June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS
3461
Frequency scanning from subwavelength aperture array Rui Yang,* Jiawei Zhang, and Hui Wang School of Electronic Engineering, Xidian University, Xi’an 710071, China *Corresponding author: [email protected] Received February 17, 2014; accepted April 25, 2014; posted May 9, 2014 (Doc. ID 206491); published June 5, 2014 Resonant transmission of microwaves is demonstrated through subwavelength holes on a semicircular radiator. Split ring resonators, offering a perfect control of the emitting apertures, are applied to determine the radiation direction and the resonant frequency. Full wave simulation shows that our design is capable of achieving wide angular scanning beams without causing any other main lobe, and the steerable beams could be easily controlled through tuning the excitation frequency. © 2014 Optical Society of America OCIS codes: (050.1220) Apertures; (050.6624) Subwavelength structures. http://dx.doi.org/10.1364/OL.39.003461
Since the initial report by Ebbesen et al. [1], extraordinary transmission (ET) through periodic arrays of subwavelength holes has become an ever increasing focus due to its practical significance for photonic devices [2–4]. It is believed that surface plasmon polaritons (SPPs) contribute to the enhanced transmission in the metallic grating with periodic apertures, which behaves as an open Fabry–Pérot resonant cavity channel [5–7]. Recent investigations have proven that ET will also exist in the SPP-free system in the microwave frequency regime, and the transmission spectra can be simply interpreted and satisfactorily predicted by an analytical model using the transmission line equivalent circuit [8,9]. In addition, the study of microwave transmission through a single subwavelength hole in the flat metal screen has also been a subject of interest, where a split ring resonator (SRR) is shown to be capable of localizing electromagnetic fields and squeezing the energy tunneling through the aperture that is much smaller than the wavelength [10,11]. Such discoveries, replacing the periodic topology of the subwavelength aperture array to achieve ET peaks, provide a convenient candidate for devising novel radiating components in microwaves. In this Letter, we shall demonstrate a frequency scanning design from subwavelength holes on a waveguide fed semicircular radiator. Besides enhancing the transmission, we show that the employed SRRs also offer a perfect control of the emitting aperture and the radiating frequency. As a result, our design is capable of achieving wide angular scanning beams without causing any other main lobe, and the steerable beams could be easily controlled by just tuning the excitation frequency. Let us consider a rectangular waveguide terminated with a metallic semicircular shorting plate radiating at the X-band, where subwavelength holes incorporated with SRRs function as the emitting windows (EWs), as shown in Figs. 1(a) and 1(b). The waveguide has the size of 22.86 mm × 10.16 mm, and the adjacent circular shorting plate thus has a diameter of 22.86 mm. The size of the holes is intentionally chosen to be very small, with a diameter of 3 mm. As a result, the energy can scarcely leak out of the radiator when it is excited at the frequency range from 8 to 12 GHz. The holes are placed on the semicircular shorting plate in terms of the steering angle of −90° < θ < 90°, with the hole center located on the yz plane of ϕ 90°. We expect to activate and open the 0146-9592/14/123461-03$15.00/0
subwavelength hole for the feeding microwaves in a different position, based on the contemporary concept of ET, so that we can manipulate the direction of the released energy. The SRR, deposited on a dielectric printed circuit board having the dimensions of 4 mm × 4 mm × 0.5 mm and the dielectric constant of εr 3.85, is used to activate the subwavelength holes by localizing the electric fields and enabling them to go resonantly through the apertures. The relative position of the hole and the SRR remains the same regardless of where we place the EWs on the semicircular shorting plate, and the SRR is placed inside the radiator at the position of 0.6 mm in front of the subwavelength hole. The projection of the hole center should be coincident with the center of the outer ring split, as shown in Fig. 1(c). The orientation of the SRR relative to the incoming electromagnetic field is of vital importance. We need to make sure that the E-field is parallel to the gap bearing sides of SRR with the incident wave passing through the SRR plane, so that it creates the strongest resonant transmission [11,12]. The resonant frequency will be tuned
Fig. 1. Schematic image of the ET radiator and the frequency scanning from the subwavelength aperture array. Three EWs are demonstrated on the semicircular shorting plate in the direction of θ −60°, θ 0°, and θ 30°. (a) Front view; (b) top view; (c) magnified picture of the purple dashed box in (a) and (b), illustrating the details of the relative position and the structural parameters of the hole and the SRR. © 2014 Optical Society of America
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OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
Table 1. Structural Parameters of the Employed SRRs for the Resonant Transmissions Frequency (GHz) 09 10 11
r (mm)
s (mm)
g (mm)
w (mm)
1.40 1.25 1.12
0.08 0.07 0.06
0.08 0.07 0.06
0.35 0.35 0.35
through the SRR structure in terms of the outer ring radius, r, the split width, s, and ring gap, g, while maintaining the ring width unchanged as w 0.35 mm in this investigation. Table 1 demonstrates the details of the structural parameters of the employed SRRs to achieve the resonant transmissions at 9, 10, and 11 GHz, respectively. The split width, s, and ring gap, g, are chosen equally with s g. The outer ring radius, r, roughly determines the resonant frequency, and the split width, s, and ring gap, g, are mainly used for the fine-tuning. Therefore, the radiation from such a design will readily be controlled in both the radiating direction and the resonant frequency by placing the properly designed SRRs in front of the subwavelength holes distributed at the desired positions on the semicircular shorting plate. Figure 2 demonstrates the E-field distributions from 9 to 11 GHz through the subwavelength holes on the semicircular shorting plate at θ −60° , θ 0° , and θ 30° , respectively. As we can visualize, there is no chance for the energy to get out of the radiator from such small apertures that are around 1∕10 wavelength in size, if we directly feed the structure from the waveguide, as shown in Figs. 2(a)–2(c). However, by placing a proper SRR in front of the hole a resonant transmission will occur at the designed frequency. In addition, the enhanced transmission holds effective regardless of where we place the SRR-hole combinations on the semicircular shorting
Fig. 2. Normalized E-field distributions through subwavelength holes on the semicircular shorting plate of the radiator at 9 GHz, θ −60° [(a), (d)]; 10 GHz, θ 0° [(b), (e)]; and 11 GHz, θ 30° [(c), (f)], respectively. (a), (b), and (c) demonstrate the E-field distributions in the radiator having no SRRs, while (d), (e), and (f) demonstrate the E-field distributions in the ET radiator with proper designed SRRs. All the near fields are normalized by 2 × 103 V∕m. The feeding microwave is directed in the z direction and its E component is directed in the x direction.
Fig. 3. Far-field radiation patterns through subwavelength holes on the semicircular shorting plate of the ET radiator at 9 GHz, θ −60° [(a), (d)]; 10 GHz, θ 0° [(b), (e)]; and 11 GHz, θ 30° [(c), (f)], respectively. (a), (b), and (c) demonstrate the 3D plots of the far-field radiations of the ET radiator, while (d), (e), and (f) demonstrate the 2D plots of the far-field radiations of the ET radiator at the yz plane of ϕ 90° . The maximum E-fields are 21.32 dB [(a), (d)], 18.63 dB [(b), (d)], and 21.58 dB [(c), (f)], respectively.
plate. For each EW at θ −60° , θ 0° , and θ 30° , we can clearly observe that the electromagnetic fields just penetrate the subwavelength holes and radiate outside freely at 9, 10, and 11 GHz, as shown in Figs. 2(d)– 2(f). The EWs on the metallic semicircular shorting plate have already included the angular displacements for the beam scanning and meanwhile offering a frequency control of the scanning angle. Therefore, we can readily obtain the frequency scanning from the subwavelength apertures by using our ET radiator, and this is also verified by the far-field plots in Fig. 3. As we can observe, ETs from EWs at 9, 10, and 11 GHz will consequently lead to the radiating main beams in the directions of θ −60° , θ 0° , and θ 30° , respectively. We can also observe that every ET offers a nearly perfect isolation between the EWs with scarcely any coupling. For instance, if the resonance transmission occurs at 10 GHz, the microwaves are only tunneling through the EW2 , as shown in Fig. 2(e). Such charming characteristics come from the fact that every EW corresponds to a unique resonance frequency within the X-band and every resonance owns a very narrow operation bandwidth of around 30 MHz, as we can observe in Fig. 4 from the reflection spectrum. Our ET radiator possesses quite low reflections at the feeding wave port that contrast sharply with the total reflection of the radiator having subwavelength holes with no SRR. These properties contribute to the high-Q frequency selective radiation from our prescribed EWs without causing any other main lobe. In conclusion, we have presented a frequency scanning design from a subwavelength aperture array based on the contemporary concept of ET at microwaves. Our proposed waveguide fed semicircular radiator, consisting of the SRR-hole as the EWs, has sufficiently demonstrated the ability to obtain wide angular scanning beams without causing other main lobes, and the steerable
June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS
3463
Universities (K5051302081) from China, Innovation Funds for Excellent Returned Overseas Chinese Talents from Xidian University, and the Newton International Fellowships (follow-on programs) from the Royal Society, UK.
Fig. 4. Graphical representation of the reflection spectrum from the radiator. (a) Return loss of the radiator with no SRR and the ET radiator in Fig. 1 within the X-band. Magnified pictures of reflections in (a) of the ET radiator at (b) 9 GHz, (c) 10 GHz, and (d) 11 GHz.
beams could simply be controlled by just tuning the excitation frequency. Rui Yang’s work has been supported by the National Natural Science Foundation of China (61301072), the Fundamental Research Funds for the Central
References 1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998). 2. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002). 3. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004). 4. C. Genet and T. W. Ebbesen, Nature 445, 39 (2007). 5. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000). 6. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003). 7. J. B. Pendry, L. Marítn-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004). 8. F. Medina, F. Mesa, and R. Marqués, IEEE Trans. Microwave Theory Tech. 56, 3108 (2008). 9. F. Medina, F. Mesa, and D. C. Skigin, IEEE Trans. Microwave Theory Tech. 58, 105 (2010). 10. A. O. Cakmak, K. Aydin, E. Colak, Z. F. Li, F. Bilotti, L. Vegni, and E. Ozbay, Appl. Phys. Lett. 95, 052103 (2009). 11. K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, Phys. Rev. Lett. 102, 013904 (2009). 12. R. Yang, Y. J. Xie, X. F. Li, Y. Y. Wang, R. Wang, and J. Jiang, Europhys. Lett. 84, 34001 (2008).
3461
Frequency scanning from subwavelength aperture array Rui Yang,* Jiawei Zhang, and Hui Wang School of Electronic Engineering, Xidian University, Xi’an 710071, China *Corresponding author: [email protected] Received February 17, 2014; accepted April 25, 2014; posted May 9, 2014 (Doc. ID 206491); published June 5, 2014 Resonant transmission of microwaves is demonstrated through subwavelength holes on a semicircular radiator. Split ring resonators, offering a perfect control of the emitting apertures, are applied to determine the radiation direction and the resonant frequency. Full wave simulation shows that our design is capable of achieving wide angular scanning beams without causing any other main lobe, and the steerable beams could be easily controlled through tuning the excitation frequency. © 2014 Optical Society of America OCIS codes: (050.1220) Apertures; (050.6624) Subwavelength structures. http://dx.doi.org/10.1364/OL.39.003461
Since the initial report by Ebbesen et al. [1], extraordinary transmission (ET) through periodic arrays of subwavelength holes has become an ever increasing focus due to its practical significance for photonic devices [2–4]. It is believed that surface plasmon polaritons (SPPs) contribute to the enhanced transmission in the metallic grating with periodic apertures, which behaves as an open Fabry–Pérot resonant cavity channel [5–7]. Recent investigations have proven that ET will also exist in the SPP-free system in the microwave frequency regime, and the transmission spectra can be simply interpreted and satisfactorily predicted by an analytical model using the transmission line equivalent circuit [8,9]. In addition, the study of microwave transmission through a single subwavelength hole in the flat metal screen has also been a subject of interest, where a split ring resonator (SRR) is shown to be capable of localizing electromagnetic fields and squeezing the energy tunneling through the aperture that is much smaller than the wavelength [10,11]. Such discoveries, replacing the periodic topology of the subwavelength aperture array to achieve ET peaks, provide a convenient candidate for devising novel radiating components in microwaves. In this Letter, we shall demonstrate a frequency scanning design from subwavelength holes on a waveguide fed semicircular radiator. Besides enhancing the transmission, we show that the employed SRRs also offer a perfect control of the emitting aperture and the radiating frequency. As a result, our design is capable of achieving wide angular scanning beams without causing any other main lobe, and the steerable beams could be easily controlled by just tuning the excitation frequency. Let us consider a rectangular waveguide terminated with a metallic semicircular shorting plate radiating at the X-band, where subwavelength holes incorporated with SRRs function as the emitting windows (EWs), as shown in Figs. 1(a) and 1(b). The waveguide has the size of 22.86 mm × 10.16 mm, and the adjacent circular shorting plate thus has a diameter of 22.86 mm. The size of the holes is intentionally chosen to be very small, with a diameter of 3 mm. As a result, the energy can scarcely leak out of the radiator when it is excited at the frequency range from 8 to 12 GHz. The holes are placed on the semicircular shorting plate in terms of the steering angle of −90° < θ < 90°, with the hole center located on the yz plane of ϕ 90°. We expect to activate and open the 0146-9592/14/123461-03$15.00/0
subwavelength hole for the feeding microwaves in a different position, based on the contemporary concept of ET, so that we can manipulate the direction of the released energy. The SRR, deposited on a dielectric printed circuit board having the dimensions of 4 mm × 4 mm × 0.5 mm and the dielectric constant of εr 3.85, is used to activate the subwavelength holes by localizing the electric fields and enabling them to go resonantly through the apertures. The relative position of the hole and the SRR remains the same regardless of where we place the EWs on the semicircular shorting plate, and the SRR is placed inside the radiator at the position of 0.6 mm in front of the subwavelength hole. The projection of the hole center should be coincident with the center of the outer ring split, as shown in Fig. 1(c). The orientation of the SRR relative to the incoming electromagnetic field is of vital importance. We need to make sure that the E-field is parallel to the gap bearing sides of SRR with the incident wave passing through the SRR plane, so that it creates the strongest resonant transmission [11,12]. The resonant frequency will be tuned
Fig. 1. Schematic image of the ET radiator and the frequency scanning from the subwavelength aperture array. Three EWs are demonstrated on the semicircular shorting plate in the direction of θ −60°, θ 0°, and θ 30°. (a) Front view; (b) top view; (c) magnified picture of the purple dashed box in (a) and (b), illustrating the details of the relative position and the structural parameters of the hole and the SRR. © 2014 Optical Society of America
3462
OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
Table 1. Structural Parameters of the Employed SRRs for the Resonant Transmissions Frequency (GHz) 09 10 11
r (mm)
s (mm)
g (mm)
w (mm)
1.40 1.25 1.12
0.08 0.07 0.06
0.08 0.07 0.06
0.35 0.35 0.35
through the SRR structure in terms of the outer ring radius, r, the split width, s, and ring gap, g, while maintaining the ring width unchanged as w 0.35 mm in this investigation. Table 1 demonstrates the details of the structural parameters of the employed SRRs to achieve the resonant transmissions at 9, 10, and 11 GHz, respectively. The split width, s, and ring gap, g, are chosen equally with s g. The outer ring radius, r, roughly determines the resonant frequency, and the split width, s, and ring gap, g, are mainly used for the fine-tuning. Therefore, the radiation from such a design will readily be controlled in both the radiating direction and the resonant frequency by placing the properly designed SRRs in front of the subwavelength holes distributed at the desired positions on the semicircular shorting plate. Figure 2 demonstrates the E-field distributions from 9 to 11 GHz through the subwavelength holes on the semicircular shorting plate at θ −60° , θ 0° , and θ 30° , respectively. As we can visualize, there is no chance for the energy to get out of the radiator from such small apertures that are around 1∕10 wavelength in size, if we directly feed the structure from the waveguide, as shown in Figs. 2(a)–2(c). However, by placing a proper SRR in front of the hole a resonant transmission will occur at the designed frequency. In addition, the enhanced transmission holds effective regardless of where we place the SRR-hole combinations on the semicircular shorting
Fig. 2. Normalized E-field distributions through subwavelength holes on the semicircular shorting plate of the radiator at 9 GHz, θ −60° [(a), (d)]; 10 GHz, θ 0° [(b), (e)]; and 11 GHz, θ 30° [(c), (f)], respectively. (a), (b), and (c) demonstrate the E-field distributions in the radiator having no SRRs, while (d), (e), and (f) demonstrate the E-field distributions in the ET radiator with proper designed SRRs. All the near fields are normalized by 2 × 103 V∕m. The feeding microwave is directed in the z direction and its E component is directed in the x direction.
Fig. 3. Far-field radiation patterns through subwavelength holes on the semicircular shorting plate of the ET radiator at 9 GHz, θ −60° [(a), (d)]; 10 GHz, θ 0° [(b), (e)]; and 11 GHz, θ 30° [(c), (f)], respectively. (a), (b), and (c) demonstrate the 3D plots of the far-field radiations of the ET radiator, while (d), (e), and (f) demonstrate the 2D plots of the far-field radiations of the ET radiator at the yz plane of ϕ 90° . The maximum E-fields are 21.32 dB [(a), (d)], 18.63 dB [(b), (d)], and 21.58 dB [(c), (f)], respectively.
plate. For each EW at θ −60° , θ 0° , and θ 30° , we can clearly observe that the electromagnetic fields just penetrate the subwavelength holes and radiate outside freely at 9, 10, and 11 GHz, as shown in Figs. 2(d)– 2(f). The EWs on the metallic semicircular shorting plate have already included the angular displacements for the beam scanning and meanwhile offering a frequency control of the scanning angle. Therefore, we can readily obtain the frequency scanning from the subwavelength apertures by using our ET radiator, and this is also verified by the far-field plots in Fig. 3. As we can observe, ETs from EWs at 9, 10, and 11 GHz will consequently lead to the radiating main beams in the directions of θ −60° , θ 0° , and θ 30° , respectively. We can also observe that every ET offers a nearly perfect isolation between the EWs with scarcely any coupling. For instance, if the resonance transmission occurs at 10 GHz, the microwaves are only tunneling through the EW2 , as shown in Fig. 2(e). Such charming characteristics come from the fact that every EW corresponds to a unique resonance frequency within the X-band and every resonance owns a very narrow operation bandwidth of around 30 MHz, as we can observe in Fig. 4 from the reflection spectrum. Our ET radiator possesses quite low reflections at the feeding wave port that contrast sharply with the total reflection of the radiator having subwavelength holes with no SRR. These properties contribute to the high-Q frequency selective radiation from our prescribed EWs without causing any other main lobe. In conclusion, we have presented a frequency scanning design from a subwavelength aperture array based on the contemporary concept of ET at microwaves. Our proposed waveguide fed semicircular radiator, consisting of the SRR-hole as the EWs, has sufficiently demonstrated the ability to obtain wide angular scanning beams without causing other main lobes, and the steerable
June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS
3463
Universities (K5051302081) from China, Innovation Funds for Excellent Returned Overseas Chinese Talents from Xidian University, and the Newton International Fellowships (follow-on programs) from the Royal Society, UK.
Fig. 4. Graphical representation of the reflection spectrum from the radiator. (a) Return loss of the radiator with no SRR and the ET radiator in Fig. 1 within the X-band. Magnified pictures of reflections in (a) of the ET radiator at (b) 9 GHz, (c) 10 GHz, and (d) 11 GHz.
beams could simply be controlled by just tuning the excitation frequency. Rui Yang’s work has been supported by the National Natural Science Foundation of China (61301072), the Fundamental Research Funds for the Central
References 1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998). 2. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, Nature 416, 61 (2002). 3. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, Nano Lett. 4, 1085 (2004). 4. C. Genet and T. W. Ebbesen, Nature 445, 39 (2007). 5. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000). 6. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003). 7. J. B. Pendry, L. Marítn-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004). 8. F. Medina, F. Mesa, and R. Marqués, IEEE Trans. Microwave Theory Tech. 56, 3108 (2008). 9. F. Medina, F. Mesa, and D. C. Skigin, IEEE Trans. Microwave Theory Tech. 58, 105 (2010). 10. A. O. Cakmak, K. Aydin, E. Colak, Z. F. Li, F. Bilotti, L. Vegni, and E. Ozbay, Appl. Phys. Lett. 95, 052103 (2009). 11. K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, Phys. Rev. Lett. 102, 013904 (2009). 12. R. Yang, Y. J. Xie, X. F. Li, Y. Y. Wang, R. Wang, and J. Jiang, Europhys. Lett. 84, 34001 (2008).
