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Abstract
A novel compact electromagnetic diode based on Fano resonance is reported, realized by combining a defective photonic crystal with a varactor-loaded split ring resonator. One-way response is achieved in a microwave waveguide system, attributed to the sharp asymmetric Fano lineshape, the strong nonlinearity enhancement, and the pronounced nonreciprocal field localization. A low threshold intensity of −1.6 dBm, a high transmission contrast up to 17.1 dB, and a maximal transmission over −16 dB are achieved within a subwavelength volume. Compared with conventional electromagnetic diode designs based on defective photonic crystals, the presence of interaction between cavity and resonator provides more flexibility in tuning the transmission properties. The findings may be beneficial for designing nonreciprocal integrated photonic devices in practical application.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetic diode (EMD) is a one-way transmission device and fundamental in all-optical signal processing [1,2]. Key indexes to evaluate the performance of EMD are small feature size, low threshold power, and large transmission contrast. For this purpose, various schemes have been proposed, including employing optical Kerr response [3–5], magneto-optic effect [6,7], electromagnetic tunneling phenomenon [8,9], interband photonic transition [10–13], and so on [14–20]. Among these methods, nonlinear one dimensional (1D) photonic crystal (PCs) with defect get increasingly attention, owing to the fact that they are easy to construct and convenient to model [21–26]. However, the transmission spectra in such structures are usually symmetric Lorentzian lineshape, with only a transmission peak. One needs to increase the input intensity to obtain a high transmission contrast. Actually, the bigger of the input intensity, the greater of the radiative damping, yielding the smaller of the transmission contrast, particularly in long-wavelength regions where dielectric loss and big volume are dominant limiting factors. This certainly restrains the range of the applications of EMDs based on defective nonlinear 1D PCs.
Recently, Fano resonance as a new paradigm for controlling mode interactions has become the focus of research. It arises from the interference of a discrete state with a continuum state [27]. This effect is originally studied in atomic systems, subsequently observed in quantum systems, and currently extended to classical systems. Numerous geometries have been designed to generate Fano resonance in solid-state-based structures, ranging from microwave to optical frequency regimes [28–33]. Compared to the conventional symmetric-shaped Lorentzian resonance, Fano resonance possesses the adjacent transmission peak-dip lineshape, the extreme weak radiation damping, and the remarkable huge field confinement. These exotic features play a pivotal role in sensing [34,35], filtering [36], and lasing [37]. Especially, the sharp asymmetric and steep dispersion of the Fano resonance profile can also be exploited to enhance the nonlinear interactions [38–41]. Only a slight increase in signal power can lead the transmission dip soon turn into the peak, making it possible to enlarge the transmission contrast and decrease the threshold power at the same time [42–44]. So it would be an effective route to incorporate Fano resonance in the defective nonlinear 1D PCs design to further promote the performance of EMDs.
In this paper, we propose and investigate a novel subwavelength EMD based on Fano resonance in an asymmetric side-coupled cavity-resonator system. The asymmetric cavity is designed with a defective microstrip PC structure (AB)2D(BA)2(BBAA). The split ring resonator (SRR) is conductively coupled with the PC cavity. A varactor diode is mounted on the SRR to serve as the nonlinear medium inclusion. The Fano resonance is created by the destructive interference between the discrete SRR mode and the continuum PC cavity mode. The unidirectional nonlinear response, together with the sharp asymmetric and steep dispersion of the Fano-type line-shape, give rise to a high-performance EMD action. A transmission contrast up to 17.1 dB and a threshold intensity low to −1.6 dBm are achieved simultaneously, with the forward transmission over −16 dB. In addition, such an EMD is shorter than one operational wavelength in transmission line at 1.32 GHz. More importantly, by introducing the SRR into the conventional .defective 1D PC, the presence of coherent interaction provides a high degree of flexibility in tuning the transmission properties. These advantages may be quite appealing from a practical point of view.
2. Results and discussions
Figure 1 presents a top-view picture of the EMD structure consisting of an asymmetry cavity (AB)2D(BA)2(BBAA) side-coupled with a varactor-loaded SRR. The sample is fabricated on a 1.0-mm-thick copper-clad F4B substrate within a total dimension of 222.0 mm × 44.0 mm. The width of the microstrip line is set to 2.7 mm to match the 50 Ω characteristic impedance. The asymmetry cavity is constructed by three Bragg mirrors and a defect layer. The Bragg mirrors (AB)2 and (BA)2 are realized by periodically etching rectangular ring (labeled B) connected with conductor fish-scale strip (marked A). The length, width, and line width of the rectangular ring are 8.5 mm, 15.0 mm, and 0.5 mm, respectively. The 8.5-mm-length×15.0-mm-width fish-scale strip has a strip width equal to 0.5 mm and a strip gap of 0.5 mm. The defect (represented D) is produced by setting the distance between (AB)2 and (BA)2 to 90 mm, giving rise to a symmetry Fabry-Perot cavity. The spatial symmetry is broken by introducing another Bragg mirror BBAA into the right side of the structure (AB)2D(BA)2, and therefore leads to the asymmetry PC cavity (AB)2D(BA)2(BBAA). The SRR with a 1.0-mm gap is arranged in the middle of the defect area. It is conductively coupled with the defect via a 0.3 mm×0.3 mm square metal strip. Its geometry parameters, as illustrated in the inset of Fig. 1, are a×a = 4.7 mm×4.7 mm. A varactor diode (Infinion BBY52) is mounted on the SRR to serve as the nonlinear medium inclusion. A commercial software CST Microwave Studio is adopted for numerical simulations. In experiments, a vector network analyzer Agilent N5222A is used to obtain the nonlinear response.
Fig. 1. Photograph of our EMD sample. The inset illustrates the configuration of the SRR and its detailed geometry parameters.
Figure 2(a) displays the simulated linear transmission spectra of the (AB)2D(BA)2(BBAA) alone, the SRR only, and the composite (AB)2D(BA)2(BBAA)-SRR structure. The spectra are investigated under the capacitor with a fixed value of C = 2.65 pF. For the individual (AB)2D(BA)2(BBAA) case, the transmission line shape is approximate to a Lorentzian. There exist a transmission peak located at around 1.374 GHz within a Bragg bandgap from 0.939 GHz to 1.755 GHz. The quality factor is mere 40 and the structure behaves as a broadband Fabry-Perot cavity. On the other hand, the single SRR exhibits a narrowband resonance. The transmission dip near 1.327 GHz indicates the magnetic dipole type excitation in metallic resonator. By combining the PC cavity and SRR, a sharp asymmetric line shape emerges, corresponding to the prominent Fano-type spectrum. The spectrum arises from interference between the narrow SRR discrete mode and the broad PC cavity spectrum. In the spectrum, the peak transmission coefficient is −5.3 dB, with a quality factor of 188 that is 4.7-fold larger than that of the individual (AB)2D(BA)2(BBAA) structure. Moreover, the transmission characteristics of the composite structure can be tuned simply by adjusting the relative positions of the PC cavity and the SRR modes. Figure 2(b) clearly illustrates that, when we alter the capacitance of the varactor from C = 1.7 pF to 3.6 pF, the difference between the transmission maximum and minimum increases at first, then reaches 47.3 dB at C = 2.4 pf, and finally decreases in relation to the SRR resonant frequency. As C = 2.4 pf, the transmission peak is located around 1.407 GHz adjacent to the transmission dip at 1.372 GHz, realizing the transmission coefficient changes rapidly from maximum to minimum. Thus, under the same condition, the narrow, sharp, and tunable features of the Fano mechanism could benefit the EMD action much more than the Lorentzian resonance based on PC cavity.
Fig. 2. (a) Transmission spectra of the (AB)2D(BA)2(BBAA) alone, the SRR only, and the composite (AB)2D(BA)2(BBAA)-SRR structure. (b) The capacitance-dependent transmission properties of the (AB)2D(BA)2(BBAA)-SRR structure.
To explore the underlying physics of Fano-type resonance of the composite (AB)2D(BA)2(BBAA)-SRR structure, the surface current distributions at the transmission peak and dip frequencies marked by I and II in Fig. 2(a) are all calculated and given in Fig. 3. For the transmission peak case, it is evident that the induced surface currents on the SRR oscillate in an anticlockwise direction, forming a magnetic dipole. The surface currents on PC-cavity is a typical standing-wave pattern. Through constructive interference between the PC-cavity and the magnetic dipole of SRR, the surface currents successfully traverse the whole composite structure. For the transmission dip case, we can find that the direction of surface currents are flipped over backward into the PC-cavity when confronted by the SRR, demonstrating clearly a destructive interference behavior. Hence, Fano-type resonance with asymmetric line shape and high quality factor Q occurs from the constructive and destructive interference of discrete SRR resonance state with broadband PC-cavity continuum state.
Fig. 3. The simulated surface current distributions under forward excitation direction in the composite (AB)2D(BA)2(BBAA)-SRR structure at the transmission peak and dip frequencies.
Figure 4 presents the simulated electric field distributions of the bare (AB)2D(BA)2(BBAA), the separate SRR, and the composite (AB)2D(BA)2(BBAA)-SRR structure. For the (AB)2D(BA)2(BBAA) structure, the electric fields at 1.374 GHz are mostly concentrated at the defect site with a standing-wave pattern. Meanwhile, due to the asymmetric reflection of the Bragg mirrors, the electric field localization under forward excitation is much larger than that under backward excitation. For the SRR structure, the electric fields at 1.327 GHz are mainly confined in the slit of SRR and almost negligible in the transmission line regardless of the incident directions. For the composite (AB)2D(BA)2(BBAA)-SRR structure at 1.371 GHz, it is seen that the coherent interaction of the two separate structures has a strong effect on the electric field distributions. Nomatter what the incident direction is, a nearly 4 times field enhancement is achieved compared with the original (AB)2D(BA)2(BBAA) structure. We also found that the difference in field maxima of the composite (AB)2D(BA)2(BBAA)-SRR structure under different excitation directions between with SRR and without SRR rises from 4.33×104 V/m to 1.25×105 V/m. Such results are beneficial to realize the low-threshold and high-contrast EMD action.
Fig. 4. The simulated electric field distributions under two opposite excitation directions in the bare PC cavity at 1.374 GHz, the separate SRR at 1.327 GHz, and their composite structure at 1.371 GHz.
To show the feasibility of the proposed (AB)2D(BA)2(BBAA)-SRR structure as EMD, the influences of the input powers with respect to different excitation directions are studied and given in Fig. 5. Apparently, the nonlinear response for two opposite incident directions shows a striking contrast. With input power increasing from −15 dBm to −5 dBm, the resonant peak under forward excitation displaces from 1.365 GHz to 1.346 GHz, whereas the transmission spectra under backward excitation are nearly unchanged. It illustrates that, the nonlinear response for forward incidence can be excited at lower input powers than that for backward incidence. Also, when the input power increases further to 2.5 dBm, the peak frequency for forward incidence displays a red-shift of 71 MHz, which correspond to backward excitation at 9 dBm. This distinct nonreciprocal nonlinear response validates the effectiveness of our EMD proposal.
Fig. 5. Measured transmission spectra of the composite cavity-resonator structure under (a) forward and (b) backward excitation with input power varying from −25 dBm to 9 dBm.
To describe the working performance of our EMD device, the maximum transmission contrast (Cmax), the maximum forward transmission (Tmax), and the unidirectional transmission are measured and presented in Fig. 6. As observed in Fig. 6(a), the Cmax increases first and then decreases, with a peak of 17.1 dB at 1.32 GHz. The Tmax is always over −16 dB and remains basically unchanged within the selected frequency range of 1.3–1.34 GHz. The above results explicitly indicate that our EMD can operate at 1.32 GHz with a maximal transmission of Tmax ≈ −15.8 dB and an excellent performance of Cmax ≈ 17.1 dB. Besides, the measured transmission spectra for different incident directions at input power of −1.6 dBm are given in Fig. 6(b). It can be found that the proposed structure has high selectivity for forward and backward incident signals at 1.32 GHz. Quantitatively, the transmission is −15.8 dB for forward excitation, whereas it is only −32.9 dB for backward excitation. That is, forward excitation enhance the nonlinear response effectively, and meanwhile, backward excitation suppress it intensely. As such, the optimal transmission contrast as high as 17.1 dB and the unidirectional transmission over −16 dB are obtained successfully.
Fig. 6. (a) Measured Cmax and forward Tmax in frequency domain. (b) Measured transmission spectra for two opposite incident directions at input power of −1.6 dBm.
In what follows, the transmission contrast depending on the input power at 1.32 GHz is also measured and depicted in Fig. 7. It is found that the transmission contrast in various input power scopes corresponds to different trends. When input power is below −1.6 dBm, the transmission contrast increases monotonously from 0.6 dB to 4.3 dB. Around −1.6 dBm of input power, the transmission contrast suddenly jumps to 17.1 dB. Further increasing input power results in the transmission contrast declines gradually but is always above 14.5 dB. When 4.2 dBm of input power is reached, the transmission contrast drops rapidly to −1.5 dB. As input power continues to increase, the transmission contrast has little changes. Therefore, the proposed structure exhibits a high-performance EMD action at 1.32 GHz as input power varies from −1.6 to 4.2 dBm.
3. Summary
In conclusion, we have experimentally demonstrated a new type of EMD based on Fano resonance in an asymmetric side-coupled cavity-resonator system. The Fano resonance arises from the coherent coupling of the PC cavity (AB)2D(BA)2(BBAA) and SRR, leading to a sharp asymmetric lineshape. The spatial asymmetry of the PC cavity gives rise to the nonreciprocity of coupling efficiencies between the PC cavity and SRR. A varactor is loaded on the SRR to function as a nonlinear medium. Combining the nonreciprocal nonlinear response with the sharp asymmetric Fano lineshape yields an excellent comprehensive EMD performance. A high transmission contrast of up to 17.1 dB, a maximal transmission over −16 dB, and a low threshold intensity of less than −1.6 dBm are attained within a subwavelength volume. Furthermore, the transmission properties of the system can be flexibly adjusted by altering the coherent interaction between the PC cavity and SRR. The present study may provide an alternative way to design compact nonlinear optical components.
Funding
National Natural Science Foundation of China (11804244, 11974261, 51607119, 91850206); Natural Science Research of Jiangsu Higher Education Institutions of China (18KJA470004); Jiangsu Province Key Discipline of China’s 13th five-year plan (20168765).
Acknowledgments
The authors thank Dr. K. J. Zhu and J. Jiang for scientific discussion and help in numerical simulations and experimental measurements.
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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