Analysis of a dual-twist Pancharatnam phase device with ultrahigh-efficiency large-angle optical beam steering

HsienHui Cheng; Achintya K. Bhowmik; Philip J. Bos

doi:10.1364/AO.54.010035

Applied Optics
Vol. 54,
Issue 34,
pp. 10035-10043
(2015)
•https://doi.org/10.1364/AO.54.010035

Analysis of a dual-twist Pancharatnam phase device with ultrahigh-efficiency large-angle optical beam steering

HsienHui Cheng, Achintya K. Bhowmik, and Philip J. Bos

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HsienHui Cheng, Achintya K. Bhowmik, and Philip J. Bos, "Analysis of a dual-twist Pancharatnam phase device with ultrahigh-efficiency large-angle optical beam steering," Appl. Opt. 54, 10035-10043 (2015)

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Abstract

It has been previously shown that a Pancharatnam phase device with a dual-twist structure can deflect light up to 60° with nearly perfect efficiency. This was beyond the limits previously assumed for these types of devices, which were considered to be optically similar to Raman–Nath gratings. In this paper we first consider the range of parameters that will allow for high efficiency and show the results for a structure that demonstrates 80° deflection. We then explore the light propagation through these devices to point out interesting intensity variations in the deflected mode of light as it traverses the deflecting layer. Finally, we explain the key to understanding the efficiency of these devices, which is not the typical parameters that are important for traditional diffractive devices, but rather the control of the polarization state of light. We provide a simple design approach for optimizing the twist angle and retardation for high efficiency.

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Properties of Input Light	Wavelength $λ_{0} = 633 nm$ Gaussian beam $W = 10 λ_{0}$ $θ_{incident} = 0 °$
FDTD Parameters	Grid resolution $Δ x = λ_{0} / 40$ $Δ t = Δ x / 2 c_{0}$
Computation Domain	Total width of grating $L = 60 λ_{0}$ source layer to computation region $A = 920$ grids computation region to NFFF layer $B = 2 λ_{0}$
Far-Field Screen	distance between PG and far field screen $D = 2 cm$ , angular resolution of far-field screen $Δ θ = (1.85 \times 10^{- 3}) °$

(a) Optimized on-axis Twist Angle $ϕ_{twist} (°)$
$Δ n$ \ Deflection Angle	$- 20 °$	$- 40 °$	$- 60 °$	$- 80 °$
0.106	60	120	250	320
0.179	55	75	160	180
0.3	40	60	85	130
(b) Optimized value of $Δ$ nd ( $λ_{0}$ )
$Δ n$ \ Deflection Angle	$- 20 °$	$- 40 °$	$- 60 °$	$- 80 °$
0.106	$0.60 λ_{0}$	$0.425 λ_{0}$	$0.525 λ_{0}$	$0.50 λ_{0}$
0.179	$0.625 λ_{0}$	$0.50 λ_{0}$	$0.55 λ_{0}$	$0.50 λ_{0}$
0.3	$0.70 λ_{0}$	$0.60 λ_{0}$	$0.50 λ_{0}$	$0.50 λ_{0}$
(c) $Δ$ nd range where intrinsic diffraction efficiency $> 90 %$ for optimized $ϕ_{twist}$ ( $λ_{0}$ )
$Δ n$ \ Deflection Angle	$- 20 °$	$- 40 °$	$- 60 °$	$- 80 °$
0.106	$0.51 λ_{0} - 0.67 λ_{0}$	$0.37 λ_{0} - 0.48 λ_{0}$	$0.46 λ_{0} - 0.57 λ_{0}$	$0.49 λ_{0} - 0.51 λ_{0}$
0.179	$0.54 λ_{0} - 0.70 λ_{0}$	$0.44 λ_{0} - 0.56 λ_{0}$	$0.43 λ_{0} - 0.60 λ_{0}$	$0.49 λ_{0} - 0.51 λ_{0}$
0.3	$0.64 λ_{0} - 0.75 λ_{0}$	$0.50 λ_{0} - 0.64 λ_{0}$	$0.45 λ_{0} - 0.55 λ_{0}$	$0.46 λ_{0} - 0.55 λ_{0}$
(d) $ϕ_{twist}$ angle where intrinsic diffraction efficiency can be $> 95 %$ (°)
0.106	45–79	100–154	213–275	317–322
0.179	31^a–79	57–101	136–184^a	None^c
0.3	20^b–60^b	46^a–74	69–103	127–133

(a) Optimized Intrinsic Diffraction Efficiency
$Δ n$ \ Deflection Angle	$- 20 °$	$- 40 °$	$- 60 °$	$- 80 °$
0.106	99.53%	98.44%	98.93%	95.27%
0.179	99.54%	99.29%	99.22%	94.55%
0.3	99.12%	98.90%	99.31%	95.82%
(b) Device Efficiency for optimized DLPPDs
$Δ n$ \ Deflection Angle	$- 20 °$	$- 40 °$	$- 60 °$	$- 80 °$
0.106	86%	84%	78%	29%
0.179	89%	91%	81%	28%
0.3	91%	85%	85%	23%
(c) Theoretical transmission due to loss of reflection for optimized DLPPDs
$Δ n$ \ Deflection Angle	$- 20 °$	$- 40 °$	$- 60 °$	$- 80 °$
0.106	91%	90%	86%	57%
0.179	89%	89%	84%	57%
0.3	88%	88%	84%	57%

Ratio of $I_{y}$ at Middle of DLPPD to Top of DLPPD
$Δ n$ \ Deflection Angle	− Deflector	+ Deflector
0.106\40°	0.10	0.83
0.179\40°	0.03	0.90
0.3\40°	0.08	0.68
0.179\60°	0.03	0.69

Properties of Input Light	Wavelength $λ_{0} = 633 nm$ Gaussian beam $W = 10 λ_{0}$ $θ_{incident} = 0 °$
FDTD Parameters	Grid resolution $Δ x = λ_{0} / 40$ $Δ t = Δ x / 2 c_{0}$
Computation Domain	Total width of grating $L = 60 λ_{0}$ source layer to computation region $A = 920$ grids computation region to NFFF layer $B = 2 λ_{0}$
Far-Field Screen	distance between PG and far field screen $D = 2 cm$ , angular resolution of far-field screen $Δ θ = (1.85 \times 10^{- 3}) °$

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Applied Optics