<i>PTX</i>-symmetric metasurfaces for sensing applications

doi:10.1007/s12200-021-1204-6

Front. Optoelectron.

2021, Vol. 14

Issue (2) : 211-220 https://doi.org/10.1007/s12200-021-1204-6

RESEARCH ARTICLE

PTX-symmetric metasurfaces for sensing applications

Zhilu YE, Minye YANG, Liang ZHU, Pai-Yen CHEN(

)

Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA

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Abstract

In this paper, we introduce an ultra-sensitive optical sensing platform based on the parity-time-reciprocal scaling (PTX)-symmetric non-Hermitian metasurfaces, which leverage exotic singularities, such as the exceptional point (EP) and the coherent perfect absorber-laser (CPAL) point, to significantly enhance the sensitivity and detectability of photonic sensors. We theoretically studied scattering properties and physical limitations of the PTX-symmetric metasurface sensing systems with an asymmetric, unbalanced gain-loss profile. The PTX-symmetric metasurfaces can exhibit similar scattering properties as their PT-symmetric counterparts at singular points, while achieving a higher sensitivity and a larger modulation depth, possible with the reciprocal-scaling factor (i.e., X transformation). Specifically, with the optimal reciprocal-scaling factor or near-zero phase offset, the proposed PTX-symmetric metasurface sensors operating around the EP or CPAL point may achieve an over 100 dB modulation depth, thus paving a promising route toward the detection of small-scale perturbations caused by, for example, molecular, gaseous, and biochemical surface adsorbates.

Keywords parity-time symmetry exceptional point (EP) laser oscillator coherent perfect absorber electromagnetic sensor radio frequency (RF) and microwave sensing optical sensing

Corresponding Author(s): Pai-Yen CHEN

Just Accepted Date: 16 March 2021 Online First Date: 15 April 2021 Issue Date: 14 July 2021

Cite this article:

Zhilu YE,Minye YANG,Liang ZHU, et al. PTX-symmetric metasurfaces for sensing applications[J]. Front. Optoelectron., 2021, 14(2): 211-220.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-021-1204-6
https://academic.hep.com.cn/foe/EN/Y2021/V14/I2/211

Fig.1 (a) Equivalent transmission line model for the PTX-symmetric sensing system and (b) its practical realization at optical frequencies, where the positive and negative elements can be realized by a passive metal sheet and an optical-pumped active metasurface respectively. In this scheme, two metasurfaces with conductances of

kG

and

− G / k

(

G = | − G | = γ Y 0

) are separated by an air gap (which is equivalent to a transmission line of characteristic admittance Y₀ and electrical length x). The system is perturbed by a variable admittance

δ Y

, which could be a reactive contribution or a conductive one

Fig.2 Evolution of eigenvalues as a function of

γ

and

k

for the PTX system in Fig. 1; here,

δ x = 10 − 3 (π / 2)

and

δ Y = 0

. We should note that if

x = π / 2

(or

δ x = 0

), the eigenvalues are unaffected by scaling factor

k

. The system can be divided into the exact symmetry phase (

γ > 2

) and the broken PTX-symmetry phase (

γ < 2

), with a discontinuous phase transition at the exceptional point (

γ = 2

). In the broken phase, two eigenvalues approach infinity (lasing state) and zero (CPA state) at the CPAL point (

γ = 2

)

Fig.3 (a) Output coefficient of the PTX-symmetric EP sensor in Fig. 1 under small perturbations

ν = δ Y/Y 0

; here,

γ = 2

and

k = 2

. Dashed line is the approximate results obtained from Eq. (3). We note that

Θ (ν)

is not affected by the sign of

δ x

. (b) Contours of output coefficient as a function of

ν

and

δ x

. The lower bound of output coefficient (or detection limit) can be minimized as

(δ x) 2

decreases

Fig.4 (a) Output coefficient

Θ (ν)

of the PTX-symmetric EP sensor with different scaling factor k; here,

γ = 2

and

δ x = 10 − 3 (π / 2)

. (b) Contours of output intensity as a function of

ν

and k. The slope of

Θ (ν)

, or sensitivity, and working range can be tuned by modifying scaling factor. When

k = 1

, the lower detection limit is approaching zero, leading to infinitesimal sensing limitation and the topmost operation range

Fig.5 (a) Output coefficient of the PTX-symmetric CPAL sensor in Fig. 1 under tiny perturbations

ν = δ Y/Y 0

; here,

γ = 2

and

k = 1

. Dashed line is the approximate results obtained from Eq. (4). (b) Contours of output coefficient as a function of

ν

and

δ x

. The upper bound (or maximum value) of the output coefficient can be greatly enhanced as

(δ x) 2

decreases

Fig.6 (a) Output coefficient

Θ (ν)

of the PTX-symmetric CPAL sensor with different scaling factor k; here,

γ = 2

and

δ x = 10 − 3 (π / 2)

. (b) Contours of output intensity as a function of

ν

and k. When

k = 2 − 1

max ? (Θ ν)

is pushed toward infinity, conforming to near-zero sensing limitation

excitation /detection port	approximate $Θ (ν)$	upper bound	lower bound
port 1 /port 1	$4 k 2 ν 2$	$4 (17 − 122) k 2 (− 3 + 22 + k 2) 2 δ x 2$	1
port 1 /port 1&2	$4 (3 + 22 + k 2) ν 2$	$4 (17 − 122) (3 + 22 + k 2) (− 3 + 22 + k 2) 2 δ x 2$	1
port 2 /port 2	$4 (17 + 122) k 2 ν 2$	$4 k 2 (− 3 + 22 + k 2) 2 δ x 2$	$17 + 122$
port 2 /port 1&2	$4 k 2 (17 + 122 + (3 + 22) k 2) ν 2$	$4 k 2 + 4 (3 − 22) k 4 (− 3 + 22 + k 2) 2 δ x 2$	$17 + 122$

Tab.1 Performance of PTX-symmetric CPAL sensor

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