# Electromagnetic field animations

Propagation of two kinds of modes in an array of broadside coupled split ring resonators inserted in the symmetry plane of an X-band rectangular waveguide (This animation and below). The animation of the mode propagating at 2 GHz represents the absolute value of the magnetic field in the left-handed (backward) wave. The cutoff frequency of the hollow waveguide fc=6.5 GHz.

Propagation of two kinds of modes in an array of broadside coupled split ring resonators inserted in the symmetry plane of an X-band rectangular waveguide (This animation and above). The animation of the mode propagating at 4 GHz represents the absolute value of the magnetic field the right-handed (forward) wave. The cutoff frequency of the hollow waveguide fc=6.5 GHz.

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Detailed metamaterial macrostructure is represented by an array of unit cells composed of split ring resonators and wires. Negative refraction is observed at 10 GHz, in the double negative frequency band (effective electric permittivity and magnetic permeability are both negative at 10 GHz).

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Detailed metamaterial macrostructure is represented by an array of unit cells composed of split ring resonators and wires. Positive refraction is observed at 15 GHz, in the double positive frequency band (effective electric permittivity and magnetic permeability are both positive at 15 GHz).

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Homogeneous metamaterial representation is based on the effective electric permittivity and magnetic permeability extracted with the PFDM method (Parameter Fitting of Dispersive Models) from the unit cell analysis. Negative refraction is observed at 10 GHz, in the double negative frequency band (electric permittivity and magnetic permeability are both negative at 10 GHz).

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Homogeneous metamaterial representation is based on the effective electric permittivity and magnetic permeability extracted with the PFDM method (Parameter Fitting of Dispersive Models) from the unit cell analysis. Positive refraction is observed at 15 GHz, in the double positive frequency band (electric permittivity and magnetic permeability are both positive at 15 GHz).

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Detailed metamaterial macrostructure is represented by a lattice of unit cells composed of split ring resonators and wires. Strong reflection and high attenuation are observed at 7 GHz, in the single negative frequency band (stopband, effective electric permittivity is negative, whereas effective magnetic permeability is positive at 7 GHz).

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Detailed metamaterial macrostructure is represented by a lattice of unit cells composed of split ring resonators and wires. Negative refraction and backward wave in the metamaterial are observed at 10 GHz, in the double negative frequency band (effective electric permittivity and magnetic permeability are both negative at 10 GHz).

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Detailed metamaterial macrostructure is represented by a lattice of unit cells composed of split ring resonators and wires. Strong reflection and high attenuation is observed at 11.5 GHz, in the single negative frequency band (stopband, effective electric permittivity is negative, whereas effective magnetic permeability is positive at 11.5 GHz). The attenuation at 11.5 GHz is significantly lower than at 7 GHz due to the lower values of the magnitudes for the real parts of permittivity and permeability.

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Detailed metamaterial macrostructure is represented by a lattice of unit cells composed of split ring resonators and wires. Positive refraction and forward wave in the metamaterial are observed at 15 GHz, in the double positive frequency band (effective electric permittivity and magnetic permeability are both positive at 15 GHz).

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Detailed metamaterial macrostructure is represented by an array of unit cells composed of split ring resonators and wires. Negative refraction is observed at 10 GHz, in the double negative frequency band (effective electric permittivity and magnetic permeability are both negative at 10 GHz). The radius of the semicircle equals 75 cm that is equivalent to 25 free space wavelengths.

No animation available!

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Homogeneous metamaterial representation is based on the effective electric permittivity and magnetic permeability extracted with the PFDM method (Parameter Fitting of Dispersive Models) from the unit cell analysis. Negative refraction is observed at 10 GHz, in the double negative frequency band (electric permittivity and magnetic permeability are both negative at 10 GHz). The radius of the semicircle equals 75 cm that is equivalent to 25 free space wavelengths.

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Polar farfield characteristics for the detailed (LHS) and effective (RHS) macrostructures at 10 GHz (double negative band, negative refraction observed). Direction of the main beam: theta = -14 deg for the detailed wedge (LHS) vs theta = -13 deg for the homogeneous wedge (RHS).

No animation available!

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. Polar farfield characteristics for the detailed (LHS) and effective (RHS) macrostructures at 15 GHz (double positive band, positive refraction observed). Direction of the main beam: theta = +22 deg for the detailed wedge (LHS) vs theta = +21 deg for the homogeneous wedge (RHS).

No animation available!

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. 3d farfield characteristics for the detailed (LHS) and effective (RHS) macrostructures at 10 GHz (double negative band, negative refraction observed). Direction of the main beam: theta = -14 deg for the detailed wedge (LHS) vs theta = -13 deg for the homogeneous wedge (RHS).

No animation available!

Simulation of the negative refraction experiment in a wedge shaped metamaterial [RA Shelby, DR Smith, and S Schultz: “Experimental verification of a negative index of refraction”, Science 292, pp. 77-79, Apr. 2001]. 3d farfield characteristics for the detailed (LHS) and effective (RHS) macrostructures at 15 GHz (double positive band, positive refraction observed). Direction of the main beam: theta = +22 deg for the detailed wedge (LHS) vs theta = +21 deg for the homogeneous wedge (RHS).

No animation available!