d s = 0.02d (M = 50).

Fig. 10
Fig. 10

Same as for Fig. 3 [TE2 (filled circles), TM1 (open circles)] but for a binary grating with d s = 0.05d (M = 20).

Fig. 11
Fig. 11

Transmission efficiencies of TE2 (filled circles) and TM1 (open circles) orders plotted as functions of N for the grating of Fig. 10 when d = 10λ.

Fig. 12
Fig. 12

Average diffraction efficiencies of the transmitted orders TE2 (filled circles) and TM1 (open circles) plotted as functions of the maximum amplitude b f of the random fabrication error for d s = 0.05d (M = 20).

Equations (21)

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

n2x=m=-+ αm exp2πimx/d,
EIx, y=expik0xx-r0y+h=-+ Rh×expikhxx+rhy,
EIIIx, y=h=-+ Th expikhxx-thy+a,
khx=2πhd+nIk0 sin ϑ,
rh=nI2k02-khx21/2nIk0|khx|ikhx2-nI2k021/2nIk0<|khx|,th=nT2k02-khx21/2nTk0|khx|ikhx2-nT2k021/2nTk0<|khx|,
EIIx, y=m=-+n=-+ Emn expikmxxAn exp-iknyy+Bn expiknyy+a0.
kny2Emn+p=-+ Emnδmpkpx2-αm-pk02=0,  m, n=0, ±1, ±2,.
HIx, y=expik0xx-r0y+h=-+ Rh×expikhxx+rhy,
HIIIx, y=h=-+ Th expikhxx-thy+a0,
HIIx, y=m=-+n=-+ Hmn expikmxxAn exp-iknyy+Bn expiknyy+a0.
GIx, y=1nx2k02HIx, yy=1nI2k02-ir0 expik0xx-r0y+h=-+ irhRh expik0xx+r0y,
GIIIx, y=1nx2k02HIIIx, yy=1nT2k02h=-+-ithTh×expikhxx-thy+a0,
GIIx, y=m=-+n=-+ Gmn expikmxxikny×-Anexp-iknyy+Bn×expiknyy+a,
Hm=k02p=-+ βm-p-1Gp=0,  m=0, ±1, ±2,,
kny2k02Gm=p=-+k02δmp-kmxαm-p-1kpxHp,  m, n=0, ±1, ±2,,
Wˆ=100expiδ,
Ei=E11,
Et=Wˆ·Ei=E1expiδ=E10+expiδ01.
k0nTE-1a0=2πl,  k0nTM-1a0=2πl,
nTEeff=1-b+bn121/2,
nTMeff=11-b+b/n121/2.

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