As a cloaking scheme, two prerequisites should be met: a clear image transfer and a hidden inner structure25. Foreground mask Ψ featured 0.7 mm × 0.7 mm is set before the entrance window of the photonic chip and this Ψ image is expected to be soundly transported through the chip without any interference with an inner structure ħ. In order to cloak the 0.44 mm × 0.35 mm ħ structure inside a chip, which is fabricated with a high power laser, we prototype up to 5,000 waveguides in three dimensions along a spindle path opening up the central space for the ħ to be hidden in (Fig. 1a).

Figure 1 (a) Principle of on-chip cloaking. Directional light through a mask of “Ψ” is incident onto the window where thousands of waveguides embedded in the chip, propagating along the waveguides to circumvent the inner structure “ħ” and re-assembling to restore the mask image “Ψ” without interference of “ħ”. (b–d) Characterization of cloaking structures with different pitches: (b) Cross sections of cloaking windows under the microscope with scale bars and duty cycles. Output images of the cloaking structures with (d)/without (c) the inner structure with pitches varying from 13 μm to 31 μm. Full size image

In this section, we characterize the cloaking structures by different pitches and optimize the performance with the introduced similarity assessment. Tomography analysis is applied to unveil the evolution of light field in the optimal one. In the end, we benchmark the robustness of the cloaking device with a continuous three-dimensional viewing angle scan.

Cloaking performance optimization

The spindle of tightly bounded waveguides seems to be a favorable choice to obtain a high resolution image. However, considering the interactions between waveguides, the pitch is obviously a crucial parameter to determine the clarity of image transfer. In our experiment, we fabricate 10 configurations of spindles with different pitches ranging from 13 μm to 31 μm and the corresponding cross sections captured using a 20× objective lens with a numerical aperture of 0.04 and 16× eyepieces are exhibited in Fig. 1b. A Gaussian beam (405 nm) is radiated through the mask at the input of the spindle and collected at the output by a CCD camera, as shown in Fig. 1c,d. Each configuration contains two sets: with (Fig. 1d) and without (Fig. 1c) the inner structure. As illustrated in Fig. 1c,d, various outputs are observed owing to different pitches. In order to evaluate their performances, a uniform statistical criterion should be set up. Therefore we introduce the normalized cross correlation (Γ)26,27, a common and convenient assessment of the similarity between two image patterns with the basic idea to compare the grey scale of each corresponding pixel between two images. Specifically, when images are converted into grey matrixes, Γ between image a and b can be represented as:

where i = 1, 2, … represents the ith pixel of the image. , is the average value of all the grey scale of pixels of a and b, respectively. According to the definition, the Γ ranges from 0 to 1; the closer to 1 the value is, the more similar two figures are to each other.

Firstly we compare the similarity of Ψ between the one only passing through the chip substrate (Fig. 2a) and the one passing through the waveguides with different pitches (Fig. 2b,c). The results (Γ a,b ; Γ a,c ) sketch that the Γ value increases steadily and reaches the peak at the pitch value of 21 μm and then decreases with the pitch getting larger. The optical coupling (crosstalk) distorts the light field propagating in the waveguides when they get too close to each other. It conforms to a monotonous tendency, which optical coupling decreases by about 85% with every pitch increase of 2 μm, according to our calculation. Due to the elliptical cross section (see Fig. 1b), the crosstalk distortion is especially intensive in the vertical direction. On the other hand, a larger pitch constraints the total volume of information in virtue of the lower waveguide density. We calculate the duty cycle, the ratio of the total cross sectional area that the waveguides occupy to the CCD active area, to quantitatively show the waveguide density. (shown in Fig. 1b).

Figure 2 Area instruction of Γ analysis and cloak characterization. (a–c) Show the output images of “Ψ”. Area i and ii represent the exact area of “Ψ” and the background, respectively: (a) Cloak off and without the inner structure “ħ”. Cloak on and (b) without “ħ”/(c) with “ħ”. (d–f) Gaussian beam without “Ψ” mask. (d) Cloak off and with “ħ”. Cloak on and (e) without “ħ”/(f) with “ħ”. Cloak characterization. (1) Γ value comparison: Ψ structure (Γ ai,bi ; Γ ai,ci ) > output image (Γ a,b ; Γ a,c ) > background (Γ aii,bii ; Γ aii,cii ) ≈ hidden ħ (Γ d,e ; Γ d,f ). (2) Γ values peak at the 21 μm pitch of the output image and Ψ structure. (3) The fluctuation of Γ values on a low level represents the numerically well cloaked ħ. Full size image

As referred in the first result (See line Γ a,b ; Γ a,c in Fig. 2), where 21 μm is regarded as the optimal pitch for transmitting the image, the maximum Γ value is still moderately large, which can be attributed to the overweight of the background (the region on the image except the Ψ) in the calculation of Γ. To estimate the influence of the background, we extract region ii in Fig. 2a–c and calculate the Γ, as shown in Fig. 2 (Γ aii,bii ; Γ aii,cii ). The result shows that the similarity of the background between different images remains at a low level (within the range of 0.18 ± 0.03).

In view of the low weight of background noise visually, we clip the structure of Ψ (Region i in Fig. 2a–c) from a uniform background and then re-calculated the Γ. As expected, the Γ values increase prominently, reaching the peak at 21 μm (Fig. 2 (Γ ai,bi ; Γ ai,ci )). Furthermore, it is the consequence of the inevitable dissipation of light between waveguides that the maximum of Γ ai,bi , peaking at 0.986, still cannot reach 1. Actually, the pitch of 21 μm reaches the image standard as high as a retina image.

In order to give a quantitative indication of that the inner structure has been well cloaked. We remove the foreground mask Ψ and compare the similarity between the output image of the chip with the uncloaked inner structure ħ (Fig. 2d), the one without the cloaked structure (Fig. 2e) and the one with the cloaked structure (Fig. 2f), respectively. Provided that the cloaking performance is not that good, we should be able to see the inner structure ħ shown in Fig. 2f and a higher Γ d,f than Γ d,e . Apparently, the results show the Γ values fluctuate around 0.13 ± 0.05, at a very low level which is hard to be distinguished from the background noise.

Tomography analysis of on-chip cloaking

To reveal the evolution of light field in the printed cloak, tomography analysis is applied to the mechanism of cloaking. We cut the chip transversely, record the data from the output and compare these experiment results with simulation ones.

We simulate this experiment by a commercial software RSoft (Beam type: Gaussian, wavelength: 405 nm, refractive index 1.5198) and derive the distribution of the light field. As shown in Fig. 3, after the beam incidence, most light circumvents the cloaked area along the waveguides, while the rest is scattered by the bulk of the chip and forms the weak white noise in the background. Also we find the light distribution in the output is quite similar with the one in the input, which means little information may have lost after the transmission.

Figure 3 Tomography of the cloaking chip. Simulative (a) and experimental (d) tomography of on-chip cloaking scheme is displayed with intensity distribution along the lateral axis in (b,c) respectively. Full size image

Inspired by the widely used tomography in biological science28,29, we perform a tomography on our cloaking chip by grinding the chip to a predefined length, which takes 1.5 hours for each millimeter removal on a polisher. As the chip gets shorter, by observing the cross section pattern, the process of the projection image splitting into two parts gradually apart from each other and then combining into one again is experimentally reproduced. Comparing the numerical results of the processed intensity distribution along the lateral axis (Fig. 3b), we can observe that the numerical one is more fluctuant, which is because the stray light smooths the fluctuation in the experiment.

Three-dimensional capacity of cloaking

Three-dimensional capacity is frequently employed to benchmark the performance of a cloaking approach. In our experiment, while our cloaking approach is only implemented in one dimension to demonstrate its feasibility, the same method can be extended to three dimensions with higher complexity of waveguide arrangement and larger number of printed waveguides. We should note that cloaking in one dimension is not that trivial in certain scenarios. For instance, the chips are packaged leaving only some specific access to the public. The components placed at appropriate locations can be well hidden on the chip in the observation direction. Interestingly, even our one-dimensional configuration has its three-dimensional capacity of cloaking in a cone, which can be understood as an effect of collective numerical aperture of waveguides.

Therefore, the tolerance for viewing angle on the chip, which shows three-dimensional capacity of cloaking, is also investigated18,19. We change the view direction by adjusting the lens behind the cloaking chip (21 μm pitch, with the inner structure) multi-directionally and align the output image with the corresponding direction as shown in Fig. 4. The sharpness, brightness and visibility decrease as the viewing angle gets large, though the Ψ does not distort. An elliptical-like region spanning 8.0° laterally and 6.7° vertically outlines the tolerance for viewing angle. Besides, the limited angle that we derive above conforms to the numerical aperture theory of an individual multimode fiber. It is remarkably interesting that, the inner structure is cloaked so well that even if the obliqueness of the viewing angle is large enough to affect the image transmission, no parts can be observed. In addition, output powers in Fig. 4a are measured and plotted correspondingly (see Fig. 4b) which describes the energy distribution in the output light cone.