The Resonance Photon-Paraphoton Conversion in Media

We propose the new approach for the direct dark matter particles observation at a laboratory. To do this one should use the violet laser to irradiate the sodium uranyl acetate-filled globular photonic crystal. In this case the laser light quanta will resonantly couple to paraphotons at uranyl unitary polaritons frequencies. Due to high density of states at the uranyl absorption edge this conversion will be extremely efficient. So there is a good opportunity to experimentally observe the paraphotons generation.


Introduction
According to the modern astrophysical data the most of the Universe's matter is "dark" [1]. So it's very important to explore this terra incognita. We consider paraphotons as candidates for the role of dark matter quanta [2][3][4][5][6][7][8][9][10][11][12][13]. In this paper we analyze the process of photon-paraphoton conversion to demonstrate the possibilities of dark particles generation at a laboratory. The paraphoton occurs when the two photons merge into the scalar bound state γ + γ pγ  .
(1) Because of two photons interaction the Lagrangian must be proportional to the square of the electric field: 2 s LgψE  .
(2) The smallness of the conversion cross section g makes the process (1) practically impossibleone has to imply the superstrong electromagnetic field to observe this in the void. In the paper we offer the new approach to solve the problemto involve medium to increase the efficiency of the photon-paraphoton conversion due to the resonant interaction of electromagnetic radiation with matter when the laser radiation's frequency is close to the polar type exciton transition frequencies for single-photon processes of absorption.

Theoretical analysis
In the electronic theory of dispersion the motion of an electron in an atom at the external field is described by the simple model (3) Here x is the electron coordinate; 0 m is its mass; 0 q is the elementary charge; 0  is the natural frequency of an electronic oscillator;  is the external field's photon frequency.
One can see that the solution for (3) On the other hand, (6) Therefore, the material medium dielectric constant depends on the external field frequency the following way: In this formula 2 2 00 0 00 the plasma frequency; the longitudinal mode frequency.
And the group velocity of the electromagnetic wave is equal to Also the effective mass of the relevant quanta (photons and polaritons) is The formulas (8)  Thus, there is a great opportunity to create the ultra-high density polariton states at material medium oscillators frequencies lj  . Because of (2) this leads to the resonant amplification for the photonparaphoton conversion. Besides, to realize (1) one has to meet the energy and the momentum conservation. This case the medium refractive index n must be equal to one. It is possible at the medium unitary polaritons [4] frequencies: the equation (8) shows that in media, there are the frequencies u  at which the absolute value of dielectric constant is equal to one: Thus, at these frequencies the medium is absolute transparent and the process (1) is welcomed. Therefore, the photon to paraphoton conversion (1) in medium is best observable for the photons of u   when u  is close to one of lj  . As seen from (13), the more factors involved in the product, the higher probability that there is such j that  1.    In the paper [19] we shown that it is possible to adjust medium natural resonant frequencies by using the photonic crystal -according the Bragg's law one should to rotate crystal to shift the lines: 2 sin m an = λ  .
(16) So it is very intriguing to analyze the conversion process (1) in the photonic crystal filled by the sodium uranyl acetate. The simplest 1D-photonic crystal is the layered medium consists of two alternating layers. Let's call them layer №1 and layer №2. Each layer has its own thickness ( i a ) and refractive index ( i n ). And for the 1D-photonic crystal the dispersion law is [20]           In case of the globular photonic crystal based on the artificial opal [21] at the practically mostly used direction at the normal to natural growth lattice plane (111): 12   12  12  21   1  2  2  arccos cos  1  cos  33  2  3   1  2  2  +  sin  1  sin  .  2  3  3 ωω k ω = n ω η D n ω ηD cc D n ω n ω ωω n ω η n ω ηD n ω n ω c c Here D is the quartz globules diameter (typically 250 D  nm); 0.26

 
is the porosity of the crystal gcc-lattice; 1 n and 2 n are layers refractive indices (the index 1 corresponds to the crystal matrix, 2for the substance in pores);  is the wave frequency and 8 3 10 c  m/s is the speed of light in the vacuum. For the 1 n there is the Sellmeier equation [22] (  is in μm):   1.
The simulation (18) - (20) results are shown by Figure 5. One can see the increased density of modes at the uranyl absorption edge due to the photonic crystal lattice. Let's analyze the group speed of light (10) in the photonic crystal with uranyl. The spectral dependences for the electromagnetic waves quanta propagation speed are presented at Figure 6. Note that in photonic crystal light deceleration is greater than without it. Moreover there are additional zero light quanta speed regions due to the photonic crystal band structure.

Discussion
The simulation shows that in medium it is possible to obtain deceleration of light velocity over to 8 orders of magnitude. Moreover, in the photonic crystal there are the zero light quanta speed spectral bands. Because of the Lagrangian proportionality to   / cv, it means that this case the conversion (1) becomes resonant and the process probability tends to 1. The theory predicts the best external field frequencies for this: it is the unitary polaritons ones at the uranyl absorption edge at the violet edge of the visible spectral region. Moreover, in discussed case we wait to observe not only spontaneous but the stimulated conversion which probability increases resonant way. We propose the sodium uranyl acetate-filled globular photonic crystal with globules of 250 nm as an active media for the potential dark matter generator under powerful laser emission excitation.

Conclusion
The results show that there is a opportunity to observe photon-paraphoton conversion at a laboratory by the using of specific media: f-element compounds. The best of them is the non-radioactive commercially available uranyl compounds. We predict the best conditions for the photon to paraphoton transformation (1) at the uranyl absorption edge. The advantage of process (1) over photon to axion conversion is the unnecessarily of the magnetic field. So it is the opportunity to make the proper conditions for dark matter quanta generation at a laboratory.