have presented, the current through the load is 2 / Z [ E: -EZ+ 1.However, in this case we can also represent the current as E / ( Z( t ) ) where E is the voltage across the load and Z( t ) is the time varying impedance. (Only R is varying with time.)we now have a relationship that gives us an exact solution for f ( E:): where 2d 7 'c Now, let us look at the circuit used in the example. Using standard circuit techniques for determining the impedance yields R / j o C R + l / j o C z( I ) = j w L + Since (d/dt>e/*l = jwelor we can replace each occurrence of j w with d/dt. After this substitution, algebraic rearrangement of (6) and (7) yields (8), which is identical to (3) when all Relative FreqLiency Relotivp FI + x i~i~i i r -y Received 12-4-89 Microwave and Optical Technology Letters, 3/3, 98-102 ABSTRACT A method is proposed for using urruy element positions plur the element excitutions in order to ohtuin both acceptable sum and diflerence patterns for a monopulse array with u two-section feed network. Preliminary resuhs ure discussed.

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Metamaterials are effectively homogeneous materials that display extraordinary dispersion. Negative index metamaterials, zero index metamaterials and extremely anisotropic metamaterials are just a few examples. Instead of using locally resonating elements that may cause undesirable absorption, there are huge efforts to seek alternative routes to obtain these unusual properties. Here, we demonstrate an alternative approach for constructing metamaterials with extreme dispersion by simply coiling up space with curled channels. Such a geometric approach also has an advantage that the ratio between the wavelength and the lattice constant in achieving a negative or zero index can be changed in principle. It allows us to construct for the first time an acoustic metamaterial with conical dispersion, leading to a clear demonstration of negative refraction from an acoustic metamaterial with airborne sound. We also design and realize a double-negative metamaterial for microwaves under the same principle.

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