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Design, fabrication and characterization of subwavelength computer-generated holograms for spot array generation

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Abstract

We report the analysis, design, fabrication and experimental characterization of novel subwavelength computer-generated holograms that produce uniform symmetric spot array. We distinguish between a polarization-sensitive and polarization-insensitive far-field reconstruction and show that a linearly polarized incident illumination is required in the former case in order to generate a symmetric reconstruction. The polarization-insensitive case generates a symmetric response independent of the illumination polarization. We show that this response is equivalent to that of a scalar-based computer-generated hologram but with an additional, independent, term that describes the undiffracted zeroth order. These findings simplify the design and optimization of form birefringent computer-generated holograms (F-BCGH) significantly. We present experimental results that verify our analysis and highlight the advantage of these novel elements over scalar-designed elements.

©2004 Optical Society of America

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Figures (4)

Fig. 1.
Fig. 1. Schematic diagram of diffractive optical element using subwavelength grating based phase modulation: subwavelngth grating with a period Λ is introduced into each cell with oriantation of the grating θ(x,y).
Fig. 2.
Fig. 2. Typical SEM cross section of the fabricated F-BCGH 1X3 element
Fig. 3.
Fig. 3. Experimentally obtained image of the Fourier transform of the F-BCGH element illuminated by a linearly polarized beam.
Fig. 4.
Fig. 4. Cross-section of Fig 3. The cross section was calculated by integrating Fig. 3 along the vertical axis.

Equations (30)

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E ¯ T ( x , y , z = 0 + ) = R = ( x , y ) 1 G = R = ( x , y ) V ¯ in
E ¯ TR ( x , y , z = 0 + ) = cos ( ϕ / 2 ) [ 1 j ] j sin ( ϕ / 2 ) exp [ + j 2 θ ( x , y ) ] [ 1 j ]
E ¯ TL ( x , y , z = 0 + ) = cos ( ϕ / 2 ) [ 1 j ] j sin ( ϕ / 2 ) exp [ + j 2 θ ( x , y ) ] [ 1 j ]
E ˜ R ( x , y ) = + E ¯ TR ( x , y ) exp [ j 2 π ( xx + yy ) ] dxdy =
cos ( ϕ / 2 ) δ d ( x , y ) [ 1 j ] j sin ( ϕ / 2 ) + exp [ j 2 θ ( x , y ) ] exp [ j 2 π ( xx + yy ) dxdy [ 1 j ] ]
E ˜ L ( x , y ) = + E ¯ TL ( x , y ) exp [ j 2 π ( xx + yy ) ] dxdy = cos ( ϕ / 2 ) δ d ( x , y ) [ 1 j ]
j sin ( ϕ / 2 ) + exp [ j 2 θ ( x , y ) ] exp [ j 2 π ( xx + yy ) dxdy [ 1 j ] = cos ( ϕ / 2 ) δ ( x , y ) [ 1 j ]
j sin ( ϕ / 2 ) { + exp [ j 2 θ ( x , y ) ] exp [ j 2 π ( x ( x ) + y ( y ) ) ] dxdy } * [ 1 j ]
E ˜ R ( x , y ) = E ˜ L ( x , y )
V ¯ in = [ cos ( χ ) exp ( j δ / 2 ) sin ( χ ) exp ( + j δ / 2 ) ] ,
V ¯ in = α [ 1 j ] + β [ 1 j ]
2 α = cos ( χ δ / 2 ) j sin ( χ + δ / 2 ) , 2 β = cos ( χ + δ / 2 ) + j sin ( χ δ / 2 )
I ( x , y ) = α 2 E ˜ R ( x , y ) 2 + β 2 E ˜ L ( x , y ) 2 = α 2 E ˜ R ( x , y ) 2 + β 2 E ˜ R ( x , y ) 2 ,
cos 2 ( χ δ / 2 ) cos 2 ( χ + δ / 2 ) = 0 ,
χ = n π / 2 or δ = m π
I L ( x , y ) = E ˜ L ( x , y ) 2 = E ˜ R ( x , y ) 2 = E ˜ R ( x , y ) 2 = I R ( x , y )
E ¯ s ( x , y , z = 0 + ) = exp [ j Φ ( x , y ) ] ,
E ¯ TR ( x , y , z = 0 + ) = E ¯ s ( x , y , z = 0 + ) ,
E ˜ R ( x , y ) = E ˜ S ( x , y ) ,
I ( x , y ) = α 2 E ˜ R ( x , y ) 2 + β 2 E ˜ L ( x , y ) 2 = E ˜ R ( x , y ) 2 = E ˜ S ( x , y ) 2 = I S ,
E ˜ R 2 = a n = 1 N δ d ( x n Δ x ) + b n = 1 N δ d ( x + n Δ x ) ,
E ˜ L 2 = b n = 1 N δ d ( x n Δ x ) + a n = 1 N δ d ( x + n Δ x )
I = E ˜ R 2 + E ˜ L 2 = ( a + b ) [ 1 N δ ( x Δ x ) + 1 N δ ( x + Δ x ) ]
E ¯ T ( x , y , z = 0 + ) = j sin ( ϕ / 2 ) sin [ 2 θ ( x , y ) ] x ̂ { cos ( ϕ / 2 ) + j sin ( ϕ / 2 ) cos [ 2 θ ( x , y ) ] } y ̂
I ( x , y ) = E ˜ x ( x , y ) 2 + E ˜ y ( x , y ) 2 = cos 2 ( ϕ / 2 ) δ d ( x , y ) + sin 2 ( ϕ / 2 ) ×
× { { sin [ 2 θ ( x , y ) ] exp ( j 2 π ( xx + yy ) ) dxdy } 2 + { cos [ 2 θ ( x , y ) ] exp ( j 2 π ( xx + yy ) ) dxdy } 2 }
I ( x = 0 , y = 0 ) = cos 2 ( ϕ / 2 ) + sin 2 ( ϕ / 2 ) { { sin [ 2 θ ( x , y ) ] dxdy } 2 + { cos [ 2 θ ( x , y ) ] } 2 }
cos 2 ( ϕ / 2 ) I ( 0 , 0 )
ϕ min = 2 cos 1 ( 1 2 N + 1 )
e = x , y ROI η I desired ( x , y ) I obtained ( x , y )
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