5 Jun 2008 - grating with good specification (high angular dispersion, high diffraction efficiency, and low polarization dependence) is strongly desired.
IJCSNS International Journal of Computer Science and Network Security, VOL.8 No.6, June 2008
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A New Binary Multi-layer Diffraction Grating Abbas Zarifkar, Reza Yousefi Iran Telecommunication Research Center, Tehran, Iran Islamic Azad University, Noor Branch, Noor, Iran
Summary In WDM communication systems, diffraction grating is an important component. Optical components such as multiplexers use diffraction grating in their structures. In these devices, a grating with good specification (high angular dispersion, high diffraction efficiency, and low polarization dependence) is strongly desired. Since reducing the reflection at the upper surface of a grating is an important issue in order to realize high optical performance, we propose a novel grating with multi-layer structure in which a thin layer is used for decreasing the reflection from the surface. A good design, which provides high optical performance in the broad wavelength band, is successfully obtained.
2. Theory
Key words:
order angle and ni and nt are incident and transmitted diffraction factors, respectively. Eq. (1) shows that for high dispersion, Λ must to be decreased in comparison with λ. In the case of Bragg condition for ith order, the diffraction efficiency is generally, but not always, maximized for the ith diffracted order [1]. Angular dispersion D of the first-order diffraction of Bragg condition is expressed by the following equation[3].
WDM, Diffraction grating.
1. Introduction For decades, diffraction gratings have been used to analyze the spectrum of light. Today, the diffraction gratings are used in optical communication components such as optical multiplexers and other integrated optical devices [1]. The diffraction gratings are required to have high diffraction efficiency, low polarization dependence and high angular dispersion [2]. It is shown that reducing the reflection at upper surface of a grating is very important in order to realize high optical performance diffraction gratings [3]. In this paper we propose a novel grating design with multi-layer structure in which a thin layer is used for decreasing the reflection from the surface and provides a high optical performance in the broad wavelength band and good polarization dependent properties. In section 2 we present a brief review of basics of diffraction grating specifications and equations. In section 3, some conventional diffraction gratings and their properties are introduced. In section 4 we simulate the proposed new structure and compare the results with structures introduced in section 3.
Manuscript received June 5, 2008. Manuscript revised June 20, 2008.
Fig. 1 shows diffraction grating operation and order of the reflected and transmitted waves. From Floquet condition and Snell’s law for the qth-order, we have: nt sin(θ q ) = ni sin(θ i ) − q
λ Λ
(1)
Where λ is the wavelength of incident light, θ i is the θ incident angle, Λ is grating period, q is qth transmitted
Fig. 1 Reflected and transmitted waves from diffraction grating with subwavelength period
D=
dθ1 2 tan(θi ) = dλ λ
(2) To increase D, Λ should be decreased and θi be increased. In our work, Λ is set to 1 μm, which is shorter than the wavelength in C-band (1.52-1.57 μm), and the incident angle θi is set to 50 deg.
IJCSNS International Journal of Computer Science and Network Security, VOL.8 No.6, June 2008
3. Existing structures of binary grating In this paper, the efficiency is calculated using rigorous coupled wave analysis (RCWA) method [1,4,5] and optimization down with stimulated annealing (SA) method [1] which is suitable for design optimization of optical devices [2]. Optimization is used to achieve a best design with high efficiency and good polarization independent property, restricted to the fixed angular dispersion. In order to inspect the proposed structures, we considered two structures as shown in Fig 2. Fig 2(a) is conventional diffraction grating structure and Fig 2(b) is new structure introduced in [3].
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Table 1 Parameters and the diffraction efficiency of the all structures.
Fig. 2(a)
2(b)
4(a)
4(b)
Parameter
h:1.64 f:0.596 n:1.87 h2:.316 h1:1.55 f:0.614 n1:1.97 n2:1.45 h1:.3759 h2:1.433 f2:0.6105 n1:1.8137 n2:2.0469 h1:.3591 h2:.5428 h3:4.6738 f3:0.6826 n1:2.1549 n2:1.9865
Δη η ave
Δ max
%
%
η ave
ave
min
max
90.5
89.5
91.6
2.3
2.3
96
95.85
96.28
0.45
0.16
94.14
93.79
94.49
0.74
0.65
97.42
96.65
98.2
1.73
0.1
ηmin , η max and η ave are respectively the minimum,
maximum and average diffraction efficiencies within the entire range of C-band including all polarizations. (η max − η min ) / η ave is the polarization dependence and Δ max / ηave is the maximum difference between efficiencies
(a)
of TE and TM modes, including wavelength dependence. Diffraction efficiencies for the first transmitted order of the structures of Fig. 2 are shown in Fig. 3. It is obvious that the first structure has low efficiency and high polarization dependent property but the second one has not only high efficiency but also very good polarization independent property.
(b) Fig. 2 Cross section of surface-relief binary diffraction grating (a) conventional structure and (b) structure introduced in [3]
The parameters and the diffraction efficiencies of the optimal design for all structures introduced in this paper are given in Table 1.
Fig. 3: Diffraction efficiency for first transmitted order of the structures shown in Fig. 2.
In [3], it is shown that the cause of the low diffraction efficiency is the Fresnel reflection at the upper/bottom
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IJCSNS International Journal of Computer Science and Network Security, VOL.8 No.6, June 2008
surfaces of a grating, and the diffraction characteristics are expected to be improved by reducing the reflection. The structure in Fig. 2(b) has been proposed based on this issue. In the next section we will introduce another method to remove reflection from surfaces of grating.
4. Proposed Structures We have modified Fig 2(a), by using of a thin layer for decreasing reflection from the surface. Width of this thin layer is 0.1 of underlying layer. This structure, after optimization is shown in Fig 4(a). This figure shows that a part of incident signal is reflected from the surface. To remove this part of reflection and increase the efficiency, the new proposed structure is presented in Fig. 4(b). Width of the second layer is half of underlying layer. Materials of the substrate and all layers except upper layer are the same and this is favorite for fabrication process. Diffraction efficiencies of the new structures for first order transmission are shown in Fig. 5.
(a)
(b) Fig. 4 Two proposed structures
Fig. 5: Diffraction efficiency for first transmitted order of the proposed structures in Fig. 4
We see that the new structures have better efficiency and polarization independent property than the conventional structure in Fig. 2(a). In comparison with Fig. 2(b), Fig. 4(a) has almost 2% lower efficiency and 0.3% lower polarization independent property while Fig. 4(b) has 2% higher efficiency and better polarization independent property. Although Fig. 2(b) has almost better frequency independent property, the structure in Fig. 4(b) has more diffraction efficiency than Fig. 2(b) in all frequencies.
5. Conclusion Reducing the reflection at upper surfaces of a grating is very important in order to realize high optical performance. Then, to control the reflection, we have proposed a novel grating with multi-layer structure in which a thin layer is used for decreasing reflection from the surface. Materials of substrate and all layers except upper layer are the same and this is favorite for fabrication process. A good design, which provides high optical performance in the broad wavelength band was successfully developed. In spite of the high angular dispersion, good optical performance with high diffraction efficiency (min > ≈ 97%) and low polarization dependence (max
