We numerically investigate the optical transmission through a compound spherical stack with conventional and metamaterial (MM) layers and also embedded MM defect. A formation of extremely narrow resonant peak with nearly complete transmittance in area of a band gap is found. We demonstrate that photon fields of certain frequencies can be strongly confined by a left-handed (LH) defect. The influence of a random deviation in the width of compound spherical layers as well the transit to the whispering gallery mode (WGM) is also discussed. 1. Introduction Controlling the electromagnetic properties of materials, going beyond the limit that is attainable with naturally existing substances, has become a reality with the advent of metamaterials [1, 2]. The range of various structured artificial structures has promised a vast variety of otherwise unexpected physical phenomena [3–5] among which the experimental realization of a negative refractive index has been one of the main advantage. A typical metamaterial combines continuous metal films (about 50？nm) with nanostrip magnetic resonators that finally yield a negative-index material. The film can be formed with a mixture of dielectric (e.g., silica) and metal, such as silver or gold, forming a semicontinuous metal film. Such structures are fabricated using techniques as the evaporation of a metal onto a dielectric substrate (see more details in review [5]). Preparation of metamaterial structure in the optical range still is an advanced task. In recent experiment [6] it has been demonstrated that the incorporation of the gain material (rhodamine 800) in the metamaterial makes it possible to fabricate an extremely low-loss and an active optical negative-index metamaterial (NIM) that is not limited by the inherent loss in its metal constituent. In this experiment the optical (NIM) structure (silver layers + rhodamine 800) is the fishnet with periodicity about 300？nm. Epoxy doped with rhodamine 800 (Rh800) and dye is used as a gain medium. The loss compensation mechanism in the sample is straightforward to understand. When Rh800 is excited by a pump pulse with sufficiently high power, a population inversion is formed inside the dye molecules. This provides amplification for a properly delayed probe pulse whose wavelength is coincident with the stimulated emission wavelength of the dye molecules (see details in [6]). Natural extension of such directions is the analysis of a compacted spherical multilayered system with embedded metamaterial layers. It is well known that except for the whispering gallery mode (WGM)
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