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Abstract
We experimentally demonstrate on-chip plasmon-induced transparency at THz frequencies using a meta-structure deposited on a 50 μm-thick dielectric subwavelength waveguide. The obvious plasmon-induced transparency results from strong coupling between the respective modes of a cut wire and a double-gap split ring resonator. The simulation and experimental results are consistent. Based on our numerical simulations of the temporal evolution of plasmon-induced transparency, a π/2 phase difference at the transparency peak between the above two modes is observed, i.e., there is energy oscillating between them that exhibits Rabi oscillation-like behavior. In addition, at the transparency peak, a strong local-field enhancement effect and high transmission can be obtained simultaneously, which can be tuned by changing the separation between the cut wire and the double-gap split ring resonator. These results will facilitate the design of THz integrated photonic devices and serve as an excellent platform for nonlinear optics and sensing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past decade, an extensive number of studies have focused on plasmon-induced transparency (PIT), which is a plasmonic classical analogue of electromagnetically-induced transparency, for its potential application in high-speed information processing chips, nonlinear optics, sensing, integrated photonic devices, and quantum optics [1–3]. PIT is caused by destructive interference between a superradiant mode (superradiant mode) and a subradiant mode (subradiant mode) [4,5]. Plenty of schemes have been proposed to produce PIT, such as using metamaterials, gold nanowire gratings, and nanocavity-coupled waveguide [6–8]. However, most PIT results were demonstrated through the off-chip incident direction that is not parallel to the chip surface, which is not conducive to integration of PIT in practical devices [9–11]. Thus, the on-chip PIT effect is very important if the effect is to be exploited in integrated photonic devices and integrated photonic chips. A number of on-chip PIT results based on the phase coupling mechanism [12,13] and near-field coupling mechanism [14–16] were reported in the literature. Nevertheless, most of these studies focus on the visible and near-infrared band, and very little research has been conducted in the terahertz regime. On-chip PIT at THz frequencies is urgently needed since THz waves are one of most promising waves due to its potential applications in sensing, material identification, and communication [17–23]. Moreover, most studies on PIT concentrate on analyzing the steady state rather than transient evolution. The studies on the steady state cannot provide an intuitive method for observing the interaction between a THz wave and functional structures, e.g. a meta-structure.
Lithium niobate (LN) subwavelength planar waveguide is an ideal on-chip platform to study THz waves, since all-feature generation, propagation, and detection capabilities are integrated on one sample [24]. In addition, time-resolved detection allows one to gather all the spatiotemporal information of propagating THz waves, which is beneficial to studying the transient interactions between THz pulses and the microstructure [25–28]. Therefore, a LN subwavelength planar waveguide also provides an excellent time-domain platform for on-chip PIT in the THz regime.
In this letter, we experimentally demonstrate on-chip PIT in the THz regime in a meta-structure deposited on the surface of a 50 μm-thick LN subwavelength waveguide. The meta-structure consists of cut metallic wires and metallic double-gap split ring resonators (DSRRs). Obvious on-chip PIT was observed in experiments and was replicated in simulation results. PIT was caused by strong coupling between the mode of a cut wire and the mode of a DSRR. The on-chip THz PIT was studied in detail by analyzing the temporal evolution with numerical simulations. The results show that the phase differences between two modes in this on-chip structure, two resonator valleys, and a PIT peak are π, 0, and π/2, respectively. The phase difference of π/2 between the two modes at the transparent peak shows that a certain amount of energy oscillates between the two modes, which appears to resemble a Rabi oscillation. Meanwhile, these results also show that the local field can be enhanced not only in the two resonator valleys, but also at the PIT peak. Therefore, strong local field enhancement and high transmission can be obtained simultaneously. The PIT and the local field enhancement can be tuned by changing the separation between the cut wires and the DSRRs. Our results will help facilitate highly sensitive THz sensing and nonlinear optics applications.
2. Structure design and fabrication
The resonators patterns in the PIT meta-structure were fabricated on a polished 50 μm-thick x-cut LN slab (11 × 10 × 0.05 mm3) using photolithography, where the optical axis was defined along the y axis in Fig. 1(a). A metal layer of 70 nm-thick Au and 5 nm-thick Ti was deposited on the LN slab. Ti acts as an adhesion layer between Au and LN. Such a meta-structure consists of two independent resonators, as shown in Fig. 1(b). The length of cut wire was L = 66 μm. The length along the x and y axes and the gap size along the y axis of the DSRR were a = 46 μm and g = 6 μm, respectively. The width of the DSRR and the cut wire was w = 6 μm. The separation between the left cut wire and the right DSRR was s = 10 μm along the x axis. The period of the meta-structure was P = 100 μm. Figure 1(c) shows a microscopic image of the fabricated structure.
Fig. 1 (a) Experimental scheme: a PIT meta-structure on a 50 μm-thick LN planar waveguide. A femtosecond pump laser was focused into a line on the front of the LN slab to generate a THz wave in the crystal slab. The coordinate system and C-axis of the crystal are also shown in the Fig. 1(a). The electric field of the THz wave was polarized along the optical axis. (b) The on-chip PIT meta-structure unit is composed of a cut wire and a DSRR, with geometric parameters L = 66 μm, w = 6 μm, a = 46 μm, P = 100 μm, g = 6 μm, and s = 10 μm. (c) Optical microscope image of the PIT meta-structure. Scale bar: 50 μm. (d) Schematic illustration of the experimental setup.
The finite-difference time-domain (FDTD) method was used to simulate the propagation of THz waves and the interaction between the waveguide mode and the meta-structure. In the model, LN was regarded as a uniaxial dielectric with no = 6.4 and ne = 5.1. The permittivity of Au was described by the Drude model ε = ε∞ − ωp2/ω2 + iωωτ with damping frequency ωτ = 4.053 × 1011Hz and plasma frequency ωp = 1.372 × 1014Hz [29]. At 0.4 THz, the permittivity of Au was chosen as ε = 1.19 × 105 + 1.84 × 106i.
3. Experimental setup
Figure 1(d) shows the experimental setup. A pump-probe system was used to record THz waves in the LN waveguide. Laser pulses from a Ti:sapphire regenerative amplifier (800 nm central wavelength, 1 kHz repetition rate, 120 fs duration) were separated into a pump beam (450 mW) and probe beam (50 mW). The y-polarized pump beam was focused into a line on the front of the LN slab with a cylindrical lens whose focal length was 150 mm after passing through a mechanical time delay line. Subsequently, the THz wave line source was generated via impulsive stimulated Raman scattering, as shown in Fig. 1(a) [30]. The generated THz fields were parallel to the C-axis of the LN crystal, i.e., along the y axis. A Cherenkov radiation cone forms in bulk LN because the femtosecond laser pulse travels faster in LN than THz waves. However, a LN slab is thin enough to act as a planar subwavelength waveguide, and the generated THz wave propagates and forms waveguide modes along the x axis [31]. These waveguide modes are transverse electric (TE) modes, i.e., the electric field component is Ey, the magnetic field components are Hx and Hz. The probe branch was frequency-doubled to 400 nm using a BBO crystal, spatially filtered to minimize high order scattering noise, and expanded to obtain a large spot before illuminating the entire sample at normal incidence. The pump beam is incident at a 15° with respect to the probe beam in order to prevent the second harmonic beam (400 nm) of pump beam generated in lithium niobate from being mixed into the probe beam. When the THz wave propagated in the slab, the refractive index of the LN crystal was changed due to the electro-optic effect. The resulting spatially dependent phase shift in the expanded probe beam is proportional to the refractive index change [30]:
where λ is the probe wavelength, L is the slab thickness, r33 is the electro-optic coefficient, and neo is the extraordinary index of refraction of LN corresponding to the probe. ETHz is the average value of THz mode experienced by the probe pulse along the z direction. However, the CCD is sensitive only to intensity. A phase-contrast imaging technique [30] was used to perform phase-to-amplitude conversion for the probe beam. For an ideal λ/4 phase plate, the measured signal from phase-contrast imaging is: with I0(x, y) the intensity envelope of the probe beam. Therefore, we can extract the phase by the operation: where S(x, y) is the signal intensity and R(x, y) is the reference intensity measured with the pump blocked. Thus, the electric field can be calculated by using the Equation (1). The image resolution was as small as 3 μm, or approximately several tenths of the wavelength in the LN crystal, providing extra fine spatial resolution.4. Results and discussion
The full spatiotemporal evolution of THz wave was extracted from the image sequence by changing the time delay between the pump and probe pulses. Because the pump beam was focused into a line along the y-axis and the signal is uniform along the y direction, it is reasonable to average the signal along the y direction. Thus, each 2D matrix containing (x, y) coordinate information was compressed to a 1D data set relating to the x-axis position only. We display the compressed 1D data set in time along the vertical axis in order to generate a space-time plot E(x, t), where the horizontal axis indicates propagation. Figures 2(a) and 2(b) show the experimental and simulated space-time plot of the THz wave propagating in the PIT meta-structure sample, respectively. In order to explain THz wave propagation, an incidence (Inci.) and reflection region (Refl.), metamaterial region (Meta.), and transmitted region (Tran.) are marked in Figs. 2(a) and 2(b). Reflection is due to the gold meta-structure, which changes the boundary conditions for the propagating THz waves [27].
Fig. 2 (a) Experimental and (b) simulated space-time plots of the propagating THz wave in the PIT meta-structure sample. Two black dashed lines show the meta-structure edges. The plots are divided into an incidence (Inci.) and reflection region (Refl.), meta-structure region (Meta. region), and transmitted region (Tran.). The horizontal axis corresponds to the x-axis of the coordinate system in Fig. 1(a). The vertical axis is the delay time between the probe and pump pulses. The black line at x = 1.22 mm in Tran. was selected for further analysis. (c)–(e) Experimental and (f)–(h) simulated dispersion curves, which were obtained by applying a 2D Fourier transform to the region shown in the red dashed rectangle in Figs. 2(a) and 2(b), corresponding to the DSRRs, cut wires, and meta-structure, respectively. The dispersion curves shown with green dashed lines are the theoretical results for a bare 50 μm-thick LN waveguide.
Figures 2(c)–2(e) show the experimental dispersion curves, which were determined by taking a 2D Fourier transform of the Tran. space-time plots [the red dashed rectangle shown in Fig. 2(a)] for the single DSRR, single cut wire, and PIT meta-structure sample, respectively, where the separation s was set to 10 μm for the latter. Figures 2(c) and 2(d) show that the curve is broken into two segments with dips at 0.42 THz and 0.43 THz for the single DSRR and single cut wire meta-structure, respectively. A transparency window appears in the dispersion curve for the PIT meta-structure instead of transmission dips for the two resonators, as shown in Fig. 2(e). Meanwhile, there are two new transmission dips on both sides of the transparency window. The transparency window and two new transmission dips result from strong coupling between the two resonators. The numerical dispersion curves in Figs. 2(f)–2(h) sufficiently reproduce our experimental results. The dispersion curves shown in the green dashed lines show theoretical results for a bare 50 μm-thick LN waveguide [31].
Figures 3(a) and 3(b) show the experimental and simulated normalized transmission spectra of the DSRRs, cut wire, and PIT meta-structure samples. We performed a Fourier transform of the time domain signals at x = 1.22 mm in the transmitted region [the black line shown in Figs. 2(a) and 2(b)] for the three meta-structures and a bare LN slab as a reference. The normalized transmission is defined as follows [2,32]:
where ET(ν) and ET,ref (ν) are the Fourier transformed y-polarized electric field through the meta-structure samples and the reference, respectively. Figure 3(a) shows a transmission valley at 0.42 THz in the single DSRR meta-structure (red line) and at 0.43 THz in the single cut wire meta-structure (blue line). The transmission valley in the single DSRR meta-structure results from a subradiant mode excited by the magnetic field component Hz of the waveguide mode [33]. The Ey distribution for this subradiant mode is shown in the red rectangle in Fig. 3(b). The transmission valley in the single cut wire meta-structure results from an superradiant mode excited by the electric field component Ey of the waveguide mode. The Ey distribution for this superradiant mode is shown in the blue rectangle in Fig. 3(b). An obvious transparency window form in the PIT meta-structure within the broad absorption band. Meanwhile, the FDTD simulation results agree well with the experimental results except some discrepancies, which include relatively small transmission deviations, small frequency shifts, and linewidth deviations at the transmission peaks and valleys for the three meta-structure samples. These discrepancies arise from the limitation of the patterning accuracy in the fabrication process. The inevitable imperfections at the edge of the unit cells lead to the small frequency shifts and the THz scattering [34]. The rough surface of the metal and the above scattering add additional loss which will broaden the bandwidth of the transparency window and reduce its transmission [34–36].Fig. 3 (a) Experimental and (b) simulated transmission spectra for the DSRR, cut wire, and PIT meta-structure samples. The inset shows the simulated Ey distributions of a single DSRR (red) and single cut wire (blue), respectively. (c)–(e) show calculated Ey distributions corresponding to the first transmission valley νL, transparency peak νT, and second transmission valley νH, respectively.
Figures 3(c)–3(e) show the Ey distribution at a certain moment for νL = 0.39 THz (located at the first transmission valley of the PIT), νT = 0.42 THz (at the transparency window peak), and νH = 0.45 THz (at the second transmission valley of the PIT), respectively. In order to further investigate the PIT behavior, we simulate the temporal evolution of Ey at point 1 near the cut wire and at point 2 near the DSRR [shown in Fig. 3(c)] using ultra-narrowband sources at frequencies of νL, νT, and νH. We define the phase of Ey at point 1 and point 2 as the phase of the respective modes in the cut wire and DSRR. Thus, we can observe the temporal evolution in the PIT meta-structure. Figures 4(a)–4(c) show the temporal evolution of Ey for the respective modes in the cut wire and DSRR at frequencies of νL, νT, and νH, respectively. One can see that the phase differences between the two modes are π, π/2, and 0 at νL, νT, and νH, respectively. The phase difference of π/2 at the transparency peak indicates that some energy oscillates between the cut wire and the DSRR. This is similar to the behavior of Rabi oscillations. Therefore, these results also indicate that the local field can be enhanced at the transmission valleys and at the transparency window.
Fig. 4 (a), (b), and (c) show the time evolution of Ey for the cut wire mode [point 1 in Fig. 3(c)] and DSRR mode [point 2 in Fig. 3(c)] at frequencies of νL, νT, and νH, respectively; the incident waves originate from the ultra-narrowband source with center frequencies of νL, νT, and νH, respectively.
To investigate the local-field enhancement effect caused by the PIT, we calculated the transmission spectrum and localization coefficient of the meta-structure with different gap separations between the DSRR and the cut wire. The transmission spectrum and localization coefficient are shown in Figs. 5(a) and 5(b), respectively. The localization coefficient is defined as
where E and E0 is the amplitude of electric field inside the waveguide below the area shown in Fig. 5(c) with and without the PIT meta-structure, respectively. One can see from Figs. 5(b) that the local field is enhanced at the transparency peak and two resonator valleys. Meanwhile, the PIT and the local field enhancement can be tuned by setting the separation between the cut wire and the DSRR. As the separation increases from 3 μm to 30 μm, the linewidth of the transparency window gradually narrows, and transmission at the transparency peak decreases correspondingly. The transparency window vanishes when s = 40 μm. However, the localization coefficients at the transparency peak increase significantly from 7.68 to 18.06 as the separation increases from 3 μm to 20 μm and decreases when s > 20 μm. One finds that the localization coefficient is 18.06 with a transmission of 0.55 when s = 20 μm. These results can be understood from the physical mechanism of PIT. The imaginary part of the linear first order susceptibility Im (χ) determines the field dissipation. For strong coupling, κ2 >> γrγd, Im(χ) ∝ 1/κ2 [35,37], where κ is the coupling strength between bright mode and dark mode, γr and γd is the damping factor of bright mode and dark mode, respectively. The decrease of coupling strength κ leads to increment in Im (χ) which corresponds to larger absorption cross-section of the meta-atom σ [35]. The linewidth of the transparency window Δλ satisfies the relation [35,37]. Thus, the weaker coupling strength κ causes the narrow linewidth of the transparency window. The transmission of the transparency window decreases due to the increased loss corresponding to larger Im(χ). In general, bright mode is similar to superradiant mode and dark mode is similar to subradiant mode. The coupling for the superradiant mode and subradiant mode in our case is analogous the coupling of bright mode and dark mode [38]. The larger the separation between the superradiant mode and the subradiant mode, the weaker the coupling strength. Therefore, as shown in Fig. 5(a), the narrow linewidth of the transparency window results from the weaker coupling strength and the transmission of the transparency window decreases due to the larger loss corresponding to an increment Im(χ) when the separation increases from 3 μm to 30 μm.Fig. 5 (a) Calculated transmission spectrum and (b) localization coefficient for the PIT meta-structure with different gap separations between the DSRR and cut wire. (c) Calculated Ey distributions corresponding to the transparency peak. The gaps between the DSRR and the cut wire are 3 μm, 8 μm, 10 μm, 20 μm, 30 μm and 40 μm, respectively.
The excitation strength of the bright mode and dark mode described by the two-resonator model [39] are
where Dr(ω) = 1 − (ω/ωr)2 − iγr(ω/ωr), Dd(ω) = 1 − (ω/ωd)2 − iγd(ω/ωd), ωr and ωd are the resonator frequency of the bright mode and dark mode, respectively. Considering the small detuning between ωr and ωd, ωr ≈ ωd. When ω ≈ ωr ≈ ωd, the excitations of the bright mode and dark mode satisfy the relation p(ω) ∝ γd/(γrγd + κ2), q(ω) ∝ κ/(γrγd + κ2). The excitation of the bright mode increases as κ decreases. The excitation of the dark mode increases firstly, then decreases as κ decreases, and reaches the maximum when . For the strong coupling, κ2 >> γrγd, q(ω) ∝ 1/κ [35]. Therefore, the excitation of the dark mode at the transparency window is inversely proportional with coupling strength κ for the strong coupling. The coupling for the superradiant mode and subradiant mode in our case is analogous the two resonator model. In Fig. 5(c), it can be seen that the local field around subradiant mode becomes stronger as the separation increases from 3 μm to 20 μm and decreases from 20 μm to 40 μm. The local field of superradiant mode increases all the time from 3 μm to 40 μm. In Fig. 5(b), the localization coefficient at the transparency peaks increases from 3 μm to 20 μm due to the enhancement of the local field for the both two modes and decreases from 20 μm to 40 μm for the decrease of local field for the subradiant mode. The PIT effect is destoyed when s ≥ 40μm, so the case for s ≥ 40μm did not study in this article. Based on above analysis, hence, we can acquire large transmission combined with strong local field enhancement when the separation between the superradiant mode and the subradiant mode is set at a specfic distance.5. Conclusion
An on-chip PIT on a LN subwavelength waveguide was experimentally investigated and simulated in THz regime. The PIT meta-structure consists of cut wires and DSRRs, which were deposited on the LN slab. An obvious PIT effect is obtained, which is caused by strong coupling between the respective modes in the cut wire and the DSRR. Temporal evolution analysis of the PIT effect using FDTD simulation reveals that a phase difference of π/2 arises between the two modes at the transparency peak. This finding is similar to what occurs in Rabi oscillation since some energy oscillates between the two modes. Moreover, a local field enhancement effect with high transmission occurs simultaneously, and this enhancement can be tuned by changing the separation between the two modes. We can determine a localization coefficient of 18.06 with transmission of 0.55 when the separation is 20 μm. It is believed that the highly confined THz fields with large transmission at the transparency window will be significant in future studies of nonlinear optics and THz wave sensing. These results provide a promising method for developing more useful and complex THz functional devices for THz integrated plasmonic circuits. This potential Rabi oscillation-like behavior is important for revealing the true nature of the coupling between modes.
Funding
National Natural Science Foundation of China (NSFC) (11874229, 61705013); The 111 Project (B07013); The Program for Changjiang Scholars and Innovative Research Team in University (IRT_13R29).
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