Fig. 1. Schematic diagram of an on-chip system consisting of multiple functional modules (a) without the cloak and (b) with the designed thermal-electromagnetic cloak, respectively. (a) A central processing unit CPU (i.e., thermal sensitive electrical element in the center region) will be affected by the gathered waste heat (indicated by red arrows) from surrounding resistive elements (blue blocks) on chip, which may make the temperature around the processing unit higher than its rated temperature or generate thermal stress/deformation due to the gradient temperature field, and then affect its working efficiency and aggravate the aging. At the same time, the CPU will disturb the EM signals (represented by yellow curves) from surrounding radiating components (e.g., the cyan antenna). (b) The designed thermal-electromagnetic cloak (colored orange) is set around the CPU in the same on-chip system. In this case, the EM signals and waste heats can be simultaneously guided around the thermal sensitive CPU. As a result, the CPU will not be affected by waste heats (or the gradient temperature field from surrounding resistive elements) and not influence radiation pattern of EM signals from surrounding radiating components. Meanwhile, the waste heat can be effectively collected by the latter cooling/recovery units.

Fig. 2. (a) Basic schematic diagram of a tubular TENM that connects two arbitrarily shaped surfaces S₁ and S₂, which can simultaneously project the thermal-electromagnetic field distribution from S₁ onto S₂ along its principal axes (blue curves). An arbitrary trapezoid element of a null medium in the (b) physical space is transformed to a compressed thin slab in the (c) reference space. The simulated results when a line current EM source and high temperature source are on the input surface S₁ of the TENM, where the normalized magnetic field (d) and the temperature field (e) are plotted, respectively. The simulated normalized magnetic field (f) and temperature field (g) for a fractal-tree shaped TENM with principal axes along the trunk, respectively, which can split both EM fields (f) and heat flux (g) from the root to the top branches. The simulated normalized magnetic field (h) and temperature field (i) for a ‘Tai Chi’ shaped TENM, respectively, which can guide both EM fields (h) and heat flux (i) around the center concealed hole. The black regions in (h) and (i) represent areas with perfect electric conductor and thermal insulation boundaries that EM fields and heat flux never touch. Details of the numerical setting are given in Supplementary Section 1.

Fig. 3. (a) Schematic diagram of graphical design method based on the directional projection property of TENM. The black and red arrow indicate the input and output fields, and the corresponding wavefronts (or isothermal surface) are represented by black/red dashed curves. Black and red solid curves inside the box are the input/output boundaries of the TENM. Blue arrowed curves indicate one possible projection. (b) A thermal-electromagnetic cloak designed by the graphical method described in (a). The input/output boundaries are designed as straight lines (conformal to the straight input/output EM wavefront and isothermal surface). The yellow region is the TENM with its principal axes along the blue arrowed lines. The green region is the concealed region. (c) A thermal-electromagnetic shifter and (d) a thermal-electromagnetic divider-deflector are designed by the same graphical method described in (a). Simulated magnetic field distributions (e, g) and temperature distributions (f, h) for the thermal-electromagnetic cloak under the case of a plane detecting wave/isotherm incidence (e, f), and a cylindrical detecting wave/isotherm incidence (g, h). Simulated magnetic field distributions (i, k) and temperature distributions (j, l) for the thermal-electromagnetic shifter (i, j) and divider-deflector (k, l) under a plane wave/isotherm incidence. (m–p) are the corresponding simulation results of (i–l) when the plane wave/isotherm is replaced by point source.

Fig. 4. (a) Reduced TENM by staggered copper and EPS boards. (b) A thermal-electromagnetic shifter realized by reduced TENM. Simulated 2D magnetic/temperature field distributions for a thermal-electromagnetic shifter with reduced TENM under (c, d) a plane TM-polarized-wave/isotherm incidence and (e, f) a line thermal/electromagnetic source. Simulated 2D magnetic/temperature field distributions for a thermal-electromagnetic cloak with reduced TENM under (g, h) a plane TM-polarized-wave/isotherm incidence and (i, j) a line thermal/electromagnetic source.

Fig. 5. (a) Schematic of the experimental setup for measuring thermal-electromagnetic cloak. Orange and green slits represent copper and EPS, respectively. Two blue thin thermal pads on the surface of a gray foam board together can simulate an on-chip environment. The black area is the concealed region for both TM-polarized EM waves and heat fluxes. Measured temperature distributions show the black protruding square on the chip will not and will influence the incident plane isothermal with cloak (b) and without cloak (c), respectively. 3D Simulated temperature distributions with cloak (d) and without cloak (e) are well matched with the measurement results in (b) and (c), respectively. 3D Simulated normalized z-component magnetic fields when a radiating component (i.e., a loop antenna) is in front of the black protruding square on the chip with cloak (f) and without cloak (g), respectively. (h) Simulated and measured normalized amplitude of magnetic fields along the marked dotted lines in (f) and (g).