Electromagnetically Induced Non-Hermitian Diffraction Grating Assisted by Incoherent Pumping

Xuedong Tian; Xingyu Liu; Yimou Liu

doi:10.3788/AOS230492

Acta Optica Sinica, Volume. 43, Issue 13, 1305002(2023)

Electromagnetically Induced Non-Hermitian Diffraction Grating Assisted by Incoherent Pumping

Xuedong Tian¹, Xingyu Liu², and Yimou Liu^2、*

Author Affiliations

¹College of Physics Science and Technology, Guangxi Normal University, Guilin 541004, Guangxi, China

²Center for Quantum Sciences, Northeast Normal University, Changchun 130024, Jilin, China

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Figures & Tables(6)

Fig. 1. Schematic diagrams of atomic equivalent three level structure, actual energy structure, and quasi one-dimensional electromagnetically induced grating. (a) Atomic equivalent three level structure; (b) actual energy structure; (c) quasi one-dimensional electromagnetically induced grating

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$Diffraction properties of PT antisymmetric grating. (a) Absorption (solid curve) and dispersion (dotted curve) spectra; (b) grating diffraction intensity angular spectrum Ip(θ); (c) transmission spectrum T(x) at end of medium L=600 μm, with relevant parameters Ωc/2π=3.0 MHz, Δp/2π=-2.27 MHz,Δc0/2π=-0.1 MHz,δc0/2π=1.0 MHz, and Λicp/2π=2.0 MHz$

Fig. 2. Diffraction properties of PT antisymmetric grating. (a) Absorption (solid curve) and dispersion (dotted curve) spectra; (b) grating diffraction intensity angular spectrum $I_{p} (θ)$ ; (c) transmission spectrum T(x) at end of medium $L = 600 μ m$ , with relevant parameters $Ω_{c} / 2 π =$ $3.0 M H z$ , $Δ_{p} / 2 π = - 2.27 M H z$ , $Δ_{c 0} / 2 π = - 0.1 M H z$ , $δ_{c 0} / 2 π = 1.0 M H z$ , and $Λ_{i c p} / 2 π = 2.0 M H z$

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$Diffraction properties of PT antisymmetric grating. (a1), (a2) Absorption (solid curve) and dispersion (dotted curve) spectra; (b1), (b2) grating diffraction intensity angular spectrum Ip(θ); (c1), (c2) transmission spectrumT(x). Detuning here are chosen as Δp/2π=Δc0/2π=0, and other parameters are same as in Fig. 2 except (a1)-(c1) Λicp=0 with L=200 μm and (a2)-(c2) Λicp/2π=2.0 MHz with L=450 μm$

Fig. 3. Diffraction properties of PT antisymmetric grating. (a₁), (a₂) Absorption (solid curve) and dispersion (dotted curve) spectra; (b₁), (b₂) grating diffraction intensity angular spectrum $I_{p} (θ)$ ; (c₁), (c₂) transmission spectrum $T (x)$ . Detuning here are chosen as $Δ_{p} / 2 π = Δ_{c 0} / 2 π = 0$ , and other parameters are same as in Fig. 2 except (a₁)-(c₁) $Λ_{i c p} = 0$ with $L = 200 μ m$ and (a₂)-(c₂) $Λ_{i c p} / 2 π = 2.0 M H z$ with $L = 450 μ m$

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$Diffraction spectra of PT antisymmetric grating. (a),(b) Diffraction spectra varying with optical depth (OD) with Λicp/2π=0, 2.0 MHz, respectively; (c1), (c2) diffraction spectra varying with incoherent pumping with OD=130$

Fig. 4. Diffraction spectra of PT antisymmetric grating. (a),(b) Diffraction spectra varying with optical depth (OD) with $Λ_{i c p} / 2 π = 0, 2.0 M H z$ , respectively; (c₁), (c₂) diffraction spectra varying with incoherent pumping with O_D=130

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$Influence of incoherent pumping and phase of coupling field detuning on diffraction spectrum. Incoherent pumping rate is (a1)-(a3) Λicp/2π=1.5 MHz; (b1)-(b3) Λicp/2π=1.0 MHz; (c1)-(c3) Λicp/2π=0.5 MHz; coupling detuning phase is (a1)-(c1) ψ=0; (a2)-(c2) ψ=π/2; (a3)-(c3) ψ=π, with L=600 μm, R = 3, and other parameters are same as in Fig. 3$

Fig. 5. Influence of incoherent pumping and phase of coupling field detuning on diffraction spectrum. Incoherent pumping rate is (a₁)-(a₃) $Λ_{i c p} / 2 π = 1.5 M H z$ ; (b₁)-(b₃) $Λ_{i c p} / 2 π = 1.0 M H z$ ; (c₁)-(c₃) $Λ_{i c p} / 2 π = 0.5 M H z$ ; coupling detuning phase is (a₁)-(c₁) $ψ = 0$ ; (a₂)-(c₂) $ψ = π / 2$ ; (a₃)-(c₃) $ψ = π$ , with $L = 600 μ m$ , R = 3, and other parameters are same as in Fig. 3

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Table 1. Comparison of different diffraction types and diffraction modes with several control parameters

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Table 1. Comparison of different diffraction types and diffraction modes with several control parameters

Diffraction mode and non-Hermitian grating type	Asymmetric diffraction			Symmetric diffraction
Diffraction mode and non-Hermitian grating type	PT-grating	Loss-type APT grating	Gain-type APT grating
Incoherent pumping （ $Λ_{i c p} / 2 π M H z$ ）	2.0	0	>0	$\forall$
O_D modulation	√	√	√	√
Phase（ $ψ / π$ ）	2m	2m	2m+1	（2m+1）/2
Modulation by sign of detuning	×	√ Diffraction direction	√ Diffraction direction	—
Asymmetric degree	Unperfect	Perfect	Near perfect	—

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Xuedong Tian, Xingyu Liu, Yimou Liu. Electromagnetically Induced Non-Hermitian Diffraction Grating Assisted by Incoherent Pumping[J]. Acta Optica Sinica, 2023, 43(13): 1305002

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Paper Information

Category: Diffraction and Gratings

Received: Feb. 3, 2023

Accepted: Mar. 6, 2023

Published Online: Jul. 12, 2023

The Author Email: Liu Yimou (liuym605@nenu.edu.cn)

DOI:10.3788/AOS230492

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology