Nhng tin b trong Quang hc, Quang ph vÃ ng dng VI ISSN 1859 - 4271

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Advances in Optics, Photonics, Spectroscopy & Applications VI ISSN 1859 - 4271The <strong>ph</strong>enomena at F , E , D are analogous to the <strong>ph</strong>enomena at A , B , C and assumingAB = EF , BC = DE we have the same conditions as (2.2) and (2.1). The reflected resonant lightcoming to the fiber center must be in <strong>ph</strong>ase with the first light, so we have:2CDn f = mλ 03 , (2.3)Where m is an integer and n f is a refractive index of the fiber.We note that AB ,CD EF are large distances. The cross section of fiber is not an ideal circle.We may change the position of observation in the surface of polymer layer and achieve thefulfillment of the conditions (2.2), (2.3). We will not take special consideration on the conditions(2.2), (2.3), sugges<s<strong>trong</strong>>tin</s<strong>trong</strong>>g that they are fulfilled.In the experiments we obtained the air-gap of 600 – 1750 nm (see Figure 2) and resonantwavelength of 537nm, so k in the equation (2.1) may be one of the values from 1 to 6. Largevalue of k is not sensible because if a large value of k gives λ 03 in the region 520-550 nm, thenthe near values of this k also give λ 03 in this region and we would have several thin lines withlarge intensity in this region of spectrum. In fact we have only one such line.PolymerAir - GapGlassFig. 2. Image of the air-gap between glass and polymer layers.III. LIGHT AMPLIFICATION BY PHOTON-ATOM INTERACTION IN CAVITYWe consider the condition of optical amplification: the green light at λ 03 passing the excitedatoms must be amplified. For this aim we must study the evolution of the state of the system ofan atom and <strong>ph</strong>otons. To study the evolution of the state we must first of all find the eigenstatesof the Hamiltonian of the system.For simplicity we consider the atoms as independent. Consider a system of an atom and<strong>ph</strong>otons. The atom has a ground state 0 a with energy ε 0 = 0 , an excited state 1 a withenergy ε 1 , an excited state 2 a with energyε 2 . Each <strong>ph</strong>oton has the wave length λ 03 accordingto the equations (2.1), (2.2) and (2.3) and the energyε 3 . The Hamiltonian of the system has theform:(0) (1)H = H + H , (2.4)(0)+H ε 1 1 + ε 2 2 + ε f f , (2.5)H(1)= 1 a a 2 a a 3++( 1 0 f + 0 1 f ) + g( 2 0 f + 0 )= gfa a a aa a a 2a, (2.6)80
Những tiến bộ <strong>trong</strong> <strong>Quang</strong> học, <strong>Quang</strong> <strong>ph</strong>ổ và Ứng dụng VI ISSN 1859 - 4271+Where f ( f ) is the <strong>ph</strong>oton creation (annihilation) operator, g is a small real interactionparameter. We assume g
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Nhng tin b trong Quang hc, Quang ph vÃ ng dng VI ISSN 1859 - 4271

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