Abstract

We make use of transformation optics technique to realize cloaking operation in the light diffusive regime, for spherical objects. The cloak requires spatially heterogeneous anisotropic diffusivity, as well as spatially varying speed of light and absorption. Analytic calculations of Photon’s fluence confirm minor role of absorption in reduction of far-field scattering, and a monopole fluence field converging to a constant in the static regime in the invisibility region. The latter is in contrast to acoustic and electromagnetic cloaks, for which the field vanishes inside the core. These results are finally discussed in the context of mass diffusion, where cloaking can be achieved with a heterogeneous anisotropic diffusivity.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Transformation optics (physics) is a promising way to achieve optical (physical) invisibility [1]. The underlying idea is to change the direction of light (or other kind of waves) rays in a manner to avoid hitting a particular area, which will be the hidden (invisible) place, without changing the propagation in the surrounding medium. This can be achieved by mimicking a deformation of a portion of the space using coordinates transformation technique, as proposed by Greenleaf et al. [2], Pendry et al. [3] and Leonhardt [4], in recent years. The same concepts have been successfully applied to control other kinds of waves in the vicinity of arbitrarily-shaped and sized objects, e.g. acoustics [5–7] and elasticity [8–12]. Pendry and his colleagues proposed also immediately after the theoretical proposal an invisibility cloak design with concentric layers of split-ring resonators (SRR), in which the waves follow curved paths. The experimental realization was achieved by Schurig et al. [13], and it consists in a cylindrical cloak made of 10 layers of periodically-arranged SRRs, of glass fibre-reinforced Polytetrafluoroethylene (PTFE), with the possibility to hide a 25 mm (copper) cylinder from microwaves, i.e. at 8.5 GHz, as expected from numerical calculations. Several other groups have since then performed similar experiments [14], in particular for other kinds of waves [15–19].

Other types of equations preserve, as well, their form under geometrical transformations like the heat equation that governs the thermal phenomena [20]. Due to the peculiarity of heat (and diffusion) waves, if cloaking exists for such diffusive processes, it has to be of different nature than its classical analogue [21–23]. Different recent studies motivated by the transformation optics technique [1,24] were subsequently proposed [25–28] to control heat flow in metamaterial devices. Experimental demonstrations were also given [29–32]. Interestingly, a mathematical proof of near-cloaking has been proposed in the time-domain, based on long time behavior of parabolic differential equations, but proving theorems in the frequency domain seems more challenging [33]. Some concept of thermal camouflaging have been also proposed [34,35].

Transformation optics applied to heat waves can lead to several interesting functionalities and uses in optoelectronics [1], by controlling the overall diffused heat, or by shielding a particular sub-component. This can be done, for example by controlling and re-directing the heat flow, by using a metamaterial surrounding cover (cloak).

In this work, we consider the propagation of diffuse photon density waves (DPDWs). These waves account for the propagation of light in turbid environments (i.e. highly scattering medium), such as human body tissues, cloud or milk [36]. In this case, photons experience multiple scattering phenomenon before being absorbed by the medium or escaping it [37]. Although the respective photons are randomly moving within the medium, in a macroscopic scale, the collection of photons behaves collectively as a density wave of photons. This DPDW is characterized, as usual wave phenomena, by a Helmholtz-like equation of motion and it experiences common wave properties, e.g. scattering [37], refraction [38], and even cloaking based on quasistatic transformation optics [39, 40] or scattering cancellation technique [41].

One important question that arises is about the value of photons’ fluence within the inner core of the cloak: Unlike for invisibility cloaks for waves for which the fields are excluded from the inner core [42], it has been numerically observed that the inner core heats up in the case of cylindrical thermal cloaks in the transient regime [20]. In this article, we would like to address this issue in the frequency regime from the viewpoint of an analytical approach (i.e. Bessel expansion of the fields, similar to Mie theory for electromagnetism), rather than from a purely numerical approach, in the specific scenario of DPDWs. The shell is composed of a metamaterial with physical parameters (anisotropic heterogeneous diffusivity and heterogeneous absorption coefficient). These properties can be calculated, by performing a coordinate transformation that preserves the DPDW equation. In particular, the heterogeneity and anisotropy of the shell’s parameters are necessary to create a space deformation in the vicinity of the object to hide. This will bend the photons incident on the structure from one side and force them to emerge in the original direction of diffusion, as if there were no perturbation (i.e. scattering).

Finally, we draw some analogies with cloaking of mass diffusion using the transformed Fick’s equation. This opens exciting perspectives not only in biological, and chemical, applications [43–46], but also in control of light in diffusive media [47].

2. Set-up of the DPDW cloaking method

It is shown in this section, that a spherical DPDW cloaking can successfully be achieved by using heterogeneous radially-symmetric shells with a heterogeneous anisotropic diffusivity, and absorption coefficient as radial functions, to hide a spherical object coated by such a shell, from the photons’ flux (or DPDWs). The geometry of the structure is schematized in Fig. 1(a), where the axis system, coordinates, as well as source and detector position are shown. We consider the three-dimensional DPDWs equation with a source and for a (complex) frequency Ω (eiωt time-harmonic dependence is assumed throughout the work, therefore Ω = −) [37],

Ωυ(x)Φ(x)+μa(x)Φ(x)+ς(x)=[D(x)Φ(x)],
with the fluence distribution field Φ(x) at position x = (r, θ, ϕ) in the spherical system of coordinates as schematized in Fig. 1(a). DPDW’ cloaking in the frequency-domain was further analyzed in [41], in the case of radial coordinates. Furthermore, the adjusted diffusivity D = 1/[3(µa + µs)] ≈ 1/(3µs), where µa and µs are the absorption and scattering coefficients, respectively. We also make use of the approximation µaµs, that is commonly known as the P1 approximation [48] and is mandatory to have the more simple form of Eq. (1). υ is the speed of light in the turbid medium and ζ a source with a Heaviside time-step variation and a Dirac spatial-dependence.

 

Fig. 1 (a) Cross-section of the DPDW structure to cloak. Schematic of the cloak: 3D scenario showing the DPDWs flux transfer, with the object to cloak in the middle (light red sphere). Different shells with different properties represent the DPDW cloak, with various parameters of the study. (b) Dispersion relation of the DPDW, giving the norm of the wavenumber versus the normalized diffusivity and frequency.

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From inspecting Eq. (1), one can deduce the dispersion relation of DPDW (i.e. that relates the frequency ω to the wavenumber k0), i.e.

k0=i(Ωυ0+μa,0)/D0,
that is very different from the linear dispersion of light in dielectric media. Here k0 is a complex number due to the absorption coefficient µa,0. This means that DPDW can only propagate for few wavelengths before getting totally attenuated, where propagating in turbid media, in contrast to light in dielectrics, and free space. This dispersion is shown in Fig. 1(b) where the amplitude of the wavenumber |k0| is given versus frequency and the relative diffusivity D/D0 of the medium, assuming a fixed absorption coefficient 1/(υ0µa,0)= 15 ns.

For homogeneous media, it is generally common to put D in front of the spatial derivatives (gradient). But, since in our study (as can be seen in Fig. 2(a)), we consider heterogeneous structures (core/shell), the gradient of the diffusivity tensor D suffers some discontinuity. The derivatives are taken in distributional sense, and accordingly one has to ensure transmission conditions, i.e. continuity of the normal component of the fluence flux D ∇Φ are encompassed in Eq. (1)].

 

Fig. 2 (a) Analysis of the scattering cross-section (SCS) behavior from a bare spherical object with varying absorption coefficient at frequency 50 MHz. (b) Plot of SCS versus frequency for different diffusivity of the bare object. Far-field scattering from (c) the bare object (sphere) and (d) the cloaked sphere, in logarithmic scale.

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The spherical coordinates (r, θ, ϕ) is considered (with r ≥ 0, 0 ≤ θ < π and 0 ≤ ϕ < 2π).

Upon a change of variable x = (r, θ, ϕ) → x′ (r′, θ′, ϕ) described by a Jacobian matrix J = (r′, θ′, ϕ′)/ (r, θ, ϕ), this equation takes the form:

Ω[det(J)/υ(x)]Φ(x)+μa(x)det(J)Φ(x)+det(J)ς(x)=(JTD(x)J1det(J)Φ(x)).

One remarks that both Eqs. (1) and (3) possess the same structure, with the noticeable difference that the transformed diffusivity

D__=JTDJ1det(J)=DJTJ1det(J)=DT1,
is tensorial, with the metric-tensor T. The absorption coefficient and inverse of speed of light are now multiplied by the determinant of the Jacobian matrix J of the coordinates transformation.

3. Analysis of DPDWs cloaking via Bessel expansion

Here, we would like to identify the coefficients of D__, as well as the expression of det(J)/υ and µadet(J) without resorting to cumbersome algebra. Indeed, symmetry dictates that the spherical cloak parameters must be independent of θ and ϕ if we use the geometric transform r′ = a + (ba)r/b, which maps the sphere 0 < rb (where it should be noted we exclude the origin) onto the shell a < r′ ≤ b. Therefore, the diffusivity tensor ought to take the from D__=diag(Dr,Dθ,Dϕ)(r) with Dθ=Dϕ, and μadet(J)=μa(r) and det(J)/υ = 1/υ′(r′). Without loss of generality, Eq. (3) takes the following form inside the anisotropic shell, depicted in Fig. 1(a):

r(Drr2Φr)+Dθsinθθ(sinθΦθ)+Dϕsin2θ2Φϕ2r2[Ωυ+μa]Φ=0,
where Dθ=Dϕ

In order to simplify this equation, we consider the separation of variables Φ(r′, θ, ϕ) = f (r′)g(θ)h(ϕ), which leads to

1Dϕr(Drr2fr)+(k2r2n(n+1))f=0,
where the angular dependence on θ has been suppressed, and where the DPDW wavenumber is defined as k2=(Ω/υ+μa)/Dϕ. The expressions of g (θ) and h(ϕ) are sought of in standard form and are the associated Legendre functions g(θ)=K0Pnm(cosθ) and and the azimuthal harmonics h(ϕ) = K1 cos() + K2 sin(), respectively.

In order to map this equation onto the standard spherical Bessel function equation with argument (r′ − a), one needs to assume that

r2Dr=(ra)2D0A,Dϕ=D0A,andk2r2=ksh2(ra)2,
where A and ksh are constants to be calculated later on.

Under these conditions, Eq. (6) takes the form

r((ra)2fr)+(ksh2(ra)2n(n+1))f=0,
which has the solution f (r′) = bn (ksh(r′ − a)) with bn a spherical Bessel or Hankel function of order n.

The total fluence field (Φ) in all regions can now be expanded. For r> b, the incident DPDW is of the form eik0rcosθ, where θ is the incidence angle, and can be expanded in spherical coordinates:

Φinc=Φ0n=0n=in(2n+1)jn(k0r)Pn(cosθ),
where the free space DPDW wavenumber is k02=(Ω/υ0+μa,0)/D0,Pn(cosθ) is the Legendre polynomial of order n and jn denotes the nth spherical Bessel function, which is related to the ordinary Bessel function Jn through the relation jn(x)=π2πJn+1/2(x). Φ0 is the amplitude of the incident DPDW field.

The scattered field can be derived by using the radiation condition (that dictates the form in terms of spherical Hankel functions)

Φscat=Φ0n=0n=cnhn(1)(k0r)Pn(cosθ),
with hn(1)() the spherical Hankel function of the first kind, and cn are coefficients to be computed using the boundary conditions (continuity of fluence Φ and its normal flux).

For a < r< b, the azimuthal invariance means that the potentials satisfy

Φsh=Φ0n=0n=dnjn(ksh(ra))Pn(cosθ),
where ksh is the wavenumber in the shell, that shall be calculated later on, and where we make use of the Bessel function jn to prevent the fields from diverging when r′ − a = 0.

Finally, inside the core of the cloak, i.e. for r< a, one has

Φint=Φ0n=0n=enjn(k0r)Pn(cosθ),
which completes the description of the temperature field in the overall space.

Regarding the boundary conditions, we know that the fluence Φ and the radial flux, i.e. Dr,Φ/r are continuous across the inner and outer (spherical) boundaries of the cloak (at radii a and b, respectively). After exploiting the orthogonality of Pn (cos θ)), we find that the coefficients cn and dn must satisfy, at the outer boundary b

in(2n+1)jn(k0b)+cnhn(1)(k0b)=dnjn(ksh(ba)),D0k0[in(2n+1)jn(k0b)+cnjn (1)(k0b)]=Dr(b)ksh×[dnjn(ksh(ba))].
From (13), we obtain
cnin(2n+1)=k0D0jn(k0b)jn[ksh(ba)]+kshDr(b)jn(k0b)jn[ksh(ba)]k0D0hn (1)(k0b)jn[ksh(ba)]kshDr(b)hn (1)(k0b)jn[ksh(ba)].

Here one needs also to compare the scattering from a single sphere that is given by the following similar expression

cnbin(2n+1)=jn(k0a)jn[k1a)]+χjn(k0a)jn[k1a)]hn (1)(k0a)jn[k1a)]χhn(1)(k0a)jn[k1a)],
with a the radius of the sphere, k0 and k1 the wavenumbers in free space and inside the sphere, respectively and
χ=k1D1k0D0,
with D0 and D1 the diffusivity in free space and inside the object, respectively.

The scattering cross-section (SCS) describes the amplitude of the scattered field in the far-field (far away from the structure). It is in a certain way, an overall measure of the visibility of any object to far observers. It is given by integrating the scattering amplitude over all the solid angles. Its expression is

SCS=4π|k0|2n=0N0(2n+1)|cn|2.
N0 is ideally taken to be N0 = ∞. But, technically, only a finite number of scattering coefficients is usually taken into account, in numerical simulations. This is justified by the fact that scattering coefficient |cn| are of order (k0a)2n+1. So, for large N0, cN0 is very small in comparison to |c0| or |ci| with iN0. In our work, we have verified that N = 10 permits to attain convergence of the SCS. It should be added here too, that absorbing objects are considered in our work. In this scenario, if one consider a receiver located far away from the object of interest, it can only measure the fields scattered from the object in the far-field region (i.e. the SCS defined in (17)). And in order to fully cloak this object, one may need to consider the more general extinction cross-section (i.e. the sum of the SCS and the absorption cross-section), and thus ideally one has to add active layers since there is residual scattering associated to absorption. However the scattering is minimized in our case using transformation optics. An in-depth discussion of similar concepts were proposed by Muehlig et al. in [49, 50].

Upon inspection of (14), we note that the coefficients cn can be made identically zero if the following two conditions are met

k0b=ksh(ba),kshDr(b)=k0D0.

Physically, the first condition means that the number of isosurfaces lines in the shell over a distance ba must be the number of isosurfaces lines in the background medium over a distance b. The second condition means that on the outer boundary of the cloak there is no scattering. When we combine these two conditions with Eq. (7), we find that

A=bba,ksh=bbak0.
The complete specification of the metamaterial within the cloak is therefore
Dr=bba(ra)2r2D0,Dθ=Dϕ=bbaD0,
and
Ω/υ+μa=b3(ba)3(ra)2r2(Ω/υ0+μa,0).
Taking into account that (21) must be valid for every frequency (Ω = −), one finally get
υ=(ba)3b3r2(ra)2υ0andμa=b3(ba)3(ra)2r2μa,0,
where it should be noted that Dr=μa=0 on the inner boundary of the cloak, where as the speed of light υ′ diverges, which makes sense, since it means that the DPDW has to travel for a much longer (actually, an infinite) path and emerge without phase difference at the other side of the shell [3]. The result of Eqs. (20)(22) is that DPDWs coordinates transformation result in anisotropic and inhomogeneous physical parameters (scattering coefficient or diffusivity and absorption coefficient). As in the case of electromagnetic or acoustic cloaks, practical realization of such cloaks necessitates the use of layered metamaterial structures [1, 24]. And this practical cloak may realize only approximate cloaking, since the ideal necessary parameters need to vanish, at some points, as stated above.

Figures 2(a) and 2(b) plot the SCS of the bare object (sphere) normalized with the diffusivity D0. In Fig. 2(a) we plot it versus the absorption coefficient. In fact, 1/υµa is homogeneous to an effective time. It shows that the SCS has a local minimum for a time of 15 ns and then converges, for a frequency of 50 MHz. In Fig. 2(b) the SCS is plotted versus frequency, but for different values of the diffusivity in the object (D1 = 1/3μs, 1)). The deduced physical parameters of the invisibility shell, as deduced from Eqs. (20)(22) can be easily realized by employing readily-available materials [37, 38, 51].

The angular dependence of the SCS is given in Figs. 2(c) and 2(d), for the bare object and the cloaked one. It shows that the cloak is efficient in reducing the scattering by many orders of magnitude.

The near-field amplitudes (given by Eq. (9)(10)) are shown in Figs. 3(a) and 3(b) for the cloaked scenario, for two different wavelengths of the DPDW. It show that the field is unperturbed by the presence of the overall structure.

 

Fig. 3 (a) Snapshot of the total normalized fluence field Φ/Φ0 around the cloak at two different wavenumbers (a) k0b = π/10 and (b) k0b = π/2. (We should mention here that colors inside the shell and core have nothing to do with color scale for normalized fluence.)

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We would like now to address the issue of the fluence field concentration in the inner core (equivalent to a temperature increase) which was observed in in the context of thermal waves in the transient regime [20]. This corresponds in our case to a field taking different non vanishing values at different frequencies. To do this, we first note that from the boundary conditions at r′ = b we have dn = in(2n + 1) (i.e. cn = 0). We therefore note that continuity of Φ and its radial flux at r′ = a lead to

in(2n+1)jn(ksh(ra))=enjn(k0r),b(ra)2(ba)r2in(2n+1)jn(ksh(ra))=enjn(k0r).
Because of the (r′ − a)2 term the in the left-hand side (of the equation) is zero in the second expression for all n, thus en = 0 for all n different from zero. Indeed, e0 does not vanish since j0(0) ≠ 0, and the fluence inside the inner core is therefore nonzero, as depicted in Figs. 4(a) and 4(b). We note that Φ takes the form
Φint=Φ0j0(k0r)Pn(cos(θ)),
which is monopole field inside the inner core, as can be seen from Fig. 4. We note that in the steady state regime, when Ω = 0, Φint = Φ0.

 

Fig. 4 Heating inside the core: Logarithmic plot of the analytical expressions of the real part of the fluence field Φ versus the distance from origin (normalized with respect to a), as obtained from (24), for a fixed angle θ.

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4. Correspondence with cloaking in mass diffusion

Let us now consider Fick’s equation. It describes, in particular, physical events where, for example, any physical quantity (e.g. energy or discrete particles) is driven inside a physical system as a result of diffusion process. This usually takes place for a random walk of the particles, until equilibrium is achieved, in a thermodynamical sense, which results in species transport without volume motion. In its simplest form, it can be written as

Ωu=(κ(x)u)+p(x,Ω),
where u represents the mass concentration evolving with frequency Ω, κ is the chemical diffusion in units of m3.s−1.

The transformed Fick’s equation can be written as

det(J)Ωu=(κ__det(J)u)+det(J)p(x,Ω),
where κ__ is given by an expression similar to that of Eq. (4). We face a problem here as the left-hand side has the factor det(J)=b3(ba)3(ra)2r2 which has no physical meaning. Of course, in the steady state, it does not play any role, so one is tempted to just disregard it. In fact, the Bessel expansion and the transformation optics technique tells us that the factor det(J) does not affect the cloaked diffusion solution. Following the previous section, we deduce that the complete specification of the metamaterial within the cloak for mass diffusion is (by normalizing to κ0 the chemical diffusion of the surrounding)
κr=bba(ra)2r2,κθ=κϕ=bba,
where it should be noted that det(J)=b3(ba)3(ra)2r2 vanishes on the inner boundary of the cloak.

One easily finds that the mass concentration inside the core of the cloak can be expressed as

uint=Uj0(k0r)P0(cos(θ)),
which is a monopole field inside the inner core. We note that in the steady state regime, when Ω = 0, uint = U.

One also notes that DPDWs and mass diffusion satisfy equivalent equations in the static limit. We further note that Fig. 4 sheds a new light on a mechanism of control of drug diffusion proposed with biochemical metamaterials: In [45], the observed delay in diffusion of a peptide drug was attributed to a strong anisotropy of effective diffusivity of a network of graphene oxyde hydrogels resembling laminated structures. Using homogenization results in [45], one can see that concentric layers of graphene oxide hydrogels lead to an effective diffusivity like in [33]. Consequently, if one surrounds a peptide drug by such a biochemical cloak, mass concentration in the core will be according to [34]. Such a uniform concentration field is reminiscent of almost trapped eigenstates studied in [52] in the context of matter wave cloaking, where the potential barrier in the Schrodinger equation (which is analogous to the one in [32]) enforced localization of matter wave inside the core. Delaying peptide drug diffusion can have interesting therapeutical applications [45].

5. Conclusions

To conclude, we have theoretically and analytically analyzed new aspects of three-dimensional DPDWs cloaking, based on the transformation coordinates technique. We have shown through numerical simulations the heating behavior of the core object, which is an important aspect that shall be taken into account in experiments. One may anticipate that making use of this design technique can make the cloaking theory one step closer to feasible realization, for heat diffusion processes. We believe that a practical realization of these concepts can be implemented easily, and leads to potential applications in sensing, thermography and/or invisibility. The range of important industrial applications is broad, and our proof-of-concept can undoubtedly foster research efforts in this emerging area of thermal cloaks and metamaterials.

Funding

Qatar National Research Fund (QNRF) through a National Priorities Research Program (NPRP) Exceptional grant, under grant number NPRP X-107-1-027 and A*MIDEX project (no ANR-11-IDEX-0001-02) funded by the Investissements d’Avenir French Government program, and managed by the French National Research Agency (ANR) are gratefully acknowledged.

Acknowledgments

MF and FHA acknowledge funding by the Qatar National Research Fund (QNRF) through a National Priorities Research Program (NPRP) Exceptional grant, NPRP X-107-1-027. SG and TP acknowledge A*MIDEX project (no ANR-11-IDEX-0001-02) funded by the Investissements d’ Avenir French Government program, managed by the French National Research Agency (ANR) with Aix Marseille University.

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31. T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014). [CrossRef]   [PubMed]  

32. H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014). [CrossRef]   [PubMed]  

33. R. Craster, S. Guenneau, H. Hutridurga, and G. Pavliotis, “Cloaking via mapping for the heat equation,” arXiv preprint arXiv:1712.05439 (2017).

34. S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017). [CrossRef]  

35. Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018). [CrossRef]   [PubMed]  

36. W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological,” IEEE J. Quantum Electron. 26, 2166–2185 (1990). [CrossRef]  

37. D. Boas, M. O’Leary, B. Chance, and A. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999 (1993). [CrossRef]  

38. M. O’leary, D. Boas, B. Chance, and A. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658 (1992). [CrossRef]  

39. R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014). [CrossRef]   [PubMed]  

40. R. Schittny, A. Niemeyer, M. Kadic, T. Bückmann, A. Naber, and M. Wegener, “Diffuse-light all-solid-state invisibility cloak,” Opt. Lett. 40, 4202–4205 (2015). [CrossRef]   [PubMed]  

41. M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016). [CrossRef]   [PubMed]  

42. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008). [CrossRef]  

43. S. Guenneau and T. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10, 20130106 (2013). [CrossRef]  

44. L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013). [CrossRef]   [PubMed]  

45. T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018). [CrossRef]   [PubMed]  

46. A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017). [CrossRef]   [PubMed]  

47. R. Schittny, M. Kadic, T. Buckman, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014). [CrossRef]   [PubMed]  

48. D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. thesis, University of Pennsylvania (1996).

49. S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013). [CrossRef]   [PubMed]  

50. S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

51. L. Renthlei, H. Wanare, and S. A. Ramakrishna, “Enhanced propagation of photon density waves in random amplifying media,” Phys. Rev. A 91, 043825 (2015). [CrossRef]  

52. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008). [CrossRef]  

References

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  1. M. Farhat, P.-Y. Chen, S. Guenneau, and S. Enoch, Transformation Wave Physics: Electromagnetics, Elastodynamics, and Thermodynamics (Pan Stanford Publishing, Singapore, 2016).
  2. A. Greenleaf, M. Lassas, and G. Uhlmann, “On nonuniqueness for calderon’s inverse problem,” Math. Res. Lett. 10, 685–694 (2003).
    [Crossref]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  4. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  5. S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
    [Crossref]
  6. H. Chen and C. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183518 (2007).
    [Crossref]
  7. M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
    [Crossref]
  8. G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
    [Crossref]
  9. M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phy. Lett. 94, 061903 (2009).
    [Crossref]
  10. N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108, 014301 (2012).
    [Crossref] [PubMed]
  11. T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
    [Crossref] [PubMed]
  12. A. Diatta, M. Kadic, M. Wegener, and S. Guenneau, “Scattering problems in elastodynamics,” Phys. Rev. B 94, 100105 (2016).
    [Crossref]
  13. D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [Crossref] [PubMed]
  14. B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
    [Crossref]
  15. M. Farhat, S. Enoch, S. Guenneau, and A. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phy. Rev. Lett. 101, 134501 (2008).
    [Crossref]
  16. M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
    [Crossref]
  17. G. Dupont, M. Farhat, A. Diatta, S. Guenneau, and S. Enoch, “Numerical analysis of three-dimensional acoustic cloaks and carpets,” Wave Motion 48, 483–496 (2011).
    [Crossref]
  18. M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85, 020301 (2012).
    [Crossref]
  19. M. Kadic, S. Guenneau, S. Enoch, and S. A. Ramakrishna, “Plasmonic space folding: Focusing surface plasmons via negative refraction in complementary media,” ACS Nano 5, 6819–6825 (2011).
    [Crossref] [PubMed]
  20. S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20, 8207–8218 (2012).
    [Crossref] [PubMed]
  21. A. Alù, “Thermal cloaks get hot,” Physics 7, 12 (2014).
    [Crossref]
  22. M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
    [Crossref] [PubMed]
  23. U. Leonhardt, “Applied physics: Cloaking of heat,” Nature 498, 440–441 (2013).
    [Crossref] [PubMed]
  24. M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
    [Crossref]
  25. T. Chen, C.-N. Weng, and J.-S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93, 114103 (2008).
    [Crossref]
  26. S. Guenneau and C. Amra, “Anisotropic conductivity rotates heat fluxes in transient regimes,” Opt. express 21, 6578–6583 (2013).
    [Crossref] [PubMed]
  27. M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).
  28. M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
    [Crossref] [PubMed]
  29. S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108, 214303 (2012).
    [Crossref] [PubMed]
  30. R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110, 195901 (2013).
    [Crossref] [PubMed]
  31. T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
    [Crossref] [PubMed]
  32. H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
    [Crossref] [PubMed]
  33. R. Craster, S. Guenneau, H. Hutridurga, and G. Pavliotis, “Cloaking via mapping for the heat equation,” arXiv preprint arXiv:1712.05439 (2017).
  34. S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017).
    [Crossref]
  35. Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
    [Crossref] [PubMed]
  36. W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
    [Crossref]
  37. D. Boas, M. O’Leary, B. Chance, and A. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999 (1993).
    [Crossref]
  38. M. O’leary, D. Boas, B. Chance, and A. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658 (1992).
    [Crossref]
  39. R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
    [Crossref] [PubMed]
  40. R. Schittny, A. Niemeyer, M. Kadic, T. Bückmann, A. Naber, and M. Wegener, “Diffuse-light all-solid-state invisibility cloak,” Opt. Lett. 40, 4202–4205 (2015).
    [Crossref] [PubMed]
  41. M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
    [Crossref] [PubMed]
  42. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
    [Crossref]
  43. S. Guenneau and T. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10, 20130106 (2013).
    [Crossref]
  44. L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
    [Crossref] [PubMed]
  45. T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018).
    [Crossref] [PubMed]
  46. A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
    [Crossref] [PubMed]
  47. R. Schittny, M. Kadic, T. Buckman, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
    [Crossref] [PubMed]
  48. D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. thesis, University of Pennsylvania (1996).
  49. S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
    [Crossref] [PubMed]
  50. S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).
  51. L. Renthlei, H. Wanare, and S. A. Ramakrishna, “Enhanced propagation of photon density waves in random amplifying media,” Phys. Rev. A 91, 043825 (2015).
    [Crossref]
  52. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008).
    [Crossref]

2018 (3)

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
[Crossref]

Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
[Crossref] [PubMed]

T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018).
[Crossref] [PubMed]

2017 (2)

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017).
[Crossref]

2016 (2)

A. Diatta, M. Kadic, M. Wegener, and S. Guenneau, “Scattering problems in elastodynamics,” Phys. Rev. B 94, 100105 (2016).
[Crossref]

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
[Crossref] [PubMed]

2015 (3)

R. Schittny, A. Niemeyer, M. Kadic, T. Bückmann, A. Naber, and M. Wegener, “Diffuse-light all-solid-state invisibility cloak,” Opt. Lett. 40, 4202–4205 (2015).
[Crossref] [PubMed]

L. Renthlei, H. Wanare, and S. A. Ramakrishna, “Enhanced propagation of photon density waves in random amplifying media,” Phys. Rev. A 91, 043825 (2015).
[Crossref]

M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

2014 (7)

T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
[Crossref] [PubMed]

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
[Crossref] [PubMed]

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).

A. Alù, “Thermal cloaks get hot,” Physics 7, 12 (2014).
[Crossref]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Buckman, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

2013 (7)

S. Guenneau and T. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10, 20130106 (2013).
[Crossref]

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
[Crossref] [PubMed]

U. Leonhardt, “Applied physics: Cloaking of heat,” Nature 498, 440–441 (2013).
[Crossref] [PubMed]

S. Guenneau and C. Amra, “Anisotropic conductivity rotates heat fluxes in transient regimes,” Opt. express 21, 6578–6583 (2013).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110, 195901 (2013).
[Crossref] [PubMed]

2012 (5)

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108, 214303 (2012).
[Crossref] [PubMed]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20, 8207–8218 (2012).
[Crossref] [PubMed]

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108, 014301 (2012).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85, 020301 (2012).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
[Crossref]

2011 (2)

M. Kadic, S. Guenneau, S. Enoch, and S. A. Ramakrishna, “Plasmonic space folding: Focusing surface plasmons via negative refraction in complementary media,” ACS Nano 5, 6819–6825 (2011).
[Crossref] [PubMed]

G. Dupont, M. Farhat, A. Diatta, S. Guenneau, and S. Enoch, “Numerical analysis of three-dimensional acoustic cloaks and carpets,” Wave Motion 48, 483–496 (2011).
[Crossref]

2009 (2)

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phy. Lett. 94, 061903 (2009).
[Crossref]

2008 (5)

M. Farhat, S. Enoch, S. Guenneau, and A. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phy. Rev. Lett. 101, 134501 (2008).
[Crossref]

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
[Crossref]

T. Chen, C.-N. Weng, and J.-S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93, 114103 (2008).
[Crossref]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008).
[Crossref]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

2007 (2)

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
[Crossref]

H. Chen and C. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183518 (2007).
[Crossref]

2006 (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[Crossref]

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

2003 (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, “On nonuniqueness for calderon’s inverse problem,” Math. Res. Lett. 10, 685–694 (2003).
[Crossref]

1993 (1)

D. Boas, M. O’Leary, B. Chance, and A. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999 (1993).
[Crossref]

1992 (1)

M. O’leary, D. Boas, B. Chance, and A. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658 (1992).
[Crossref]

1990 (1)

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[Crossref]

Alu, A.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
[Crossref]

Alù, A.

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
[Crossref] [PubMed]

M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

A. Alù, “Thermal cloaks get hot,” Physics 7, 12 (2014).
[Crossref]

Alwakil, A.

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

Amra, C.

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

S. Guenneau and C. Amra, “Anisotropic conductivity rotates heat fluxes in transient regimes,” Opt. express 21, 6578–6583 (2013).
[Crossref] [PubMed]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20, 8207–8218 (2012).
[Crossref] [PubMed]

Bagci, H.

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
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M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
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Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
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T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
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G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
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M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phy. Lett. 94, 061903 (2009).
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R. Schittny, M. Kadic, T. Buckman, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
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R. Schittny, A. Niemeyer, M. Kadic, T. Bückmann, A. Naber, and M. Wegener, “Diffuse-light all-solid-state invisibility cloak,” Opt. Lett. 40, 4202–4205 (2015).
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R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
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T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
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S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
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S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Castaldi, G.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).

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H. Chen and C. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183518 (2007).
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D. Boas, M. O’Leary, B. Chance, and A. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999 (1993).
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M. O’leary, D. Boas, B. Chance, and A. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658 (1992).
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H. Chen and C. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183518 (2007).
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T. Chen, C.-N. Weng, and J.-S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93, 114103 (2008).
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Chen, P.

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
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Chen, P.-Y.

M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
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M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
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M. Farhat, P.-Y. Chen, S. Guenneau, and S. Enoch, Transformation Wave Physics: Electromagnetics, Elastodynamics, and Thermodynamics (Pan Stanford Publishing, Singapore, 2016).

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T. Chen, C.-N. Weng, and J.-S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93, 114103 (2008).
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T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018).
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R. Craster, S. Guenneau, H. Hutridurga, and G. Pavliotis, “Cloaking via mapping for the heat equation,” arXiv preprint arXiv:1712.05439 (2017).

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S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
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S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
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D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
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Cunningham, A.

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

de Lustrac, A.

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
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Diatta, A.

S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017).
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A. Diatta, M. Kadic, M. Wegener, and S. Guenneau, “Scattering problems in elastodynamics,” Phys. Rev. B 94, 100105 (2016).
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G. Dupont, M. Farhat, A. Diatta, S. Guenneau, and S. Enoch, “Numerical analysis of three-dimensional acoustic cloaks and carpets,” Wave Motion 48, 483–496 (2011).
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Dintinger, J.

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Dupont, G.

G. Dupont, M. Farhat, A. Diatta, S. Guenneau, and S. Enoch, “Numerical analysis of three-dimensional acoustic cloaks and carpets,” Wave Motion 48, 483–496 (2011).
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Enoch, S.

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85, 020301 (2012).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
[Crossref]

M. Kadic, S. Guenneau, S. Enoch, and S. A. Ramakrishna, “Plasmonic space folding: Focusing surface plasmons via negative refraction in complementary media,” ACS Nano 5, 6819–6825 (2011).
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G. Dupont, M. Farhat, A. Diatta, S. Guenneau, and S. Enoch, “Numerical analysis of three-dimensional acoustic cloaks and carpets,” Wave Motion 48, 483–496 (2011).
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M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
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M. Farhat, S. Enoch, S. Guenneau, and A. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phy. Rev. Lett. 101, 134501 (2008).
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M. Farhat, P.-Y. Chen, S. Guenneau, and S. Enoch, Transformation Wave Physics: Electromagnetics, Elastodynamics, and Thermodynamics (Pan Stanford Publishing, Singapore, 2016).

Farhat, M.

S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017).
[Crossref]

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
[Crossref] [PubMed]

M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
[Crossref]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85, 020301 (2012).
[Crossref]

G. Dupont, M. Farhat, A. Diatta, S. Guenneau, and S. Enoch, “Numerical analysis of three-dimensional acoustic cloaks and carpets,” Wave Motion 48, 483–496 (2011).
[Crossref]

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phy. Rev. Lett. 101, 134501 (2008).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, and S. Enoch, Transformation Wave Physics: Electromagnetics, Elastodynamics, and Thermodynamics (Pan Stanford Publishing, Singapore, 2016).

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Galdi, V.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
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M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).

Gao, D.

T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
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H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
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B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
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A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008).
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A. Greenleaf, M. Lassas, and G. Uhlmann, “On nonuniqueness for calderon’s inverse problem,” Math. Res. Lett. 10, 685–694 (2003).
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Guenneau, S.

T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018).
[Crossref] [PubMed]

S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017).
[Crossref]

A. Diatta, M. Kadic, M. Wegener, and S. Guenneau, “Scattering problems in elastodynamics,” Phys. Rev. B 94, 100105 (2016).
[Crossref]

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
[Crossref] [PubMed]

M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110, 195901 (2013).
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S. Guenneau and C. Amra, “Anisotropic conductivity rotates heat fluxes in transient regimes,” Opt. express 21, 6578–6583 (2013).
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S. Guenneau and T. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10, 20130106 (2013).
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S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20, 8207–8218 (2012).
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M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85, 020301 (2012).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
[Crossref]

G. Dupont, M. Farhat, A. Diatta, S. Guenneau, and S. Enoch, “Numerical analysis of three-dimensional acoustic cloaks and carpets,” Wave Motion 48, 483–496 (2011).
[Crossref]

M. Kadic, S. Guenneau, S. Enoch, and S. A. Ramakrishna, “Plasmonic space folding: Focusing surface plasmons via negative refraction in complementary media,” ACS Nano 5, 6819–6825 (2011).
[Crossref] [PubMed]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phy. Lett. 94, 061903 (2009).
[Crossref]

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phy. Rev. Lett. 101, 134501 (2008).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, and S. Enoch, Transformation Wave Physics: Electromagnetics, Elastodynamics, and Thermodynamics (Pan Stanford Publishing, Singapore, 2016).

R. Craster, S. Guenneau, H. Hutridurga, and G. Pavliotis, “Cloaking via mapping for the heat equation,” arXiv preprint arXiv:1712.05439 (2017).

Han, T.

T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
[Crossref] [PubMed]

Hasan, S. B.

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Horsley, S.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
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Hutridurga, H.

R. Craster, S. Guenneau, H. Hutridurga, and G. Pavliotis, “Cloaking via mapping for the heat equation,” arXiv preprint arXiv:1712.05439 (2017).

Justice, B.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Kadic, M.

A. Diatta, M. Kadic, M. Wegener, and S. Guenneau, “Scattering problems in elastodynamics,” Phys. Rev. B 94, 100105 (2016).
[Crossref]

R. Schittny, A. Niemeyer, M. Kadic, T. Bückmann, A. Naber, and M. Wegener, “Diffuse-light all-solid-state invisibility cloak,” Opt. Lett. 40, 4202–4205 (2015).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Buckman, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110, 195901 (2013).
[Crossref] [PubMed]

M. Kadic, S. Guenneau, S. Enoch, and S. A. Ramakrishna, “Plasmonic space folding: Focusing surface plasmons via negative refraction in complementary media,” ACS Nano 5, 6819–6825 (2011).
[Crossref] [PubMed]

Kanté, B.

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008).
[Crossref]

Lai, Y.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
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Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008).
[Crossref]

A. Greenleaf, M. Lassas, and G. Uhlmann, “On nonuniqueness for calderon’s inverse problem,” Math. Res. Lett. 10, 685–694 (2003).
[Crossref]

Lederer, F.

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Leonhardt, U.

U. Leonhardt, “Applied physics: Cloaking of heat,” Nature 498, 440–441 (2013).
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U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
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Li, B.

T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
[Crossref] [PubMed]

Li, J.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
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Li, Y.

Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
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Luo, H.

Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
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M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
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M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
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Milton, G. W.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
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Mitchell-Thomas, R. C.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
[Crossref]

Moccia, M.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).

Mock, J.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Movchan, A.

M. Farhat, S. Enoch, S. Guenneau, and A. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phy. Rev. Lett. 101, 134501 (2008).
[Crossref]

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
[Crossref]

Movchan, A. B.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phy. Lett. 94, 061903 (2009).
[Crossref]

Mühlig, S.

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Naber, A.

Narayana, S.

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108, 214303 (2012).
[Crossref] [PubMed]

Nicolet, A.

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
[Crossref]

Niemeyer, A.

O’Leary, M.

D. Boas, M. O’Leary, B. Chance, and A. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999 (1993).
[Crossref]

M. O’leary, D. Boas, B. Chance, and A. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658 (1992).
[Crossref]

Pavliotis, G.

R. Craster, S. Guenneau, H. Hutridurga, and G. Pavliotis, “Cloaking via mapping for the heat equation,” arXiv preprint arXiv:1712.05439 (2017).

Pendry, J.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Pendry, J. B.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

Prahl, S.

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[Crossref]

Puvirajesinghe, T.

T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018).
[Crossref] [PubMed]

S. Guenneau and T. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10, 20130106 (2013).
[Crossref]

Puvirajesinghe, T. M.

S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017).
[Crossref]

Qiu, C.-W.

Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
[Crossref] [PubMed]

T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
[Crossref] [PubMed]

Quevedo-Teruel, O.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
[Crossref]

Rahm, M.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

Ramakrishna, S. A.

L. Renthlei, H. Wanare, and S. A. Ramakrishna, “Enhanced propagation of photon density waves in random amplifying media,” Phys. Rev. A 91, 043825 (2015).
[Crossref]

M. Kadic, S. Guenneau, S. Enoch, and S. A. Ramakrishna, “Plasmonic space folding: Focusing surface plasmons via negative refraction in complementary media,” ACS Nano 5, 6819–6825 (2011).
[Crossref] [PubMed]

Renthlei, L.

L. Renthlei, H. Wanare, and S. A. Ramakrishna, “Enhanced propagation of photon density waves in random amplifying media,” Phys. Rev. A 91, 043825 (2015).
[Crossref]

Rockstuhl, C.

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Salama, K.

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
[Crossref] [PubMed]

Sato, Y.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108, 214303 (2012).
[Crossref] [PubMed]

Savo, S.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).

Scharf, T.

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

Schittny, R.

R. Schittny, A. Niemeyer, M. Kadic, T. Bückmann, A. Naber, and M. Wegener, “Diffuse-light all-solid-state invisibility cloak,” Opt. Lett. 40, 4202–4205 (2015).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Buckman, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110, 195901 (2013).
[Crossref] [PubMed]

Schurig, D.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Shi, X.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
[Crossref] [PubMed]

Smith, D.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Smith, D. R.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Song, R.

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

Starr, A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Stenger, N.

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108, 014301 (2012).
[Crossref] [PubMed]

Sun, H.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
[Crossref] [PubMed]

Tassin, P.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
[Crossref]

Thiel, M.

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Thong, J. T.

T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
[Crossref] [PubMed]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008).
[Crossref]

A. Greenleaf, M. Lassas, and G. Uhlmann, “On nonuniqueness for calderon’s inverse problem,” Math. Res. Lett. 10, 685–694 (2003).
[Crossref]

Veynante, D.

Wanare, H.

L. Renthlei, H. Wanare, and S. A. Ramakrishna, “Enhanced propagation of photon density waves in random amplifying media,” Phys. Rev. A 91, 043825 (2015).
[Crossref]

Wegener, M.

A. Diatta, M. Kadic, M. Wegener, and S. Guenneau, “Scattering problems in elastodynamics,” Phys. Rev. B 94, 100105 (2016).
[Crossref]

R. Schittny, A. Niemeyer, M. Kadic, T. Bückmann, A. Naber, and M. Wegener, “Diffuse-light all-solid-state invisibility cloak,” Opt. Lett. 40, 4202–4205 (2015).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, T. Buckman, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110, 195901 (2013).
[Crossref] [PubMed]

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108, 014301 (2012).
[Crossref] [PubMed]

Welch, A.

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[Crossref]

Weng, C.-N.

T. Chen, C.-N. Weng, and J.-S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93, 114103 (2008).
[Crossref]

Wilhelm, M.

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108, 014301 (2012).
[Crossref] [PubMed]

Willis, J. R.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[Crossref]

Xu, H.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
[Crossref] [PubMed]

Yang, T.

Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
[Crossref] [PubMed]

Yodh, A.

D. Boas, M. O’Leary, B. Chance, and A. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999 (1993).
[Crossref]

M. O’leary, D. Boas, B. Chance, and A. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658 (1992).
[Crossref]

Zeng, L.

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

Zerrad, M.

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

Zhang, B.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
[Crossref] [PubMed]

Zhi, Z.

T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018).
[Crossref] [PubMed]

Zhu, J.

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
[Crossref]

Zolla, F.

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
[Crossref]

ACS Nano (1)

M. Kadic, S. Guenneau, S. Enoch, and S. A. Ramakrishna, “Plasmonic space folding: Focusing surface plasmons via negative refraction in complementary media,” ACS Nano 5, 6819–6825 (2011).
[Crossref] [PubMed]

Appl. Phy. Lett. (1)

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phy. Lett. 94, 061903 (2009).
[Crossref]

Appl. Phys. Lett. (2)

H. Chen and C. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183518 (2007).
[Crossref]

T. Chen, C.-N. Weng, and J.-S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93, 114103 (2008).
[Crossref]

IEEE J. Quantum Electron. (1)

W. Cheong, S. Prahl, and A. Welch, “A review of the optical properties of biological,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[Crossref]

J. Opt. (2)

S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, “Cloaking and anamorphism for light and mass diffusion,” J. Opt. 19, 103002 (2017).
[Crossref]

M. McCall, J. B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, and et al., “Roadmap on transformation optics,” J. Opt. 20, 063001 (2018).
[Crossref]

J. R. Soc. Interface (2)

S. Guenneau and T. Puvirajesinghe, “Fick’s second law transformed: one path to cloaking in mass diffusion,” J. R. Soc. Interface 10, 20130106 (2013).
[Crossref]

T. Puvirajesinghe, Z. Zhi, R. Craster, and S. Guenneau, “Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide,” J. R. Soc. Interface 15, 20170949 (2018).
[Crossref] [PubMed]

Math. Res. Lett. (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, “On nonuniqueness for calderon’s inverse problem,” Math. Res. Lett. 10, 685–694 (2003).
[Crossref]

Nat. Commun. (2)

T. Bückmann, M. Thiel, M. Kadic, R. Schittny, and M. Wegener, “An elasto-mechanical unfeelability cloak made of pentamode metamaterials,” Nat. Commun. 5, 4130 (2014).
[Crossref] [PubMed]

Y. Li, X. Bai, T. Yang, H. Luo, and C.-W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9, 273 (2018).
[Crossref] [PubMed]

Nature (2)

M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
[Crossref] [PubMed]

U. Leonhardt, “Applied physics: Cloaking of heat,” Nature 498, 440–441 (2013).
[Crossref] [PubMed]

New J. Phys. (4)

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[Crossref]

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla, and A. Nicolet, “A homogenization route towards square cylindrical acoustic cloaks,” New J. Phys. 10, 115030 (2008).
[Crossref]

S. A. Cummer and D. Schurig, “One path to acoustic cloaking,” New J. Phys. 9, 45 (2007).
[Crossref]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Isotropic transformation optics: approximate acoustic and quantum cloaking,” New J. Phys. 10, 115024 (2008).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phy. Rev. Lett. (2)

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3d acoustic cloaking shell,” Phy. Rev. Lett. 100, 024301 (2008).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phy. Rev. Lett. 101, 134501 (2008).
[Crossref]

Phys. Rev. A (1)

L. Renthlei, H. Wanare, and S. A. Ramakrishna, “Enhanced propagation of photon density waves in random amplifying media,” Phys. Rev. A 91, 043825 (2015).
[Crossref]

Phys. Rev. B (4)

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85, 020301 (2012).
[Crossref]

B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[Crossref]

A. Diatta, M. Kadic, M. Wegener, and S. Guenneau, “Scattering problems in elastodynamics,” Phys. Rev. B 94, 100105 (2016).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, “Frequency-selective surface acoustic invisibility for three-dimensional immersed objects,” Phys. Rev. B 86, 174303 (2012).
[Crossref]

Phys. Rev. E (1)

D. Boas, M. O’Leary, B. Chance, and A. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999 (1993).
[Crossref]

Phys. Rev. Lett. (6)

M. O’leary, D. Boas, B. Chance, and A. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658 (1992).
[Crossref]

S. Narayana and Y. Sato, “Heat flux manipulation with engineered thermal materials,” Phys. Rev. Lett. 108, 214303 (2012).
[Crossref] [PubMed]

R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, “Experiments on transformation thermodynamics: molding the flow of heat,” Phys. Rev. Lett. 110, 195901 (2013).
[Crossref] [PubMed]

T. Han, X. Bai, D. Gao, J. T. Thong, B. Li, and C.-W. Qiu, “Experimental demonstration of a bilayer thermal cloak,” Phys. Rev. Lett. 112, 054302 (2014).
[Crossref] [PubMed]

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Ultrathin three-dimensional thermal cloak,” Phys. Rev. Lett. 112, 054301 (2014).
[Crossref] [PubMed]

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108, 014301 (2012).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4, 021025 (2014).

Physics (1)

A. Alù, “Thermal cloaks get hot,” Physics 7, 12 (2014).
[Crossref]

Proc. R. Soc. A (1)

M. Farhat, P. Chen, S. Guenneau, H. Bağcı, K. Salama, and A. Alù, “Cloaking through cancellation of diffusive wave scattering,” Proc. R. Soc. A 472, 20160276 (2016).
[Crossref] [PubMed]

Sci. Rep. (4)

L. Zeng and R. Song, “Controlling chloride ions diffusion in concrete,” Sci. Rep. 3, 3359 (2013).
[Crossref] [PubMed]

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “A self-assembled three-dimensional cloak in the visible,” Sci. Rep. 3, 2328 (2013).
[Crossref] [PubMed]

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

M. Farhat, P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

Science (5)

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref] [PubMed]

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Wave Motion (1)

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[Crossref]

Other (4)

M. Farhat, P.-Y. Chen, S. Guenneau, and S. Enoch, Transformation Wave Physics: Electromagnetics, Elastodynamics, and Thermodynamics (Pan Stanford Publishing, Singapore, 2016).

R. Craster, S. Guenneau, H. Hutridurga, and G. Pavliotis, “Cloaking via mapping for the heat equation,” arXiv preprint arXiv:1712.05439 (2017).

D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. thesis, University of Pennsylvania (1996).

S. Mühlig, A. Cunningham, J. Dintinger, M. Farhat, S. B. Hasan, T. Scharf, T. Bürgi, F. Lederer, and C. Rockstuhl, “Reply to the comment on” a self-assembled three-dimensional cloak in the visible” in scientific reports 3, 2328,” arXiv preprint arXiv:1310.5888 (2013).

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Figures (4)

Fig. 1
Fig. 1 (a) Cross-section of the DPDW structure to cloak. Schematic of the cloak: 3D scenario showing the DPDWs flux transfer, with the object to cloak in the middle (light red sphere). Different shells with different properties represent the DPDW cloak, with various parameters of the study. (b) Dispersion relation of the DPDW, giving the norm of the wavenumber versus the normalized diffusivity and frequency.
Fig. 2
Fig. 2 (a) Analysis of the scattering cross-section (SCS) behavior from a bare spherical object with varying absorption coefficient at frequency 50 MHz. (b) Plot of SCS versus frequency for different diffusivity of the bare object. Far-field scattering from (c) the bare object (sphere) and (d) the cloaked sphere, in logarithmic scale.
Fig. 3
Fig. 3 (a) Snapshot of the total normalized fluence field Φ/Φ0 around the cloak at two different wavenumbers (a) k0b = π/10 and (b) k0b = π/2. (We should mention here that colors inside the shell and core have nothing to do with color scale for normalized fluence.)
Fig. 4
Fig. 4 Heating inside the core: Logarithmic plot of the analytical expressions of the real part of the fluence field Φ versus the distance from origin (normalized with respect to a), as obtained from (24), for a fixed angle θ.

Equations (28)

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Ω υ ( x ) Φ ( x ) + μ a ( x ) Φ ( x ) + ς ( x ) = [ D ( x ) Φ ( x ) ] ,
k 0 = i ( Ω υ 0 + μ a , 0 ) / D 0 ,
Ω [ det ( J ) / υ ( x ) ] Φ ( x ) + μ a ( x ) det ( J ) Φ ( x ) + det ( J ) ς ( x ) = ( J T D ( x ) J 1 det ( J ) Φ ( x ) ) .
D _ _ = J T D J 1 det ( J ) = D J T J 1 det ( J ) = D T 1 ,
r ( D r r 2 Φ r ) + D θ sin θ θ ( sin θ Φ θ ) + D ϕ sin 2 θ 2 Φ ϕ 2 r 2 [ Ω υ + μ a ] Φ = 0 ,
1 D ϕ r ( D r r 2 f r ) + ( k 2 r 2 n ( n + 1 ) ) f = 0 ,
r 2 D r = ( r a ) 2 D 0 A , D ϕ = D 0 A , and k 2 r 2 = k sh 2 ( r a ) 2 ,
r ( ( r a ) 2 f r ) + ( k sh 2 ( r a ) 2 n ( n + 1 ) ) f = 0 ,
Φ inc = Φ 0 n = 0 n = i n ( 2 n + 1 ) j n ( k 0 r ) P n ( cos θ ) ,
Φ scat = Φ 0 n = 0 n = c n h n ( 1 ) ( k 0 r ) P n ( cos θ ) ,
Φ sh = Φ 0 n = 0 n = d n j n ( k s h ( r a ) ) P n ( cos θ ) ,
Φ int = Φ 0 n = 0 n = e n j n ( k 0 r ) P n ( cos θ ) ,
i n ( 2 n + 1 ) j n ( k 0 b ) + c n h n ( 1 ) ( k 0 b ) = d n j n ( k s h ( b a ) ) , D 0 k 0 [ i n ( 2 n + 1 ) j n ( k 0 b ) + c n j n   ( 1 ) ( k 0 b ) ] = D r ( b ) k s h × [ d n j n ( k s h ( b a ) ) ] .
c n i n ( 2 n + 1 ) = k 0 D 0 j n ( k 0 b ) j n [ k s h ( b a ) ] + k s h D r ( b ) j n ( k 0 b ) j n [ k s h ( b a ) ] k 0 D 0 h n   ( 1 ) ( k 0 b ) j n [ k s h ( b a ) ] k s h D r ( b ) h n   ( 1 ) ( k 0 b ) j n [ k s h ( b a ) ] .
c n b i n ( 2 n + 1 ) = j n ( k 0 a ) j n [ k 1 a ) ] + χ j n ( k 0 a ) j n [ k 1 a ) ] h n   ( 1 ) ( k 0 a ) j n [ k 1 a ) ] χ h n ( 1 ) ( k 0 a ) j n [ k 1 a ) ] ,
χ = k 1 D 1 k 0 D 0 ,
S C S = 4 π | k 0 | 2 n = 0 N 0 ( 2 n + 1 ) | c n | 2 .
k 0 b = k s h ( b a ) , k s h D r ( b ) = k 0 D 0 .
A = b b a , k s h = b b a k 0 .
D r = b b a ( r a ) 2 r 2 D 0 , D θ = D ϕ = b b a D 0 ,
Ω / υ + μ a = b 3 ( b a ) 3 ( r a ) 2 r 2 ( Ω / υ 0 + μ a , 0 ) .
υ = ( b a ) 3 b 3 r 2 ( r a ) 2 υ 0 and μ a = b 3 ( b a ) 3 ( r a ) 2 r 2 μ a , 0 ,
i n ( 2 n + 1 ) j n ( k s h ( r a ) ) = e n j n ( k 0 r ) , b ( r a ) 2 ( b a ) r 2 i n ( 2 n + 1 ) j n ( k s h ( r a ) ) = e n j n ( k 0 r ) .
Φ int = Φ 0 j 0 ( k 0 r ) P n ( cos ( θ ) ) ,
Ω u = ( κ ( x ) u ) + p ( x , Ω ) ,
det ( J ) Ω u = ( κ _ _ det ( J ) u ) + det ( J ) p ( x , Ω ) ,
κ r = b b a ( r a ) 2 r 2 , κ θ = κ ϕ = b b a ,
u int = U j 0 ( k 0 r ) P 0 ( cos ( θ ) ) ,

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