PT-symmetric coherent perfect absorber with graphene

Mustafa Sarısaman; Murat Tas

doi:10.1364/JOSAB.35.002423

$PT$ -symmetric coherent perfect absorber with graphene

Mustafa Sarısaman and Murat Tas

Journal of the Optical Society of America B
Vol. 35,
Issue 10,
pp. 2423-2432
(2018)
•https://doi.org/10.1364/JOSAB.35.002423

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Mustafa Sarısaman and Murat Tas, "PT-symmetric coherent perfect absorber with graphene," J. Opt. Soc. Am. B 35, 2423-2432 (2018)

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Related Topics
Table of Contents Category
- Light Sources and Amplifiers
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Optical materials (160.4670)
- Optical properties (160.4760)
- Coherent optical effects (270.1670)
- Laser theory (270.3430)
- Absorption (300.1030)

About this Article
History
- Original Manuscript: April 12, 2018
- Revised Manuscript: August 4, 2018
- Manuscript Accepted: August 7, 2018
- Published: September 10, 2018

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Abstract

We investigate $PT$ -symmetric coherent perfect absorbers (CPAs) in the TE mode solution of a linear homogeneous optical system surrounded by graphene sheets. It is revealed that the presence of graphene sheets plays a role to adjust the enhancement of absorption in a CPA. We derive exact analytic expressions and work through their possible impacts on lasing threshold and CPA conditions. We point out the roles of each parameter governing an optical system with graphene, and we show that optimal conditions of these parameters give rise to enhancement and possible experimental realization of a CPA laser. The presence of graphene leads the required gain amount to reduce considerably based on its chemical potential and temperature. We obtain that the relationship among system parameters decides the measure of CPA conditions. We find that graphene features that contribute to the resonance effect in graphene sheets are rather preferable to build a better CPA.

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$z = 0$	$a_{2} + b_{2} = a_{1} + b_{1}$ , $a_{2} - b_{2} = u_{+}^{(2)} a_{1} - u_{-}^{(2)} b_{1}$
$z = 1$	$a_{2} e^{i K_{2}} + b_{2} e^{- i K_{2}} = a_{3} e^{i K_{3}} + b_{3} e^{- i K_{3}}$ ${\tilde{n}}_{2} (a_{2} e^{i K_{2}} - b_{2} e^{- i K_{2}}) = {\tilde{n}}_{3} (a_{3} e^{i K_{3}} - b_{3} e^{- i K_{3}})$
$z = 2$	$a_{3} e^{2 i K_{3}} + b_{3} e^{- 2 i K_{3}} = a_{4} e^{2 i K} + b_{4} e^{- 2 i K}$ $a_{3} e^{2 i K_{3}} - b_{3} e^{- 2 i K_{3}} = u_{-}^{(3)} a_{4} e^{2 i K} - u_{+}^{(3)} b_{4} e^{- 2 i K}$

	Spectrally Singular Waves	Time-Reversed Waves	CPA Waves
Region $I$	$b_{1} e^{i K (x \tan θ - z)}$	$b_{1}^{*} e^{- i K (x \tan θ - z)}$	$a_{4}^{*} e^{- 2 i K} e^{- i K (x \tan θ + z)}$
Region $I V$	$a_{4} e^{i K (x \tan θ + z)}$	$a_{4}^{*} e^{- i K (x \tan θ + z)}$	$b_{1}^{*} e^{2 i K} e^{- i K (x \tan θ - z)}$

	With Graphene			–	Without Graphene
$θ$	0°	−40°	−80°		0°	−40°	−80°
$λ$	807.996 nm	808.008 nm	807.993 nm		808.006 nm	808.001 nm	808.009 nm
$g$	$10.859 {cm}^{- 1}$	$10.104 {cm}^{- 1}$	$9.002 {cm}^{- 1}$		$11.433 {cm}^{- 1}$	$10.458 {cm}^{- 1}$	$9.025 {cm}^{- 1}$
$κ$	$- 6.982 \times 10^{- 5}$	$- 6.496 \times 10^{- 5}$	$- 5.788 \times 10^{- 5}$		$- 7.351 \times 10^{- 5}$	$- 6.724 \times 10^{- 5}$	$- 5.803 \times 10^{- 5}$
$\| ρ \|$	1.9053	1.8883	1.7817		0.5824	0.7597	1.5929
$δ ϕ$	146.106°	148.620°	179.940°		135.008°	135.007°	135.004°

	$T = 50 K$ and $μ = 0.027 eV$			–	$T = 200 K$ and $μ = 0.0005 eV$
$θ$	0°	−40°	−80°		0°	−40°	−80°
$λ$	807.995 nm	808.007 nm	807.991 nm		807.994 nm	808.007 nm	807.991 nm
$g$	$10.872 {cm}^{- 1}$	$10.119 {cm}^{- 1}$	$9.014 {cm}^{- 1}$		$10.819 {cm}^{- 1}$	$10.064 {cm}^{- 1}$	$8.971 {cm}^{- 1}$
$κ$	$- 6.990 \times 10^{- 5}$	$- 6.506 \times 10^{- 5}$	$- 5.796 \times 10^{- 5}$		$- 6.956 \times 10^{- 5}$	$- 6.471 \times 10^{- 5}$	$- 5.768 \times 10^{- 5}$
$\| ρ \|$	1.6713	1.6324	1.6591		1.6291	1.5982	1.6632
$δ ϕ$	157.613°	162.139°	160.031°		153.293°	158.044°	160.507°

$z = 0$	$a_{2} + b_{2} = a_{1} + b_{1}$ , $a_{2} - b_{2} = u_{+}^{(2)} a_{1} - u_{-}^{(2)} b_{1}$
$z = 1$	$a_{2} e^{i K_{2}} + b_{2} e^{- i K_{2}} = a_{3} e^{i K_{3}} + b_{3} e^{- i K_{3}}$ ${\tilde{n}}_{2} (a_{2} e^{i K_{2}} - b_{2} e^{- i K_{2}}) = {\tilde{n}}_{3} (a_{3} e^{i K_{3}} - b_{3} e^{- i K_{3}})$
$z = 2$	$a_{3} e^{2 i K_{3}} + b_{3} e^{- 2 i K_{3}} = a_{4} e^{2 i K} + b_{4} e^{- 2 i K}$ $a_{3} e^{2 i K_{3}} - b_{3} e^{- 2 i K_{3}} = u_{-}^{(3)} a_{4} e^{2 i K} - u_{+}^{(3)} b_{4} e^{- 2 i K}$

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