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A microparticle resonance model, describing the interaction between an LCR circuit coupled with a bipole, is established for the accurate simulation of Metamaterials. The quantum dynamic descriptions of both an LCR circuit and a bipole are harmonic oscillators. The coupling effect will induce a frequency (the resonance frequency) shift, thereby affecting the resonance occurrence of LCR-circuit Metamaterials. Resistance R has effects on the resonance frequency and effective parameters of Metamaterials, but its scale varying does not cause a fluctuation except in some situations, such as R2 or 1/R2 is the same quantity order of inductance L ( $$R^{2} \ge 1 /L$$ for the cases of parallel and series connections of R with L and C, respectively. The use of temperature adjustment (altering R) to adjust the LCR-circuit resonance frequency is proposed for the realization of a tunable Metamaterial.

Based on the separate discussions on dispersion and nonlinear effects, the parametric gain operator is established to exhibit the pump field’s impact in the process of the fast and wide spectral expansion. The condition of inducing sideband is that sin [ ∑ n = 2 ∞ ( − 1 ) n + 1 n ! β n ω n d z ] = 0 has a solution with the intensity fluctuations or cos [ ∑ n = 2 ∞ ( − 1 ) n + 1 n ! β n ω n d z ] = 0 has a solution with a initial phase. The initial intensity fluctuation results in a coherent white source while the initial phase modulation cuts down this band’s width but brings the nearby blue-shift or red-shift solitons which depend on the dispersion coefficients. Furthermore, this parametric gain operator can be used to describe the phenomenon of CW pump inducing solitons.

The evolution of ASE noise and the generation of nonlinear phase shift are analyzed based on the travelling wave solution of ASE noise and its probability density function by solving the Fokker-Planck equation including dispersion effect. Nonlinear effect has strong impact on ASE noise. After the transmission in non-zero dispersion shift fibers + dispersion compensation fibers, due to the nonlinear effect, ASE noise is enhanced. Detailedly, the real part of ASE decreases but the image part increases greatly compared to that with dispersion effect only. Nonlinear phase shift, related to the image part of ASE noise, occurs in this kind of link. The impact of signal intensity on ASE noise induces fluctuations to the both curves of ASE noise and nonlinear phase shift as functions of time, respectively. Furthermore, it results in the non-Gaussian distribution of ASE noise probability density function (side-bands occurring) and brings more than 1 dB additive BER.

The normalized phase-amplitude representation and the Darboux figure are first defined. Then as an example, we establish the quantum optics description for the field in photonic crystal fibers in the defined representation. The field is evolved from one Darboux state to another state in the Darboux figure. By the continuous inputting (pump) of light, the waves induced by nonlinear effects become stronger (the wave frequency number remains constant at the same distance, and their intensities accumulate). The blueshifted waves induced by the third-order resonant susceptibility are not strong enough to cover other nonlinear effect and turn weak along the length (pump turns weak).