1. Introduction

Optical bound states in continuum (BICs), as the special electromagnetic eigenstates in optical transmission media whose frequency is located in the radiation continuum but is completely localized, have attracted extensive attention of optical researchers in recent years [1–5]. Optical BICs are a strong resonance effect between light and matter. Theoretically, the resonance linewidth is zero, and the quality (Q) factor is infinite. BICs are decoupled from the radiation continuum, so that it cannot be accessed in general. However, for an optical resonance system supporting BICs, such as photonic crystal or optical metasurface, adjusting the excitation wave vector, periodic boundary, shape, size or other physical parameters of this system can make BICs weakly coupled with far field radiation and leak into free space [6–10], thus allowing us to access and use BICs. Optical BIC with radiation leakage is called quasi-BIC (q-BIC), and its Q factor is non infinite and far greater than that of other resonance states.

Optical BICs supported by metasurfaces have been reported in a variety of applications, such as filtering [11], sensing [12], micro-antenna [13], polarization manipulation [14], image-based applications [15–19], micro-lasing [20], nonlinear optics and vortex optics [21–23]. The reported image-based applications of optical BICs include fingerprint encoding imaging of the optical information of biochemical molecules [15,16], and inducing object edge optical information to enhance and identify object edges [17]; these two applications are based on the far-field physical properties of q-BICs under periodic unit cell arrangement and can be classified as far-field image-based applications. Relatively speaking, near-field image-based applications of optical BICs also exist [19]. For a unit cell without periodic arrangement, the far field physical attribute of q-BIC is no longer valid, but the near-field radiation characteristics of q-BIC still exist and its variation trend is related to the far-field radiation variation trend of q-BIC in periodic structure [19]. This effect may be applied to near-field imaging and displaying devices where the number of pixels corresponds to the number of unit cells one by one. Unfortunately, although the far field image-based applications of optical BICs have been proved theoretically and experimentally, the near field image-based applications are still in theoretical demonstration and are being questioned due to the lack of experimental evidence.

In this letter, for the first time, we carried out experimental verification for the image-based applications of optical BICs. A terahertz (THz) near-field displaying metarsurface is designed, in which each display pixel is based on only one unit cell. Each unit cell after periodic expansion supports q-BIC with different far-field radiation intensity. Although a single unit cell loses its far field property under periodic effect, its near field property still exists. The electric field distribution of the metasurface in the near-field region was observed by a special two-dimensional THz detector, and the established image was successfully displayed. The near-field displaying at q-BIC frequency and non q-BIC frequency are studied. It is found that the near-field displaying results correspond to the change trend of far-field radiation intensity of periodic unit cells, indicating that the near-field displaying function is indeed induced by q-BIC effect, which experimentally proves the feasibility of near-field image-based applications of optical BICs. Finally, we demonstrate the potential application of such near-field displaying in the field of information encryption, and this effect may also be extended to more fields.

2. Simulation and Experiment

The sample is made of all silicon dielectric material (ε=11.9 ρ>5000 Ω·cm [24]), and its unit cell structure is shown in Fig. 1(a). The unit cell periodic constant is P = 160 µm. If the geometric center in the unit cell plane is taken as the coordinate origin, the in-plane center coordinates (x, y) of two identical elliptical bars can be expressed as (-40 µm, 0) and (40 µm, 0), respectively. The height of the silicon elliptical bars is h₁ = 200 µm, and the thickness of the silicon substrate is h₂ = 300 µm. A pair of elliptical bars with in-plane rotational symmetry (C₂ symmetry) can support the optical BICs mode. The long axis of the elliptical bars is L = 130 µm, and the short axis is W = 30 µm. When two elliptical bars rotate with an angle of θ in the plane in opposite directions around their geometric centers, the structural C₂ symmetry broken will support the q-BIC mode with radiation leakage. The leakage rate and transmission amplitude of q-BIC are controlled by angle θ. Each unit cell is taken as a near-field displaying pixel of the sample. These unit cells are asymmetric elliptical bars with different θ, which radiate different electromagnetic field intensities in the near-field region to correspond to different grayscales of the image to be displayed.

 

Fig. 1. (a) Unit cell diagram of near-field displaying metasurface sample, one unit cell corresponds to one pixel; (b) two-dimensional near-field THz detection system for characterization.

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In this work, the COMSOL software with frequency-domain finite element technique is used for all simulation analysis, where Floquet periodicity boundary is used for x-y direction. The sample was prepared by inductively coupled plasma (ICP) etching technology, using SF₆ as the etching gas. The characterization system of THz near-field displaying is shown in Fig. 1(b), which is based on the transformation of the classic THz time-domain spectrometer (THz-TDS). Therefore, most of the system is similar to the THz-TDS. A beam splitter is used to divide the femtosecond pulse laser into two paths, one path of laser is transmitted to the THz emission port through the reflectors R1-R5, and the THz generation uses the femtosecond pulse light to excite the photoconductive antenna. The THz time-domain signal is generated by adjusting the delay of the optical path composed of reflectors R2 and R3. The THz signal is collimated by an ellipsoid mirror, and the polarization state is controlled by a polarizer. The THz beam incidents on the back of the metasursurface sample, and its light spot is enough to evenly cover the sample. Another channel of femtosecond laser is transmitted to the THz receiver through the reflectors R6-R8 and a scattering compensation device. Before the femtosecond laser is transmitted to the THz receiver, a fiber coupler is used to couple the spatial light into the fiber, and the dispersion in the fiber is pre-compensated by the dispersion compensation device between R6 and R7. The output light of the optical fiber finally shines on a commercial terahertz near-field probe through a small reflector. The probe is also based on a photoconductive antenna that can detect the E_z component of the THz electric field on the sample surface. Finally, the amplitude and phase information within the required frequency range can be obtained by Fourier transformation of the obtained THz time-domain signal. In order to obtain the near-field THz electric field distribution on the entire sample surface, the THz probe, optical fiber coupling output port and a small reflector are fixed on a two-dimensional mobile platform. By moving the platform in the x and y directions, the probe completes the scanning on entire sample surface to obtain a two-dimensional THz near-field detection map.

3. Results and discussion

The BICs can be identified by analyzing the pattern symmetry and the change of Q factor. The relationship among eigenfrequency, radiative Q factor and θ is shown in Fig. 2(a)-(b). Here, only eigenstates located at high symmetrical point (i.e. Γ point) are considered, which corresponds to radiation wave vector in the z direction perpendicular to the unit cell surface. As shown in Fig. 2(a), when θ = 0°, the transverse magnetic (TM) eigenmode located near 0.95 THz can be found. At this time, the structure meets C₂ symmetry. This physical property can be described mathematically as f(x, y) = f(-x, -y). With θ changing to 15°, the C₂ symmetry of the structure is broken, enhancing the degree of asymmetry, and the eigenfrequency at Γ point is tuned to around 0.97 THz. The corresponding radiative Q factor is shown in Fig. 2(b). It can be seen that when θ = 0°, TM intrinsic mode has infinite Q factor, and Q factor decreases exponentially with θ increasing. The abscissa and ordinate axes of Fig. 2(b) are expressed in logarithm, as shown in Fig. 2(c). The relationship between Q factor and θ presents Q ∝ θ^-2. The change trend of Q factor conforms to the Q factor characteristics of symmetry-protected BIC [25]. With the symmetry breaking, the change in far-field transmission spectra are obvious, where BIC is transformed to q-BIC with the sharp resonance spectrum, as shown in Fig. 2(d). Another characteristic of symmetry-protected BIC is that the symmetry of BIC mode is incompatible with the symmetry of radiation continuum [26]. Therefore, the electromagnetic distribution is further analyzed to determine the eigenmode. It is required for TM mode to detect the distribution of z component electric field amplitude E_z, as shown in Fig. 2(e). At 0.95 THz, the E_z distribution of radiation continuum is compared with that of BIC mode. The radiation continuum is excited by the normally incident far-field x-polarized THz wave. Please note that the electromagnetic distribution monitored under far-field x-polarized wave excitation is radiation continuum mode rather than BIC mode, due to the far-field non-excitable property of BIC. Since the BIC is a far-field non-excitable electromagnetic eigenstate, its electromagnetic field distribution can only be obtained by solving its eigenfield. The results show that the radiation continuum is odd symmetric, i.e. E_z(x, y) = -E_z(-x, -y), but the BIC eigenstate with zero radiation leakage is even symmetric, namely E_z(x, y) = E_z(-x, -y). These phenomena prove the mode incompatibility between the radiation continuum and BIC mode, and such BIC is an even bound mode completely hidden in the odd radiation continuum.

 

Fig. 2. (a) The rotation angle θ dependent eigenfrequency, and the corresponding radiative quality factor expressed as (b) linear from and (c) logarithm form. (d) The far-field transmission spectra comparison for BIC and q-BIC, where q-BIC spectrum with θ = 3° are selected (e) The normalized electric field amplitude E_z for BIC mode and radiation continuum mode.

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Under the normal incidence of x-polarized THz wave, the far-field transmission spectra of periodically arranged unit cells at different rotation angles θ are shown in Fig. 3. The displacement of the q-BIC peak position in Fig. 3(a) is consistent with the eigenfrequency shift in Fig. 2(a), and the transmission amplitude of the unit cells depends on the angle θ, which is the premise of realizing near-field displaying. When each pixel corresponds to only one unit cell, the unit cell no longer has the far-field radiation properties in the case of periodic expansion, but the near-field radiation amplitude trend still exists and is similar to far-field radiation trend. To prove this, we first extract transmission amplitudes at different frequencies and plot them in Fig. 3(b) to determine the near-field radiation amplitude trend that different unit cells should have. These representative frequencies are 0.8 THz, 0.92 THz, and 0.97 THz. These frequencies show some particularities: I) at 0.8 THz, the amplitudes of different unit cells are similar and difficult to distinguish; II) at 0.92 THz, the amplitude of different unit cells can be distinguished gradually, but the amplitude discrimination is far less than that of 0.97 THz; III) at 0.97 THz related to q-BIC, the amplitude differentiation of different unit cells reaches the maximum, and has a good monotonic variation characteristic with θ. It can be expected that when a unit cell corresponds to a pixel one by one in a display array, the near-field amplitude should show the following trends: I) at 0.8 THz, it is difficult to distinguish the electric field intensity between different pixels; II) at 0.92 THz, the electric field intensity between different pixels can be distinguished, but the contrast is weak; III) at 0.97 THz, the electric field intensity between different pixels should have the best contrast.

 

Fig. 3. (a) The relationship between the far-field transmission spectra and the rotation angle θ, as the x-polarized THz exciting periodic unit cells. (b) The comparison of amplitude values at three representative frequencies.

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A near-field displaying metasurface sample with the test results are shown in Fig. 4. We selected an 80 × 80 pixel “panda head” as the original grayscale image, and selected six basic unit cells (θ = 0°, 3°, 6°, 9°, 12° and 15°) to represent six grayscales. The construction process of the metasurface sample is as follows. Extract the grayscale value of each pixel in the original image, and redefine these values according to six grayscales, as shown in Fig. 4(a). The six grayscales in order correspond to six basic unit cells. For example, the pixel with the highest grayscale value (the brightest) corresponds to the unit cell with θ = 0°, and the pixel with the lowest grayscale value (the darkest) corresponds to the unit cell with θ = 15°. Here, each pixel only corresponds to one unit cell, thus finally it forms an 80 × 80 pixel metasurface. The sample schematic diagram and physical image are shown in Fig. 4(b). Use the system shown in Fig. 1(b) to test the distribution of the spatial electric field amplitude E_z of the metasurface sample on a plane in the near-field region. The test probe is located 200 µm away from the sample surface, which is lower than the operating wavelength, and is a typical near-field region. The results are shown in Fig. 4(c)-(e). It can be seen that at 0.8 THz, due to the small difference of transmission amplitude of different unit cells, the contrast of imaging results is poor with indistinct outline (Fig. 4(c)), and the original image can hardly be presented. At 0.92 THz, although the transmission amplitude of different cells varies monotonously with θ, the contrast is significantly lower than that at 0.97 THz (Fig. 4(d)). At the 0.97 THz related to q-BIC, the results successfully reproduce the original image with obvious contrast, and the grayscale distribution is in good agreement with that of the original image (Fig. 4(e)). These experimental results are in good agreement with the predictions, which proves the feasibility of near-field displaying of BICs. It should be noted that there is a dark spot on the tongue of the panda, which is a bad point, and this is due to the damage of the sample in this area. Also, the panda image of sample can be directly observed by eyes, which is actually a coincidence (the reasons are described in section S1 in Supplement 1). Soon, we will find that the visual pattern with naked eyes can be designed to be completely different from the real information.

 

Fig. 4. (a) The process of grayscale value extraction and metasurface reconstruction; (b) the physical photos and scanning electron microscopy images of sample with side and top views, where the white scale bar is 100 µm; (c-e) experimental results of THz near-field displaying at different frequencies.

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The use of silicon materials also has special advantages, that is, it is convenient to add a free degree of dynamic switch control for BIC near-field displaying. By changing the Si conductivity to modify the complex eigenfrequency to enhance the absorption loss of electromagnetic waves [27,28], it can be found that while the transmittance of the unit cells decreases, the transmission intensity difference among these unit cells also reduces significantly, as shown in Fig. 5(a). This trend will also be shown in the change of near-field intensity. As a result, the contrast of the image decreases or even disappears to complete the switching of near-field displaying status from ‘ON’ to ‘OFF’. The photo-generated carriers in sample are excited by the 1064 nm continuous wave pump, as shown in Fig. 5(b). The Si conductivity can be increased to 80 S/m when the pump power is increased to 0.65 W. It is easy to find that the contrast of the tested image decreases significantly until it disappears, as shown in Fig. 5(c). In the experiment, the optical switch control of BIC near-field displaying is realized.

 

Fig. 5. (a) The simulated transmission amplitude at 0.97 THz for different Si conductivities (the data with Si conductivity less than 0.02 S/m is the same as that in Fig. 3(b)). (b) The schematic diagram for the optical pump with 1064 nm continuous wave (CW). (c) The experimental results for displaying at 0.97 THz (the image without pump is the same as that in Fig. 4(e)).

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The main achievement we have obtained is to prove the relationship between near-field and far-field transmission trends of q-BIC through the near-field displaying experiment, which has not been proved before, and may show potential application in the following field: the pattern seen by the naked eye can be completely different from real THz pattern designed through the special arrangement of unit cells, and this feature can be applied to the field of information encryption. The confidential information is edited as a disposable key containing frequency, polarization and other information, which is restored through the near-field displaying, where the pattern seen by the naked eye can be used as a disguise. We demonstrate the signal transmission for two binary-coded letters, such as ‘AB’, which have 16-bit binary codes, namely ‘01000001 01000010’, as shown in Fig. 6(a). It is easy to imagine that these binary codes can be realized by encoding the x-polarized wave transmission intensities at 0.97 THz of symmetric unit cell and asymmetric unit cell (θ=15°) to ‘1’ and ‘0’ respectively, but this method is also easy to be cracked. To enhance the difficulty of information decoding, we can further consider the different incident and transmission polarization states to enhance the complexity of coding. For symmetric unit cell supporting BIC, the transmission intensities of incident x- and y- polarized waves are high, and their values are generally the same and can be coded as 1, recorded as Cx = Cy = 1. For asymmetric unit cell with θ=15°, the q-BIC mode is only sensitive to x polarization, so an extremely low transmittance is obtained at 0.97 THz, which is coded as Cx = 0, while the y polarization transmission wave still maintains a high transmittance, which is coded as Cy = 1 (see section S2 in Supplement 1). Obviously, after the asymmetric unit cell is rotated by 90°, the corresponding transmission code will be switched to Cx = 1 and Cy = 0. Next, define the logical operator ‘AND’ as Cx × Cy. When both Cx and Cy are 1, we have Cx × Cy = 1, otherwise Cx × Cy = 0. Further, we can use the value of the logic operation Cx × Cy to correspond to binary codes of ‘AB’, and the corresponding unit cells are shown in Fig. 6(d). When the binary code of the letter is ‘1’, that is, Cx × Cy = 1, in which Cx = 1 and Cy = 1, and the structure satisfying this condition is a symmetric unit cell; when the binary code of the letter is ‘0’, that is, Cx × Cy = 0, there are two cases to meet the conditions, one is that Cx = 0 and Cy = 1, and the second one is that Cx = 1 and Cy = 0, which respectively correspond to the asymmetric unit cell before and after 90° rotation. Herein, we set 16-bit Cx to ‘01000001 01000010’ and 16-bit Cy to ‘01110011 11100110’, and it easy to found that values of 16-bit Cx × Cy are equal to binary codes of ‘AB’, i.e. Cx × Cy = ‘01000001 01000010’. It should be mentioned that code of Cx and Cy is not unique, and multiple code arrangements can make values of the Cx × Cy can correspond to binary codes of ‘AB’. Then, arrange the 16 unit cells in Fig. 6(d) as a 4 × 4 form to complete the creation of the metasurface carrying ‘AB’ information, as shown in Fig. 6(b). By detecting the near-field intensity distributions of the metasurface under the excitation of x- and y- polarizes waves at 0.97 THz, the Cx and Cy can be got, and then the original information will be revealed by performing the logic operation Cx × Cy, as shown in Fig. 6(c). The idea of using values of logic operation Cx × Cy to correspond to the binary codes of ‘AB’ contains the effect induced by multiple polarization states, which is more complex than directly using the electric field intensity coding under a single polarization state, so the transmitted information is more confidential.

 

Fig. 6. The conceptual design and simulation results for information encryption application. (a) Information encoding process considering polarization state; (b) the corresponding metasurface with 4 × 4 pixels, where one pixel corresponds to 3 × 3 identical unit cells; (c) by detecting the near-field intensity distributions of different polarization states at the q-BIC frequency of 0.97 THz, the coded information of Cx and Cy are obtained, and then the original information is showed by performing the logic operation Cx × Cy.

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Of course, the information encryption application shown in Fig. 6 is not limited to the use of frequency and polarization. As mentioned in Fig. 5, the use of silicon material provides a free degree of dynamic displaying control, and such physical attribute related to Si conductivity change can also be incorporated into the information encryption application shown in Fig. 6 to further enhance the key strength. In addition, the applications of near-field displaying supported by BIC may be extended to more fields. By using q-BIC coding, the intensity of the incident THz field can be adjusted at the pixel level to prepare a high-resolution near-field mask, which is helpful for high-resolution non-destructive detection of hidden objects (such as circuits in chips) [29]. Some substances have specific resonance peaks in THz band; the frequency tuning attribute of q-BIC can be used to design a near-field array with resonant frequency covering the matter feature peak [15], so as to realize the image-based coding of the THz feature information of the matter with the smallest device volume. Meanwhile, compared with BIC far-field displaying (that one pixel is composed of multiple identical unit cells), BIC near-field displaying (that one pixel corresponds to one unit cell) does not require a large number of unit cells, which not only compresses the image size, but also improves the image resolution.

4. Conclusion

In summary, we have designed an all-silicon dielectric near-field displaying metasurface that supports THz q-BIC, where each display pixel is based on only one unit cell. The electric field distribution of the metasurface in the near-field region is observed by a special two-dimensional THz detector, and the established image is successfully displayed. In addition, the near-field displaying results at different frequencies are studied and compared. It is found that the display quality is closely related to the q-BIC frequency, which confirms that this near-field displaying function is based on the q-BIC. This work proves the feasibility of the near-field image-based application of optical BICs for the first time, which may play a role in many fields such as information encryption.