Abstract

Design of broadband diffractive elements is studied. It is shown that dielectric polarization gratings can be made to perform the same optical function over a broad band of wavelengths. Any design of paraxial-domain diffractive elements can be realized as such broadband elements that may, e.g., give constant diffraction efficiencies over the wavelength band while the field propagation after the elements remains wavelength-dependent. Furthermore, elements producing symmetric signals are shown to work with arbitrarily polarized or partially polarized incident planar broadband fields. The performance of the elements is illustrated by numerical examples and some practical issues related to their fabrication are discussed.

© 2005 Optical Society of America

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References

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Appl. Opt. (3)

Geophys. J. R. Astr. Soc. (1)

J. C. Samson, �??Descriptions of the polarization states of vector processes: applications to ULF magnetic fields,�?? Geophys. J. R. Astr. Soc. 34, 403�??419 (1973).
[CrossRef]

J. Mod. Opt. (1)

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, �??Fourier array illuminators with 100% efficiency: analytical Jones-matrix construction,�?? J. Mod. Opt. 47, 2351�??2359 (2000).

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

Opt. Commun. (3)

G. Piquero, R. Borghi, A. Mondello and M. Santarsiero, �??Far field of beams generated by quasi-homogeneous sources passing through polarization gratings,�?? Opt. Commun. 195, 339�??350 (2001).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. Di Fabrizio, and M. Gentili, �??Analytical derivation of optimum triplicator,�?? Opt. Commun. 157, 13�??17 (1998).
[CrossRef]

D.-E. Yi, Y.-B. Yan, H.-T. Liu, Si-Lu, and G.-F. Jin, �??Broadband achromatic phase retarder by subwavelength grating,�?? Opt. Commun. 227, 49�??55 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (12)

J. A. Davis, J. Adachi, C. R. Fernández-Pousa, and I. Moreno, �??Polarization beam splitters using polarization diffraction gratings,�?? Opt. Lett. 26, 587�??589 (2001).
[CrossRef]

C. R. Fernández-Pousa, I. Moreno, J. A. Davis, and J. Adachi, �??Polarizing diffraction-grating triplicators,�?? Opt. Lett. 26, 1651�??1653 (2001).
[CrossRef]

F. Wyrowski, �??Upper bound of efficiency of diffractive phase elements,�?? Opt. Lett. 16, 1915�??1917 (1991).
[CrossRef] [PubMed]

H. Lajunen, J. Tervo, and J. Turunen, �??High-efficiency broadband diffractive elements based on polarization gratings,�?? Opt. Lett. 29, 803�??805 (2004).
[CrossRef] [PubMed]

Y. Kanamori, M. Sasaki, and K. Hane, �??Broadband antireflection gratings fabricated upon silicon substrates,�?? Opt. Lett. 24, 1422�??1424 (1999).
[CrossRef]

I. R. Hooper and J. R. Sambles, �??Broadband polarization-converting mirror for the visible region of the spectrum,�?? Opt. Lett. 27, 2152�??2154 (2002).
[CrossRef]

D. Yi, Y. Yan, H. Liu, S. Lu, and G. Jin, �??Broadband polarizing beam splitter based on the form birefringence of a subwavelength grating in the quasi-static domain,�?? Opt. Lett. 29, 754�??756 (2004).
[CrossRef] [PubMed]

C. Sauvan, P. Lalanne, and M.-S. L. Lee, �??Broadband blazing with artificial dielectrics,�?? Opt. Lett. 29, 1593�??1595 (2004).
[CrossRef] [PubMed]

F. Gori, �??Measuring the Stokes parameters by means of a polarization grating,�?? Opt. Lett. 24, 584�??586 (1999).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, �??Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,�?? Opt. Lett. 27, 1141�??1143 (2002).
[CrossRef]

J. Tervo and J. Turunen, �??Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,�?? Opt. Lett. 25, 785�??786 (2000).
[CrossRef]

S. Astilean, Ph. Lalanne, P. Chavel, E. Cambril, and H. Launois, "High-efficiency subwavelength diffractive element patterned in a high-refractive-index material for 633 nm", Opt. Lett. 23, 552�??554 (1998).
[CrossRef]

Proc. Phys. Soc. (1)

L. Mandel, �??Intensity fluctuations of partially polarized light,�?? Proc. Phys. Soc. 81, 1104�??1114 (1963).
[CrossRef]

Other (6)

J. Turunen, �??Diffraction theory of microrelief gratings,�?? in Micro-Optics: Elements, Systems, and Applications, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), Chapter 2.

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

H. R. Philipp, �??Silicon Dioxide (SiO2) (Glass),�?? in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, Orlando, 1985), pp. 749�??763.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic Press, San Diego, 1990), Section 3.4.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Geometry of a form-birefringent, y-invariant, sub-wavelength-period grating with period d, modulation depth h, minimum transverse feature size g, and refractive indices n 0, n 1, n 2, and n 3.

Fig. 2.
Fig. 2.

Diffraction efficiencies of the 1→3 beam splitter based on a scalar design, realized as a polarization grating, η 0=η ±1 (solid line), and as a surface-relief phase grating, η 0 (dashed line) and η ±1 (dash-dotted line).

Fig. 3.
Fig. 3.

Diffraction efficiency of a 1→2 beam splitter made of TiO2 using subwavelength grating with parameters d=220 nm, f=0.6, and h=750 nm (dashed line), h=800 nm (solid line), and h=850 nm (dotted line).

Fig. 4.
Fig. 4.

Diffraction efficiency of a 1→2 beam splitter made of TiO2 using subwavelength grating with parameters d=220 nm, h=800 nm, and f=0.55 (dashed line), f=0.60 (solid line), and f=0.65 (dotted line).

Equations (38)

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T ( x , y ) = [ t cos 2 θ ( x , y ) + t sin 2 θ ( x , y ) ( t t ) sin θ ( x , y ) cos θ ( x , y ) ( t t ) sin θ ( x , y ) cos θ ( x , y ) t sin 2 θ ( x , y ) + t cos 2 θ ( x , y ) ] ,
t = t exp ( i kn h ) ,
t = t exp ( i kn h ) ,
ϕ ( λ ) = arg t arg t = kh ( n n )
J i = α J R + β J L
J R = 1 2 ( 1 i )
J L = 1 2 ( 1 i ) .
α = ( E i x i E i y ) 2 ,
β = ( E i x + i E i y ) 2 ,
E ( x , y ) = T ( x , y ) J i .
E ( x , y ) = α E R ( x , y ) + β E L ( x , y )
E R ( x , y ) = 1 2 ( t + t ) J R + 1 2 ( t t ) exp [ i 2 θ ( x , y ) ] J L
E L ( x , y ) = 1 2 ( t + t ) J L + 1 2 ( t t ) exp [ i 2 θ ( x , y ) ] J R
t ± t = exp ( i arg t ) [ 1 ± exp ( i ϕ 0 ) ]
E ( x , y ) = m = n = J m , n exp [ i 2 π ( mx d x + ny d y ) ] ,
J m , n = 1 d x d y 0 d x 0 d y E ( x , y ) exp [ i 2 π ( mx d x + ny d y ) ] d x d y
η m , n = J m , n 2
J m , n = T m , n ( 0 ) J i + α T m , n ( 1 ) J L + β T m , n ( 1 ) J R
T m , n ( 0 ) = 1 2 ( t + t ) δ 0 , 0 ,
T m , n ( ± 1 ) = 1 2 ( t t ) t m , n ( ± 1 ) ,
t m , n ( ± 1 ) = 1 d x d y 0 d x 0 d y exp [ ± i 2 θ ( x , y ) ] exp [ i 2 π ( mx d x + ny d y ) ] d x d y .
η m , n = T m , n ( 0 ) 2 + α T m , n ( 1 ) 2 + β T m , n ( 1 ) 2 + 2 Re [ α * T m , n ( 0 ) * β T m , n ( 1 ) ] + 2 Re [ β * T m , n ( 0 ) * α T m , n ( 1 ) ]
η m , n = α T m , n ( 1 ) 2 + β T m , n ( 1 ) 2
η m , n = T m , n ( 0 ) 2 + T m , n ( 1 ) 2 = 1 4 t + t 2 δ 0 , 0 + 1 4 t t 2 t m , n ( 1 ) 2 .
θ ( x , y ) = θ ( x ) = π x D ,
η 0 = 1 4 t + t 2
η ± 1 = 1 8 t t 2 ( 1 E i x E i y sin ϑ ) ,
η m , n = ( α 2 + β 2 ) T m , n ( 1 ) 2 = T m , n ( 1 ) 2
η 0 , 0 = T 0 , 0 ( 0 ) 2 + T 0 , 0 ( 1 ) 2 + ( t 2 t 2 ) Re [ α β * t 0 , 0 ( 1 ) ]
J ( r , ω ) = [ J xx ( r , ω ) J xy ( r , ω ) J yx ( r , ω ) J yy ( r , ω ) ] = [ E x * ( r , ω ) E x ( r , ω ) E x * ( r , ω ) E y ( r , ω ) E y * ( r , ω ) E x ( r , ω ) E y * ( r , ω ) E y ( r , ω ) ] ,
J t = T J i T ,
J ( r , ω ) = n = 1 2 λ n ( ω ) ϕ n ( r , ω ) ϕ n ( r , ω )
J t = T ( λ 1 J 1 + λ 2 J 2 ) T = λ 1 T J 1 T + λ 2 T J 2 T ,
η m , n = λ 1 η 1 m , n + λ 2 η 2 m , n ,
η m , n = ( λ 1 + λ 2 ) η 1 m , n = η 1 m , n .
t ( x , λ ) = exp [ i Φ ( λ ) sin ( 2 π x D ) ] ,
Φ ( λ ) = 2 π ( n 2 n 1 ) h 0 λ
η m ( λ ) = J m 2 [ Φ ( λ ) 2 ] ,

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