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Abstract
The determination of chirality of circularly polarized light (CPL) is of great significance to the development of various optical techniques. In this paper, a miniature circular polarization analyzer (CPA) based on surface plasmon polariton (SPP) interference is proposed. The proposed CPA consists of a micron scale long sub-wavelength slit and two groups of spatially arranged periodic sub-wavelength rectangular groove pairs, which are etched in a metal layer. Under the illumination of a CPL with a given chirality, the proposed CPA is capable of forming SPP-mediated interference fringes with different periods in far field. The chirality of CPL can be directly and quantitatively differentiated by the frequency value of the far field SPP-mediated interference fringes. Different from the existing SPP-based CPAs, the proposed CPA can directly image the chirality information in far field, avoiding near-field imaging of the SPP field.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization is an important property of the transverse electromagnetic waves that describe the vector distribution of electric field oscillation. On a plane perpendicular to the propagation direction, the trajectory depicted by the end of the electric vector of circularly polarized light (CPL) is a circular trajectory. According to the rotation direction of electric vector (also known as chirality), CPL can be divided into left-handed CPL and right-handed CPL. Analyzing the concrete chirality of CPL is a significant issue in practical applications, such as analysis of the physiological properties of chiral molecules, polarimetric imaging techniques and for development of various optical technologies [1]. Surface plasmon polaritons (SPPs) are a kind of near field surface wave that propagates along the interface between metal and dielectric materials [2,3]. Owing to its unique properties, such as a short wavelength and localized field enhancement, SPPs are expected to be a good carrier for designing highly integrated and miniaturized plasmonic devices [4–8]. By carefully designing the geometrical parameters and changing the arrangements of artificial metal microstructures, the plasmonic devices (such as metasurfaces) can be specifically designed to be sensitive to the polarization of incident light [9–20].
For instance, SPP-based plasmonic devices have been designed as CPAs to analyze the chirality of the CPL [21–31]. The main principle of these CPAs described above is that: the specially designed structures of these CPAs are sensitive to the polarization of incident CPL, and can produce strong polarization dependent optical response. Under the illumination of CPL with different chiralities, the intensity distribution of the generated SPP field will be different, which can be used as a criterion to judge the chirality of CPL. However, the SPP field is generated in near field. In order to obtain the intensity distribution of the SPP field, near field microscopic imaging techniques, such as near field scanning optical microscopes (NSOM), must be used. Thus, these proposed CPAs have some limits in practical applications for high cost, bulky optical components and long time-consuming.
To avoid using NSOM, a practical polarization controlled CPA working in the THZ frequency range is proposed [32]. According to the chirality of the CPL, this CPA can selectively focus SPPs at two separate locations. By placing two photodiodes at the position of the two SPP foci and differentially detecting the intensities of the two foci, the chirality of the CPL can be directly detected. However, the two photodiodes are required to be accurately placed at the focus position.
On the other hand, some Archimedes-spiral-based devices that can work solely depend on far-field detection (e.g. transmission spectrum, reflection spectrum or microscope image) have been proposed and experimental realized [16,17,33,34]. These devices are also sensitive to the chirality of incident CPLs. However, the devices designed in these reference papers are not directly used as CPAs to identify the chirality of circularly polarized light. If these devices are used as CPAs, the far field patterns can be used to judge the chirality of CPL qualitatively.
In the end, in this paper, a miniature CPA using surface plasmon interference is designed. Compared with many previous SPP-based CPAs, the detection information for analyzing chirality of CPLs can be directly obtained in far field, avoiding near-field imaging of the SPP field, thereby can effectively reduce the detection cost and improve the detection speed. What's more, the chirality of CPL can be directly and quantitatively differentiated by the frequency value of the far field SPP-mediated interference fringes.
2. Device structure and working principle
In this section, the device structure and working principle of the proposed CPA are introduced. The innovation of this paper is to introduce surface plasmon interference fringe pattern interrogation technique for the analysis of the chirality of CPLs. This technique has been utilized to design a plasmonic interferometer for high throughput sensing or a fast Fourier transform plasmon resonance spectrometer [35,36].
Figure 1(a) shows the schematic diagram of a group of periodic sub-wavelength rectangle-grooves pair, in which the two column grooves are perpendicular to each other. The length, width and height of a sub-wavelength rectangle-groove unit are 200 nm, 40 nm and 120 nm. Δx denotes the spacing between two columns of sub-wavelength grooves along x axis. Δy denotes the spacing between two adjacent groove units along y axis. Here, let Δx=0.153 μm, Δy=0.2 μm. It has been proved in Ref. [11] that, such two parallel columns of sub-wavelength rectangular grooves etched in metal film are sensitive to the chirality of the incident CPLs. Under the illumination of left-handed CPL or right-handed CPL, directional launching of SPPs can be obtained. Specific working principle of this structure to realize the directional launching of SPPs can learn from Ref. [11].
Fig. 1. Schematic diagram of CPA. (a) two columns of periodic sub-wavelength rectangle-grooves, (b) schematic diagram of CPA on x-y plane, and (c) functional testing optical path.
Figure 1(b) shows the schematic diagram of the proposed CPA on x-y plane. The proposed CPA consists of a micron scale long sub-wavelength slit (named ‘S’) and two groups of periodic sub-wavelength rectangular groove pairs (respectively named ‘G1’ and ‘G2’). Each group contains two columns of sub-wavelength rectangle-grooves, which are perpendicular to each other. The design process of the CPA’s structure is simple. Firstly, the two columns of sub-wavelength rectangular grooves shown in Fig. 1(a) are designed and regarded as a whole. It can be rotated in x-y plane. With this approach, ‘G1’ and ‘G2’, which have different tilt angles, are designed and specifically placed on both sides of the long slit. The angle between ‘G1’ and ‘S’ (i.e., y-axis) is defined as θ1 = 10°. The angle between ‘G2’ and ‘S’ is defined as θ2=20°. For ‘G1’ and ‘G2’, the length, width and height of a sub-wavelength rectangle-groove unit are the same as in Fig. 1(a). All of these micro/nano structures are etched in a silver thin film. The thickness of the silver film is 150 nm. The length, width and height of the long slit are 32 μm, 100 nm and 150 nm, respectively.
Figure 1(c) shows the schematic diagram of the functional testing experiment for the proposed CPA. A collimated CPL plane wave normally illuminates the CPA along the negative direction of z-axis. The wavelength of incident CPL is λo=633 nm. At 633 nm, the dielectric permittivity of the silver is ε=−15.9317+i1.07633. The corresponding wavelength of SPP is λspp=612.8 nm. The function of the proposed CPA is investigated and numerically demonstrated by the commercial software Lumerical FDTD Solutions. The corresponding simulated results will be given and discussed in next section. The following work is to analyze the basic working principle of the structure.
On the one hand, structures of ‘G1’ and ‘G2’ are sensitive to the chirality of the incident CPLs. A simulation can be introduced to verify the unidirectional SPP launching functions of ‘G1’ and ‘G2’. In this simulation, the long slit ‘S’ shown in Fig. 1(b) are removed. Figure 2 shows the corresponding phase distribution of the SPP field generated by ‘G1’ and ‘G2’. The results indicate that the ‘G1’ and ‘G2’ can directionally launch SPP under illumination of CPL. For instance, in Fig. 2(a), under illumination of the left-handed CPL, the launched SPP waves propagate perpendicularly away toward the left side of the ‘G1’ and ‘G2’. On the contrary, in Fig. 2(b), under illumination of the right-handed CPL, the launched SPP waves propagate perpendicularly away toward the right side of the ‘G1’ and ‘G2’. Meanwhile, the SPP wave generated by the ‘G1’ or ‘G2’ can be regarded as a plane wave [11]. The directional propagation direction of the SPP plane wave is related to the tilt angle of ‘G1’ and ‘G2’. From the geometric relationship shown in Fig. 1(b), the angle between the direction of SPP plane wave generated by ‘G1’ and the x axis is θ1; the angle between the direction of SPP plane wave generated by ‘G2’ and the x axis is θ2.
Fig. 2. Simulation results of the phase distribution of the generated SPP field generated by the ‘G1’ or ‘G2’ under illumination of (a) left-handed CPL, and (b) right-handed CPL.
On the other hand, the micron scale long sub-wavelength slit is not sensitive to the chirality of the incident CPLs. It means no matter what the chirality of the incident CPL is, bidirectional launched SPP waves would be excited by ‘S’. The propagation direction of the bidirectional launched SPP plane wave generated by ‘S’ is parallel to the x axis.
Therefore, when the proposed CPA is normally illuminated by a collimated left-handed CPL, the SPP plane wave generated by ‘G2’ interferes with the SPP plane wave generated by ‘S’ at the lower part of the slit, resulting in periodic interference fringe pattern. While the SPP plane wave generated by ‘G1’ will not meet the SPP plane wave generated by ‘S’ at the upper part of the slit, thus there will be no interference at the upper part of the slit. On the contrary, under illumination of a collimated right-handed CPL, the SPP plane wave generated by ‘G1’ propagates toward the slit and interferes with the SPP wave generated by ‘S’ at the upper part of the slit, resulting in periodic interference fringe pattern. Meanwhile, the directional propagating SPP plane wave generated by ‘G2’ cannot meet the SPP plane wave generated by ‘S’ at the lower part of the slit. As a result, there will be no interference at the lower part of the slit.
Then, the generated SPP interference fringe patterns are transmitted through the slit to the bottom side of the metal film and reconverted back to the photons, resulting in periodic interference fringe pattern in far field [35,36]. In the end, the far field SPP-mediated interference fringe patterns can be collected by an objective and eventually imaged by a standard CMOS or CCD camera in far field.
3. Results
Figure 3 shows the intensity distribution of the SPP field generated at a distance of zo=-200 nm from the bottom of the metal surface. From Fig. 3, it can be seen that, two different types of SPP interference field are generated in near field by the designed CPA under illumination of CPL with different chiralities. The results are consistent with the working principle discussed above. The detailed results are as follows:
Fig. 3. The generated near field SPP spatial intensity distributions on x-y plane at zo=-200 nm by the designed CPA under illumination of (a) left-handed CPL, and (b) right-handed CPL.
Figure 3(a) corresponds to the result of left-handed CPL incidence. At the slit position, the lower half of the interferogram obviously presents periodic bright and dark regions, indicating respectively constructive and destructive interference. The periodic interference fringe pattern is produced by the interference of the SPP plane wave generated by ‘G2’ and the SPP plane wave generated by ‘S’ at the slit position. However, there are no periodic bright and dark regions in the upper half of the interferogram, indicating no interference occurs in this region. This is due to the fact that the SPP plane wave generated by ‘G1’ will not meet the SPP plane wave generated by ‘S’ at the slit position, thus there will be no interference at the upper part of the slit.
Figure 3(b) corresponds to the result of right-handed CPL incidence. Different from the result shown in Fig. 3(a), the upper half of the interferogram obviously presents periodic bright and dark regions at the slit position. This periodic interference fringe pattern is produced by the interference of the SPP plane wave generated by ‘G1’ and the SPP plane wave generated by ‘S’ at the slit position. While the SPP plane wave generated by ‘G2’ will not meet the SPP plane wave generated by ‘S’ at the slit position, thus no interference occurs at the lower part of the slit.
According to optical interference theory, the spatially period of interference fringes is determined by T=λspp/sin(θ), where θ=θ2=20° for the case of left-handed CPL incidence, θ=θ1=10° for the case of right-handed CPL incidence. Therefore, it can be calculated that: T2=0.6128 μm/sin(20°) = 1.792 μm for the case of left-handed CPL incidence, T1=0.6128 μm /sin(10°) = 3.529 μm for the case of right-handed CPL incidence. Thus, the period of the SPP interference patterns produced at the slit position in near field is determined by the tilt angle of G1’or ‘G2’ and the chirality of the incident CPL. The larger the tilt angle, the smaller the period is.
Figures 4(a) and 4(b) show the generated far field SPP-mediated interference fringe pattern at a distance of zo=-6 μm from the bottom of the metal surface under illumination of left-handed CPL and right-handed CPL, respectively. It is similar to the interferogram generated in near field as shown in Fig. 3. Half of the interferogram obviously presents periodic interference fringes, while the other half has no obvious interference fringes. The interferogram shows the intensity distribution of the light fields in the spatial domain. In the following, we will discuss how to derive the chirality information of CPL from the main frequency value.
Fig. 4. The generated far field SPP-mediated interference fringe pattern at a distance of zo=-6 μm by the designed CPA under illumination of (a) left-handed CPL, and (b) right-handed CPL.
Figure 5 shows the scheme for calculating the frequency of far field SPP-mediated interference fringes. The region marked with black rectangular wireframe shown in Figs. 4(a) and 4(b) are respectively extracted and presented in Figs. 5(a) and 5(b). The size of the region are xɛ[-0.15 μm, 0.95 μm], and yɛ[-24.3 μm, 8.2 μm]. The intensity line profile along y axis at xɛ[-0.15,0.95] is then extracted. After a sum calculation, the intensity line profiles along y axis are plotted in Figs. 5(c) and 5(d), respectively. The period of interference fringes can be deduced from this graph. Here, in order to quickly extract the period of the interference fringe, the fast Fourier transform method is performed.
Fig. 5. Simulation results of extracting chirality information of CPL from far-field SPP-mediated interference fringes pattern. (a) and (b) SPP intensity profiles at the region of xɛ[-0.15 μm,0.95 μm], yɛ[-24.3 μm, 8.2 μm], z=-6μm, (c) and (d) the intensity line profiles along y-axis, (e) and (f) fast Fourier transform of (c) and (d).
Figures 5(e) and 5(f) show the intensity profiles in the frequency domain, which are generated by the fast Fourier transform of the intensity profile in the spatial domain shown in Figs. 5(c) and 5(d). The main frequency value in the frequency domain gives information about the chirality of the incident CPLs.
For right-handed CPL incidence, the main frequency value is f1=0.3074. The period of interference fringes corresponds to T1’=1/f1=3.253 μm. Compared to the theoretic value T1=0.6128 μm/sin(10°) = 3.529 μm, the absolute error is 0.276 μm.
For left-handed CPL incidence, the main frequency value is f2=0.6149. The period of interference fringes corresponds to T2’=1/f2=1.626 μm. Compared to the theoretic value T2=0.6128 μm/sin(20°) = 1.792 μm, the absolute error is 0.166 μm. In both cases, the absolute error is less than the wavelength of SPP.
The results indicated that different periods and main frequencies of the SPP-mediated interference pattern can be utilized to judge the chirality of incident CPL. When the period is approximately equal to 3.253 μm(main frequency is 0.3074), the circularly polarized light is right-handed CPL. When the period is approximately equal to 1.626 μm(main frequency is 0.6149), the circularly polarized light is left-handed CPL. In addition, the error between the theoretical value and the simulated value can be controlled in a small range. Thus, the chirality of CPL can be inferred from the period of interference fringes in far field, namely the main frequencies in the frequency domain.
Taking into account the possible errors in the experimental measurement, we can take the average frequency value as the criterion. If we take f=(f1+f2)/2 = 0.46 as the criterion of interference fringe frequency, when the fringe frequency is greater than 0.46, the incident CPL is left-handed CPL; when the fringe frequency is less than 0.46, the incident CPL is right-handed CPL.
4. Discussion
The SPP-mediated far field interference pattern is controlled by both the tilting angle of ‘G1’ or ‘G2’ and the chirality of the incident CPL. In this paper, there are two simple rules to follow to select the angles between slit S and G1/G2:
- (1) According to the formula of interference fringe period T=λspp/sin(θ), the smaller the angle, the larger the period will be. In this paper, we consider that the angle should be smaller, then the interference fringe period will be larger, which is convenient for imaging observation.
- (2) Meanwhile, under the illumination of CPL with different chirality, the period of the generated interference fringes should be different. In this paper, we choose the angles θ1=10° and θ2=20°, T1=0.6128 μm/sin(10°) = 3.529 μm, T2=0.6128 μm/sin(20°) = 1.792 μm. The value of T1 is about twice the value of T2. We can also choose other angles between slit S and G1/G2. For instance, θ1 = 5° andθ2=18°.
Meanwhile, one can see that, the minor peaks (especially at around frequency=1.076) appear in Figs. 5(e) and 5(f). Next, the reasons for the occurrence of these minor peaks are discussed.
Keeping the structural parameters of the proposed CPA unchanged, the incident light is changed from CPL to linearly polarized light, and the generated interference fringes in near field and far field are shown in Figs. 6(a) and 6(b), respectively. Comparing Fig. 6(a) and Figs. 3(a) and 3(b), it can be seen that, interference fringes appeared in both the upper and lower parts of the slit under linear polarized light illumination. This difference can be attributed to this reason: under linear polarized light illumination, the sub-wavelength rectangular groove array in the device (G1 and G2) no longer has the functionality of unidirectionally launching SPP waves. The region marked with black rectangular wireframe shown in Fig. 6(b) is extracted and shown in Fig. 6(c). Figures 6(d) and 6(e) show the intensity profile in the spatial domain and intensity profile in the frequency domain, respectively. The calculation method is the same as that in Fig. 5.
Fig. 6. The generated near field (a) and far field (b) interference fringe pattern by the designed CPA under illumination of linearly polarized light, (c) SPP intensity profile extract from the region marked with black rectangular shown in (b), (d) the intensity line profile along y-axis, (e) fast Fourier transform of (d).
Figure 7(a) shows the intensity profile in the frequency domain, which is obtained by combining Fig. 6(e) and Fig. 5(e) into one picture. Figure 7(b) shows the intensity profile in the frequency domain, which is obtained by combining Fig. 6(e) and Fig. 5(f) into one picture. From Fig. 6 and Fig. 7, one can see that, the minor peak (at around frequency=1.076) appears in Fig. 6(e), Fig. 7(a) and Fig. 7(b). By comparing Fig. 5(c), Fig. 5(d) and Fig. 6(d), it can be seen that in region at yɛ[-10 μm, 6 μm], the intensity profile also shows a periodic distribution. It can also be clearly seen in Fig. 6(a) that periodic interference fringes are generated in the middle region of the intensity profile(marked with a black circle). This periodic fringe is independent of the polarization state of the incident light. In other words, whether the incident light is CPL or linearly polarized light, this periodic fringe will appear. And the corresponding fringe frequency is approximately equal to 1.1.
Fig. 7. Comparison between spectra of (a) left handed CPL and linearly polarized light; (b) right handed CPL and linearly polarized light.
There are two reasons to explain the source of this interference fringe. On the one hand, under the illumination of CPL, the rectangular groove arrays G1 and G2 did not achieve a completely directional excitation of SPP waves. On the other hand, under the illumination of CPL, the SPP generated at the lowermost end of the G1 and the uppermost area of G2 can no longer be regarded as a plane wave, but as a spherical wave. Therefore, regardless of whether the incident light is CPL or linearly polarized light, interference fringes are generated in the intersection area between the lowermost end of G1 and the uppermost end of G2. Thus, the minor peaks (at around frequency=1.1) that appear in Figs. 5(e) and (f) can not be eliminated by changing the titling angles. It should be pointed out that in data analysis, we focus on the main maximum peak. The existence of this minor peak (at around frequency=1.1) does not affect the feasibility of the function of the device designed in this paper.
By the Fourier transform of the SPP-mediated far field interference fringe patterns, the frequency value (or period) of the interference fringe pattern used as a criterion for distinguishing chirality can be quickly obtained. Thus, the chirality information of the incident CPL can be fast judged. In practical applications, the interference fringes can be further enlarged by a microscope objective lens and then collected by a standard CCD or CMOS camera [35,36].
5. Conclusions
In this letter, a hybrid metallic structure that consists of a micron scale long sub-wavelength slit and two groups of spatially arranged periodic sub-wavelength rectangular groove pairs is designed as a SPP based miniature CPA. The performance of the proposed CPA is numerically demonstrated by using Lumerical FDTD Solutions software. The simulated results indicates that, under illumination of CPL with different chirality, two different types of SPP-mediated interference patterns can be generated in far field above the metal surface. Fast Fourier transform of the SPP-mediated interference pattern in the spatial domain provides the frequency value of the interference pattern in the frequency domain. The frequency value (or period) is utilized to analyze the chirality of incident CPLs. Compared with the previous SPP-based CPAs using NSOM to detect the SPP filed in near field, the proposed CPA is capable of differentiating the chirality of incident CPL in far field, which shows superior characteristics and relatively lower detection cost. This is the main motivation of the proposed SPP based CPA in this paper.
Funding
National Natural Science Foundation of China (11974107, 61775140).
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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