Design and analysis of a broadband terahertz polarization converter with significant asymmetric transmission enhancement

Journal Pre-proof Design and analysis of a broadband terahertz polarization converter with significant asymmetric transmission enhancement Pan Wu, Chen Qi, Ma Yong, Wang Xueyin, Ren Xinyu

PII: DOI: Reference:

S0030-4018(19)31008-9 https://doi.org/10.1016/j.optcom.2019.124901 OPTICS 124901

To appear in:

Optics Communications

Received date : 30 July 2019 Revised date : 9 October 2019 Accepted date : 4 November 2019 Please cite this article as: P. Wu, C. Qi, M. Yong et al., Design and analysis of a broadband terahertz polarization converter with significant asymmetric transmission enhancement, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124901. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Journal Pre-proof

Design and Analysis of a Broadband Terahertz Polarization Converter with Significant Asymmetric Transmission Enhancement Pan Wu

Chen Qi*

Ma Yong

Wang Xueyin

Ren Xinyu

College of Photoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

pro

of

Abstract—A tri-layered terahertz metamaterial based on the gratings-polarization converter-gratings (GPCG) structure is proposed, which is composed of a double L structure array sandwiched by two orthogonal metallic sub-wavelength gratings (SWGs). Simulation results show that two cascaded Fabry-Perot-like resonance cavities result in broadband polarization conversion with significant asymmetric transmission (AT) phenomenon. The improved polarization conversion rate (PCR) is over 0.99 from 0.20THz to 1.97THz with a relative bandwidth of 163.13%, almost 1.74 times that of other work, and the enhanced AT parameter is beyond 0.8 from 0.37THz to 1.73THz with a relative bandwidth of 129.52%. Moreover, in a wide range of incident angles, the proposed metamaterial maintains great AT performance, thus showing great potential applications in circulators, direction-dependent polarization converters and polarization-sensitive sensing and imaging. Index Terms—terahertz; asymmetric transmission; polarization conversion; metamaterial

performance is urgently needed. I

INTRODUCTION

Asymmetric transmission (AT), firstly proposed by

structures, can achieve fascinating electromagnetic (EM)

in total transmission between opposite propagations, which

properties such as negative refraction [1], optical illusion

in essence originates from the different polarization

[2], invisibility cloaking [3] and polarization conversion

conversion abilities of the medium for two cross-polarized

[4-10],

waves.

by

adjusting

its

structures

and

re-

Metamaterials (MMs), artificial sub-wavelength periodic

Fedotov et al [11] in 2006, manifests itself as a difference

periodic

The

AT belongs

to

a

Lorentz

reciprocal

phenomenon, and behaves as diode-like effect, therefore,

EM waves, and is of great importance with various

can be used in direction-dependent polarization converters

urn al P

arrangements. Polarization is an inherent characteristic of applications,

ranging

from

sensing

to

optical

communication. Natural existing birefringent crystal is

and polarization-controlled devices in polarization-sensitive sensing and imaging [11-12].

traditionally used to control the polarization state by

Numerous artificial structures are designed to realize the

accumulating phase difference through the relative long

AT effect of EM waves, such as composite gratings [12-13],

propagation

narrow

the holes in metallic plates [14-15], photonic crystals [18]

bandwidth and bulk configuration. Recently, MMs have

and MMs [18-35], the most commonly used ones. Menzel

been used to manipulate EM wave polarization state [4-10]

C et al [32] experimentally demonstrated and theoretically

with the advantages of small size, easy integration and high

analyzed the AT effect of a 3D low-symmetry MM. Peng Y

efficiency.

X et al [33] realized the AT phenomenon through

distance,

thus

suffering

from

polarization conversion caused by the mutual induction of

classified into transmissive and reflective modes. In 2017,

bright and dark modes in plasmonic metasurfaces.

Ma et al [5] proposed a reflective MM, and its PCR

Serebryannikov A E et al [34] combined chirality and

exceeds 0.8 from 0.37 to 1.05THz with a relative

tunneling through complementary split-ring resonator

bandwidth of 96%. In 2013, Abasahl B et al [8] proposed a

structures to achieve AT effect. However, MMs using these

plasmonic structure with perturbation that achieved

methods have drawbacks of limited efficiency and narrow

linear-to-circular conversion in transmissive mode. In 2018,

bandwidth, thus preventing their practical applications.

Jo

Polarization converters (PCs) based on MMs can be

Song et al [10] proposed a transmissive polarization

Multilayered MMs can also achieve AT effect with the

conversion meta-device, and its PCR is greater than 0.95

combination of sub-wavelength gratings (SWGs) and

from 9.0GHz to 12.3GHz. Usually, reflective PCs have

metallic

more excellent performance than transmissive ones.

polarization conversion abilities. In 2016, Cheng et al [28]

Therefore, broadband transmissive PC with nearly perfect

proposed a MM composed of a split disk array sandwiched

author. E-mail address: [email protected] 

* Corresponding

array,

which

realize

direction-dependent

Journal Pre-proof

Supposing

by two orthogonal SWGs, and its AT parameter of linearly

the

device

does

not

contain

any

polarized wave is beyond 0.9 from 0.23THz to 1.17THz. In

magneto-optical material, the reciprocity theorem can be

2018, Wang et al [29] achieved AT effect for linearly

expressed as [19]:

polarized wave by SWGs-double split rings-SWGs MM,

tiif ( b )  tiif ( b ) ,

and its AT parameter is greater than 0.8 in the range of 124~244THz. In this way, MMs can achieve AT effect and polarization

conversion

simultaneously.

However,

broadband multilayered MM is still in exploration.

(3)

| tijf ( b ) |  | t bji( f ) | .

Thus, the AT parameter of linearly polarized wave can be simplified as:

In this paper, a tri-layered terahertz MM based on

of

△x | t yxf |2  | t byx |2

gratings-polarization converter-gratings (GPCG) structure

| t f |2  | t f |2 yx

is proposed, and its AT parameter of y-polarized wave is

(4)

xy

 △ , y

beyond 0.80 from 0.37THz to 1.73THz. Besides, in the

where △x and △y are the AT parameters of x- and

conversion rate (PCR) of forward incident y-polarized

y-polarized wave, respectively, and tfij is the cross-polarized

wave is greater than 0.99 with a relative bandwidth of

coefficient for the forward propagation.

pro

frequency range of 0.35~1.59THz, the polarization

127.84%, and in the frequency range of 0.20~1.97THz, the

According

PCR of backward incident x-polarized wave is more than

cross-coupling

0.99 with a relative bandwidth of 163.13%. Specifically,

polarized waves for forward and backward propagations

the design idea and physical mechanism of MMs based on

manifests the asymmetric transmission effect. Note that the

GPCG structure are illustrated. Therefore, MMs using

AT effect can be achieved by designing the MMs with

GPCG structure can achieve excellent AT effect and nearly

different polarization conversion capabilities for two

perfect polarization conversion performance for linearly

polarized waves.

Eq.

and

(4),

the

difference

polarization

conversion

between of

two

re-

polarized waves in terahertz band.

to

Obviously, great AT effect for linearly polarized wave

can be achieved when the following conditions are met:

THEORETICAL ANALYSIS

urn al P

II

tijf  0, t jif  1 .

Matrix is often used to describe the relationship between

Accordingly, the AT parameter of linearly polarized wave is

the incident wave and the transmitted wave:

 Extr   t xx  tr     E y   t yx

t xy   Exin   Exin   T    in  ,  t yy   E yin   Ey 

(5)

close to 1 with the diode-like transmission characteristic

(1)

under the above conditions. To measure the polarization conversion ability of the

where the superscript tr and in represent the transmitted

proposed MM, PCR is calculated using the following

wave and the incident wave, respectively, the subscript x

formula:

and y respectively indicate the x-/y-polarized wave, txx and

tyy are the co-polarized coefficients, txy and tyx are the cross-polarized coefficients.

PCR p 

| tqp |2 | tqp |2  | t pp |2

,

(6)

where the subscript p and q represent the polarization state

the difference between the total transmission of forward

of the incident and transmitted wave, respectively, i.e. tqp

propagation and that of backward propagation, which is

(tpp) is the coefficient when the incident wave is p-polarized

used to measure the asymmetric transmission ability of the

wave and the transmitted wave is q-(p-)polarized wave.

Jo

The asymmetric transmission parameter △ is defined as

device, and can be expressed as:

△i  Ti f  Ti b

 (| tiif |2  | t jif |2 )  (| tiib |2  | t bji |2 ),

III STRUCTRUE DESIGN (2)

where the subscript i and j denote the polarization state of

The unit cell of the proposed metamaterial is presented in Fig.1, which is composed of a double L structure array sandwiched with two orthogonal metallic SWGs. The top

the EM waves, the superscript f and b indicate forward

metal SWGs are along x-axis with a spacing of f=5.0μm

propagation (along the -z direction) and backward

and a width of f1=10.0μm. Five equally spacing strips

propagation (along the +z direction).

consist a meta-atom (the length along y-axis of the

Journal Pre-proof

meta-atom equals to 4f+5f1), and the symmetry axis of the

converted into x-polarized wave by the PC and then the

meta-atom coincides with that of the unit cell. The bottom

x-polarized wave will be transmitted through SWGs. But

metal SWGs are along y-axis with a spacing of ff=13.0μm

when y-polarized wave is incident along the backward

and a width of ff1=11.0μm, and are placed in a similar

propagation direction, it will be reflected by the gratings

manner to the top SWGs. The middle metallic layer

and cannot pass through the metamaterial. As for

consists of two centrally symmetrical L-shaped patterns, of

x-polarized wave, it will be totally reflected at SWGs when

which the parameters are as follow: w1=11.0μm, w2=9.0μm,

normally incident for the forward propagation and be

w3=9.0μm, l1=14.0μm, l2=38.0μm, l3=58.0μm.

converted into y-polarized wave when incident for the

performed by using the CST Microwave Studio software.

backward propagation. Therefore, this composite MM has

of

Numerical simulations of the proposed MM were

excellent AT characteristic in theory.

The unit cell boundary conditions were applied to the x and

Note that, the ideal PC is required in the above model.

y directions and the open (add space) boundary was defined

However, to our best knowledge, no ideal single layer transmissive linear polarization converter in terahertz region is reported. Therefore, part of the incident

material and its thickness is t=0.5μm. The substrates

y-polarized wave in the forward propagation is converted

between two metal layers were quartz with a permittivity of

into its cross-polarized wave and part of it remains the

3.75, a loss tangent of 0.0004 and a thickness of d=30.0μm.

same polarization state which is reflected by the bottom y-direction metallic SWGs. A Fabry-Perot resonant cavity

y -pol.

(b)

is formed [26] and the interference in multi-reflection

re-

(a )

pro

in the z direction. In the simulation, copper with an electric conductivity of 5.8×107S/m was used as the metallic

process can enhance the polarization conversion ability,

f z

Px

f1

y

x

This PCG structure has great polarization conversion performance for forward incident y-polarized wave [25],

x-pol.

thus only PCRx is discussed here. However, since some EM

Py

urn al P

y -pol. y -pol.

when compared with single layer PC, as shown in Fig.3(c).

wave is transmitted out at the polarization converter, the AT phenomenon is not obvious. As shown in Fig. 3(a) and (b),

(c )

w3

(d )

tyx and tyy are negligible while the co-polarized coefficient

txx cannot be ignored, and the cross-polarized coefficient txy

l3

has three obvious peeks. △y is similar to txy with three obvious peeks and the maximum of △y is 0.74. From

w1

l1

1.13THz to 1.37THz, △y ≥ 0.6. The PCG structure can

w2

l2

improve the polarization conversion performance and

ff1

ff

Fig.1. Geometry detail of the proposed metamaterial. (a) Perspective view of the unit cell. (b) Top layer. (c) Middle double L metallic pattern. (d) Bottom layer.

IV BI-LAYERED MODEL AND ANALYSIS

Jo

The initial idea is combining polarization converter (PC)

simultaneously realize the AT effect, but the bandwidth is narrow. Sub-wavelength gratings paralleling to y -axis

Linear polarization converter

y -pol.

x-pol.

x-pol.

with SWGs to realize different polarization conversion abilities for two polarized waves, instead of breaking symmetry, to achieve AT effect. The polarization

y -pol.

y -pol.

x-pol. y

converter-gratings (PCG) model is shown in Fig.2. The incident linearly polarized wave will be converted into its cross-polarized wave by the ideal PC, and the SWGs work as a polarizer. Consequently, when the y-polarized wave is incident along the forward propagation direction, it will be

z Fig.2. The schematic of the ideal polarization converter-gratings model.

Journal Pre-proof

(b) 0.8

0.8

AT parameter

0.6 txx txy

0.2 0.0 0.0

0.5

tyx tyy

1.0

1.5

0.6

PCRx

0.8

x-pol. x-pol. y -pol. 0.5

1.0

1.5

2.0

x-pol.

Frequency/THz

y -pol. y

double L array only double L + SWGs

z

0.6

Fig.4. The schematic of the GPCG model.

0.4

1.5

2.0

Fig.3. (a) Transmission coefficients and (b) AT parameter of y-polarized wave when linearly polarized wave is incident on non-ideal polarization converter-gratings structure in forward direction. (c) PCRx of double L array only and PCG structure.

0.8 0.6

pro

1.0

Transmission

0.5

Frequency/THz

V

(b) 1.0

(a) 1.0

0.2 0.0 0.0

Sub-wavelength gratings paralleling to y -axis

y -pol.

0.2

Frequency/THz

(c) 1.0

Linear polarization converter

0.4

0.0 0.0

2.0

Sub-wavelength gratings paralleling to x -axis

of

0.4

0.8 0.6 0.4 0.2 △y 0.0 1.01.11.21.31.41.5

△y

AT parameter

Transmission

(a) 1.0

0.4

txx txy

0.2

0.0 0.0

0.5

1.0

tyx tyy

1.5

2.0

0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 0.0

△x △y 0.5

Frequency/THz

1.0

1.5

2.0

Frequency/THz

Fig.5. (a) Transmission coefficients and (b) AT parameter when linearly polarized wave is incident on GPCG structure in forward direction.

THI-LAYERED MODEL AND ANALYSIS

When the x-polarized wave is incident backward and the

results that the bi-layered PCG structure cannot realize the

y-polarized wave is incident forward, the PCRs are

expected AT effect in practice. It is necessary to add

calculated as follow:

re-

From the above analysis, it reveals from simulation

another orthogonal metallic SWGs in front of the PC to

form the proposed gratings-polarization converter-gratings

PCR x 

urn al P

(GPCG) structure, as shown in Fig.4. The forward incident

y-polarized wave is converted into an elliptically polarized

PCR y 

wave at PC. The x-polarized component is transmitted out through the bottom SWGs. The y-polarized component is

PCR x 

reflected by the top x-direction SWGs. The aforementioned

process repeats and only a small part of the incident

y-polarized wave without polarization conversion is

| t |  | t xxb |2 | t xyf |2 | t xyf |2  | t yyf |2

, (7)

.

According to Eq. (3), Eq. (7) can be simplified as follow:

reflected by the y-direction SWGs and then converted into elliptically polarized wave which is transmitted and

| t byx |2 b 2 yx

PCR y 

| t xyf |2 | t xyf |2  | t xxf |2

,

| t xyf |2

(8)

. | t xyf |2  | t yyf |2

transmitted through the top gratings. This GPCG structure

By using the combination structure of SWGs, the

cascades two Fabry-Perot-like resonant cavities, thus

transmitted wave of the MM is highly polarized ideally

enhancing the asymmetric transmission phenomenon and

used for polarization conversion, as shown in Fig.6.

broadening the bandwidth [26-30]. Comparing Fig.3 and 5

From Eq. (8) and Fig.5(a), one can conclude that PCRx ≠

shows that tyx and tyy are still negligible, txx decreases

PCRy because of tfxx ≠ tfyy. By analyzing the structure and the

tyy

transmission performance of the middle polarization

significantly increased with a maximum of 0.958. The

converter, metallic double L pattern has different

bandwidth is obviously broadened and △y is beyond 0.8 in

transmission and polarization conversion performance for

the range of 0.37~1.73THz. Hence, the tri-layered GPCG

x- and y-polarized wave because the structure is not

Jo

while

obviously.

△

is

significantly

increases

y

structure can significantly enhance the AT performance

equivalent in the x and y direction. In Fig.6(a), the PCR of

compared with the initial PCG structure.

backward incident x-polarized wave is beyond 0.9 in the range of 0.13~2.00THz and is over 0.99 from 0.20THz to 1.97THz with a 163.13% relative bandwidth. In Fig.6(b), the PCR of forward incident y-polarized wave is beyond 0.9 in the range of 0.25~1.99THz and is over 0.99 from

Journal Pre-proof (a)

0.35THz to 1.59THz with a 127.84% relative bandwidth. In short, the proposed MM achieves excellent polarization

(2)

conversion function in the broadband range. (b)1.0

0.8

0.8

0.4 0.2 0.0 0.0

PCRx 0.5

1.0

1.5

2.0

0.6 0.4 0.2 0.0 0.0

PCRy 0.5

1.0

1.5

2.0

Frequency/THz

Frequency/THz

Fig.6. (a) PCR of the backward incident x-polarized wave (b) PCR of the forward incident y-polarized wave.

(b)

To further illustrate the transmitted wave, Stokes

pro

as: S0  t yy2  t xy2 ,

S3  2t yy t xy sin  ,

re-

(9)

S 2  2t yy t xy cos  ,

where δ=arg(txy)-arg(tyy). And the polarization azimuth angle ψ and ellipticity angle χ are used to describe the figure of merit for linear polarization conversion as: tan 2  S 2 / S1 ,

(10)

Fig.8. The distribution of real part pf cross-polarized electric field on the surface of the bottom substrate layer for (a) 1.78THz and (b) 2.10THz incidence.

The physical mechanism of polarization conversion is

analyzed by simulated the real part of the cross-polarized

urn al P

sin 2   S3 / S0 .

(1)

(2)

parameters are introduced to describe the polarization state

S1  t yy2  t xy2 ,

of

0.6

PCR

PCR

(a) 1.0

(1)

As shown in Fig. 7, the polarization azimuth angle is

electric field on the top surface of the bottom substrate as

close to 90° in the frequency range of 0.42~0.81THz and

shown in Fig.8. In Fig.8(a), the cross-polarized electric

1.46~1.97THz, and that is close to -90° from 0.81THz to

fields in zone (1) and zone (2) maintain consistent at

1.46THz. In the frequency range of 0.29~1.90THz, the

1.78THz, i.e., the cross-polarized electric fields in zone (1)

ellipticity angle is close to 0°. This means that the incident

and zone (2) possess a close phase, which results in mutual

y-polarized wave can be nearly perfect converted into

promotion. On the contrary in Fig.8(b), the sign of the

x-polarized wave by the proposed MM.

cross-polarized electric fields in zone (1) and zone (2) is



90 60

0 -30 -60

phases of the cross-polarized electric fields in the two

5

zones is close to π, thus reducing the polarization

0

-5

0.5

1.0

Jo

-90 0.0

opposite at 2.10THz, which means the difference of the

10

1.5

χ/deg

ψ/deg

30



conversion. The mutual promotion of the cross-polarized

-10

electric field results in the broadband polarization

-15

conversion [26].

-20 2.0

Frequency/THz

Fig.7. Polarization azimuth angle ψ and ellipticity angle χ for y-polarized wave along the forward direction

Now, the influence of the proposed GPCG MM with

different geometric parameters, mainly including lengths (l1, l2, l3) and widths (w1, w2, w3) of the L-shaped structure, the spacing (ff) and width (ff1) of the bottom SWGs and substrate thickness d, on AT performance is discussed. Figure 9 shows the AT parameter of y-polarized wave and PCR of both x-/y-polarized waves with different l1. As l1 increases, △y in the low frequency range slightly changes while in the high frequency range, △y increases

Journal Pre-proof

significantly and the bandwidth with △y beyond 0.6

unchanged in the frequency range of 0~1.35THz, while the

becomes narrow. However, PCRx and PCRy almost remain

last dip declines with a decrease in w1. As w2 increases, the

the same with different value of l1 in the considered

first two dips of △y decrease while the last two dips are

frequency range. The influence of l2, l3, w1, w2 and w3 on

increased. However, in this case, the bandwidth for △y

PCRx and PCRy resembles that of l1, so it is not discussed

above 0.6 obviously becomes narrow. Things are different when w3 increases. As one can see from Fig.10 (e), in the

here.

frequency range over 1.66THz, △y is basically the same

(a) 1.0

except for an abrupt peak at 1.93THz when w3 equals 13μm. l1=10μm l1=14μm l1=18μm 0.5

1.0

0.8

0.4 0.2 0.5

1.0

1.5

y

0.6

l1=10μm l1=14μm l1=18μm

0.4 0.2

2.0

0.0 0.0

0.5

1.0

1.5

0.0 0.0

2.0

0.6

l2=34μm l2=36μm l2=38μm 0.5

1.0

1.5

Frequency/THz

2.0

0.5

1.0

1.5

0.6

w1=7μm w1=11μm w1=15μm

0.4 0.2 0.5

1.0

1.5

Frequency/THz (e) 1.0

△y

0.8 0.6 0.4 0.2 0.0 0.0

0.4

0.6

w2=5μm w2=9μm w2=13μm

0.4 0.2

0.0 0.0

0.5

1.0

1.5

0.5

ff=9μm ff=13μm ff=17μm

1.0

1.5

0.6

2.0

Frequency/THz

1.0

1.5

2.0

ff1=5μm ff1=11μm ff1=17μm

0.4 0.2 0.0 0.0

2.0

0.5

1.0

1.5

2.0

Frequency/THz

(f) 1.0

(e) 1.0

Frequency/THz

2.0

0.6

0.5

Frequency/THz 0.8

0.8

2.0

0.8

0.8 △y

0.0 0.0

0.0 0.0

2.0

Frequency/THz

(d) 1.0

(c) 1.0

0.0 0.0

0.2

△y

0.0 0.0

0.2

(d) 1.0

0.0 0.0

l3=54μm l3=58μm l3=62μm

0.4

1.5

ff1=5μm ff1=11μm ff1=17μm

0.4

0.8

PCRy

0.2

1.0

0.2

urn al P

0.4

0.5

0.6

(c) 1.0 PCRx

0.6

△y

0.8

△y

0.8

ff=9μm ff=13μm ff=17μm

Frequency/THz

Fig.9. (a)AT parameter, (b)PCRx and (c)PCRy with different l1. (b) 1.0

0.4 0.2

Frequency/THz

Frequency/THz

(a) 1.0

0.6

△

l1=10μm l1=14μm l1=18μm

0.8

0.8

re-

0.6

(b) 1.0

(a) 1.0

0.8

PCRy

PCRx

2.0

Frequency/THz (c) 1.0

(b) 1.0

0.0 0.0

1.09THz) or 13μm (at 0.71THz).

1.5

△y

0.0 0.0

an abrupt dip with △y below 0.6 when w3 is 5μm (at

PCRx

0.2

PCRy

0.4

of

But in the frequency range of 0.40~1.66THz, there exists

0.6

pro

△y

0.8

0.6 ff=20μm ff=24μm ff=28μm

0.4 0.2 0.0 0.0

0.5

1.0

1.5

Frequency/THz

2.0

0.5

0.0 0.0

ff1=5μm ff1=11μm ff1=17μm 0.5

1.0

1.5

2.0

Frequency/THz

Fig.11. (a)AT parameter, (c)PCRx and (e)PCRy with different ff. (b)AT parameter, (d)PCRx and (f)PCRy with different ff1.

Then the influence of structure parameters of SWGs on

AT performance is discussed. As demonstrated before, two

w3=5μm w3=9μm w3=13μm

0.5

1.0

1.5

cascaded F-P cavities are formed between SWGs and the middle double L structure array, and the top and the bottom

2.0

SWGs have similar function, thus only the spacing and

Frequency/THz

Jo

Fig.10. AT parameter with different (a)l2, (b)l3, (c)w1, (d)w2, and (e)w3.

width of the bottom SWGs are discussed here. As shown in Fig. 11, the spacing ff almost has no effect on △y and PCRx,

Figure 10 shows how the △y depends on l2, l3, w1, w2 and

and slightly affects PCRy. With an increase of ff1, the PCRx

w3. As shown in Fig.10 (a), the third dip of △ obviously

is almost unchanged, △y fluctuates significantly in the high

drops and the bandwidth for △y over 0.6 almost keeps the

frequency range, and the bandwidth of PCRy becomes

same when l2 decreases. As for l3, the four dips change

wider. The bottom SWGs are along y-axis so have little

y

significantly. With an increase of l3, the third dip increases

effect on PCRx. At the same time, when the width of the

while the other three dips decline, especially for the first

SWGs increases, less y-polarized wave can transmit the

and the last dips which have sharp reduction (see Fig.

MM, making PCRy close to 1 in a wider frequency range.

10(b)). Next the influence of widths of L-shaped structure

In order to obtain the bandwidth as wide as possible and

is discussed, as shown in Fig. 10 (c)-(e). △y almost remains

make △y almost all greater than 0.8 in the entire bandwidth,

Journal Pre-proof

structure parameters of L-shaped pattern and SWGs are (a)

△y

optical F-P cavity, when the optical path difference is

1.0

0.4 0.2

1.5

2.0

0.0 0.0

θ=0° θ=10° θ=20° θ=30°

0.5

1.0

1.5

2.0

Frequency/THz

Fig.13. (a)Asymmetric transmission and (b)PCR of incident x-polarized wave with different θ.

of

(2m  1)c . 4nd

0.5

0.6

The incident wave cannot be strictly perpendicular to the

Using the relationship λ=c/v, Eq. (9) is rewritten as:

vm 

θ=0° θ=10° θ=20° θ=30°

Frequency/THz

satisfied: (9)

0.4

0.0 0.0

wave is attenuated when the following condition is

(2m  1) . 2

0.8

0.6

0.2

(2m+1)λ/2, destructive interference occurs, that is, the EM

2nd 

(b) 1.0

0.8

Next the influence of substrate thickness d on AT performance is discussed. According to the theory of

1.0

PCRx

selected as mentioned in the section III.

metamaterials in practical circumstances, thus the influence of incident angle θ on AT phenomenon and PCR is

Therefore, the frequency spacing at which destructive

discussed. As shown in Fig.13(a), △y almost remains

interference occurs is: vq  vm 1  vm 

[2( m  1)]c 2(m  1)c c   . 4nd 4nd 2nd

pro

(10)

unchanged expect a significant decrease near 1.08THz. The AT effect is still obvious in the range of 0.35~1.79THz

(11)

when θ increases to 20°. However, when θ increases to 30°,

As can be seen in Eq. (11), the frequency spacing decreases

the △y decreases rapidly in the frequency range over

d=30μm

below 1.6THz. This is because when θ is small, the y

d=50μm

(a) 1.0

d=70μm

PCRx

0.4

influence of θ on the y component of the incident EM

0.6 0.4

0.5

1.0

1.5

waves becomes dominant. Therefore, PCRx remains

d=30μm d=50μm d=70μm

0.2

unchanged in the low frequency and deteriorates rapidly in

urn al P

△y

change too much. However, when θ is increasing, the

0.8

0.6

0.0 0.0

component of the oblique incident EM waves does not

(b) 1.0

0.8

0.2

1.6THz while the AT effect is still obvious in the frequency

re-

with the increase of d.

2.0

0.0 0.0

0.5

1.0

1.5

2.0

Frequency/THz

Frequency/THz

the high frequency, as shown in Fig. 13(b). Overall, the

proposed MM has great AT performance and polarization

Fig.12. (a)Asymmetric transmission and (b)PCR of incident x-polarized wave with different d.

conversion ability in a wide range of incident angles, which is beneficial to practical applications.

The influence of d on the proposed MM with other structure parameters unchanged is shown in Fig.12. △y

varies approximately periodically and the period decreases

V

CONCLUSION

In this paper, a tri-layered MM based on GPCG structure

as d increases, which is consistent with the above analysis.

is proposed. The AT parameter of y-polarized wave is

However, the phase variation introduced by the MM will

beyond 0.8 from 0.37THz to 1.73THz and the highest AT

lengthen

The

parameter 0.958 is achieved. PCRs of backward incident

Fabry-Perot-like cavity in the proposed MM has a longer

x-polarized wave and forward incident y-polarized wave

cavity length than the thickness of the substrate. As in Fig.

are beyond 0.99 in the range of 0.20~1.97THz and

12 (b), PCRx is basically unchanged except for a few

0.35~1.59THz, respectively. Simulation results show that

frequency points, showing that the polarization conversion

the proposed metamaterial achieves excellent asymmetric

equivalent

optical

Jo

the

path

[36].

ability remains almost the same when d changes. Therefore,

transmission performance and nearly ideal polarization

the substrate thickness of the GPCG structure can be

conversion characteristic in broadband and the two

changed according to actual requirements and production

performances are independent on the angle of the incident

conditions. The GPCG structure can be used as

waves. The AT parameter and PCR has been compared with

polarization-dependent band-pass filters.

some other AT and PC devices listed in Table 1. With these features, the proposed metamaterial shows great potential applications in circulators, filters and direction-dependent polarization conversion.

Journal Pre-proof

Table 1 Comparation of the proposed MM with a few reported AT and PC devices PC/AT device

Structure

AT parameter (relative bandwidth)

PCR (relative bandwidth)

Xu et al [4]

Double split rings reflective MM

-

≥0.90(87.7%)

PC

Ma et al [5]

Metal/insulator/metal meta-atom

-

≥0.80(96%)

PC

Xu et al [7]

H-shaped MM

-

≥0.90(94%)

PC

Lee et al [9]

Dielectric-resonator MM

-

≥0.9(66%)

AT

Liu et al [20]

complementary U-shaped MM

[email protected], [email protected]

-

AT

Liu et al [27]

GPCG

≥0.5 (120%)

-

AT

Wang et al [29]

GPCG

≥0.8 (65.22%)

-

AT

Cheng et al [37]

Complementary cut-wire integrated with Si

≥0.8 (17.22%)

≥0.9(17.22%)

GPCG

≥0.8 (129.52%)

≥0.99 (163.13%)

pro

Proposed MM

of

PC

terahertz frequencies[J]. Optics Express, 2017, 25(22):

Funding

27616-27623.

This work was supported by New Direction Cultivation Project

of

Chongqing

University

of

Posts

[7] Xu J, Li R, Qin J, et al. Ultra-broadband wide-angle

and

linear polarization converter based on H-shaped

Telecommunications (A2014-116), the Key Research of

Chongqing

University

of

Posts

metasurface[J].

and

Optics

Express,

2018,

26(16):

20913-20919.

re-

Program

Telecommunications on Interdisciplinary and emerging field

[8] Abasahl B, Dutta-Gupta S, Santschi C, et al. Coupling

(A2018-01), Chongqing Research Program of Basic

strength can control the polarization twist of a

Research and Frontier Technology (No. cstc2016jcyjA0301);

plasmonic antenna[J]. Nano letters, 2013, 13(9):

Project 61405001 supported by NSFC and the Venture &

4575-4579.

Returnees (No. cx2018121).

References

[9] Lee W S L, Ako R T, Low M X, et al.

urn al P

Innovation Support Program for Chongqing Overseas

Dielectric-resonator

metasurfaces

for

broadband

terahertz quarter-and half-wave mirrors[J]. Optics Express, 2018, 26(11): 14392-14406.

[10] Song K, Su Z, Silva S, et al. Broadband and

[1] Suzuki T, Kondoh S. Negative refractive index

high-efficiency

transmissive-type

nondispersive

metasurface in the 2.0-THz band[J]. Optical Materials

polarization

Express, 2018, 8(7): 1916-1925.

Materials Express, 2018, 8(8): 2430-2438.

conversion

meta-device[J].

Optical

[2] Lai Y, Ng J, Chen H Y, et al. Illusion optics: the optical

[11] Fedotov V A, Mladyonov P L, Prosvirnin S L, et al.

transformation of an object into another object[J].

Asymmetric propagation of electromagnetic waves

Physical Review Letters, 2009, 102(25): 253902.

through a planar chiral structure[J]. Physical Review

[3] Schurig D, Mock J J, Justice B J, et al. Metamaterial

electromagnetic cloak at microwave frequencies[J]. Science, 2006, 314(5801): 977-980.

[4] Xu J, Li R, Wang S, et al. Ultra-broadband linear converter

based

Jo

polarization

metasurface[J].

Optics

Express,

on

anisotropic

2018,

26(20):

26235-26241.

Letters, 2006, 97(16): 167401.

[12] Liu J, Li Z, Liu W, et al. High‐Efficiency Mutual Dual‐Band Asymmetric Transmission of Circularly Polarized

Waves

with

Few‐Layer

Anisotropic

Metasurfaces[J]. Advanced Optical Materials, 2016, 4(12): 2028-2034.

[13] Li Y, Dong G, Zhao R, et al. Dual-band asymmetric

[5] Ma S, Wang X, Luo W, et al. Ultra-wide band reflective

transmission and circular dichroism in hybrid coupled

metamaterial wave plates for terahertz waves[J]. EPL

plasmonic metamaterials[J]. Journal of Physics D:

(Europhysics Letters), 2017, 117(3): 37007.

Applied Physics, 2018, 51(28): 285105.

[6] Jiang Y, Wang L, Wang J, et al. Ultra-wideband high-efficiency

reflective

[14] Xu S, Hu F, Chen M, et al. Broadband terahertz

linear-to-circular

polarization converter and asymmetric transmission

polarization converter based on metasurface at

based on coupled dielectric‐metal grating[J]. Annalen

Journal Pre-proof

Der Physik, 2017, 529(10): 1700151.

metamaterials polarization converter[J]. Journal of

[15] Zhu R, Wu X, Hou Y, et al. Broadband Asymmetric Light Transmission at Metal/Dielectric Composite

Lightwave Technology, 2018, 36(12): 2322-2327. [27] Liu D Y, Li M H, Zhai X M, et al. Enhanced

Grating[J]. Scientific reports, 2018, 8(1): 999.

asymmetric transmission due to Fabry-Perot-like

[16] Peng N, Li X, She W. Nonreciprocal optical

cavity[J]. Optics Express, 2014, 22(10): 11707-11712.

transmission through a single conical air hole in an Ag

[28] Cheng Y, Gong R, Wu L. Ultra-broadband linear

film[J]. Optics Express, 2014, 22(14): 17546-17552.

polarization conversion via diode-like asymmetric

[17] Li X, Liu W, She W. Asymmetric optical transmission

transmission with composite metamaterial for terahertz

B, 2018, 35(4): 886-891.

waves[J]. Plasmonics, 2017, 12(4): 1113-1120. [29] Wang C, Zhou X, Tang D, et al. Ultra-broad band

[18] Fei H, Wu M, Xu T, et al. A broadband

diode-like

transmission

of

linearly

polarized waves based on the three-layered chiral

transmission device based on generalized total reflection principle[J]. Journal of Optics, 2018, 20(9):

asymmetric

pro

polarization-insensitive on-chip reciprocal asymmetric

structure[J]. Optik, 2018, 164: 171-177.

[30] Cheng Y, Fan J, Luo H, et al. Dual-band and

095004.

high-efficiency circular polarization conversion via

[19] Li M L, Zhang Q, Qin F F, et al. Microwave linear

asymmetric

polarization rotator in a bilayered chiral metasurface

complementary

chiral

metamaterial

U-shaped

anisotropic

[31] Ji R, Wang S W, Liu X, et al. Giant and broadband

[20] Liu D, Xiao Z, Ma X, et al. Dual-band asymmetric of

with

Materials Express, 2019, 9(3): 1365-1376.

re-

Optics, 2017, 19(7): 075101.

transmission

metamaterial in the terahertz region[J]. Optical

based on strong asymmetric transmission[J]. Journal of

transmission

of

through silver film with a hyperbolic air hole[J]. JOSA

based

structure[J].

Physics A, 2015, 118(3): 787-791.

circular asymmetric transmission based on two

on

cascading

Applied

polarization

conversion

cavities[J].

Nanoscale, 2016, 8(15): 8189-8194.

[32] Menzel C, Helgert C, Rockstuhl C, et al. Asymmetric transmission of linearly polarized light at optical

transmission of linearly and circularly polarized waves

metamaterials[J]. Physical review letters, 2010,

in metamaterial due to symmetry-breaking[J]. Applied

104(25): 253902.

urn al P

[21] Liu D J, Xiao Z Y, Ma X L, et al. Asymmetric

Physics Express, 2015, 8(5): 052001.

[33] Peng Y X, Wang K J, He M D, et al. Electromagnetic

[22] Xiao Z Y, Zou H L, Xu K K, et al. An implemented

near-field coupling induced polarization conversion

method of asymmetric transmission for arbitrary

and

polarization

metasurfaces[J]. Optics Communications, 2018, 412:

base

in

multi-layered

chiral

meta-surface[J]. Journal of Magnetism and Magnetic Materials, 2017: 278-285.

asymmetric

transmission

in

plasmonic

1-6.

[34] Serebryannikov A E, Beruete M, Mutlu M, et al.

[23] Liu D Y, Zhai X M, Yao L F, et al. Asymmetric

Multiband

one-way

polarization

conversion

in

transmission with double bands based on chiral twisted

complementary split-ring resonator based structures by

double-split-ring

Optics

combining chirality and tunneling[J]. Optics express,

[24] Xu Y, Shi Q, Zhu Z, et al. Mutual conversion and

[35] Liu D, Xiao Z, Ma X, et al. Broadband asymmetric

asymmetric transmission of linearly polarized light in

transmission and polarization conversion of a linearly

bilayered chiral metamaterial[J]. Optics Express, 2014,

polarized wave based on chiral metamaterial in

22(21): 25679-25688.

terahertz region[J]. Wave Motion, 2016, 66: 1-9.

resonators[J].

Jo

Communications, 2014, 323: 19-22.

[25] Ma H, Wu R X. Asymmetric transmission of linearly polarized

wave

in

all-dielectric

2015, 23(10): 13517-13529.

[36] Yu N, Genevet P, Kats M A, et al. Light propagation

chiral

with phase discontinuities: generalized laws of

metamaterial[C]//2016 Progress in Electromagnetic

reflection and refraction[J]. science, 2011, 334(6054):

Research Symposium (PIERS). IEEE, 2016: 658-661.

333-337.

[26] Jing X, Gui X, Zhou P, et al. Physical explanation of Fabry–Pérot

cavity

for

broadband

bilayer

[37] Cheng Y, Luo H, Chen F, et al. Photo-excited switchable broadband linear polarization conversion

Journal Pre-proof

via asymmetric transmission with complementary

Continuum, 2019, 2(8): 2391-2400.

Jo

urn al P

re-

pro

of

chiral metamaterial for terahertz waves[J]. OSA

Journal Pre-proof

of

Declaration of interests    The authors declare that they have no known competing financial interests or personal relationships  that could have appeared to influence the work reported in this paper.    ☐The authors declare the following financial interests/personal relationships which may be considered  as potential competing interests:    

re-

pro

 

Jo

urn al P