Propagation Properties of Vortex Airy Beams Through Electromagnetically Induced Transparency Medium

Sendong Xu

doi:10.3788/LOP202259.0126002

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 1 >Page 0126002 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 1, 0126002 (2022)

Propagation Properties of Vortex Airy Beams Through Electromagnetically Induced Transparency Medium

Sendong Xu^*

Author Affiliations

School of Science, Zhejiang University of Science and Technology, Hangzhou , Zhejiang 310023, China

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DOI: 10.3788/LOP202259.0126002 Cite this Article Set citation alerts

Sendong Xu. Propagation Properties of Vortex Airy Beams Through Electromagnetically Induced Transparency Medium[J]. Laser & Optoelectronics Progress, 2022, 59(1): 0126002 Copy Citation Text

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Abstract

In order to study the propagation characteristics of vortex Airy beams through electromagnetically induced transparency medium, the analytical expression is obtained for vortex Airy beams passing through the electromagnetically induced transparency medium based on the ABCD matrix optics theory. The propagation properties of vortex Airy beams passing through the electromagnetically induced transparency medium are obtained by using the formula. The results show that the center lobe is distorted due to the superimposition of the Airy beam and the vortex. The center lobe is reconstructed and the revival of the vortex after a long distance. In addition, it is feasible to controlling the intensity and the location of vortex Airy beams via manipulation Rabi frequency of the electromagnetically induced transparency medium.

Keywords

electromagnetically induced transparency medium light intensity matrix optics Rabi frequency vortex Airy beams

ε = 1 + \frac{N β_{e}}{1 - N β_{e} / 3}

，（1）

β_{e} = \frac{i {|D_{13}|}^{2}}{ε_{0} ℏ D} [\frac{γ_{2}}{2} + i (Δ_{p} - Δ_{c})] [\frac{γ_{2^{'}}}{2} + i (Δ_{p} - Δ_{c^{'}})]

，（2）

D = (\frac{Γ_{3}}{2} + i Δ_{p}) [\frac{γ_{2}}{2} + i (Δ_{p} - Δ_{c})] [\frac{γ_{2^{'}}}{2} + i (Δ_{p} - Δ_{c^{'}})] + \frac{1}{4} Ω_{c^{'}}^{*} Ω_{c^{'}} [\frac{γ_{2}}{2} + i (Δ_{p} - Δ_{c})] + \frac{1}{4} Ω_{c}^{*} Ω_{c} [\frac{γ_{2^{'}}}{2} + i (Δ_{p} - Δ_{c^{'}})]

，（3）

\begin{array}{l} E (x, y, 0) = f_{A i} (\frac{x}{w_{x 0}}) e x p (\frac{a x}{w_{x 0}}) f_{A i} (\frac{y}{w_{y 0}}) \\ e x p (\frac{a y}{w_{y 0}}) {[(x - x_{d}) + i (y - y_{d})]}^{l} \end{array}

，（4）

f_{A i} (x) = \frac{1}{2 π} \int_{- \infty}^{\infty} e x p (- \frac{i u^{3}}{3} - i x u) d u

。（5）

E (x, y, z) = \frac{i k_{0}}{2 π B} \iint E (x_{0}, y_{0}, 0) e x p \{- \frac{i k_{0}}{2 B} [A ({x_{0}}^{2} + {y_{0}}^{2}) - 2 (x x_{0} + y y_{0}) + D (x^{2} + y^{2})]\} d x_{0} d y_{0}

，（6）

(\begin{matrix} A & B \\ C & D \end{matrix}) = (\begin{matrix} 1 & \frac{z}{n} \\ 0 & 1 \end{matrix})

（7）

E (x, y, z) = \frac{B}{k_{0} A^{2}} e x p [Q (x, y, z)] (P_{1} + P_{2} + P_{3})

，（8）

\begin{array}{l} Q (x, y, z) = \frac{a}{A} (\frac{x - 2 x_{c}}{w_{x 0}} + \frac{y - 2 y_{c}}{w_{y 0}}) + (\frac{- i k_{0} D}{2 B} + \frac{i k_{0}}{2 A B}) (x^{2} + y^{2}) + \\ i [\frac{B^{3}}{12 A^{3} {k_{0}}^{3}} (\frac{1}{{w_{x 0}}^{6}} + \frac{1}{{w_{y 0}}^{6}}) - \frac{a^{2} B}{2 A k_{0}} (\frac{1}{{w_{x 0}}^{2}} + \frac{1}{{w_{y 0}}^{2}}) - \frac{B}{2 A^{2} k_{0}} (\frac{x}{{w_{x 0}}^{3}} + \frac{y}{{w_{y 0}}^{3}})], \end{array}

（9）

P_{1} = \frac{k_{0}}{B} f_{A i} (\frac{x - x_{c}}{A w_{x 0}} - \frac{i a B}{A k_{0} {w_{x 0}}^{2}}) f_{A i} (\frac{y - y_{c}}{A w_{y 0}} - \frac{i a B}{A k_{0} {w_{y 0}}^{2}}) [x - A x_{d} - 2 x_{c} + i (y - A y_{d} - 2 y_{c})]

，（10）

P_{2} = \frac{- i}{w_{x 0}} [f_{A i'} (\frac{x - x_{c}}{A w_{x 0}} - \frac{i a B}{A k_{0} {w_{x 0}}^{2}}) + a f_{A i} (\frac{x - x_{c}}{A w_{x 0}} - \frac{i a B}{A k_{0} {w_{x 0}}^{2}})] f_{A i} (\frac{y - y_{c}}{A w_{y 0}} - \frac{i a B}{A k_{0} {w_{y 0}}^{2}})

，（11）

P_{3} = \frac{1}{w_{y 0}} [f_{A i'} (\frac{y - y_{c}}{A w_{y 0}} - \frac{i a B}{A k_{0} {w_{y 0}}^{2}}) + a f_{A i} (\frac{y - y_{c}}{A w_{y 0}} - \frac{i a B}{A k_{0} {w_{y 0}}^{2}})] f_{A i} (\frac{x - x_{c}}{A w_{x 0}} - \frac{i a B}{A k_{0} {w_{x 0}}^{2}})

，（12）

x_{c} = A x_{d} + 2 x_{c}, y_{c} = A x_{d} + 2 y_{c}

。（13）

z_{0} = 2 n k_{0} w_{x 0} \sqrt[]{- w_{x 0} x_{d}}

。（14）

Sendong Xu. Propagation Properties of Vortex Airy Beams Through Electromagnetically Induced Transparency Medium[J]. Laser & Optoelectronics Progress, 2022, 59(1): 0126002

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