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LETTER ARTICLEwww.lpr-journal.org

Tunable Visible Cloaking Using Liquid Diffusion

Xiaoqiang Zhu, Li Liang, Yunfeng Zuo, Xuming Zhang, and Yi Yang*

A method is introduced for the design of invisibility cloaks inspired by fluiddynamics that is different from traditional transformation optics. Theinhomogeneous refractive index of the liquid cloak controlled by the naturalliquid diffusion is analogous to its counterpart designed by transformationoptics. Here, a tunable liquid visible cloak is experimentally presented by thenatural diffusion of miscible flows. This method avoids the use of complexnanostructures in its solid counterpart, and provides a simple and low-costapproach. This implies that optofluidics can be used as a technology to makereal-time reconfigurable transformation optic devices.

1. Introduction

Thanks to the intensive research efforts in transformation op-tics (TO), devices can be designed to control electromagneticwaves precisely.[1,2] Using initial TO method, cloaks of electro-magnetic wave and DC fields have been well realized.[3–7] Theseperfect cloaks are often metamaterial-based, relying on the res-onance of metallic structures and thus have a limited rangeof working wavelength.[3–6] Complex electromagnetic parame-ters such as singular points, also block the realization of cloaks,using special coordinate transformation could simplify thepermittivity and permeability.[8,9] Based on the traditional trans-formation optics, a new design method, quasiconformal trans-formation optics (QCTO),[10] has been put forward for experi-mental demonstrations. A new kind of diffusion cloak withoutusing transformation optics also shows great potiential in thecloaking area. A number of colloidal particles are added to thecloak and form the diffusive media, the diffusive light can propa-gate like heat flows in such media and conceal the objects insidethe cloak.[11–14] This new method eliminates the metamaterial-based materials and broadens the applied frequencies of devices.In particular, compared with the other methods that require theanisotropy of medium properties,[3] the QCTO method provides

X. Zhu, L. Liang, Y. Zuo, Prof. Y. YangSchool of Physics & TechnologyKey Laboratory of Artificial Micro/Nano Structure of Ministry ofEducationWuhan UniversityWuhan 430072, ChinaE-mail: [email protected]. X. ZhangDepartment of Applied PhysicsHong Kong Polytechnic UniversityHong Kong 999077, Hong Kong

The ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/lpor.201700066

DOI: 10.1002/lpor.201700066

a relatively simple solution because itallows the use of isotropic media,[15–18]

which leads to the devices becoming om-nidirection, broadband and polarizationindependent, showing its practical appli-cation value. Based on QCTO methods,invisible cloaks of broadband,[19,20] opti-cal frequencies[15–17] and visible light[18]

have been demonstrated. However, thedemonstrated QCTO devices often in-volve nanofabricated structures[15–18] toform the effective gradient-index profile,making it difficult for use with visiblelight since the feature sizes should be

much smaller than the wavelength. As a result, the devices usingthe QCTOmethod with low cost and a simple fabrication processis still demanding.The QCTO devices demonstrated always use solid materials

to realize the gradient-index profile, the commonly used solidmedia (like metals, silicon and silicon compounds) have limi-tations in complex nanofabrication, tiny object size and the so-called effective refractive-index condition. By contrast, optoflu-idic systems make use of liquids as the optical media and enjoywide tunabilities of geometry and refractive index by simply ad-justing the flow rates or replacing the liquids.[21–31] The previousresearch has seen the association between fluid-mechanics equa-tion and transformation optics,[32] and one of our recent stud-ies well demonstrated such a potential by using three misciblelaminar flows to generate a tunable refractive-index field so asto manipulate the light focusing and interference properties.[21]

This shows that the liquids media have the potential to be naturalQCTOmaterials, and as a result, the optofluidic system providesa versatile platform for widely tunable QCTO devices.In this letter, we employ convection-diffusion of miscible lam-

inar flows to form an inhomogeneous refractive-index profile.In contrast to the transformation-optics method, the refractive-index profile is formed in amicrofluidic channel, and shows anal-ogy with the profile of QCTO when the flow rates of liquids arelow. An optofluidic system is applied to operate the convection-diffusion among liquids, and a series of simulations and exper-imental results confirm the workablity of the optofluidic cloak.An experimentally switchable optical cloak is demonstrated, byemploying miscible laminar flows to switch the cloaking state.To illustrate the liquid cloaks, we use three miscible laminar

flows, as shown in Figure 1. As the object to be hidden, a bumpis placed at the bottom of the main channel (i.e., the region ofcloak).When themain channel is filled with one kind of liquid (ordifferent liquids but the refractive-index profile is mismatched toa low flow rate profile), the incoming rays are scattered by thebump to form a deformed image. As a result, the existence ofthe bump is detectable, corresponding to the “cloak-off” state (seeFigure 1a). In contrast, when the miscible flows are pumped into

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Figure 1. Switchable optofluidic carpet cloak using miscible liquids. a)“Cloak-off” state, in which themain channel (i.e., the region of the cloak) isfilled with a homogeneous liquid to have the same refractive index, or filledwith different liquids but having the inappropriate refractive-index profile.When light is irradiated onto a bump (i.e., the object to be hidden), therays are scattered by the bump to form a deformed image. b) “Cloak-on”state, in which the main channel is filled with miscible liquids to obtain aparticular refractive-index profile by diffusion. The rays experience no scat-tering and form a normal image, as if there were no bump.

the main channel at very slow velocities, the mutual diffusion ofliquids generates the right refractive-index profile that graduallydeflects the rays to conceal the scattering effect by the bump. Asa result, a normal image is formed, as if there were no bump.This corresponds to the “cloak-on” state (see Figure 1b). Usingliquid media can avoid the nanofabricating processing for invis-ible cloaks and brings the advantage of reconfigurability. Thisshows the potential of liquid materials in playing an importantrole in transformation-optics design.

2. Method and Design

2.1. Method

The physical mechanism is based on our new finding that theconvection-diffusion equation for flow dynamics at low flow ve-locity has nearly the same form as QCTO. More specifically, theflow dynamics of the laminar flows in the microchannel is gov-erned by the convection-diffusion equation:[33]

∂C∂t

= D∇2C − U∇C + R (1)

where C is the concentration of the liquids, U is the velocity ofthe fluids, D is the diffusion coefficients among the liquids and

R is the source for a chemical species. This equation determinesthe concentration distribution of the mixed liquids. Under theconditions of no chemical reaction (R = 0), the steady state (i.e.,�C/�t= 0) and very slow flow velocity (i.e.,U → 0), Eq. (1) leadsto the Laplace equation of concentration as expressed by

∇2C → 0 (3)

Since the core flow has a higher refractive index than thecladding flows, the molar concentration and refractive index ofthe mixed liquid have an one-to-one relationship. According tothe data in the literature, it is found that the relationship of molarconcentration and refractive index are not the same for differnetmixed liquid types.[37] Here, ethylene glycol andDIwater are usedas materials, and the molar concentration and refractive index oftheir mixture are fitted (Supplementary Figure S1). Combiningthe fitting result and Eq. (3), the refractive index of the mixturenc satisfies:

∇2(n2c ) → 0 (4)

For a quasiconformal transformation optics from physical co-ordinates (x, y) to virtual coordinates (X, Y).

n2quasi = XxYy − XyYx (5)

The refractive index of the lower boundary (boundary withbump) nl = f (x, y), and for a certain transformation, the nl is adetermined value. Appling the boundary condition nl = f (x, y)to Eq. (4), calculating the results of several models using a finite-elementmethod (shown in Supplementary Figure S2). It is foundthat n2c has a very similar profile as n2quas i . These results meanthat if the boundary condition nl = f (x, y) is satisfied by the liq-uid, the liquid can form a refractive-index profile very similar tothe profile obtained by the quasiconformal transformation usingconvection-diffusion. The ratio of diffusion and convection canbe described by a nondimensional number, the Peclet number(Pe), here Pe = u (W1 +2W2)/D, u is the average velocity of flu-ids, W1 is the width of core inlet, and W2 is the width of eachcladding inlet. The physical meaning of Pe is the relative strengthof the convection with respect to the diffusion. Detailed theoreti-cal discussions in Supplementary Section 1, and SupplementaryFigure S3 show the relationship between Pe and the influence ofconvection.

2.2. Design

In the switchable cloaking device, the convection-diffusion of theliquids determines the refractive-index profile. After the liquidsare pumped in from three inlets, they start to mix with each otherby convection-diffusion. As discussed in the method, for an ideal2D-liquid cloak, the boundary condition nl = f (x, y) should besatisfied. Countless inlets are needed for an absolutely ideal liq-uid cloak. However, in a real application, the number of inletsis limited. In the experimental model in this work, there is onepoint with the highest refractive index and two points with thelowest refractive index. Three inlets are applied in themodel withtheir centers having the highest or lowest refractive index. The



Figure 2. Design and modeling of the switchable optofluidic cloak. a) Diagram of only the fluidic parts and dimensions of the inlets. In the verticaldirection, the device consists of two layers, the upper layer has three inlets and one outlet to convey liquids whereas the lower layer has only one outletbut no inlets. The lower layer provides more space for diffusion and its bottom is gold coated to act as a reflecting boundary. The inset shows thecross-sectional view near the entrance part of the inlets. b) A typical refractive-index profile is required for the “cloak-on” state. c) The cross-sectionalview taken by the optical microscope.

widths of the inlets are calculated carefully to ensure minimumerrors, and a discussion is in Supplementary Figures S4 to S6.Furthermore, we can change the profile of the cloak by turningthe flow rate, ratio and flow directions. To make the result accu-rate, the designed refractive index in the inlets is very close to therefractive index of singular points. Our experimental model canbe seen in Figure 2 and Supplementary Figure S6. As shown inFigure 2a, the chip has a two-layer structure. The upper layer isused to convey liquids, and the lower-layer is the cloak part forthe convection-diffusion of liquids. A reflector coated with goldis also provided by the lower layer, as shown in Figures 2a andc. In the experiment model, the channel widths W1 and W2 are190 and 80 μm, respectively (see Figure 2a). The cloaked area isshown in Figure 2b, whose height H and width Wb are 14 and1000 μm, respectively. In this design, the flow rate at “cloak-on”state is 13.2 nl/min (Pe= 0.94) and the refractive-index profile forthe flow rate of 13.2 nl/min is simulated inFigure 3c, showing thesuitability for quasiconformal mapping. The simulated profile istransformed from the concentration profile by putting the fittedrelationship of concentration and refractive index to the concen-tration profile (the details are given in Supplementary materialS1). The concentration profile is calculated by a finite-elementmethod using the convection-diffusion equation. Other choices

of liquid media give different critical flow rates because of thedifferent diffusion coefficients and different refractive indices.

3. Experimental

For an experimental demonstration, the microstructure of thecloak device was fabricated using polydimethylsiloxane (PDMS)by the soft lithographic processes. All liquids were stored in50-μl glass syringes and driven by the syringe pumps (LongerPump, TS-1A) that support the precision control of flow ratedown to 6.5 nl/min. The experiments were performed underan inverted microscope (NIKON, Ti-U). A 532-nm green laser(CNI, MGL-FN-532/1) and a white-light laser source (Fianium,AOTF, WhiteLase SC400) were used as the light sources. Thefluorescent dye Rhodamine B was added into the liquids forvisualization of the propagation path of light. In the experimentof liquid convection-diffusion, in order to see the refractive-indexprofile clearly, the core liquid of ethylene glycol was dyed withhigh-concentration Rhodamine B and looked light yellow underthe mercury lamp, whereas the cladding liquid of DI water wasdyed with low-concentration Rhodamine B and looked dark red(in the experiment of light propagation, the concentration of the



Figure 3. Convection-diffusion mapping formed by the switchable optofluidic cloak. a), b) and c) are the simulation results, d), e) and f) are the exper-imental results. The core and cladding liquids are dyed by a fluorochrome with different concentrations so that d), e) and f) reflect the gradient-indexprofile. a) and d) The simulated and measured results of the refractive-index profile when only the core liquid is used to fill the region of cloak. b) and e)The simulated and measured results when the fluids have high flow rates (Pe >>0.94). c) and f) The simulated and measured results when the fluidshave low flow rates (Pe = 0.94).

fluorescent dye in both liquids is the same). The convection-diffusion between fluorescent dyes can indirectly reflectthe convection-diffusion between different liquids. The low-concentration fluorescent can be used to make a light path inthe liquid visible and indirectly reflect the intensity of light.[34,35]

The intensity of light inspired by the fluorescent dye If = I0ψ1Cf

exp(–ψ2Cf), where ψ1 and ψ2 are constant when the dielectricconstant is invariable, Cf is the concentration of the fluorescentdye, at a low-concentration of the fluorescent dye, the If hasa linear relationship with Cf.[35] The simulated results of theconvection-diffusion mappings in Figures 3a–c match well withthe corresponding measured results in Figures 3d–f.Light-propagation experiments are conducted to verify the ef-

fect of the optofluidic cloak, and the results are shown in Fig-ure 4. In the initial state, the cloaking region is filled with onlyethylene glycol from the core inlet, the refractive index is uni-form in the whole region, as in Figure 3d. The correspondinglight propagation in Figure 4d shows that the reflected beam fansout into several strands due to the scattering of the bump, whichagrees well with the simulation in Figure 4a. Therefore, the bumpis detectable and the cloak is in the “cloak-off” state. The inten-sity distributions of the reflected beams for the experimental andthe simulated result are compared in Figure 4g, both match ap-proximately. The confocal images in Supplementary Figure S6show the consistency of media in thickness. This means thatthe distribution of light is homogeneous in the z-direction, andthe light excited by low-concentration fluorescent can representthe light distribution. Next, when the flow rate is 60 nl/min(larger than the critical value 20 nl/min) for all inlets, both theconvection and the diffusion take effect, and the refractive-indexprofile takes up the whole cloaking region, as shown in Figure3e. In this case, the reflected beam is also scattered according tothe experimental result in Figure 4e and the simulation result inFigure 4b), thus the cloak is still off. The intensity distributionsin Figure 4h share a similar profile. Finally, when the flow ratereduces to to 13.2 nl/min (below the critical value 20 nl/min),the diffusion becomes dominant so that the refractive-index pro-file is confined to the inlet region as Figure 3f. Under this condi-tion, the reflected beam becomes a single beam (experiment in

Figure 4f, simulation in Figure 4c and the intensity profiles inFigure 4i), and the scattering of the bump is concealed entirely,corresponding to the “cloak-on” state. Due to the absorption ofthe gold reflector at visible frequencies, the reflected beams haveweaker intensities than the incident beam (Figures 4d–f). Thelaser is collimated by a fabricated microlens, the microlens has acurvature of 14.3 mm–1. Such a collimated lens is always appliedin microfluidic systems.[30,36] For the liquid cloak, the media aredielectric. Therefore, the bandwidth can be very wide because itdoes not rely on the resonant effect in themedia. The liuqid cloakhas been tested at the wavelengths of 400, 488 and 588 nm. Fig-ures S7a, d and g show the light paths in the “cloak-off” state. Itcan been seen that the reflected beams fan out. Figures S7b, e andh show the light paths in the “cloak-on” state, the reflected beamsremain as a single beam. The intensity analysis is plotted in Fig-ures S7c, f and i. Supplementary Figure S9 shows the results ofdifferent situations. Figures S9b and c show the light paths of theQCTOmethod and the fluid-dynamicsmethod, respectively. Thisshows the cloak formed by the convection-diffusion is analogousto the quasiconformal mapping, and it works well to switch be-tween the “cloak-off” state and the “cloak-on” state by adjustingthe refractive-index profile. Supplementary Figure S9 shows thesimulation results for different situations, Figures S9b and c, re-spectively, show the light path of the QCTOmethod and the fluid-dynamics method. This shows the cloak formed by convection-diffusion is analogous to quasiconformal mapping, and can op-erate well as a cloak.In the experimental results, the width of the inlets and the

height of microchannel are controlled in an acceptable range.In addition, we demonstrated the results with other wavelengths(400, 488 and 588 nm) and another incident angle of 15°. Theseerror analyses and extra experimental results can be seen in Sup-plementary Figures S4–S8.

4. Conclusions

In conclusion, we introduced a method to design invisibilitycloaks by fluid dynamics, whose refractive-index profile is formed



Figure 4. Light propagation in the switchable optofluidic cloak. a) and d) The simulated and experimental results of light propagation corresponding tothe refractive-index profiles in Figures 3a and d. The cloak is “off”, and the incident beam is not affected by the cloak. The reflected beam looks scatteredwith a power gap. The contrasted reflected beams of a) and d) is shown in g). b) and e) The simulated and experimental results of light propagationunder the profiles of Figures 3b and e. The influence of convection does not disappear, the Peclet number is not small enough. The refractive-indexprofile is inappropriate for the “on-state”, and the reflected beam is still scattered. The contrasted reflected beams of b) and e) is shown in h). c) and f)The simulated and experimental results of light propagation under the profiles of Figures 3c and f. The flow rate is low enough, and the Peclet number issmall enough. Here, the profile is appropriate for the “on-state” and the reflected beam is single. The contrasted reflected beams of c) and f) are shownin i).

by natural convection-diffusion of liquids. The optofluidic cloakis controllable via the flow rates of fluids and the refractive-index profile shows analogy with the profile obtained from qua-siconformal mapping when the flow rates are low. Simulationsand experiments are carried out to confirm the performanceof the liquid cloak. This implies that optofluidics can be usedas natural technology by analogy with transformation-opticaldevices.

Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.

AcknowledgementsThis work was financially supported by the National Natural ScienceFoundation of China (No. 11774274, 61378093 and 61377068), Qing-dao National Laboratory for Marine Science and Technology (No.QNLM2016ORP0410) and the State Oceanic Administration, People’s Re-public of China “marine environmental monitoring and upgrading” and

Research Grants Council of Hong Kong (N PolyU505/13, 152184/15E,152127/17E). We also acknowledge assistance with nanofabrication pro-vided by the Center for Nanoscience and Nanotechnology at Wuhan Uni-versity.

Conflict of InterestThe authors have declared no conflict of interest.

Keywordsconvection-diffusion; invisible cloak; optofluidic

Received: March 20, 2017Revised: September 19, 2017

Published online: November 6, 2017

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