High-Efficiency Two-Port Encapsulated Low-Contrast Grating withSuppressed Zeroth Order under Normal Incidence

Author NameAffiliation
Bowen GongDepartment of Engineering and Transportation, South China University of Technology, Guangzhou 510640, China
Huiying WenDepartment of Engineering and Transportation, South China University of Technology, Guangzhou 510640, China
Hongtao LiGuangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou 511443, China

Abstract:
A two-port encapsulated low-contrast grating with suppressed zeroth order under normal incidence is described in this paper. Based on such grating configuration, the improved efficiency and spectral bandwidth of the first order for TE and TM polarizations with a designed period of 1860 nm can be obtained. On the one hand, some of the accurate grating parameters were numerically optimized utilizing a rigorous coupled-wave analysis; on the other hand, the inherent physical mechanism suppressing the zeroth order through an encapsulated fused-silica grating was adequately interpreted on account of a simplified modal method. Encapsulated grating with a cover layer cannot be simply considered as adding a coating on it. Compared with reported surface-relief grating, all parameters of encapsulated grating should be re-optimized and the optimized performances of encapsulated grating were greatly improved. Therefore, the encapsulated grating can be potentially applied in writing fiber Bragg gratings.
Key words:encapsulated gratingsuppression of the zeroth orderimproved diffraction efficiencyimproved spectral bandwidth
DOI：10.11916/j.issn.1005-9113.20016
CLC NUMBER:O436
Fund:

Bowen Gong, Huiying Wen, Hongtao Li. High-Efficiency Two-Port Encapsulated Low-Contrast Grating with Suppressed Zeroth Order under Normal Incidence[J]. Journal of Harbin Institute of Technology (New Series), 2021, 28(5): 28-37. DOI: 10.11916/j.issn.1005-9113.20016
Fund Sponsored by the National Natural Science Foundation of China (Grant No.51578247) Corresponding author Huiying Wen. E-mail: hywen@scut.edu.cn
Hongtao Li. E-mail: 18814116735@163.com Article history Received: 2020-03-09



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High-Efficiency Two-Port Encapsulated Low-Contrast Grating with Suppressed Zeroth Order under Normal Incidence
Bowen Gong¹, Huiying Wen¹, Hongtao Li²
1. Department of Engineering and Transportation, South China University of Technology, Guangzhou 510640, China;
2. Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou 511443, China
Received: 2020-03-09
Sponsored by the National Natural Science Foundation of China (Grant No.51578247)
Corresponding author: Huiying Wen. E-mail: hywen@scut.edu.cn;
Hongtao Li. E-mail: 18814116735@163.com.

Abstract: A two-port encapsulated low-contrast grating with suppressed zeroth order under normal incidence is described in this paper. Based on such grating configuration, the improved efficiency and spectral bandwidth of the first order for TE and TM polarizations with a designed period of 1860 nm can be obtained. On the one hand, some of the accurate grating parameters were numerically optimized utilizing a rigorous coupled-wave analysis; on the other hand, the inherent physical mechanism suppressing the zeroth order through an encapsulated fused-silica grating was adequately interpreted on account of a simplified modal method. Encapsulated grating with a cover layer cannot be simply considered as adding a coating on it. Compared with reported surface-relief grating, all parameters of encapsulated grating should be re-optimized and the optimized performances of encapsulated grating were greatly improved. Therefore, the encapsulated grating can be potentially applied in writing fiber Bragg gratings.
Keywords: encapsulated gratingsuppression of the zeroth orderimproved diffraction efficiencyimproved spectral bandwidth
0 Introduction Advantageous applications of the suppression of the zeroth order based on micro-optic integrated grating can be found in Bragg-grating device^[1], high-efficiency-efficiency multilayer dielectric gratings^[2], distributed feedback semiconductor lasers^[3-7], high-volume extreme-ultraviolet lithography^[8], and red (660 nm) vertical cavity surface-emitting lasers^[9]. In particular, in order to ensure the single longitudinal mode operation, many reports focused on decreasing the efficiency of zeroth order and increasing the efficiency of the first order^[3-7]. In addition, a sampled Bragg grating could cancel the zeroth-order well, and that could be applied in dual-wavelength lasing generation and OCDMA En/decoding^[10]. In fact, the suppression of the zeroth-order binary diffraction gratings has been reported with good performance based on some conventional construction methods. Gamet et al.^[11] reported a high-contrast binary grating that cancels the zeroth order, which included a ridge of Si₃N₄ with a high refractive index and a substrate of SiO₂ with a relatively low refractive index. Sun et al.^[12] designed a phase mask grating structure comprised of a high-index HfO₂ grating ridge and a fused-silica substrate to suppress the zeroth order with excellent properties. Trost et al.^[8] investigated and fabricated Mo/Si multilayers grating that could successfully achieve a high IR-suppression in the zeroth order. In Refs. [11-12], researchers employed the high-contrast grating to cancel the 0th order. Their designed grating is composed of a grating ridge with high-refractive-index material (e.g., Si₃N₄ or HfO₂) and a grating substrate with low-refractive-index material (e.g., fused silica). To manufacture such high-contrast grating, high-refractive-index material should be primarily deposited on the fused-silica substrate by using low-pressure chemical vapor deposition (LPCVD) method. However, to fabricate the proposed low-contrast grating, the grating can be directly fabricated using phase mask and etching with no additional material deposited on the substrate. Therefore, compared with fabricating low-contrast grating, high-contrast and multi-layer gratings can be manufactured with disadvantages of higher cost and more complicated production processes.
Although the various binary grating configurations reported above can not only cancel the zeroth order well but also yield excellent properties, the complex grating structures restricted them from delving into actual optical applications. Unlike a conventional two-port low-contrast grating beam splitter under Bragg incidence^[13] or second Bragg incidence^[14], it is not easy for low-contrast grating to suppress the zeroth order under normal incidence. In recent years, Wang^[15] numerically designed low-contrast surface-relief fused-silica binary grating based on a rigorous coupled-wave analysis (RCWA)^[16] and a modal method^[17]. Intriguingly, when the designed grating period exceeded 2λ, it could also cancel the zeroth order very well. However, the obtained efficiencies of the first orders were only 46.15% and 43.60% for TE (electric field oscillating parallel to the grating ridges) and TM (magnetic field oscillating parallel to the grating ridges) polarizations, respectively. In practice, in order to implement a fiber Bragg grating with high efficiency, the results for the first order should be improved.
In this paper, encapsulated fused-silica low-contrast binary diffraction grating was theoretically and numerically designed based on a numerical RCWA optimization and a theoretical simplified modal method (SMM) explanation. The validity can be indirectly verified by some reported grating-based works. For numerical calculation and theoretical analysis, some grating-based elements have been designed and studied by the same rigorous coupled-wave analysis and modal methods. Through lithography and dry etching, the designed elements have been demonstrated in experiments^[18-20]. Therefore, the encapsulated low-contrast grating presented in this paper can be potentially verified by using similar techniques. Encapsulated grating with a cover layer cannot be simply considered as adding a coating on it. Compared with a surface-relief low-contrast grating^[15], all the parameters of encapsulated surface-relief low-contrast grating should be re-optimized. In addition, the encapsulated grating can effectively reduce reflection and improve the transmission efficiency. More importantly, our optimization results show enhancement in the efficiencies of the first order and incident spectral bandwidths for two polarizations. In addition, the fabrication tolerance of the grating was also investigated.
In this paper, the encapsulated low-contrast grating was firstly numerically optimized by RCWA for two-port with the suppressed zeroth order under normal incidence. Secondly, the physical mechanism for propagation was explained by modal method. Thirdly, the spectral bandwidth was investigated. Lastly, the performance by encapsulated grating in this paper was compared with reported surface-relief grating. Different from other conventional optical devices, the sub-wavelength grating has the merit of high spatial frequency, and it can be interesting if the proposed sub-wavelength grating is employed to be directly written into a fiber Bragg grating by using zeroth-order nulled phase mask technique. In addition, a 32-nm broad spectral bandwidth for the proposed grating can be of potential assistance for developing future dense wavelength division multiplexing (DWDM) system.
1 Grating Design and Optimization The encapsulated fused-silica grating with suppression of the zeroth order is presented schematically in Fig. 1. The whole grating structure is comprised of a cover layer, grating ridge, grating groove, and a substrate. It is worth noting that the grating cover layer, ridge, and substrate are constitutive of the fused silica with a refractive index of n₂=1.45. The grating groove is air, with a refractive index of n₁=1.00. A plane wave (TE or TM polarization) vertically irradiates the top of the grating and the grating only diffracts into the positive and negative first orders with two diffraction angles of θ₁ and θ_-1, respectively. In the grating parameters, the duty cycle of f can be defined as the ratio of grating ridge of b to grating period of d. Brückner et al.^[21] reported an encapsulated subwavelength grating resonant reflector. Based on guided-mode resonant theory, they numerically calculated the optimized cover layer with very thin thickness of 337 nm^[21]. Since coupling efficiency of reflective higher grating orders for grating modes are very weak, the tolerance of the cover layer thickness is rather low. Different from the above reported work, Clausnitzer et al.^[22] designed and fabricated a transmission encapsulated grating for reducing the reflection. In that work, they chose 2-mm-thick fused-silica grating substrate and 3-mm-thick fused-silica grating cover layer for reducing the Fresnel reflection in the whole simulation and measurement process. As a matter of fact, if the cover layer is too thin, the grating diffraction efficiency can be easily affected by the different cover layer thickness. However, if the cover layer is thick enough, the diffraction efficiency cannot be influenced by the thickness of cover layer. In this work, in order to simplify actual fabrication process and save fabrication cost, the grating substrate and cover layer with thicknesses of 2 mm and 3 mm were selected in a real device, respectively.
Fig.1
Fig.1 Schematic illustration of low-contrast fused-silica encapsulated grating with suppressed zero order


The grating groove depth and period are h and d, respectively. As the efficiency of the negative first order is equal to that of the positive first order, only the efficiency of the first order needs to be considered in this paper. Fig. 2 depicts the diffraction efficiency of the first order versus the groove depth and grating period for TE polarization (Fig. 2(a)) and TM polarization (Fig. 2(b)). Different color of contour line corresponds to different diffraction efficiency from 0 to 45%. As can be seen from the optimized groove depth of 1.22 mm and the grating period of 1860 nm, improved diffraction efficiencies of 46.572% and 44.649% in the first order are obtained for TE and TM polarizations with a given duty cycle of 0.21, respectively.
Fig.2
Fig.2 Optimized grating groove depth and period versus diffraction efficiency of the first diffraction order with the optimized duty cycle of 0.21 and incident wavelength of 800 nm for TE polarization and TM polarization based on RCWA


After determining the grating parameters, the efficiency of each order around the optimized period and grating groove depth can be obtained. Fig. 3 shows the efficiency versus the grating period and groove depth with a duty cycle of 0.21 under normal incidence. Different color corresponds to different diffraction efficiency from 0 to 50% or 45% as exhibited in the scaling of pseudo color. In Fig. 3, with a depth of 1.22 μm and a period of 1860 nm, efficiencies of just 2.749% and 4.059% can be diffracted into the zeroth order for TE and TM polarizations, respectively. Therefore, the designed encapsulated fused-silica low-contrast grating can be shown to suppress the zeroth order under normal incidence. As a matter of fact, in a practical dry etching process, fabrication errors appear naturally. Thus, some of the grating parameters (i.e., grating groove depth and grating duty cycle) can deviate from the optimized grating results. One may have to consider fabrication tolerances for effectively and expediently manufacturing a grating device.
Fig.3
Fig.3 Efficiency of the zeroth order and the first order versus encapsulated grating depth and period with a given grating duty cycle of 0.21 and wavelength of 800 nm for TE polarization in the zeroth order, TE polarization in the first order, TM polarization in the zeroth order, and TM polarization in the first order


Duty cycle is also an important parameter in grating. When the duty ratio of the manufactured grating deviates, the effect of zero-order elimination will be affected. As the duty cycle and grating groove depth diverge from the grating parameters, the available fabrication tolerances can be acquired from Fig. 4. Different color corresponds to different diffraction efficiency from 0 to 50% or 45% as shown in the scaling of pseudo color. In Fig. 4, within the range of 0.19 < f < 0.23 and 1.21 μm < h < 1.23 μm, it can be simultaneously found the efficiencies of the first order more than 46% for TE polarization and 44.5% for TM polarization. Moreover, efficiencies of the zeroth order for both polarizations are low, which are less than 5%.
Fig.4
Fig.4 Efficiency versus fabrication tolerances of grating depth and duty cycle with the optimized grating period of 1860 nm and wavelength of 800 nm for TE polarization in the zeroth order, TE polarization in the first order, TM polarization in the zeroth order, and TM polarization in the first order


2 Theoretical Interpretation Based SMM Although one can directly obtain the accurate grating parameters by optimizing and calculating the RCWA code simply based on a numerical operation, it does not help to delve into the inherent physical essence of grating. At this point, a forceful SMM is employed to explain the intact coupling mechanism in the grating region. In fact, the operating principle of SMM can be treated as a Mach-Zehnder interferometer. As for the low-contrast fused-silica encapsulated grating, the incident plane light can stimulate five grating modes in such grating region under normal incidence. Each mode propagates in the grating ridge with a different effective index, and the effective index for each polarization can be calculated based on following the eigenfunctions for the TE polarization^[17]:
$\begin{aligned}F\left(n_{\text {eff }}^{2}\right)=& \cos k_{1}(1-f) d \cdot \cos k_{2} f d-\\& \frac{k_{1}^{2}+k_{2}^{2}}{2 k_{1} k_{2}} \cdot \sin k_{1}(1-f) d \cdot \\& \sin k_{2} f d=\cos \delta d\end{aligned}$ (1)
For the TM polarization:
$\begin{aligned}F\left(n_{\text {eff }}^{2}\right)=& \cos k_{1}(1-f) d \cdot \cos k_{2} f d-\\& \frac{n_{2}^{4} k_{1}^{2}+k_{2}^{2}}{2 n_{2}^{2} k_{1} k_{2}} \cdot \sin k_{1}(1-f) d \\& \sin k_{2} f d=\cos \delta d\end{aligned}$ (2)
where
$\begin{aligned}&k_{i}=k_{0} \sqrt{n_{i}^{2}-n_{\text {eff }}^{2}} \\&\delta=k_{0} \sin \theta, k_{0}=2 n_{2} {\rm{ \mathsf{ π} }} / \lambda\end{aligned}$ (3)
Under normal incidence, F(n_eff²) is equal to 1; utilizing an optimized duty cycle of 0.21 and a period of 1860 nm, the two eigenfunctions can be solved. Therefore, the five effective indices for the five grating modes in each polarization are as follows:
$n_{0, \text { eff }}^{\mathrm{TE}}=1.3128, n_{1, \text { eff }}^{\mathrm{TE}}=0.9774 $
Or
$n_{2, \text { eff }}^{\mathrm{TE}}=0.9633, n_{3, \text { eff }}^{\mathrm{TE}}=0.7034, n_{4, \text { eff }}^{\mathrm{TE}}=0.6368$
$n_{0, \text { eff }}^{\mathrm{TM}}=1.2483, n_{1, \text { eff }}^{\mathrm{TM}}=0.9702$
$n_{2, \text { eff }}^{\mathrm{TM}}=0.9645, n_{3, \text { eff }}^{\mathrm{TM}}=0.6773, n_{4, \text { eff }}^{\mathrm{TM}}=0.6533$
For each polarization, an energy exchange takes place between the incident light and each grating mode. The exchange ability can be quantified based on the following overlap integral^[18]:
$\begin{aligned}t_{m}^{\mathrm{in}}=&\left\langle E_{y}^{\mathrm{in}}(x) \leftrightarrow u_{m}(x)\right\rangle=\\& \frac{\left|\int_{0}^{d} E_{y}^{\mathrm{in}}(x) u_{m}(x) \mathrm{d} x\right|^{2}}{\int_{0}^{d}\left|E_{y}^{\mathrm{in}}(x)\right|^{2} \mathrm{~d} x \int_{0}^{d}\left|u_{m}(x)\right|^{2} \mathrm{~d} x}\end{aligned}$ (4)
where E_yⁱⁿ(x) and u_m(x) are the incident light and amplitude of electric field in mth grating mode, respectively. According to the calculation of the overlap integral, for the TE polarization, it is obtained that the incident light exchanges mainly 40.62% and 56.36% of its energy with mode 0 and mode 2, respectively. For TM polarization, light can exchange 38.42% and 47.33% of its energy with mode 0 and mode 2, respectively. It can be seen that energy exchanges between the incident wave and mode 1, mode 3, and mode 5 are limited, thus only mode 0 and mode 2 are considered during the whole modal coupling course. To intuitively observe the modes inside the grating, three modal profiles are prohibited in Fig. 5, where mode 0 and mode 2 are symmetrical modes in a grating period, while conversely, mode 1 is an asymmetrical mode in the grating region.
Fig.5
Fig.5 Distributions of modal profiles with the fixed duty cycle of 0.21 and wavelength of 800 nm in an individual period of 1860 nm for TE polarization and TM polarization


At the bottom of low-contrast grating, different modes can be coupled into different diffraction orders. The theoretical efficiencies of the diffraction orders are determined as^[18]
$\eta_{0}=1-4 M(1-M) \sin ^{2}(\Delta \phi / 2) $ (5)
$\eta_{1}=4 N^{2} \sin ^{2}(\Delta \phi / 2) $ (6)
$M=\frac{1}{d} \int_{0}^{d} t_{0}^{\mathrm{in}} u_{0}(x) \mathrm{d} x$ (7a)
$N=\left|\frac{1}{d} \int_{0}^{d} t_{0}^{\mathrm{in}} u_{0}(x) \cos \frac{2 {\rm{ \mathsf{ π} }}}{d} x \mathrm{~d} x\right|$ (7b)
$\Delta \phi=\frac{2 {\rm{ \mathsf{ π} }}}{\lambda}\left(n_{0, \text { eff }}-n_{2, \text { eff }}\right) h$ (7c)
where M and N are transmission coefficients, Δ? represents the accumulated phase difference.
Based on the solution for the amplitude of the electrical or magnetic field and energy exchanging values, the results for two transmission coefficients can be obtained. Therefore, the calculated results for M and N are 0.4062 and 0.3035 for TE polarization, respectively. On account of the optimized grating parameter, a phase difference of 3.3489 is obtained. For TM polarization, M, N, and Δφ are 0.3842, 0.2874, and 2.7193, respectively. From the results obtained, the diffraction efficiencies of the zeroth and the first orders can be inferred based on SMM. For TE polarization, a theoretical efficiency of 4.55% in the zeroth order can be obtained. For TM polarization, a theoretical efficiency of 9.52% is calculated. Therefore, such low-contrast fused-silica encapsulated grating can also theoretically suppress the zeroth order based on SMM. In addition, except SMM, some new frameworks for grating also appear, which can bring more profoundly significant meanings in new grating theory^[23-24].
In order to compare the difference calculated by these two methods, the rigorous coupled-wave method and the simplified modal method were used to study the beam splitting effect of the grating. Fig. 6 depicts the contrast of diffraction efficiencies on account of RCWA and SMM corresponding to the groove depth of the low-contrast encapsulated grating for the two polarizations. The results of the numerical calculation based on RCWA appear consistent with those of the theoretical interpretation based on SMM. In essence, the suppression of the zeroth order can be well illustrated and realized using accurate numerical optimization and powerful theoretical predication based on the two-beam interference theory. As shown in Fig. 6, because of ignoring the modal inflection by using the SMM, the calculated diffraction efficiencies are different in some degree by using SMM and RCWA. Furthermore, the modal reflection can be neglected by using SMM for calculating diffraction efficiencies.
Fig.6
Fig.6 Contrast in diffraction efficiencies on account of RCWA and SMM corresponding to the groove depth of the low-contrast encapsulated grating with a duty cycle of 0.21 and period of 1860 nm for TE polarization and TM polarization


3 Discussion of Incident Spectral Bandwidth In order to confirm whether the grating in this article has practical value, the spectral bandwidth needs to be analyzed.In fact, the chromatic dispersion of the fused silica in the study of the spectral bandwidth should be considered. In order to fully investigate such performance, the comparison of diffraction efficiencies of the first and the zeroth orders can be calculated based on considering and ignoring chromatic dispersion conditions with different incident wavelengths as shown in Fig. 7. It can be concluded from Fig. 7 that the differences obtained by comparing corresponding efficiencies for two conditions are comparatively small. Thus, the grating diffraction efficiency cannot be greatly influenced by the chromatic dispersion of the fused silica.
Fig.7
Fig.7 Calculated comparison of diffraction efficiencies of the first and the zeroth orders based on considering and ignoring chromatic dispersion conditions with different incident wavelengths for TE polarization and TM polarization


As demonstrated in Fig. 7(b), efficiencies of the TE-polarized light in the first order are in excess of 46% in the spectral scope of 782-818 nm. Efficiencies in excess of 44% within the wide spectrum of 751-814 nm are obtained for the TM-polarized light. Thus, for both polarizations, a broad incident spectral region of 782-814 nm is obtained. To guarantee high efficiencies in the first order and suppress efficiencies in the zeroth order, it is identified that efficiencies less than 5% in the zeroth order for TE and TM polarizations are acquired within a wide wavelength range of 775-810 nm.
In order to prove that the encapsulated grating can effectively reduce reflection and improve the transmission efficiency, the reflection spectra are shown in Fig. 8, which illustrates the comparison of reflection efficiencies in the 0th order and the 1st order between encapsulated grating and surface-relief grating with the optimized grating duty cycle of 0.21 and grating depth of 1.22 μm for TE and TM polarizations under normal incidence. As can be seen from Fig. 8, efficiencies in the 0th order for two polarizations of the encapsulated grating are much lower than the calculated results of the surface-relief grating. Therefore, based on the calculated results in Fig. 8(a) and (b), it can be concluded that the designed encapsulated grating can cancel the 0th order better than that of surface-relief grating with the given grating duty cycle of 0.21 and grating depth of 1.22 μm at a wavelength of around 800 nm.
Fig.8
Fig.8 Comparison of reflection efficiencies in the 0th order and the 1st order between encapsulated grating and surface-relief grating with the optimized grating duty cycle of 0.21 and grating depth of 1.22 μ m for TE and TM polarizations under normal incidence


The proposed encapsulated low-contrast grating requires additional processes to cover the top layer compared with the surface-relief grating structures. Therefore, the fabrication process should be described in detail. First, chromium layer and positive photoresist layer are evaporated on the cleaned fused-silica wafer. Next, a holographic lithography technology based on laser interference and chromium mask are employed to form the needed grating pattern. After that, the grating can be transferred into inductively coupled plasma equipment used for etching and the needless chromium mask can be removed using chemical solution. Finally, the fused-silica surface-relief grating can be fabricated. For manufacturing the encapsulated fused-silica grating, a cleaned and dried fused-silica wafer should first be prepared. Next, the as-prepared surface-relief grating should be kept clean and dry in high pressure environment.Finally, by means of applying the 5 kg weight, the upper surface of grating and the covered fused-silica wafer are activated and contacted using oxygen plasma under 100 ℃ for 72 h.
It is certain that the diffraction efficiencies of the surface-relief grating are lower than the efficiencies of the encapsulated grating due to the Fresnel reflections. To solve such problem to improve the laser-damaged threshold of the designed device, and reduce the reflections of the proposed encapsulated grating, an optical anti-reflection film can be added on the surface of the encapsulated grating. Such film has relatively low refractive index. In order to realize the destructive interference of the reflective light, the thickness of anti-reflection film should be designed as 200n nm (n represents the positive integer), where our optimized incident wavelength is 800 nm. Meanwhile, the optical path difference (OPD) of two adjacent reflective lights can reach π. Ultimately, the reflective lights can be well suppressed based on this optical interference effect.
In fact, compared with the research in Ref.[15], the improvement of many important optical performances may be achieved in this work. Therefore, many important optical performances comparison between the reported work in Ref.[15] and our work is in Table 1. Firstly, with the optimized grating parameters, the improvement of efficiency in the 1st order compared with the efficiency in Ref.[15] can be obtained. Next, when the efficiencies in 1st order for TE and TM polarization are more than 45.44% and 43.11%, respectively, the ranges of fabrication tolerance for duty cycle of 0.03 or grating depth of 0.08 μ m or period of 180 nm of our grating can be much wider than reported duty cycle of 0.02 or grating depth of 0.06 μ m or period of 105 nm in Ref.[15]. Finally, based on the optimized parameters in Ref.[15] and our work, the spectral bandwidth in range of 785-805 nm in Ref.[15] and in range of 782-818 nm in our work can be calculated, where efficiencies are more than 46% for TE polarization in the 1st order and efficiencies can be more than 43.5% for TM polarization in the 1st order. Therefore, our spectral bandwidth of 36-nm window is much broader than the reported 20-nm window in Ref.[15]. In brief, it is an efficient approach that can restrain the reflection and improve the transmission efficiency. In addition, it can provide an effective way to enhance the performances of the various diffraction grating elements.
表 1
Table 1 Performances comparison between the reported work in Ref.[15] and our work with the optimized various grating parameters Related work TE(%)/TM(%), max(η_1st) Fabrication tolerance η_1st^TE > 45.44%, η_1st^TM > 43.11%Spectral bandwidth(nm) η^TE _1st > 46%, η_1st^TM > 43.5%
f or h(μm) or d(nm)
Reported work 46.150/43.600 0.29-0.31 (0.02) 1.05-1.11 (0.06) 1642-1747 (105) 785-805(20)
This work 46.572/44.649 0.20-0.23 (0.03) 1.19-1.27 (0.08) 1778-1958 (180) 782-818(36)

Table 1 Performances comparison between the reported work in Ref.[15] and our work with the optimized various grating parameters


4 Conclusions In this paper, a low-contrast fused-silica encapsulated binary grating for suppressing the zeroth order with a relatively simple configuration was theoretically and numerically designed based on RCWA and SMM. Compared with the reported high-contrast and multi-layer gratings for canceling the zeroth order^[11-12], the designed grating has the merits of easy fabrication and low cost. Compared with the reported surface-relief low-contrast fused-silica grating^[15], the encapsulated grating not only suppresses the zeroth order effectively but also brings improved high diffraction efficiency into the first order. Through optimization, the moderate fabrication tolerance and wider incident spectral bandwidths with an optimized period of 1860 nm can be found. Since the encapsulated fused-silica low-contrast grating has been achieved experimentally^[25], the grating has such potential application domains as fiber Bragg gratings with the merits of high efficiency in the first order, and low efficiency in the zeroth order.
On the one hand, it should be noted that the proposed encapsulated dielectric low-contrast diffraction grating is quite different from the reported surface-relief dielectric transmission grating with suppressed zeroth diffraction order in Ref.[15]. Firstly, the grating in Ref.[15] is a simple surface-relief grating configuration, while, in this paper, an encapsulated low-contrast binary grating with a fused-silica cover wafer was designed, which can be functioned as a Fabry-Perot resonator. Secondly, the efficiency of the first order in Ref.[15] is not so high. Nevertheless, a cover layer coated on our designed grating device can improve the transmission efficiency of the first order by suppressing the Fresnel reflection on the surface of the grating and protect grating surface against scratches^[26-27]. Furthermore, compared with the surface-relief grating^[15], once the surface of grating can be coated on a cover layer, the encapsulated grating parameters need to be redesigned. Last but not the least, the incident performance is not mentioned in Ref.[15]. However, in this paper, an important broad incident spectral bandwidth of 32-nm window has been investigated, which can be conveniently integrated into DWDM system.

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