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Abstract
Due to the characteristic of surface plasmon polaritons (SPP) excitation, radial polarized beams and circular polarized beams are widely used for plasmonic lens and plasmonic near field focusing. In this paper, a plasmonic lens based on in-plane total internal reflection (TIR) scheme is proposed and numerically demonstrated to achieve the simultaneous nanofocusing of azimuthal and radial polarized beams. By means of the in-plane TIR mechanism, the operation bandwidth of lens ranges from visible light to mid-infrared. The proposed structure has been utilized in the design of a plasmonic liquid refractive index sensor and is expected to find potential applications in near-field optical energy focusing, near-field imaging and sensing.
© 2017 Optical Society of America
1. Introduction
In recent years, plasmonic near field focusing [1–13] has been widely studied, and therefore enlightened a number of applications such as near field optical vortex generation [3–5], circular polarization analysis [6–9], near field optical energy focusing [10], enhanced Raman spectral imaging [11] and micro-manipulation [12, 13]. The surface plasmon polaritons (SPP) excitation schemes under linear and circular polarization have been investigated in detail and shown various promising applications [1–3, 5–10]. On the other hand, the SPP excitation with more complex incident beams such as cylindrical vector beams has also been discussed. Although plasmonic lenses for cylindrical vector beams have been proposed [4, 14–17], these studies mainly focused on the radial polarized incidence or component. Since slit structure on metal can excite SPP under the incidence of TM polarized incident beam [17–19], and radial polarization is TM polarized to ring slit and spiral slit, therefore the SPP propagating towards the center of lens can be excited. In contrast, the azimuthal polarization is TE polarized to ring slit and spiral slit, no SPP is excited [4, 16, 20, 21] and plasmonic lens for azimuthal polarization focusing is rarely studied.
Achieving azimuthal polarization focusing makes an efficient use of incident power and improves the performance of plasmonic device such as circular polarization analyzer. To focus azimuthal polarized beam, it is essential to control the SPP excitation direction. Manipulating SPP excitation direction with azimuthal polarized incident beam was firstly demonstrated by Chen et al [20]. By utilizing the triangle aperture structure supporting symmetric and asymmetric modes under different polarized incidences, directional excitation of SPP was realized. On the other hand, although SPP in-plane refraction and reflection have been theoretically predicted and experimentally observed [22, 23], its capability of controlling SPP propagation direction has not been properly discussed and only few studies on the applications of in-plane refraction and reflection have been reported [24, 25]. In-plane total internal reflection (TIR) possesses the advantage of deflecting SPP with high efficiency, which provides an alternative route for azimuthal polarization nanofocusing.
In this paper, a plasmonic lens which could achieve simultaneous nanofocusing of both azimuthal and radial polarized beam is proposed and numerically demonstrated. The proposed device consists of a conventional ring slit plasmonic lens [14] and an in-plane TIR lens (IPTIRL). We first investigate the characteristic of SPP in-plane TIR in three layer plasmonic waveguide structure and obtain the relationship between effective index of SPP and zirconium dioxide layer thickness, which is utilized for designing the IPTIRL. The IPTIRL is composed of a zirconium dioxide layer, which is further etched to form several in-plane prisms, and a gold film base. Through the slits etched in gold film, the energy of incident azimuthal polarized beam is coupled to SPP, which is further focused into a sub-wavelength-size spot at lens center. Performance of IPTIRL under different incident wavelength are investigated with the results confirm the broadband operation characteristic of IPTIRL. We then investigate the plasmonic lens which could achieve simultaneous nanofocusing of both azimuthal and radial polarized beam, simulation results indicate our design realize the anticipation. Base on IPTIRL structure, a liquid refractive index sensor is also proposed and numerically investigated, simulation results show good agreement with the theoretical analyses. The IPTIRL structure is expected to have potential applications in near-field optical energy focusing, near-field imaging and sensing.
2. Principle
The SPP are electromagnetic modes confined in the perpendicular direction of dielectric-conductor interface, which arise from the coupling of electromagnetic fields to the oscillations of conductor's electron plasma [26]. The effective index of SPP [24] is determined by both dielectric and conductor that form the interface:
Where εm and εd are the relative permittivity of conductor and dielectric, respectively. And the propagation constant of SPP [24, 26] is:Where k0 = 2π/λ is the wave number in vacuum.When SPP travel at different interfaces, refraction, reflection, and focusing can occur. For two different dielectric-conductor interfaces (DCI) shown in Figs. 1(a) and 1(b), the effective indices of SPP are assumed to be neff1 and neff2 (neff1>neff2), corresponding to the propagation constants of β1 and β2. When SPP travel from DCI 1 to DCI 2 along the in-plane direction, the SPP energy will be reflected back to DCI 1 or coupled to DCI 2 (refraction). According to the interface condition for electromagnetic fields [27], the direction of reflection and refraction can be determined.
Fig. 1 (a) Schematic diagram of SPP travel through different dielectric-conductor interfaces; (b) schematic diagram of SPP in-plane reflection and refraction; (c) SPP with incident angle of 39.5°, which is larger than critical angle.
At the in-plane interface, continuity of tangential component of electric field requires that the propagation constants satisfy relationship βτ1 = βτ2, where βτ1 and βτ2 are the tangential propagation constants in DCI 1 and DCI 2, respectively. When the in-plane incident angle equals to θc = arcsin(neff2/neff1), βτ2 = βτ1 = β1sin(θ) = k0neff2, and SPP are excited in DCI 2 and propagate along the in-plane interface. Therefore, when the incident angle is larger than θc, there will not be refracted SPP propagate in DCI2.
Figure 1(c) shows the case of SPP TIR, which is simulated by commercial finite-element software COMSOL Multiphysics. In the simulation, DCI 1 consists of gold and zirconium dioxide, and DIC 2 consists of gold and air. Here, the reason we choose zirconium dioxide as the dielectric material of DCI 1 is that zirconium dioxide has a relative high refractive index and could create a large effective index difference between DCI 1 and DCI 2. Therefore, the range of incident angle in in-plane TIR regime can be wider, which allows a more flexible design of the in-plane TIR device. At wavelength of 800nm, the refractive indices of gold and zirconium dioxide [28, 29] are nAu = 0.15 + 4.91i and nZrO2 = 2.14, respectively. The effective indices at DCI 1 and DCI 2 are calculated to be 2.37 and 1.02 using Eq. (1). Thus, the critical angle of in-plane TIR, which can be expressed as θc = arcsin(neff2/neff1), is 25.5°. However, the incident angle in this case is 39.5°, larger than the critical angle. It is clear to see that almost all the energy is reflected. Only a few energy penetrates the in-plane interface, and this proportion energy is bounded at the in-plane interface.
3. IPTIRL structure
The IPTIRL structure is depicted in Fig. 2. A gold film of thickness of 150nm is deposited on silica substrate, then 12 slits are etched on the gold film [see Fig. 2(a)]. The length and width of the slits are 500nm and 150nm, respectively. All the slits are arranged along a circle (the radius of the circle is 2μm) and their long axis of symmetry is perpendicular to the electric field of azimuthal polarization. Except for the slits, some additional structures should be etched or deposited on the gold film, which serve as alignment markers [30, 31] for subsequent procedures. Then, depositing a zirconium dioxide layer of on the gold film, followed by etching procedure that produces the in-plane prisms. The alignment markers will be used as reference in etching procedure. In practice, etching zirconium dioxide is not so easy. Since the design requires a dielectric material with high refractive index, other material with relative lower refractive index and acceptable fabricate feasibility can be selected, such as zinc monoxide, which has been extensively studied in nano-fabrication [32, 33]. We change the dielectric material to zinc monoxide and conduct comparison simulations (other parameters stay unchanged). Simulation results confirm that IPTIRL with zinc monoxide layer also has the capability of focusing azimuthal polarized beam, but the amplitudes of focusing spot is lower. This is due to the parameters are not optimal for IPTIRL with zinc monoxide layer.
Fig. 2 Schematic diagrams of the IPTIRL are shown in (a) and (b); (c) is the schematic diagram of zirconium dioxide layer; (d) is the zoom in of area A in (c).
From Fig. 2(c) one can see that in-plane isosceles triangle prisms are placed on one side of each slit. The vertex angle and sides of the prisms [see Fig. 2(d)], which are designed with geometrical optics principle, are 101° and 650nm, respectively. According to the geometric relation, the incident angle of SPP at the base of prisms is 39.5°. Here, the sides of the prisms are longer than the length of slits. This design is from the perspective of geometric optics, which makes sure all the rays from slits are reflected to the center of device. At incident wavelength of 800nm, 1100nm and 1400nm, the amplitudes of focusing spot, which are normalized to the incident field, are 1.10, 3.30 and 3.60, respectively. While for prisms with side length of 500nm (size of the slits is also 500nm × 150nm), the normalized amplitude of focusing spot under above mentioned incident wavelength are 1.46, 3.47 and 1.44, respectively. At shorter wavelength, the amplitude differences of focusing spot between these two configures are small, but at 1400nm, the latter configuration shows poor focusing performance. Therefore, we adopt the configuration in which the prisms have longer side length.
To realize SPP in-plane TIR, the incident angle at the base of prisms must reach critical angle. Since the thickness of the zirconium dioxide layer is directly related to the effective index of SPP, it is necessary to analyze SPP mode characteristic under different thicknesses of zirconium dioxide layer. Consider a semi-infinite space of gold and air, and a zirconium dioxide layer is placed on the gold. The thickness of zirconium dioxide layer will affect the characteristic of SPP. As shown in Fig. 3, the effective indices of SPP increase with the thickness of zirconium dioxide layer and approach to a constant described by Eq. (1). It is obvious that when the thickness of zirconium dioxide become large enough, the gold region and zirconium dioxide layer can be treated as semi-infinite space. According to the characteristic of SPP and properties of materials, the proposed plasmonic lens can operate in a wide frequency range from visible light to mid-infrared. Thus, by carefully designing the incident angle and thickness of zirconium dioxide layer, the operation frequency range can be controlled. In the following discussion, we set the thickness of zirconium dioxide layer as 450nm.
Fig. 3 Relationship between effective index of SPP mode and thickness of zirconium dioxide layer under different wavelength.
The performance of proposed plasmonic lens is analyzed by commercial finite-different time-domain software Lumerical FDTD Solutions. In our FDTD simulations, perfectly matched layer (PML) boundary condition is applied, and the azimuthal polarized beams with wavelength of 800nm, 1100nm and 1400nm are launched into the device from the substrate. In all the simulations, the transverse field distribution of incident beams have Laguerre-Gaussian profile of E01(r), which can be described as:
Where is the associated Laguerre polynomial of order p and index l; the , l and p is the radial coordinate, radial index and azimuthal index, respectively. And the spot size corresponding to the Gaussian beam radius, donated as w0, is set to be 5μm in all the simulations. A detector is placed at the center of the device, which is 50nm above the gold film in the zirconium dioxide layer, and the xy-plane contains detector is also defined as observation plane. Figure 4 shows the SPP electric field distributions on observation plane. The amplitudes of electric field are normalized to the incident field (e.g. E/E0, where E represents the observed electric field distribution and E0 is the amplitude of incident field). From Fig. 4 one can see that all the azimuthal polarized beams are focused to the center of the device. The sizes of focusing spots, which are defined as the full-width at half-maximum (FWHM), are respectively 192nm, 351nm and 325nm under the above mentioned incident wavelengths [see Figs. 4(d) to 4(f)]. Compared with longer incident wavelength, the amplitude of focusing spot under incident wavelength of 800nm is weaker, the reason is that the width of slit is not suitable for this wavelength. In the following discussion we will mainly focus on longer wavelength.Fig. 4 Electric field of generated SPP (a)-(c) and corresponding electric field distribution along x-axis (d)-(f). The amplitude of each field is normalized to incident field. The observation plane is 50nm above the gold film. Wavelength of each case: (a) (d): 800nm; (b) (e): 1100nm; (c) (f): 1400nm.
To make use of the incident energy efficiently, more slits and prisms could be added to the device, and consequently the size of the device will increase. As mentioned above, all the slits distribute along a circle. If we fix the radius of this circle, the number of the prisms reduces as the size increases, besides, the length of the slits is also limited by the size of prisms. Table 1 shows three IPTIRLs with different slits and prisms. To maintain the same structure parameters as shown in Fig. 2, the side length of prisms in each device is 150nm longer than the slits, and the slits are also arranged along a circle whose radius is 2μm. Simulation conditions are the same as before, incident wavelength of 1100nm and 1400nm are investigated. Figure 5 shows the normalized electric field on observation plane. From Figs. 5(a) and 5(d) one can see that IPTIRL 1 has the lowest amplitudes of focusing spot under both incident wavelengths. As for IPTIRL 2, the focusing performance is slightly better than IPTIRL 3 under incident wavelength of 1100nm, but the focusing performance is much poor under incident wavelength of 1400nm. Therefore, the length of the slits will limit the operating wavelength. When determining the parameters of IPTIRL, the size of slits should be in priority.
Table 1. IPTIRLs with different slits and prisms
Fig. 5 Normalized electric field on observation plane under different configuration and incident wavelength. The incident wavelength of (a) device 1, (b) device 2 and (c) device 3 are1100nm, and the incident wavelength of (d) device 1, (e) device 2 and (f) device 3 are1400nm.
4. Azimuthal and radial polarization focusing
The proposed IPTIRL structure is designed for azimuthal polarized incidence, and there is seldom focusing effect when applied to radial polarization. Figure 6(a) shows the distribution of electric field on observation plane under radial polarized incidence at wavelength of 1100nm, and Fig. 6(b) is the corresponding electric field distribution on xOz plane. As shown in Fig. 6, although there is a tiny spot at the center of the IPTIRL [see Fig. 6(a)], the SPP excitation efficiency is considerably low [see Fig. 6(b)].
Fig. 6 (a) Normalized electric field of generated SPP under radial polarized incidence at wavelength of 1100nm on observation plane; (b) Normalized electric field distribution on xOz plane corresponding to (a), in this figure, radial polarized beam is launched from the substrate (z<0), since the structures on gold film (0<z<0.15μm) are not compatible with radial polarized beam, only a few energy is coupled to SPP and propagate on gold - zirconium dioxide interface, and the discontinuity of field at z = 0.6μm arise from the boundary of zirconium dioxide (0.15μm<z<0.6μm) and air (z>0.6μm).
To realize simultaneous nanofocusing of both azimuthal and radial polarization, we combine the IPTIRL structure with conventional ring slit plasmonic lens. As shown in Fig. 7(a), a ring slit with width of 150 nm is added to the gold film, and its inner radius is 2.25 μm. The parameters of IPTIRL structure are kept the same as the last section, and the wavelength of incident beam is also 1100 nm. The normalized electric fields on observation plane under azimuthal and radial polarized incidence are shown in Figs. 7(c) and 7(d), respectively. It can be seen that both azimuthal and radial polarized incidence are focused into a tiny spot at the center of the device. Compared with Fig. 4(b), the pattern in Fig. 7(c) shows a bit of difference. The spot sizes of center spot under both incidence are 241nm [see Fig. 7(f) and 7(g)], smaller than the case of pure IPTIRL under azimuthal polarized incidence. This difference may originates from the change of structural parameters. Although the configuration of IPTIRL in last section has a wild operating frequency, the parameters still can be optimized for specific wavelength. Figure 7(e) is normalized electric field on xOz plane. Compared with Fig. 6(b), the focusing efficiency of radial polarization is improved obviously. It is worth noting that the IPTIRL structure can be combined with other structures such as spiral structure [9] or symmetry broken structure slit [34] to improve the performance of circular polarization analysis and linear polarization focusing.
Fig. 7 (a) A ring slit is added to the gold film; (b) schematic diagram of the plasmonic lens which achieving simultaneous nanofocusing of both azimuthal and radial polarization; normalized electric field of generated SPP under (c) azimuthal polarized incidence and (d) radial polarized at incidence wavelength of 1100nm on observation plane; (e) electric field distribution on xOz plane corresponding to (d), ring slit remarkably improve the coupling efficiency between incident radial polarized beam and SPP, the discontinuity of field at z = 0.6μm arise from the boundary of zirconium dioxide (0.15μm<z<0.6μm) and air (z>0.6μm); (f) and (g) are electric field distributions along x-axis corresponding to (c) and (d), respectively.
5. IPTIRL-based refractive index sensor
According to previous discussion, there is no doubt that in-plane TIR is a feasible way to control the propagation direction of SPP. However, the propagation direction of SPP can also be inflected if the in-plane reflection is not TIR, and the difference of whether the reflection is TIR is the reflectivity. Usually, the reflectivity increase with the difference of effective indices between two DCIs. Thus, by tuning the background index of the device and making the device work at internal reflection regime, the intensity of center focusing spot can be adjusted. Based on this principle, our device can be used for liquid index detection. Here, we also utilize FDTD method to investigate the device’s performance in different background refractive indices. Background refractive indices range from 1.3 to 1.45 with step of 0.03 are investigated, which cover many common liquids. The parameters of the device are chosen as the same as that shown in Fig. 2, and an azimuthal polarized beam of wavelength of 1400nm is launched into the device. As the background refractive index approaches to 1.3, the TIR critical angle increase to about 40°. Thus, when the background refractive index increase from 1.3, the refractivity decrease. Simulation results are shown in Fig. 8. Figures 8(a) to 8(f) show the normalized electric fields of SPP on the observation plane, and the normalized intensities (e.g. I/I0 = |E/E0|2, where I is the electric field intensity to be observed and I0 is the intensity of incident field) of center focusing spots are shown in Fig. 8(g). We set the intensity of center focusing spot as 0dB under background refractive index of 1.3, and the intensity does decrease with the background refractive index. An average sensitivity of −20.47dB/RIU is achieved. Linear and quadratic polynomial fitting is applied to the result in Fig. 8(g), the quadratic polynomial presents R2 = 0.9939, which indicates the plasmonic lens has a good quadratic response to the background refractive index.
Fig. 8 Normalized electric field distribution of generated SPP under different background refractive indices nbg: (a) nbg = 1.3; (b) nbg = 1.33; (c) nbg = 1.36; (d) nbg = 1.39; (e) nbg = 1.42; (f) nbg = 1.45; (g) relationship between background refractive index and normalized electric intensity of center focusing spot. Red line: quadratic polynomial fitting; blue dash line: linear fitting; R2: coefficient of determination in the fittings.
Compared with previous work [35–38], the sensitivity of our sensor is lower. However, one should note that most of reported schemes were based on resonance structures [35–38]. Resonance structures do provide exotic intensity sensitivity near resonant wavelength, but the detected refractive index range is extremely narrow [35, 37, 38]. To detect a larger refractive index range, wavelength interrogation technique should be applied, which increase the system complexity. Compared with sensors based on resonance structure, our scheme has the capability of detecting much larger refractive index range. As mentioned above, the detection range of the sensor is 0.15 refractive index unit, and the detection range can be extended by choosing higher refractive index dielectric material and optimizing the in-plane incident angle. In addition, the size of our sensor is much smaller when compared with previous work [35–37].
The sensor structure proposed in this section is a demonstration of the application of proposed IPTIRL. To the best of our knowledge, refractive index sensor based on the sensing regime of in-plane reflection has not been proposed. The sensitivity of the sensor is related to the geometric shape, material, thickness of the dielectric layer and in-plane incident angle. By optimizing the above mentioned parameters, the sensitivity could be further improved.
6. Conclusion
An IPTIRL structure for azimuthal polarized beam focusing has been proposed and numerically demonstrated. By utilizing in-plane TIR, SPP generated from azimuthal polarized beam can be focused into a sub-wavelength spot at the center of device. The FWHM of focusing spots are 192nm, 337nm and 325nm under incident wavelength of 800nm, 1100nm and 1400nm, respectively. By combining the IPTIRL structure with conventional ring slit structure, a plasmonic lens achieving simultaneous nanofocusing of both azimuthal and radial polarization is also achieved. At wavelength of 1100nm, both azimuthal and radial polarized incidence can be focused into a tiny focusing spot with FWHM of 241nm. A liquid refractive index sensor based on the IPTIRL structure is also investigated. The sensor has a good quadratic response to the background refractive index and an average sensitivity of −20.47 dB/RIU in background refractive index from 1.3 to 1.45 is achieved. Benefiting from the TIR mechanism, the proposed plasmonic lens possesses a wide operating bandwidth from visible light to mid-infrared if the parameters of the device are carefully designed. We expect the proposed device has the potential in near-field optical energy focusing, near-field imaging and sensing.
Funding
Fundamental Research Funds for the Central Universities (2017YJS009).
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