Impact of Kerr Effect on the Performance of Optical Invisibility Cloak Designed by Transformation Optics

Po-Han Fu, Hsiu-Chih Yeh, Wei-Chi Hsu, and Ding-Wei Huang* Graduate Institute of Photonics and Optoelectronics National Taiwan University Taipei, Taiwan R.O.C. [email protected]

Abstract — The impact of the Kerr effect on an optical probing electric field. As probing intensity increases, more invisibility cloak designed by transformation optics is studied. electromagnetic power penetrates into the cloak to reach the For the annular cloak made of meta-materials with Kerr object inside. According to the analyses above, when the nonlinearity, the of the cloak may vary with the optical cloak is made of meta-materials with Kerr nonlinearity, intensity of the probing electromagnetic waves. As the probing the cloaking performance will be impaired severely as the intensity increases, the refractive index distribution of the probing intensity increases. annular cloak deviates from its original optimal value. As a result, the cloaking performance of the optical invisibility cloak is impaired severely.

Keywords — optical cloak; Kerr effect; Optical invisibility cloaks designed by transformation optics were proposed in recent years [1]. With the optimal design of the isotropic or anisotropic distribution of the or permeability of the annular cloak region for a certain probing electromagnetic wavelength, the object inside the cloak is not detectable. The implementation of such cloaks was demonstrated with the meta-materials at microwave Fig. 1. (a)–(d) Normalized total electric fields and (e)–(h) normalized frequency [2] and optical frequency [3]. For the optimal scattered electric fields as the probding electromagnetic waves propagating performance of the optical cloak designed by transformation through the optical cloak under the probing electric fields at 0.01, 2, 4, and 6 optics, the distribution of the material parameters for a certain ×1010 V/m, respectively. probing wavelength should stick to the formulation to guarantee the lowest penetration field inside the cloak and lowest scattering and distortion of the electromagnetic waves outside the cloak. However, if the annular cloak is made of meta-materials with the Kerr effect [4], the refractive index (or permittivity) distribution of the cloak may vary with the intensity of the probing electromagnetic waves so that the cloak may become less optimal. Consequently, the performance of the optical cloak would be impaired. In this study, the finite element analysis software COMSOL Multiphysics® is used to conduct numerical simulations of the responses of the electromagnetic waves passing through the optical cloak. In addition to the formulation for the material parameters based on the transformation optics, the Kerr nonlinearity of the material of the cloak is also considered in Fig. 2. The power inside the cloak as a function of the probing electric field. the simulation models to analyze the impact of the Kerr effect on the performance of the optical cloak under different The authors acknowledge the financial support from intensity of the probing electromagnetic waves. In the model, National Science Council, Taiwan R.O.C. under the grant the outer and inner diameters of the annular cloak are 5 and 2.5 number NSC 102-2221-E-002-175 μm, respectively. The probing wavelength is 500 nm. The 10 probing electric field varies from 0.01 to 7×10 V/m. REFERENCES Figure 1 shows the simulation results of the of the [1] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic normalized total electric field (a)-(d) and the normalized fields,” Science, vol. 312, no. 5781, pp. 1780–1782, 2006. scattered electric fields as the probing electromagnetic waves [2] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. propagating through the optical cloak under different probing Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science, vol.314, no. 5801, pp. 977–980, 2006. electric fields at 0.01, 2, 4, and 6 ×1010 V/m, respectively. The [3] W. Cai, U. Chettiar, A. Kildishev, and V. M. Shalaev, “Optical cloaking results of the total fields and scatted fields imply a clear trend with ,” Applied Physics Letters, vol. 1, no. 11, pp. 224– that the distortion of the electromagnetic fields outside the 227, 2007. cloak becomes more severe as the probing intensity increases. [4] P. Weinberger, "John Kerr and his Effects Found in 1877 and 1878". Figure 2 shows the power inside the cloak as s function of the Philosophical Magazine Letters, vol. 88, 897–907, 2008.