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Abstract
[Opt. Express 31, 261562023 [CrossRef] ] shows an anomalous absorption of the echelle grating in TM polarization light near the pseudo-Brewster angle. On top of that, more generally, we relate the absorptions of echelle grating to the Al materials with an absorption spectral band. The blaze diffraction efficiencies (DEs), absorption strengths and electric field distributions, and the energy of non-blaze diffraction orders of the echelle are analyzed in detail. The computing reveals that the interaction between the incident light for TM polarization and the echelle structure leads to amplifying the absorption strength of Al materials with an absorption spectral band from visible to near IR. The deepening groove depth not only suppresses the absorption strength of the Al-echelle grating under TM polarization closer to the absorption spectra of Al materials but improves the light-collecting ability (LCA) at both polarizations. Therefore, the DE differences of different blaze wavelengths for the wideband blaze are explained. The Ag materials echelle with lower absorption is to further validate the results. From the point of view of the effects of absorption and LCA, the novel echelles with high DE can be designed and fabricated.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Echelle gratings are gratings with rough groove density but finely ruled groove shapes that work at high diffraction angles and orders [1–4]. Harrison introduced the concept of echelle gratings to precisely measure the wavelengths of complex atomic spectra and molecular spectra for the first time in 1949 [4]. In general, planar blazed gratings employ a low-order diffraction spectrum for which high angular scattering can only be achieved by increasing the number of etched grooves per millimeter of the grating [5]. However, due to manufacturing technology and cost, it has become difficult to accurately and uniformly etch 2400 lines/mm. In contrast, echelle gratings have fewer lines per millimeter, a larger blaze angle, a higher working order, a higher dispersion rate, and a very high spectral resolution of up to 106 [6,7]. In addition, the diffraction orders of echelle gratings are generally larger, from more than a few dozen to more than a hundred orders. Also, the spectrum of these spectral orders is often concentrated in a smaller angular range where the blaze efficiency is the highest. This means that echelle gratings can take advantage of the broadband blaze in the ultraviolet to infrared wavelength band [8]. Therefore, since the introduction of the echelle grating, it has played an important role in astronomy [9,10], spectral analysis [11,12], photolithography [13,14], optical communication [15,16], and thermospheric imaging [17].
Diffraction efficiency (DE) is one of the most critical parameters for echelle gratings, and its magnitude largely determines the energy transfer characteristics of applications such as high-resolution spectrometers, photolithography, and wavelength-division multiplexing, which are of great interest to researchers [12–16]. The DE of the echelle grating is defined as the ratio of the energy of the diffracted light to the energy of the incident light, and its magnitude is determined by the reflection and absorption properties of the grating surface material and the groove structure of the grating when given the incidence conditions [18–20]. Among them, the groove structure of the echelle grating, as the most variable factor, has been the focus of research. Early on, Engman et al. proposed that reducing the apex angle of the groove of the echelle grating could eliminate the defect effect of large groove edges and thus improve the DE [20,21]. Subsequently, Loewen et al. simulated and analyzed the variation curves of DE of echelle gratings with incident wavelength and incident angle to guide the application of echelle gratings [8]. Zhang et al. proposed that the high DE of echelle gratings mainly depended on optimizing the blaze angle and the groove depth and optimized and developed the r-2 echelle grating of 79 lines/mm [22]. To reduce the intensity difference between the spectral center and the edge, Shi et al. [23] changed the double-faced echelle grating into a multi-faceted grating, which broadened the spectral distribution of the grating in the spectral plane. Yang et al. studied the polarization effect of the echelle grating. They pointed out that polarization sensitivity could be suppressed by increasing the depth of the grooves, which could improve the DE [24]. Sadlowski et al. effectively suppressed the polarization sensitivity and achieved enhanced DE by plating a gold coating on the surface of an echelle grating [25]. In addition, the studies on the reflection and absorption properties of gratings have mainly focused on subwavelength structures. For example, Zhou et al. designed two Ti/Si/SiO2/Ti absorbers that can realize average absorption of 92% and 87% in the spectral ranges of 14-30 µm and 8-30 µm, respectively [26]. Pors et al. proposed a coupler that allows for high-efficiency unidirectional polarization-controlled excitation of surface plasmon polaritons [27]. To our knowledge, there is only one work on the absorption properties of echelle gratings, which points out the anomalous absorption of TM-polarized light by echelle gratings near the pseudo-Brewster angle [28]. It should be mentioned that this study only investigates the strong absorption effect of echelle gratings under a very large incident angle close to grazing incident just for the echelle grating with a right apex angle and a very large blaze angle not for the echelle with a deep groove depth and the high diffraction efficiencies.
It is obvious from the above investigations that increasing the groove depth and modulating the grating surface can improve the DE of an echelle grating. However, most of these studies do not provide particular reasons for improving DE. The research on the effect of DE on echelle grating absorption is nearly non-existent. If these related contents can be supplemented, it will undoubtedly bring new understanding and guidance to the optimized design and manufacture of echelle gratings.
In this paper, the effect of different groove depths on the DE of echelle gratings is analyzed in detail from two new perspectives: absorption and LCA. As far as we know, this is the first time to combine these two perspectives to study the DE of the echelle grating. Sec. 3 discusses the efficiency behaviors of echelle gratings under different conditions. Firstly, the phenomenon of significant diffraction energy loss at different wavelengths for a conventional Al-echelle grating with an apex angle of 90° is pointed out. Then, the diffraction performance of echelle gratings with various groove depths at various wavelengths is compared, and it is demonstrated that deepening the grating groove can reduce the diffraction energy loss. Further, in Sec. 4, spectral maps are used to analyze the LCA and absorption characteristics of echelle gratings with various groove depths at two polarizations, and specific reasons for the enhancement of DE by deep-groove gratings are provided. Next, the absorption behavior and the physical mechanism of the absorption enhancement of Al-echelle gratings under TM polarization are analyzed by combining the absorption bands of Al and the electric field distribution diagrams. Finally, in Sec. 5, the consistency from the Al and Ag gratings results confirms the findings and illustrates the generalizability of those findings. This work gives the reason for the difference in DE between different blaze wavelengths as well as essentially reveals the effect brought about by the groove depth on the DE, which undoubtedly brings many new views to the field of echelle gratings.
2. Grating model
Figure 1 shows the groove structure of the echelle grating. As shown in Fig. 1, the grating structure consists of two layers from top to bottom: the grating layer and the substrate. The z-axis is the normal direction of the grating, while the direction of the grating groove is parallel to the y-axis. The echelle grating's apex angle, blaze angle, period, and groove depth are denoted by α, β, d, and h, respectively. In particular, the grating period and the blaze angle are set to 12.5 µm and 64.43°, respectively, during the following study. The grating layer and substrate materials are aluminum, whose refractive index is given in Ref. [29]. In addition, the incident light source is a monochromatic plane wave, in which TM-polarized lines are in the xz plane and perpendicular to the direction of the incident light, while TE polarization is perpendicular to the xz plane. With constant values of grating period and blaze angle, the echelle grating with different apex angles will have different groove depths. For example, when the apex angle of the echelle grating is changed from the traditional right angle to an acute angle, its groove will become deeper. Moreover, PCGrate software based on the boundary integral equation method performs all the number simulation calculations in this paper.
3. Efficiency behavior of echelle grating under different conditions
3.1 Differences in DE of different wavelengths for echelle grating
We calculated the non-polarization DE as a function of incident wavelength for the echelle grating with an apex angle of 90° in Littrow mounting, as shown in Fig. 2. Here, the non-polarization DE is the average of the diffraction efficiencies at TE and TM polarizations. In Fig. 2, the spectral lines from left to right represent the −50th to −21st diffraction orders, respectively. Among them, the wavelength at the peak of the spectral line is the blaze wavelength of the corresponding diffraction order. The relationship between different blaze orders (m) and blaze wavelengths (λ) can be expressed by the following equation:
where θ refers to the angle of incidence and is set to 64.43°. Generally speaking, the echelle grating has the characteristic of a broadband blaze, meaning that the spectral lines in the spectrogram should be horizontal. For example, the spectral lines of the echelle grating with infinite conductivity in Fig. 2 tend to be in a horizontal state. However, in Fig. 2, it can be seen that the peaks of the spectral lines from left to right of the Al echelle grating are first in a state of rapid decline, followed by a slow rise and fall, and finally a rapid rise. In this case, the diffraction spectrum in the figure shows a concave trend. This indicates that the grating does not maintain its high efficiency in realizing broadband blaze. This phenomenon is caused by the weaker LCA and the higher absorption of the echelle grating when its groove is shallow, especially at TM polarization. This conclusion will be demonstrated in the following.
Fig. 2. The differences of non-polarization diffraction efficiency as a function of blaze wavelength for the echelle grating with Al and infinite conductivity.
3.2 Better blaze characteristics from echelle grating with deep groove depth both for TE and TM polarizations
First, we investigated the efficiency behavior of the echelle grating at different groove depths. Figure 3 shows the DE versus wavelength for echelle gratings with apex angles of 90° (groove depth of 4866.76 nm) and 80° (groove depth of 6660.25 nm) for TM and TE polarizations, respectively. Here, the corresponding blaze orders at different wavelengths (data points) are labeled in the figure. The 200-1050 nm wavelength band is selected as the studied wavelength band owing to its common use in high-resolution spectrometers. As shown in Fig. 3(a), the DE of the deep-groove grating at TE polarization is significantly improved relative to that of the shallow-groove grating over the entire investigated spectrum. Notably, the diffraction efficiencies of the deep- and shallow-groove gratings (D-SGGs) have the same trend with wavelength, decreasing slowly from the short to the long wavelength. This also leads to the difference between the two diffraction efficiencies remaining about 10%. In Fig. 3(b), the DE of the deep-groove grating at TM polarization is higher than that of the shallow-groove grating almost throughout the studied spectrum. In the 300-900 nm wavelength band, the improvement in the efficiency of the deep-groove grating relative to the shallow-groove grating remains above 10%.
Fig. 3. Diffraction efficiency of the blazed diffraction orders as a function of the blaze wavelength for Al-echelle grating with groove depths of 4866.76 nm and 6660.25 nm, respectively: (a) TE polarization, (b) TM polarization.
In addition, the fluctuation of the spectral lines of the grating in TM polarization is significantly larger than that in TE polarization, especially for the shallow-groove grating. Of these, the efficiency of the shallow-groove grating shows a rapid decrease after 450 nm and reaches a minimum near 600 nm, and begins to rise. This also results in the difference between the efficiencies of the D-SGGs reaching a maximum of nearly 37% near 600 nm. These results show that the spectral trend of the grating in TM polarization will dominate the non-polarization spectrum of the grating to some extent. In addition, combining Figs. 2 and 3, it can also be seen that the depression phenomenon in the spectral map of the right-angle grating is effectively resolved with deeper grooves, the most obvious being near the wavelength of 600 nm. Based on the above analysis results, the following preliminary conclusions can be drawn: The DE of the echelle grating with deeper grooves is significantly improved throughout the entire studied spectrum; this efficiency improvement exists in both polarizations, but the contribution from the TM polarization dominates in most of the spectra.
4. Absorption and energy distribution of non-blaze diffraction orders of echelle gratings
The substrate of the echelle grating is thick enough to make the grating virtually without transmission. In this case, the energy of the incident light is concentrated in the blaze order, dispersed in other non-blaze orders, and absorbed by the grating. For this reason, the reasons for the improved DE of the deep-groove grating will be investigated in the following, both in terms of light concentration and absorption. Here, the lower the total DE of the non-blaze order, the better the LCA of the grating.
Figure 4 shows the total DE of non-blaze orders as a function of wavelength for echelle gratings with different groove depths at two polarizations. Here, the non-blaze orders are the diffraction orders other than the corresponding blaze order labeled in the figure. In Fig. 4(a), the trends of the efficiency curves of D-SGGs at TE polarization are almost the same. Among them, the total efficiency of the non-blaze order of the deep-groove grating is lower than that of the shallow-groove grating throughout the spectrum, and the difference between the two efficiencies stays near 10%. Notably, the efficiency difference in Fig. 4(a) is almost the same as that in Fig. 3(a), both numerically and in the changing trend. Therefore, we deduce that the enhancement of DE by the deep-groove grating is mainly attributed to the improvement of LCA. In Fig. 4(b), the deep-groove grating in TM polarization has a higher LCA than the shallow-groove grating for most of the spectra (200-920 nm). Among them, the increase in the LCA of the deep-groove grating relative to the shallow-groove grating remains smooth in the 200-450 nm wavelength band. However, the LCA of the shallow groove grating decreases rapidly after 450 nm wavelength and reaches a minimum at around 600 nm wavelength, resulting in the deep-groove grating having a much higher LCA than the shallow-groove grating here. In addition, it is easy to find that the trend of the efficiency difference between the two curves in Fig. 4(b) is basically the same as that in Fig. 3(b), except that there is a certain difference in the magnitude of the values. This indicates that the enhancement of DE of the deep-groove grating relative to the shallow-groove grating at TM polarization is somewhat controlled by the increase in the LCA, especially near the wavelength of 600 nm. To visualize the LCA of the gratings at different wavelengths, the diffraction distributions of the D-SGGs at wavelengths of 451.03 nm (blaze order of −50th), 644.33 nm (blaze order of −35th), and 902.05 nm (blaze order of −25th) for the two polarizations are given in Figs. 4(c, d), respectively. From Figs. 4(c, d) show that the diffracted energy of D-SGGs is mainly distributed near the blaze order. Among them, the efficiency of the deep-groove grating is higher at the blaze order, while the efficiency of the shallow-groove grating is higher at non-blaze orders. Overall, the LCA of the echelle grating is enhanced in the studied spectra at different polarizations after the grating groove is deepened.
Fig. 4. Total diffraction efficiency of all the non-blazed diffraction orders as a function of the blaze wavelength for Al-echelle grating with the groove depths of 4866.76 nm and 6660.25 nm, respectively: (a) TE polarization, (b) TM polarization. Distributions of diffraction energy at wavelengths of 451.03 nm, 644.33 nm, and 902.05 nm for Al-echelle with the groove depths of 4866.76 nm and 6660.25 nm, respectively: (c) TE polarization, (d) TM polarizations.
Furthermore, we investigated the absorption characteristics of the echelle gratings with different groove depths. Figure 5 shows the absorption spectra of D-SGGs under TE and TM polarizations. In Fig. 5(a), the absorption of the D-SGGs at TE polarization is basically the same, and the efficiency difference between the two within the whole spectrum is close to 0. This result further proves that the improvement of the DE of the deep-groove grating at TE polarization is mainly contributed by its high LCA. In Fig. 5(b), the deep-groove grating in TM polarization can be seen to suppress absorption relative to the shallow-groove throughout the spectrum. Among them, the suppression of absorption of the deep-groove grating relative to the shallow-groove grating is more than 10% within the −45th order to the −25th order (the maximum value reaches 16.5%). In addition, an interesting phenomenon can be observed in Fig. 5: The absorption curves of D-SGGs at both polarizations show a general trend of gradually increasing from short to long wavelengths, reaching a maximum near the 820 nm wavelength and then starting to decline rapidly. As a whole, the absorption of the grating is much higher in the TM polarization than in the TE polarization, especially since the maximum absorption of the shallow-groove grating under the TM polarization is close to 35%.
Fig. 5. Absorption at different blazed wavelengths for Al-echelle grating with groove depths of 4866.76 nm and 6660.25 nm, respectively: (a) TE polarization, and (b) TM polarization.
In order to explain the above phenomenon, we give the real and imaginary parts of the refractive index of Al and its attenuation coefficient in Fig. 6(e). Here, the attenuation coefficient is defined as the ratio of the imaginary part of the refractive index to the real part. Then the absorption spectra of the Al mirror at both polarizations are calculated for different incident angles, as shown in Figs. 6(a, b). From Figs. 6(a, b), the Al mirror has a distinct absorption band (near 800 nm wavelength) at both polarizations. Significantly, the lowest point of the Al attenuation coefficient is at the same location as this absorption band. This suggests that the Al attenuation coefficient may dominate the appearance of the absorption band. In particular, the absorption band and efficiency under TM polarization are larger than those under TE polarization, especially at large incidence angles. Additionally, the absorption spectra under TE and TM polarizations have a common point: The absorption of the mirror decreases rapidly when the wavelength exceeds 920 nm. These results are undoubtedly in agreement with the absorption spectral lines in Fig. 5, including the trend of the spectrum lines, the peak position, and the absorption and the bandwidth for TM polarization are higher than those for TE polarization. To better visualize these results, a comparison of the absorption spectra of the Al grating and the Al mirror is given in Figs. 6(c, d). It should be mentioned that for the Al grating, the incident light is perpendicular to the working surface and does not directly illuminate the un-working surface. Therefore, the absorption spectra of the Al mirror are calculated in the case of normal incidence. In Fig. 6(c), the absorption curves of D-SGGs under TE polarization basically coincide with those of the Al mirror. This result indicates that Al metal's absorption basically dominates Al grating's absorption under TE polarization. In Fig. 6(d), although the overall trends of the three spectral lines are basically the same, the absorption of the D-SGGs is undoubtedly higher than that of the Al mirror. This result further illustrates that the absorption of the metal itself will control the absorption of the Al grating. However, in TM polarization, the absorption of the Al grating will be further enhanced relative to the Al itself under TM polarization. Especially in the absorption band of Al, the absorption enhancement effect of the grating is further enlarged. This is one of the reasons why the spectral line in Fig. 2 shows an obvious depression in the wavelength range of 800-900 nm. Fortunately, the absorption of the Al grating can be suppressed by deepening the groove, thus redistributing the energy of the diffraction order and enhancing the efficiency of the blazed order. To prove this point, Fig. 6(f) gives the relationship between the absorption of the middle-step grating with groove depth at different polarizations. In Fig. 6(f), the absorption of the Al grating at TE polarization is insensitive to the groove depth, which is basically the same as that of the Al mirror. At TM polarization, the absorption of the Al grating is gradually suppressed with the increase of the groove depth (from 3 µm to 12 µm) and gradually converges to the absorption of the Al mirror. These results are consistent with the above point.
Fig. 6. Absorption spectra of Al mirror at different incident angles: (a) TE polarization, (b) TM polarization. Absorption of Al grating (θ = 64.43°) and Al mirror (θ = 0°) at different blazed wavelengths: (c) TE polarization, (d) TM polarization. (e) Relationship between the real and imaginary parts of the refractive index of Al and its attenuation coefficient as a function of wavelength. (f) Absorption of the echelle grating as a function of groove depth.
As a result, the following conclusions can be obtained by combining Figs. 3–6: Under TE polarization, the improvement of the DE of the deep-groove grating is mainly provided by the improvement of the LCA; under TM polarization, the improvement of the DE of the deep-groove grating comes from better LCA on the one hand, and from the effective suppression of the light absorption on the other hand, which combine to realize the improvement of the efficiency of the blaze order.
Then, we further researched the physical mechanism of light absorption enhancement in the echelle grating at different groove depths. The absorption peak in Fig. 5(b) is chosen as the target wavelength (835.24 nm, blaze order of −27th), and the electric field distributions of the D-SGGs at both polarizations are shown in Fig. 7. In Figs. 7(a, b), it can be seen that most of the electric field energy of the D-SGGs at TE polarization is mainly distributed in the air, which verifies the low-absorption property of the Al grating at TE polarization. However, the electric fields of the D-SGGs under TM polarization are different. In Figs. 7(c, d), the un-working surfaces of the D-SGGs under TM polarization generate surface waves and experience some transverse transmission, which is the phenomenon of excited surface plasmon polariton (SPP) [30]. Due to the generation of SPP, part of the electric field energy is mainly distributed on the un-working surface of the gratings. The difference is that the surface waves on the un-working surface of deep-groove grating are weaker, while those of shallow-groove grating are stronger. Therefore, the enhancement of light absorption at different groove depths for the echelle grating can be attributed to the generation of SPP. This also explains the phenomenon in Fig. 5, i.e., why the absorption curves of the Al grating only show significant absorption enhancement at TM polarization. In addition, the deepening of the groove of the echelle grating can effectively suppress the intensity of the surface wave, thus reducing its optical absorption. This phenomenon is mainly because the boundary space of the echelle grating is different in the case of shallow and deep grooves. According to the electromagnetic theory of gratings, the electric or optical field is distributed in the groove space, from the incident beam to the edge of the un-working surface. The closer the incident optical field is to the edge of the groove, the stronger the interaction between them [22]. As shown in Fig. 1, a deep-groove grating creates more edge space relative to a shallow-groove grating, making the light field farther away from the edge of the un-working surface, gradually weakening the interaction between them.
Fig. 7. Electric field distributions at 835.24 nm wavelength for Al-echelle grating with groove depths of 4866.76 nm and 6660.25 nm, respectively: (a, b) TE polarization, (c, d) TM polarization. The observed ranges in the x and z directions are −12500 nm to 12500 nm and 0 nm to 8800 nm, respectively.
5. Diffraction performance of echelle grating made of Ag materials with low absorption spectrum band
To further verify the above findings and extend them to other metallic materials, the diffraction properties of the Ag echelle grating are studied at different groove depths. Since Ag has a strong absorption band in the wavelength range from UV to 400 nm, the spectral range of 400-1200 nm is chosen for the study. The diffraction efficiency versus wavelength for Ag gratings with groove depths of 4886.76 nm and 25205.11 nm are given in Figs. 8(a, b). The blaze order corresponding to each data point has been labeled in the figure. As seen in Figs. 8(a, b), the diffraction efficiencies of the echelle grating at both polarizations are substantially improved after deepening the grating groove. Further, the LCA of the Ag grating is discussed in Figs. 8(c, d). As shown in Figs. 8(c, d), the LCA of the deep-groove grating is undoubtedly much higher than that of the shallow-groove grating, especially at the TM polarization. Among them, combined with Figs. 8(a, c), it can be found that the improvement in DE of the deep groove grating relative to the shallow groove grating under TE polarization almost comes from the improvement in LCA. In TM polarization, the improvement in DE of the deep groove grating relative to the shallow groove grating is largely dominated by the LCA. These results are undoubtedly in agreement with the findings for Al gratings.
Fig. 8. Diffraction efficiencies of blazed and non-blazed diffraction orders as a function of blaze wavelengths for Ag-echelle grating with groove depths of 4866.76 nm and 25205.11 nm, respectively: (a, c) TE polarization, (b, d) TM polarization.
Finally, we discuss the absorption properties of Ag gratings with different groove depths in Fig. 9. Here, Figs. 9(a, b) show the absorption spectra of the Ag mirror versus the incident angle for TE and TM polarizations. Figure 9(c) shows the real and imaginary parts of the refractive index of Ag and its attenuation coefficient. Figure 9(d) shows the absorption of Ag gratings with different groove depths and Ag mirror for different blaze wavelengths for TE and TM polarizations. From Fig. 9(c), the attenuation coefficient of Ag gradually increases and stays at a higher level from 400 nm wavelength towards the long wavelength. As shown in Figs. 9(a, b), there are obvious absorption bands near 400 nm wavelength for the Ag mirror under TE and TM polarizations, which coincides with the lowest position of the attenuation coefficient of the Ag. In the range of small incident angles, the absorption of the mirror decreases significantly with increasing wavelength, especially after 550 nm when the absorption drops to less than 4%. This phenomenon is consistent with the trend of the absorption spectral lines in Fig. 9(d). In particular, at TE polarization, the absorptions of the D-SGGs and the mirror are almost identical. Under TM polarization, the Ag gratings have a further enhancement in absorption relative to the Ag mirror. Significantly, the deep-groove grating effectively suppresses the absorption enhancement of the structure, making the absorption of the deep-groove grating very close to that of the mirror. These results are undoubtedly in agreement with the findings in Al gratings, further proving the reliability of the above conclusions.
Fig. 9. Absorption spectra of Ag mirror at different incident angles: (a) TE polarization, (b) TM polarization. (c) Relationship between the real and imaginary parts of the refractive index of Ag and its attenuation coefficient as a function of wavelength. (d) Absorption of Ag grating (θ = 64.43°) and Ag mirror (θ = 0°) at different blazed wavelengths.
6. Conclusion
To summarize, we have researched the effects of the absorption characteristics and LCA of echelle gratings in different groove depths on the DE. According to research, the shallow-groove Al-echelle grating cannot maintain the high efficiency of the broadband blaze in the Littrow mounting. This is especially true in the visible wavelength band, where the loss of diffracted energy is very obvious. Deepening the groove while other conditions remain unchanged can effectively improve the DE of the Al-echelle grating, in which the TM polarization is dominant over TE polarization. The calculation results indicate that the deep-groove grating's enhancement of DE can be ascribed to improved LCA and effective absorption suppression. Specifically, the high LCA of the deep-groove grating contributes significantly to the improvement in DE in TE polarization. Under TM polarization, the enhancement of DE by deep-groove gratings is provided by improving LCA and absorption suppression. Further research shows that the absorption behaviors of Al gratings at different polarizations are dominated by the Al absorption band, particularly the absorption peaks appearing near the wavelength of 800 nm. Moreover, the electric field analysis shows the phenomenon that the absorption of the Al grating under TM polarization is enhanced due to the SPP excitation on the un-working surface This is why absorption in TM polarization is substantially higher than in TE polarization. Fortunately, deepening the echelle groove efficiently suppresses the SPP intensity at the un-working surface, reducing absorption. Finally, the findings related to Al-echelle gratings are successfully extended to Ag gratings, showing that the derived conclusions are somewhat generalizable. These results close a gap in the research of the absorption characteristics of echelle gratings and may provide fresh understanding and recommendations for the future design and fabrication of high-efficiency echelle gratings.
Funding
National Outstanding Youth Science Fund Project of National Natural Science Foundation of China (U21A20509); Canton Science and Technology project (202007010001); Canton Pearl River Talent planning.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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