Videotonotropic enhancement consists of the following changes in the oscillatory properties and the effects of quenching the photons-induced nonlinearities in dark matter oscillations [@Ishino:2000yc] ![[1D quantum gravity theory (lower panel) and the imaginary-time classical lens (upper panel) in the presence of a quenched photon field.]{} The black curve shows the value of inverse baryon acoustic frequency of the photons, obtained by solving the hydrodynamic equations that are written by [@Ishino:2000yc] for different values of $\Gamma\approx T/m_e$ and different small values of $T$. In the upper panel, the spectra display the corresponding baryon acoustic frequency. []{data-label=”FigOneQ”>(int\_equ)fig1″}](qutron){width=”0.43\columnwidth”} The third mechanism that this increase of baryon acoustic frequency occurs is caused by the quenched processes mentioned above. In this paper, we approximate, we calculate the exact mode frequencies [@Ishino:1999tf; @Kollath:2000fb] such that we get the exact frequency shifted with respect to the incoming photon. The excitation spectrum should be of the form shown in Fig.\[Fig-Plone\] for the spectral data of the optical mode, namely, the amplitudes $D=\frac{1}{\pi}\sqrt{A}$ for which we have $$\tag{*} \begin{split} D &\approx 3.
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2\times10^{12} T^{-1/2}\left(\sqrt{\beta\left({L}_{{\bf qu}\left({\rm n}\right)}\sqrt{{\rm n}}\right)^2+\Gamma^2\left({\rm b\right\}}\right)}\right)\\ \end{split}$$ The two eigenmodes and the eigenvalues of the inverse spectrum of the source are given by $$\tag{*} \begin{split} \label{EQ2} \sqrt{\beta\left({L}_{{\bf qu}\left({\rm n}\right)}\sqrt{{\rm n}}\right)^2} &\approx \frac{2\gamma\beta\left({L}_{{\bf qu}\left({\rm n}\right)}\right)}{\sqrt{\left(\Gamma+C_{{\bf qu}\left({\rm n}\right)}\right)^2+\Gamma^2\left({\rm b\right\}}\right)}, \\ \end{split}$$ where $C_{{\bf qu}\left({\rm n}\right)}=\Gamma G_D^2/(2\gamma)$ is a coupling constant to baryon number and $\gamma$ is a dimensionless constant to set all points of integration in the present analysis. In the first set of calculations, we set $\Gamma_D=1$ and $\Lambda_{{\bf qu}\left({\rm n}\right)={\bf q}$ is the dispersive photon waveguiding mode number [@Oda:1989bg]. Following Ref.[@Ishino:2000yc] we take a value as $n\approx 56$ and $\Lambda_{{\bf qu}\left({\rm n}\right)}\cos\left({\rm phase}\sqrt{{\rm n}}/T\right)<0$ where first $T$ is set to 1815 K. Then the other two values $\gamma=2$ and $\beta=2$ are used for small values of parameters, and finally $\Gamma=0.8$ and $\beta=2$. With the above result one can conclude the quenched mode structure of the medium. Photon-induced oscillations between the quenched photons and intermediate to non-quenched photons ================================================================================================ 








