Article Cite This: ACS Photonics 2019, 6, 1774−1779
pubs.acs.org/journal/apchd5
Broadband on-Chip Terahertz Asymmetric Waveguiding via PhaseGradient Metasurface Ride Wang,† Qiang Wu,*,†,‡ Wei Cai,*,†,‡,§ Qi Zhang,† Hao Xiong,† Bin Zhang,∥ Jiwei Qi,†,‡ Jianghong Yao,†,‡ and Jingjun Xu*,†,‡
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Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education, TEDA Institute of Applied Physics and School of Physics, Nankai University, Tianjin 300457, China ‡ Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China § Renewable Energy Conversion and Storage Center, Nankai University, Tianjin 300071, China ∥ College of Science, Civil Aviation University of China, Tianjin, 300300, China ABSTRACT: As fundamental elements, optical diodes are required for on-chip optical communications and computing. However, it is still a challenge to realize ultracompact devices working in the terahertz (THz) range. Here an optical diode device with a bandwidth up to 100 GHz that is able to produce a highly asymmetric THz propagation was designed by coupling a gradient metasurface and subwavelength waveguide modes. This system is based on the breaking of the momentum symmetry at the interface with phase discontinuities. The asymmetric transmission process generated by THz mode conversion is detected by employing time-resolved phase contrast imaging. The results agree well with full-wave electromagnetic simulations. Moreover, the performance of the working bandwidth and the ratio of transmission of the device can be optimized by the induced arbitrary scattering phase. These performances indicate that this design provides a very effective method and a versatile platform for on-chip information processing by preventing undesired light interference in the integrated system. KEYWORDS: on-chip asymmetric propagation, phase-gradient metasurface, terahertz time-resolved phase contrast imaging, lithium niobate
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previous work it was demonstrated that these coupled devices may be an excellent platform for enhanced on-chip analyte sensing in the terahertz (THz) region.24 The combination of a metasurface and a rectangle waveguide may provide a new solution for the realization of ultracompact optical diodes. Currently, novel integrated devices using rod-shaped metasurfaces have been demonstrated despite being limited to the infrared and microwave region.22,25 In addition, at spectroscopically important THz frequencies,26−29 asymmetric transmissions relying on the polarization conversion have been reported.30 However, the design of a device that may facilitate the optical integration over a broadband in the THz region still remains unexplored. This paper presents an innovative device to produce a highly asymmetric propagation in a broadband of the THz spectrum on an integrated platform by combining gradient metasurfaces with subwavelength waveguides, which is based on the principle of the momentum symmetry breaking at the interfaces with phase discontinuities. By engineering the degrees of freedom of a metasurface, the device could work with up to a 100 GHz bandwidth. Its asymmetric transmission behavior was directly observed by using time-resolved phase contrast imaging associated with the dispersion relation, along
ptical diodes enable the asymmetric transmission of light in information communication and optical computing.1,2 In contrast to common electrical diodes equipped with a semiconductor p−n junction, optical diodes are inherently complex due to the time-reversal symmetry of light−matter interaction. Considerable effort has been dedicated to studying their asymmetric transmission behavior. This effect is based on the nonreciprocal physical response associated with the breaking of time-reversal symmetry by the magneto-optical effect,3−6 nonlinear optics,7,8 and indirect interband photonic transition.9,10 An ideal optical isolator can be designed by using any of these approaches; however, large devices are always required, and it is challenging to integrate them on a chip. In contrast, the optical-diode phenomenon can be realized in a simpler way by employing various reciprocal structures with spatial symmetry breaking, such as chiral or hyperbolic metamaterials,11−13 bilayer metallic strips,14,15 digital metamaterials,16 U-shaped resonators,17 and photonic crystals.18,19 Despite this, major challenges, including the miniaturization of asymmetric transmission devices and the increase of the operation bandwidth still exist and are not favorable for the integration of on-chip photonic systems. Recently, a specially designed metasurface combined with rectangle waveguides with a small cross section as an ideal model for integration that could obtain asymmetric transmission based on breaking spatial symmetry has attracted much interest.20−23 In a © 2019 American Chemical Society
Received: April 8, 2019 Published: June 12, 2019 1774
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Figure 1. Schematic diagram of the asymmetric propagation and the asymmetric optical power transmission, phase and resonator response of optical microrods. (a) Graphical representation of the device, which supports the highly asymmetric transmission due to the gradient metasurface, works at about f = 0.38 THz. The upper panel shows the unit cell dimensions of the microrod with its periodicity, Λx = 30 μm, and its width, w = 10 μm. The offset of the microrod array from the rectangle waveguide central axis is g = 20 μm (distance between two black dashed lines). The rotation of the microrods (red dashed line) from the optical axis of LN (y direction, blue dashed line) is θ = 40°. The LN subwavelength rectangular waveguide measures 200 μm in width and 50 μm in thickness. The waveguide mode transmits along the x axis. (b) The full-wave simulation shows that in the forward direction the incident TE00 mode converts into the TE10 mode and that the effective wavelength increases. (c) The incident TE00 mode is blocked in the backward direction. (d) Optical power transmission spectra in the opposite propagation direction. The solid and dashed lines show the power transmission of the whole field and of the waveguide, respectively. (e) The forward−backward transmittance shows that a highly asymmetric transmission is maintained over a broad bandwidth. (f) Phase and amplitude of scattered light from microrods placed on the top of LN is obtained as a function of the microrod length.
Table 1. Design Parameters To Achieve Unidirectional Transmission device and modal index change
microrod lengths (μm)
117.3, 109.3, 105.0, 101.7, 99.5, 97.7, 96.3, 95.2, 93.7, 92.7, 91.2, 90.1, 88.7, 87.8, 86.5, 85.4, 84.3, 83.2, TE00 → TE10, 3.22 → 2.04 82.5, 81.4, 80.3, 79.2, 78.2, 77.1, 76.0, 74.9, 73.4, 72.4, 71.3, 70.2, 69.2, 66.9, 65.8, 64.7, 63.3, 61.8, 60.4, (f = 0.38 THz) 58.9, 57.1, 55.3, 53.9, 52.1, 50.2, 48.1, 45.9, 43.7, 41.5, 39.4, 36.5, 32.8, 26.7, 16.2
with full-wave simulations, which agree well with the experimental results. The findings presented in this paper promise novel applications in an ultracompact footprint and shine a light on the next generation of on-chip communication functional devices. The perspective view of the sample is shown in Figure 1a. The device supports a highly asymmetric optical power transmission because the unidirectional phase gradient introduces a breaking in the momentum symmetry. The gradient metasurface consists of 52 phased gold microrods patterned on the top surface of lithium niobate (LN) subwavelength rectangle waveguide. The width of a single microrod is w = 10 μm and the distance between the two adjacent microrods is Λx = 30 μm. It should be noted that there exist two degrees of freedom: the offset of the microrod array from the waveguide central axis, g = 20 μm, and the
rotation (deg)
offset (μm)
Δϕ (deg)
Λx (μm)
40
20
3.5
30
microrod rotation around the optical axis of the LN waveguide (y direction), θ = 40°. The parameters of the gradient microrods are shown in detail in Table 1. The numerical calculations to validate the design are performed with a commercial 3D finite-difference time-domain (FDTD) solutions software. A column of dipoles was placed in the LN rectangle waveguide as a source to excite the waveguide mode. Its polarization was aligned with the LN crystallographic optical axis. The gold microrod is set to perfect electrical conductor (PEC) due to the conductivity of it in the THz band at the order of 107 S/m. The simulated area boundaries were all set to the perfectly matched layer. Figure 1b,c depicts the mode evolutions in two opposite propagation directions at f = 0.38 THz. This indicates that the optical power transmission is asymmetric. One can see that, in the forward direction, the incident TE00 mode is converted into the TE10 1775
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Figure 2. Design of metasurfaces with a simultaneous working bandwidth and transmission control and spatial electric field distribution with different elements. (a, b) Forward and backward transmission of microrod arrays with different offsets and rotation degrees of freedom. (c, d) Nearfield spatial electric field distribution of the microrod on the top of the LN waveguide with different offsets and rotations. Black dashed lines indicate the location of the LN rectangle waveguide cross-section.
mode with 73.2% high transmission. This is in sharp contrast to the backward direction, where the optical power is blocked by a limited reflection or by a high optical scattering, which results in a low output energy. The broadband transmission spectra of the device in the opposite propagation directions are shown in Figure 1d (solid line). These results reveal that the transmittance along the forward and backward transmissions is distinct. A much broader spanning of forward−backward transmittance (>100) reaches up to 100 GHz, ranging from f = 0.28 and 0.38 THz, as shown in Figure 1e. In this section, the physical mechanism behind this performance is investigated. A beam of light penetrates into the metal microrod, which is coupled into surface electromagnetic waves and travels back and forth along the surface. This process is accompanied by the excited charge oscillations of the microrod. As a result, the surface wave and the oscillating charge are coupled, which is our well-known as surface plasmon. The abrupt phase shift over the free-space wavelength scale can be introduced via the strong interaction between light and the localized surface plasmons. The phase of the surface plasmon of the microrod can be controlled by spatially tailoring the length of the microrod. Thereby, the phase change between the scattered light wave from the optical microrod relative to that of the incident light wave sweeps a range of ∼π,31,32 as shown in Figure 1f. The design in Figure 1a is based on the concept of using phase discontinuity to control guided waves by consecutive scattering events at the microrod array. A gradient metasurface with a discontinue constant phase difference, Δϕ, and a subwavelength period, Λx, between adjacent microrods introduces a unidirectional phase gradient, Δϕ . This is equivalent to a unidirectional
kxout = kxin − N
Δϕ Λx
where kin/out = k0nin/out, k0 = 2πc/f is the free-space wavevector, x nin and nout are the index of the input and converted waveguide mode, respectively. Moreover, f is the working frequency, c is the light velocity in vacuum, and N is the number of effective actions to complete the transformation of different waveguide modes. For example, the index decreases from 3.22 to 2.04 in the TE00-to-TE10 mode conversion in the LN subwavelength rectangle waveguide at f = 0.38 THz, where Δϕ = 3.5° and Λx = 30 μm. The Δϕ induced by the metasurface imparted to the Λ_
guided mode conversion process. The large number of effective interactions occurs over a propagation distance of 1.54 mm (the length of the microrod array), which is only 1.95× larger than the free-space wavelength λ0 = 0.789 mm. These indicators suggest that such a device has reduced the footprint substantially and can work in a broad THz band compared to an existing traditional asymmetric device. Furthermore, an analysis of the effects of two degrees of freedom (the different offset and rotations on forward and backward transmission) is provided in this section. Figure 2a,b shows that the forward and the backward transmissions are approximately zero when both rotation and offset are zero. This is a peculiar phenomenon which cannot support asymmetric transmission by combining the metasurface and the subwavelength rectangle waveguide. Interestingly, the forward transmission would be improved and works in broadband as either of two elements changed. The scattering spatial electric field distribution of the microrods attached to the surface of a subwavelength dielectric LN waveguide may be used to explain the aforementioned outcome. For the TE00 incident, when the microrod is at the center of the waveguide and its orientation is aligned with the y axis, the horizontally polarized near-field component has no spatial overlap with any other mode, as shown in Figure 2c. In this case, the radiation field of the microrod cannot form a stable mode inside the
Λ_
momentum keff along the surface. As a result, the microrod arrays have a collective action on the waveguided modes. The total imparted compensating momentum required for mode conversion satisfies the following formula, 1776
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subwavelength waveguide. However, when a microrod is displaced from the center of the waveguide (for example, by 20 μm) and is oriented at a nonzero angle (for example, 40°), its near-field component has a nonzero spatial overlap with the TE10 mode, as shown in Figure 2d. A steady mode field distribution is then formed at the cross-section of the subwavelength rectangle waveguide. Thus, the various electric field distributions in the waveguide, caused by the microrod scattering on the surface of waveguide, can be implemented by gradual engineering of the relative position of the microrod to the waveguide. Therefore, the realization of forward transmission needs two conditions: (i) a gradient metasurface has to provide an additional momentum to match the momentum conservation; (ii) the microrod near-field component has to exist as a nonzero spatial overlap with a particular mode on the cross section of the waveguide. By properly choosing the location of the microrods on the waveguide top surface and their orientation, selective coupling between two waveguide modes was obtained. Contrary to the previous results, the change of these elements does not affect the backward transmission, as shown in Figure 2b. Additionally, the transmission is approximately zero in a wide spectral range due to the additional momentum, which is unidirectional. This phenomenon provides the possibility to build on-chip asymmetric transmission devices. The distinct behavior of asymmetric waveguide propagation can be best described and analyzed by the transmission process of the optical power associated with dispersion relation based on the pump−probe systerm. A Ti:sapphire regenerative amplifier is separated into a probe beam and a pump beam so that the standard ultrafast detection in Figure 3a is achieved. The y-polarized pump beam is tracked through a mechanical delay line and a blazed grating, which are imaged into the LN slab by a cylindrical lens (with focal length of 20 cm) to produce linearly polarized narrow THz waves.33 One notices that the THz electric fields and polarization of the pump beam are aligned with the optical axis of the LN crystal. On the basis of the electro-optic effect,34 A time- and space-dependent change of LN refractive index is induced as the THz wave propagates inside the LN slab. The 400 nm probe branch is expanded to irradiate the whole sample, whose phase is modulated immediately after the sample. This produces a shift, which is proportional to the refractive index.35,36 By relying on the 4f system, the phase-to-amplitude conversion is performed. Then changing the time delay between the arrival time of the pump and the probe pulses on the sample, a full spatiotemporal evolution of THz wave is achieved from the image sequence. Based on this experiment, through the extraction of the intensity information from the image recorded at each time delay, the signals are integrated into a row vector along the y direction. By displaying the integrated row vectors in time along the vertical axis one generates a space-time map.37 Figure 3b−e shows the space−time plots of the LN subwavelength rectangle waveguide decorated with a gradient metasurface. In these images, the conversion, dispersion and reflection processes are presented. In order to more clearly interpret the propagation properties of optical power in the sample, the incidence (Inci.) and reflection region (Refl.), the metasurface region (Meta.) and transmitted region (Tran.) were added. Concerning the forward transmission, one can notice in Figure 3b,c that the coupled TE00 mode passes through the metasurface smoothly and is transformed into another mode.
Figure 3. (a) Schematic diagram of the experimental setup. The 800 nm pump beam (red) is diffracted by a 1200 lines/mm blazed grating. The diffraction passes through a cylindrical lens with a focal length of 20 cm and strikes the 50 μm thick LN slab, generating THz waves. The probe beam (blue) is frequency-doubled to 400 nm via a BBO crystal and irradiates the whole sample at normal incidence. The focal length of the 4f system is f = 10 cm, with the phase plate placed in the Fourier plane of the first lens. The signal is collected with a CCD after the lens group. The inset diagram shows the microscope image of a sample. The microrods are placed on the top surface of the LN subwavelength rectangle waveguide. The gradient metasurface consists of 52 microrods with a 20 μm offset from the central waveguide and 40° rotation from optical axis. (b−e) Experimental and simulation results of forward and backward temporal evolution. The space−time plots of the hybrid structure with the image intensity show the transmission of THz electric field which was extracted from the LN subwavelength rectangle waveguide. These plots are divided into three regions: incidence (Inci.) and reflection region (Refl.), metasurface region (Meta.), and transmitted region (Tran.). The two black dashed lines are the metasurface edges.
However, the energy is blocked in the backward direction, as shown in Figure 3d,e, because there is no lower order waveguide mode to match the increased momentum of the TE00 mode. Meanwhile, the continuous wiggles in the “Meta.” result from the consecutive oscillation of the microrods electric field in Figure 3e. In the experiment result (Figure 3d), the energy has been reflected and scattered before reaching the interface x ∼ 2.1 mm. As a result, it is clear that the hybrid structure supports asymmetrical transmission. According to the spatiotemporal data, the frequency information on the transmission can be easily acquired. Figure 4a−f shows the corresponding dispersion diagrams of the experiment and the numerical simulation, which were obtained by applying a 2D Fourier transform to the Inci. and Tran. in 1777
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Figure 4. Dispersion curves. (a, b) Transverse electric modes of LN subwavelength rectangle waveguide are obtained experimentally and by performing numerical simulation using the 2D Fourier transform of the Inci. space−time plot in Figure 3b−e. They are related to processes of the forward and backward incidence, respectively. The first three transverse electric modes of the subwavelength LN rectangular waveguide with 200 μm width and 50 μm thickness are shown in (b). (c, e) Experimental dispersion curves of the Tran. modes. (d, f) The corresponding simulations, showing good agreement with experiments.
Figure 3b−e. When the THz wave is in Inci., it is mainly coupled as the TE00 mode, as shown in Figure 4a,b. After that, concerning the forward transmission, it is gradually converted into the TE10 mode, as shown in Figure 4c,d. Nevertheless, in the process of backward transmission, the optical power is obstructed and only a low energy leaks out (Figure 4e,f). When compared with the amplitude of the incident field, the leakage can be almost neglected. The experimental results show a high accuracy and consistency with the simulation results reported in Figure 1d (dashed lines). Moreover, the microrod array allows the device to achieve a broadband performance because of an inverse relation between the device dimension and its working bandwidth.38
THz devices. The gradient metasurface could be used to break the symmetry between optical pumps and generated optical signals and thus help to relax the phase matching requirement in the on-chip wavelength conversion process. This would open a door for THz integrated functional devices. The aforementioned features make this device attractive as a potential component for future on-chip highly integrated photonic information processing systems.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. *E-mail:
[email protected].
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CONCLUSION In this paper, a device with a highly asymmetric propagation over a broadband THz spectrum has been presented via the strong interaction between a gradient metasurface and a THz waveguide mode. The metasurface converts the waveguide modes by consecutive optical scattering. The scattering phase and the different mode field distribution in the waveguides were controlled by designing the metasurface. As a result, the working bandwidth and the ratio of the transmission of the asymmetric propagation were optimized. Such excellent properties in the THz frequencies could not be achieved with other devices previously presented. The size of the photonic integrated devices based on this kind of metasurface is smaller than for conventional devices since they do not require any external assistance, such as the introduction of magnetic fields or a radio frequency modulation. Based on the experiments and the simulations, the process of transmission and mode conversion demonstrates the reasons and the characteristics of the asymmetric transmission. This process may contribute to a deeper investigation of other functional
ORCID
Qiang Wu: 0000-0003-3189-2219 Wei Cai: 0000-0002-4451-5239 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (11574158, 11874227, 61705013, 91750204, 11774185), the 111 Project (B07013), the Program for Changjiang Scholars and Innovative Research Team in University (IRT_13R29), the Tianjin Natural Science Foundation (18JCQNJC02100), and the Fundamental Research Funds for the Central Universities (Nankai University (63191522, 63191738)).
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