Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Current Optics and Photonics 2019; 3(5): 438-444
Published online October 25, 2019 https://doi.org/10.3807/COPP.2019.3.5.438
Copyright © Optical Society of Korea.
Feng Kuang^{1}, Feng Li^{2}, Zhihong Yang^{2,*}, and Hong Wu^{2,*}
Corresponding author: yangzhihong@njupt.edu.cn, wuhong@njupt.edu.cn
In this theoretical study, a line-defect photonic-crystal waveguide hosted in an annular photonic crystal was demonstrated to provide high-performance slow light with a wide band, low group-velocity dispersion, and a large normalized delay-bandwidth product. Combined with structural-parameter optimization and selective optofluid injection, the normalized delay-bandwidth product could be enhanced to a large value of 0.502 with a wide bandwidth of 58.4 nm in the optical-communication window, for a silicon-on-insulator structure. In addition, the group-velocity dispersion is on the order of 10^{5} (ps^{2}/km) in the slow-light region, which could be neglected while keeping the signal transmission unchanged.
Keywords: Annular photonic crystals, Slow light, Normalized delay-bandwidth product
In recent years, slow light in photonic-crystal waveguides (PCWs) has attracted much attention, since the effect remains excellent at room temperature and corresponding devices can be fabricated using traditional semiconductor technologies, providing many potential advantages in signal processing, optical storage [1], tunable delay [2], modulator and filter [3-5]. Generally a PCW is obtained by introducing a line defect into a perfect PC structure, which results in waveguide modes within the photonic band gap of the host PC and excites slow light near the Brillouin zone’s edges. The slow-light performance parameters of the PCWs to which attention is usually paid are the group index
An annular photonic crystal (APC) [15] is an unusual type of PC structure composed of a two-dimensional (2D) lattice of annular dielectric rods in air, or annular air voids in a dielectric background. This structure has been proposed to achieve a large absolute band gap [16], polarization-independent slow light [17], and polarization beam splitting [18]. Because it is a composite unit, an APC presents more possibilities than a normal PC in dispersion engineering. Therefore, in this research we chose an APC as the host of the PCWs, to explore the possibility of obtaining flat-band slow light. Combined with structural-parameter modification and selective optofluidic injection, optimized APCWs can support high-performance slow light with a constant group index, broad bandwidth, and low group-velocity dispersion.
Inspired by reference 16, we designed an APC slab based on a triangular lattice above a SiO_{2} layer with a refractive index of 1.45. The remaining portion within the slab was silicon (Si) with a refractive index
To save calculation time, it was necessary to calculate the dispersion properties of the APC slabs using a 2D simulation instead of a 3D simulation. As 2D approximation methods, the effective-index method [19, 20] and effective-period method [12, 21] have been successfully applied to the design of PC devices. Especially in Ref. [21], the latter method was shown to provide more accurate estimation of device behavior than the former. Therefore, we utilized 2D simulations by means of the effective-period method. In this method, the 2D effective period for our structure was calculated to be , where
A line-defect APC waveguide with as formed by removing a row of annuli in the
Based on previous work, some parameters are known to influence the dispersion, to obtain polarization-independent waveguiding and slow light in 2D APCWs [17, 22]. Such parameters include the radii and positions of the first two rows of the annuli, the width of the waveguide, and so on. To achieve a flat band, we altered the outer radius
The normalized delay-bandwidth product (NDBP), a comprehensive index for evaluating the slow-light performance of an APCW, can be calculated by [23, 24]
where and Δ
Usually the region of dispersion in relation to group index values within [5, 25] can be defined as an acceptable region for slow light applications.
Applying the above criterion, the group indices corresponding to
Next, to improve the dispersion, optofluid infiltrations with different refractive indices
As can be seen in Fig. 4(a), for
Then we turned to the case of
TABLE 1. Details of the group indices and the corresponding GVD, flat band’s center wavelength
To illustrate the advantages of APCs over normal PCs in slow-light dispersion engineering, we compared the results of our current work to the previously reported results proposed by line-defect PCWs hosted in 2D air-hole or rod PCs. Our best NDBP value of 0.502 was higher than the results reported in Ref. [26] (NDBP = 0.48), Ref. [7] (NDBP = 0.465), and Ref. [12] (NDBP = 0.469).
As shown in Fig. 5(a), it can be found that in the same dispersion curve there are two regions where the slopes of the curves differ greatly. One region has a larger slope, because the corresponding group index is small, resulting in a large group velocity, called a
Another important issue for slow-light devices is group-velocity dispersion (GVD), which causes pulse broadening and signal distortion [24]. The GVD, calculated by evaluating
To verify the PWE results, numerical simulations were performed using the two-dimensional FDTD method with a boundary treatment of perfectly matched layers. In the simulation, we studied the transmission characteristics of an optical pulse in the infiltrated waveguide of Fig. 5 with
In summary, we investigated the slow light in a line-defect APCW. By altering the outer radius of the second row of the annular air holes adjacent to the center of the waveguide, and selectively injecting optoliquid as a post-processing method, high-performance slow light with a wide bandwidth of 58.4 nm, large NDBP value of 0.502, and low GVD of 10^{5} (ps^{2}/km) could be obtained in the optical-communication window for a silicon-on-insulator structure. Our numerical results demonstrate that this approach allows researchers to exploit the proposed structure for ultracompact low-dispersion devices in the slow-light regime. Admittedly, the current work does not provide an exhaustive parameter search. Other APCW geometries might provide better performance.
Current Optics and Photonics 2019; 3(5): 438-444
Published online October 25, 2019 https://doi.org/10.3807/COPP.2019.3.5.438
Copyright © Optical Society of Korea.
Feng Kuang^{1}, Feng Li^{2}, Zhihong Yang^{2,*}, and Hong Wu^{2,*}
^{1}
Correspondence to:yangzhihong@njupt.edu.cn, wuhong@njupt.edu.cn
In this theoretical study, a line-defect photonic-crystal waveguide hosted in an annular photonic crystal was demonstrated to provide high-performance slow light with a wide band, low group-velocity dispersion, and a large normalized delay-bandwidth product. Combined with structural-parameter optimization and selective optofluid injection, the normalized delay-bandwidth product could be enhanced to a large value of 0.502 with a wide bandwidth of 58.4 nm in the optical-communication window, for a silicon-on-insulator structure. In addition, the group-velocity dispersion is on the order of 10^{5} (ps^{2}/km) in the slow-light region, which could be neglected while keeping the signal transmission unchanged.
Keywords: Annular photonic crystals, Slow light, Normalized delay-bandwidth product
In recent years, slow light in photonic-crystal waveguides (PCWs) has attracted much attention, since the effect remains excellent at room temperature and corresponding devices can be fabricated using traditional semiconductor technologies, providing many potential advantages in signal processing, optical storage [1], tunable delay [2], modulator and filter [3-5]. Generally a PCW is obtained by introducing a line defect into a perfect PC structure, which results in waveguide modes within the photonic band gap of the host PC and excites slow light near the Brillouin zone’s edges. The slow-light performance parameters of the PCWs to which attention is usually paid are the group index
An annular photonic crystal (APC) [15] is an unusual type of PC structure composed of a two-dimensional (2D) lattice of annular dielectric rods in air, or annular air voids in a dielectric background. This structure has been proposed to achieve a large absolute band gap [16], polarization-independent slow light [17], and polarization beam splitting [18]. Because it is a composite unit, an APC presents more possibilities than a normal PC in dispersion engineering. Therefore, in this research we chose an APC as the host of the PCWs, to explore the possibility of obtaining flat-band slow light. Combined with structural-parameter modification and selective optofluidic injection, optimized APCWs can support high-performance slow light with a constant group index, broad bandwidth, and low group-velocity dispersion.
Inspired by reference 16, we designed an APC slab based on a triangular lattice above a SiO_{2} layer with a refractive index of 1.45. The remaining portion within the slab was silicon (Si) with a refractive index
To save calculation time, it was necessary to calculate the dispersion properties of the APC slabs using a 2D simulation instead of a 3D simulation. As 2D approximation methods, the effective-index method [19, 20] and effective-period method [12, 21] have been successfully applied to the design of PC devices. Especially in Ref. [21], the latter method was shown to provide more accurate estimation of device behavior than the former. Therefore, we utilized 2D simulations by means of the effective-period method. In this method, the 2D effective period for our structure was calculated to be , where
A line-defect APC waveguide with as formed by removing a row of annuli in the
Based on previous work, some parameters are known to influence the dispersion, to obtain polarization-independent waveguiding and slow light in 2D APCWs [17, 22]. Such parameters include the radii and positions of the first two rows of the annuli, the width of the waveguide, and so on. To achieve a flat band, we altered the outer radius
The normalized delay-bandwidth product (NDBP), a comprehensive index for evaluating the slow-light performance of an APCW, can be calculated by [23, 24]
where and Δ
Usually the region of dispersion in relation to group index values within [5, 25] can be defined as an acceptable region for slow light applications.
Applying the above criterion, the group indices corresponding to
Next, to improve the dispersion, optofluid infiltrations with different refractive indices
As can be seen in Fig. 4(a), for
Then we turned to the case of
TABLE 1.. Details of the group indices and the corresponding GVD, flat band’s center wavelength
To illustrate the advantages of APCs over normal PCs in slow-light dispersion engineering, we compared the results of our current work to the previously reported results proposed by line-defect PCWs hosted in 2D air-hole or rod PCs. Our best NDBP value of 0.502 was higher than the results reported in Ref. [26] (NDBP = 0.48), Ref. [7] (NDBP = 0.465), and Ref. [12] (NDBP = 0.469).
As shown in Fig. 5(a), it can be found that in the same dispersion curve there are two regions where the slopes of the curves differ greatly. One region has a larger slope, because the corresponding group index is small, resulting in a large group velocity, called a
Another important issue for slow-light devices is group-velocity dispersion (GVD), which causes pulse broadening and signal distortion [24]. The GVD, calculated by evaluating
To verify the PWE results, numerical simulations were performed using the two-dimensional FDTD method with a boundary treatment of perfectly matched layers. In the simulation, we studied the transmission characteristics of an optical pulse in the infiltrated waveguide of Fig. 5 with
In summary, we investigated the slow light in a line-defect APCW. By altering the outer radius of the second row of the annular air holes adjacent to the center of the waveguide, and selectively injecting optoliquid as a post-processing method, high-performance slow light with a wide bandwidth of 58.4 nm, large NDBP value of 0.502, and low GVD of 10^{5} (ps^{2}/km) could be obtained in the optical-communication window for a silicon-on-insulator structure. Our numerical results demonstrate that this approach allows researchers to exploit the proposed structure for ultracompact low-dispersion devices in the slow-light regime. Admittedly, the current work does not provide an exhaustive parameter search. Other APCW geometries might provide better performance.
TABLE 1. Details of the group indices and the corresponding GVD, flat band’s center wavelength