Startseite Azimuthally and radially polarized orbital angular momentum modes in valley topological photonic crystal fiber
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Azimuthally and radially polarized orbital angular momentum modes in valley topological photonic crystal fiber

  • Zhishen Zhang ORCID logo , Jiuyang Lu , Tao Liu , Jiulin Gan , Xiaobo Heng , Minbo Wu , Feng Li EMAIL logo und Zhongmin Yang EMAIL logo
Veröffentlicht/Copyright: 29. September 2021
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Nanophotonics
Aus der Zeitschrift Nanophotonics Band 10 Heft 16

Abstract

Artificially tailoring the polarization and phase of light offers new applications in optical communication, optical tweezers, and laser processing. Valley topological physics provides a novel paradigm for controlling electromagnetic waves and encoding information. The proposed fiber has the inner and outer claddings possessing opposite valley topological phases but the same refractive indices, which breaks through the polarization constraints of the traditional fiber. Robust valley edge states exist at the domain walls between the inner and outer claddings because of bulk edge correspondence. The valley topological fiber modes exhibit the unprecedented radial and azimuthal polarization with high-order azimuthal index. Those topological modes are robust against the disorder of the fiber structure. These results enable guide and manipulate the optical polarization and angular momentum in fiber with high fidelity. The proposed fiber has the potential to become a powerful optical spanner for the application of bio-photonics.

Keywords: azimuthally and radially polarized modes; orbital angular momentum fiber; valley topological photonic crystal

1 Introduction

Polarization and phase are two important properties of light and spatially arranging the polarization and phase [1–3] leads to intriguing applications in optical communication [4, 5], optical tweezers [6, 7], and laser processing [8, 9]. The azimuthally and radially polarized modes [10] have the higher efficiency for the stable trapping of polar nanoparticles [6] and the laser machining in the polar materials [8]. The helically phased beams carry the orbital angular momentum (OAM) [11, 12], which have the extensive applications, such as high-capacity optical communications [5], multidimensional micro-manipulation [7], and the three-dimensional microstructure machining [9]. Recent work [1, 2, 13] has shown that the polarization and phase of light can be tailored arbitrarily in free space. Compared with the free space, the fiber has advantages in high beam quality and long transmission distance. The azimuthally/radially polarized OAM fiber will combine the advantages of the azimuthally/radially polarized lights, the OAM lights, and the fiber lights, and leads to the potential application as the low-energy great-strength optical spanner into biological tissues. However, the arbitrary combination of polarization and phase in fiber is still challenging. The polarization and phase of fiber modes rely heavily on the azimuthal index. According to the wave equation [14], the refractive indices contrast between fiber core and cladding divides the fiber modes into three categories, the linear or circular polarized modes, the azimuthally polarized modes, and the radially polarized modes. The latter two cases can only be achieved with zero azimuthal index [14]. Due to the high-order azimuthal index of the OAM modes [12], there is no report about the azimuthally and radially polarized OAM modes in fiber.

Most recently, the concept of the band structure topology [15–22] plays a new approach for controlling characteristics of the fiber modes and offers tremendous opportunities in realizing the revolutionary photonic crystal fibers (PCFs) [23–27] with low loss, novel mode field and polarization distributions, and large bandwidth. The Dirac fiber [23] modifies the envelope amplitude of fiber mode by the Dirac equation. The one-way fiber [24] perfectly immunes the backscattering loss based on the Weyl crystals. The Dirac-vortex fiber [27] supports the single polarization mode over one octave bandwidth by the vortex winding number. The valley topological photonic crystal [20, 28], [29], [30], [31], [32], [33], [34], [35] provides an extra degree of freedom to encode the information and has been investigated in the directional optical waveguide [30–33] and the robust photonic delay line [20]. Furthermore, the paired valley topological photonic crystals for guiding the valley topological states have the same effective refractive indices, which is fundamentally different from the waveguides based on the total internal reflection [14] or photonic bandgap [36]. The valley topology may enable us to design waveguide without refractive indices contrast and obtain novel optical fibers with controllable polarization and phase.

Here, we achieve the unprecedented azimuthally and radially polarized orbital angular momentum (OAM) modes in valley topological photonic crystal fiber (TPCF). The proposed TPCF has the inner and outer claddings with the same refractive indices but opposite valley Chern numbers. By eliminating the refractive indices contrast between fiber core and cladding, the three characteristic equations for the different polarized fiber modes now have the identical expressions, which breaks through the polarization constraints of the azimuthal index in the traditional fiber. The topological fiber modes are composed of the clockwise and counterclockwise resonance of topologically protected states in the enclosed interface. The polarization of topological fiber mode is consistent with the corresponding topological state that is parallel or perpendicular to the interface. The topological fiber modes, characterized with the azimuthal/radial polarization, have high azimuthal index and synthesize the polarized OAM modes. Due to the topological protection, the polarization characteristics and the confinement losses of the fiber modes are robust to the local perturbation. These findings may enable the creation of novel polarized orbital angular momentum fiber for optical trapping and laser micromachining.

2 Results

2.1 Topological properties in quasi two dimensional (2D) systems

As depicted in Figure 1a, the design consists of a triangular lattice of the three-hole units in the transverse plane and invariant structure in the longitudinal direction. The lattice constant, the hole radius, and the center-to-center distance of the three-hole unit are set as a = 3.1 μm, r = 0.2a, and h = 3 a / 6 , respectively. The rotation angle of the three-hole α controls the topological properties of the photonic crystal. The refractive index of the substrate and holes are set as 1.444 and 1. Compared with the in-plane propagation in the 2D photonic topological insulators, the light can propagate in directions that lie outside the transverse section in quasi-2D systems due to the additional vertical dimension. More specifically, both the topological photonic band gap (TPBG) and edge states can be constructed under a non-zero longitudinal wave constant k z , just like the ordinary (nontopological) photonic bandgaps and the Dirac cones [14]. The band topology of quasi-2D valley topological photonic crystal is analytically descripted by the effective Hamiltonian H K / K ′ = ± v D ( σ x δ k x + σ y δ k y ) ± ( Δ 1 δ k y + Δ 2 ) σ z (see Supplementary Information 1),where K/K′ are the corner points in the first Brillouin Zone, v D is the group velocity, ( δ k x , δ k y ) = ( k x − K x ( ′ ) , k y − K y ( ′ ) ) is the reciprocal vector measured from the K/K′ points, σ x , y , z are the Pauli matrices. Δ1 δk y is considered as the k z -induced perturbation, which does not break the degenerate states at K/K′ points but change the bands near the K points. Δ2 is the structure-induced perturbation strength because of the breakdown of inversion symmetry, will lift the degenerate states at K/K′ points and open a topological nontrivial gap. The k z acts on the electromagnetic fields of the pseudospin states (insets in Figure 1a), the gap size and center frequency of topological gap, which will expand the parameter scope of the photonic topological insulators, such as reducing the requirement of the substrate refractive index. Figure 1a shows the dependence of the topological bandgap as k z varies. The topological gap is opened with / 2 π k z a > 0.6 , and gradually increases to the maximum with / 2 π k z a = 2 .

Figure 1: Topological gap and edge states with a non-zero k z . (a) Topological bandgap (gray region) as k z varies. The black line indicates the dispersion of the substrate material. The downright inset shows the three-hole unit. The top left insets are the electric field distributions of lower and upper bands at K point correspond to labels p and q, respectively. The green cones denote the Poynting vectors. (b) Interface formed by the upper phase A and lower phase B. (c) Electric field distribution of the horizontally polarized edge state. (d) Electric field distribution of the vertically polarized edge state. The blue arrows indicate the polarization characteristics.
Figure 1:

Topological gap and edge states with a non-zero k z . (a) Topological bandgap (gray region) as k z varies. The black line indicates the dispersion of the substrate material. The downright inset shows the three-hole unit. The top left insets are the electric field distributions of lower and upper bands at K point correspond to labels p and q, respectively. The green cones denote the Poynting vectors. (b) Interface formed by the upper phase A and lower phase B. (c) Electric field distribution of the horizontally polarized edge state. (d) Electric field distribution of the vertically polarized edge state. The blue arrows indicate the polarization characteristics.

The out-of-plane topological edge states are supported at the interface between two photonic crystals with the opposite valley Chern number. In quasi-2D valley topological photonic crystal, the band inversion occurs when the rotation angle (α) changes its plus-minus. So the photonic crystal with −60° < α < 0° (phase A) and 0° < α < 60° (phase B) have the opposite valley Chern number. Figure 1b schematically shows the interface that is formed by the upper phase A and lower phase B. Two edge states (Figure 1c and d) with the horizontal and vertical polarization are achieved with / 2 π k z a = 2.6372 . Due to bulk-boundary correspondence, there should be only one edge state with hybrid polarization at the interface. However, the horizontally and vertically polarized component will have different longitudinal wave constant because of the shape birefringence of the interface. So this hybrid polarized edge state is further split into two horizontally and vertically polarized states. The electric fields of the edge states [37] with the out-plane propagation are expressed as

(1) φ x = ( c 1 ψ 1 x + c 2 ψ 2 x ) ⋅ e i ( δ k x ⋅ x + δ k y ⋅ y ) ⋅ e − | m v D y | ⋅ e i ( K D x ⋅ x + K D y ⋅ y + k z ⋅ z ) ⋅ e − i ω x t ⋅ e x

(2) φ y = ( c 1 ψ 1 y + c 2 ψ 2 y ) ⋅ e i ( δ k x ⋅ x + δ k y ⋅ y ) ⋅ e − | m v D y | ⋅ e i ( K D x ⋅ x + K D y ⋅ y + k z ⋅ z ) ⋅ e − i ω y t ⋅ e y

where ψ 1,2 is the electric field of counterclockwise or clockwise pseudospin states at the K points, subscript x/y represents the electric field component parallel or perpendicular to the interface, e (x/y) is the unit vector, m = ω D Δ / v D 2 is the equivalent mass, and ω D is the Dirac frequency. ω (x/y) is the frequency of edge state, which is influenced by the wave vector (k x , k y , k z ) and the polarization. (k Dx , k Dy , k z ) is the wave vector at K/K′ points.

2.2 Topological fiber modes formed by the out-of-plane edge states

When the interface is rolled into the tubular structure, the forward (backward) edge state will form a stable clockwise (counterclockwise) propagation fiber mode. Mathematically, the interface contour of the TPCF is converted into the equal-perimeter circle with the coordinate transformation (l x , l y ) ⇔ (θ, r − l y ), where l x =  Lθ /2π is the length of interface related to the arc angle θ, L is the perimeter of the enclosed interface, and l y is the least length to the interface. In succession, the wave vector (k x , k y ) is also converted into ( 2 π k θ L , k r ) . The key of this transformation is that the global formation mechanisms of topological fiber modes are changeless although the local mode field distribution may have some deviation. So the mode is described by a cylindrical wave function [14].

(3) d d r 2 + 1 r 2 d d θ 2 + 1 r d d r Φ + ( k θ 2 + k r 2 ) Φ = 0

It is important that the core is zero-thickness and the inner and outer claddings have the same (k θ , k r ). So the mode field distribution Θ is proportional to R(r)e ivθ , where

(4) R ( r ) = I v k θ 2 + k r 2 ⋅ r , 0 ≤ r ≤ r 0   K v k θ 2 + k r 2 ⋅ r , r ≥ r 0  

I v and K v are the v-th modified Bessel functions of the first and second kinds, and r 0 =  L /2π . Due to the same subexpressions inside the I v and K v , the characteristic matrix of the equations formed by the boundary condition of continuity is singular and the polarization of fiber mode is not determined (see Supplementary Information 2). The polarization properties of fiber modes are directly derived from the out-of-plane edge states in the enclosed interface between the inner and outer claddings. The horizontally and vertically polarized edge states are converted into the radially and azimuthally polarized modes in TPCF. The longitudinal electric field in TPCF is

(5) E z ( θ , r ) ∝ u e ( θ , r ) ⋅ e i θ e ( θ , r ) ⋅ e − | m v D ( r − r 0 ) | ⋅ e i ( k θ ⋅ θ ) ⋅ e i [ k r ( r − r 0 ) ] ⋅ R ( r )

where u e ( θ , r ) ⋅ e i θ e ( θ , r ) is the initial distribution of the edge state. When the θ ranges from 0 to 2π, the additional phase difference induced by the edge state is 0. So the k θ should be the integer v for keeping the periodicity in the azimuthal direction, which coincide with the phase distribution of the OAM modes in TPCF (Figure 3). In other words, only the edge states that meet the resonance condition can form the fiber modes. The vector modes in TPCF are the interference patterns resulting from the clockwise and counterclockwise rotation of topologically protected states in the enclosed interface between the inner and outer claddings.

2.3 Radially and azimuthally polarized OAM modes in TPCF

Figure 2a shows the cross-section of valley topological photonic crystal fiber, whose inner and outer claddings are the phase A and phase B, respectively. The fiber core interface is set as the triangle-clique instead of the hexagon to avoiding that two kinds of interfaces appeared alternately. The layers of the inner and outer claddings are respectively set as 2 and 5, and the parameters of units are the same as Figure 1a. The optimization of the fiber structural parameters is shown in Supplementary Information 3. The fiber vector modes at 1550 nm are computed by the finite element method. As shown in Figure 2, the proposed TPCF supports multiple fiber modes in topological gap. The topological fiber modes are classified as the azimuthally polarized ( AP v m e / o ) and radially polarized ( RP v m e / o ) modes, as the HE v m e / o and EH v m e / o modes in conventional fibers, where the subscript v and m are the azimuthal and radial indices, the superscript e and o represent the even and odd vector modes. It is important that those unique radially and azimuthally polarized modes in TPCF are resulted from the single polarization of the topologically protected edge states, but not the enclosed contour shape of fiber core. To prove that assertion, the triangle-clique core fiber is designed and multiple hybrid polarized modes are observed (Supplementary Information 4). Also, the polarized modes in TPCF can be the higher azimuthal index, which are fundamentally different from the TE0m and TM0m mode in conventional fibers, whose eigenvalue equations limit the zero azimuthal index. For each azimuthal index, there are two degenerate modes (the even and odd modes) with the same propagation constant due to two complementary interference patterns of the clockwise and counterclockwise edge states. However, when the number of bright spots in fiber mode is the multiples of three, this degeneracy is lifted due to the C 3v symmetry of the fiber cross-section. As shown in Figure 2b and c, the AP vm and RP vm modes have the similar electric field distributions and orthogonal polarization distributions, for both fundamental modes ( A P 11 o and R P 11 o ) and the high order modes (AP21 and RP21). All the modes in the proposed fiber have the confinement loss no more than the magnitude of 5 × 10−4 dB/km. The higher azimuthal index (v) of mode is, the larger confinement loss is. The AP v m e / o modes have the less confinement loss than the RP v m e / o modes.

Figure 2: Azimuthally and radially polarized modes in TPCF. (a) Fiber dispersion in topological gap. The top left inset is the structure of the valley topological photonic crystal fiber. The downright inset is the enlarged view of fiber dispersion in solid line box. (b) Dispersions and the electric field distributions of the RP 11 o ${\text{RP}}_{11}^{o}$ , RP 21 e ${\text{RP}}_{21}^{e}$ , and RP 21 o ${\text{RP}}_{21}^{o}$ modes. (c) Dispersions and the electric field distributions of the AP 11 o ${\text{AP}}_{11}^{o}$ , AP 21 e ${\text{AP}}_{21}^{e}$ , and AP 21 o ${\text{AP}}_{21}^{o}$ modes. The blue arrows indicate the polarization characteristics.
Figure 2:

Azimuthally and radially polarized modes in TPCF. (a) Fiber dispersion in topological gap. The top left inset is the structure of the valley topological photonic crystal fiber. The downright inset is the enlarged view of fiber dispersion in solid line box. (b) Dispersions and the electric field distributions of the RP 11 o , RP 21 e , and RP 21 o modes. (c) Dispersions and the electric field distributions of the AP 11 o , AP 21 e , and AP 21 o modes. The blue arrows indicate the polarization characteristics.

The unprecedented radially and azimuthally polarized orbital angular momentum (OAM) fiber modes are created based on the synthetic formula [38] (even mode ± i ⋅ odd mode) for the degenerate modes. For example, Figure 3 shows the electric field and phase distributions of the azimuthally and radially polarized OAM modes in TPCF with topological charge l = 1, which are synthesized by APOAM l − 1,1 ± = AP l 1 e ± i ⋅ AP l 1 o and RPOAM l − 1,1 ± = RP l 1 e ± i ⋅ RP l 1 o . The differences among the effective indices of the adjacent modes are larger than 1 × 10−4, which will greatly decrease the mode coupling. The spiral phase distribution (Figure 3d and i) validates that the topological charge of OAM mode is l = 1. As shown in Figure 3a and b, the energy mainly concentrates to the azimuthal component. The polarization extinction ratio is defined as PER = P 1 / P 2 , where P 1 and P 2 are the power of major and minor polarization components, respectively. For the APOAM 11 + mode, the polarization extinction ratio is 20 dB. For the RPOAM 11 + mode (Figure 3f and g), the energy mainly concentrates to the radial component and the polarization extinction ratio is 17.9 dB. To investigate the propagation feature of APOAM 11 + and RPOAM 11 + modes, we further simulate the transmissions of OAM modes along the proposed TPCF (100 μm long) based the finite-difference time-domain method. As shown in Figure 3c and h, both polarized OAM modes propagate stably without attenuation. The helical phase distributions (Figure 3e and j) are coincident with Figure 3d and i, which indicate that both modes have the helical wavefront and propagate in spiral manner. The azimuthally and radially polarized OAM modes are remarkably different from the linear and circular polarization OAM modes in the reported OAM fiber. Proposed valley topological photonic crystal fiber brings new development potential for the OAM fiber applications such as the optical trapping and laser micromachining.

Figure 3: Azimuthally and radially polarized orbital angular momentum fiber modes. (a–e) Azimuthal electric field, radial electric field, propagating electric field, phase distribution, and propagating phase of APOAM 11 + ${\text{APOAM}}_{11}^{+}$ ; (f–j) Azimuthal electric field, radial electric field, propagating electric field, phase distribution, and propagating phase of RPOAM 11 + ${\text{RPOAM}}_{11}^{+}$ . The blue lines in (a) and (g) donate the location of the vertical sections for the propagating fields.
Figure 3:

Azimuthally and radially polarized orbital angular momentum fiber modes. (a–e) Azimuthal electric field, radial electric field, propagating electric field, phase distribution, and propagating phase of APOAM 11 + ; (f–j) Azimuthal electric field, radial electric field, propagating electric field, phase distribution, and propagating phase of RPOAM 11 + . The blue lines in (a) and (g) donate the location of the vertical sections for the propagating fields.

The modes in TPCF are topologically robust against the structure disorder. In order to show this stability, we introduce the random offset ∈ (−δ, δ) to TPCF in the random directions (Figure 4a inset). For each δ, 40 simulations are conducted. Figure 4 shows the polarization extinction ratio and confinement loss of AP21 mode in the defective TPCFs. The fluctuating ranges of both two cases slowly increase with the increasing δ. When / h δ is 3%, the polarization extinction ratio is higher than 15 dB and the confinement loss is less than 0.003 dB/km, which is enough for most OAM applications. The performance deterioration in the defective TPCFs is because of the coupling between the AP21 mode and the leaky modes triggered by the disordered fiber claddings. This coupling effect is greatly inhibited for two reasons. First, the defect modes are not allowed in the topological gap unless the symmetry for the topological protection is broken. Therefore, the difference between the equivalent refractive indices of the AP21 mode and the leaky modes increases. Second, there is the phase mismatch between the AP21 mode and the leaky modes. Although the disorder only causes less coupling between two oppositely directed topological modes, the clockwise topological resonance modes propagating in the disordered TPCF can turn into the counterclockwise modes. The disorder will destroy the degeneration of the even mode and odd mode, and introduces the additional phase difference. Based on the synthetic formula (even mode ± i ⋅ odd mode), the rotation direction of mode will be changed when the additional phase difference equal to π. It is worth emphasizing that the TPCF is not a one-way waveguide due to the invariant structure along the propagating direction. The backscattering wave can be excited with the longitudinal nonuniform defects.

Figure 4: Fiber modes against the in-plane disorder. (a) Confinement loss of AP21 mode of TPCF. All holes in fiber occur the random offsets δ and inset shows the disorder cell with the red dashed lines. h is the distance between the hole and the center of cell. (b) Polarization extinction ratio of AP21 mode of TPCF. Insets are the azimuthal and radial electric field of the perturbed AP21 mode, whose polarization extinction ratio is labeled by the star.
Figure 4:

Fiber modes against the in-plane disorder. (a) Confinement loss of AP21 mode of TPCF. All holes in fiber occur the random offsets δ and inset shows the disorder cell with the red dashed lines. h is the distance between the hole and the center of cell. (b) Polarization extinction ratio of AP21 mode of TPCF. Insets are the azimuthal and radial electric field of the perturbed AP21 mode, whose polarization extinction ratio is labeled by the star.

3 Discussion

For experimental considerations, the proposed TPCF can be realized by the stack-and-draw method, which has been used for fabricating various PCFs with circular holes array. Due to the non-zero longitudinal wave constant, the TPBG is formed with the relatively low index contrast. So the TPBG can be constructed by numerous glasses, such as SiO2, Schott SF4, and As2S3. The operating wavelength can be turned to arbitrary transparent band of substrate materials by adjusting the size of primitive cell in claddings. While the above analysis has been limited to the valley topological photonic crystal with three-holes units, other 2D photonic topological insulators, such as the photonic crystals with C 6v -symmetric unit cells [18], can also be implemented for the TPCF with the same guiding mechanism.

In conclusion, a novel TPCF is proposed with the radially and azimuthally polarized orbital angular momentum (OAM) fiber modes. The proposal TPCF is composed of inner and outer claddings that are the honeycomb lattices with the upwards and downwards three-holes units. The guiding mechanism based on the topologically protected edge state is established and the topological fiber modes are studied systematically. Due to the topological protection, the modes of the TPCF are robust against the in-plane disorder. The proposal TPCF further enriches the principles of fiber design, by enhancing the performances through controllable modes, polarization, and defect-immune propagation feature. It also offers a new platform for exhibiting the novel topological phenomena in quasi-2D systems.

4 Methods

Our simulations were performed by the COMSOL RF module and the Lumerical FDTD Solutions. The bandgaps in Figure 1a was calculated by a hexagonal primitive cell with different k z -vector under the Floquet periodic boundary conditions. The electric field distributions of the edge states (Figure 1c and d) were calculated by the interface formed by the upper phase A (1 × 10 units) and lower phase B (1 × 10 units) with ( k x , k y , k z ) = ( / 3 a 2 π , 0 , 2 π / 2.6372 a ) . The dispersions and the electric field distributions of fiber modes (Figures 2 and 4) were calculated by the cross-section (Figure 2a inset) with the perfectly matched layer. In the defective fiber simulations, all holes in fiber occur the random offsets δ. The confinement loss was calculated by L loss = 20 ln ⁡ 10 ⋅ 2 π 1.55 × 1 0 − 6 ⋅ I m [ n eff ] × 1 0 3 ( d B / k m ) , where Im[n eff] was the imaginary part of the mode equivalent refractive index. The OAM fiber modes (Figure 3a, b, and d) were synthesized by APOAM 11 + = AP 21 e + i ⋅ AP 21 o and the modes (Figure 3f, g, and i) were synthesized by RPOAM 11 + = AP 21 e + i ⋅ AP 21 o . The propagating electric field and phase of OAM fiber modes (Figure 3c, e, h, and j) were calculated by a three-dimensional FDTD model (the proposed fiber with 100 μm long) and the perfectly matched layer boundary conditions were used. The mode sources were set as AP 21 e + i ⋅ AP 21 o and RP 21 e + i ⋅ RP 21 o , respectively.

Corresponding authors: Zhongmin Yang, School of Physics and Optoelectronic Technology, South China University of Technology, Guangzhou, Guangdong 510640, China; State Key Laboratory Luminescent Materials and Devices and Institute of Optical Communication Materials, South China University of Technology, Guangzhou 510640, China; and South China Normal University, Guangzhou 510006, China, E-mail: ; and Feng Li, Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China, E-mail:

Funding source: Guangdong Key Research and Development Program

Award Identifier / Grant number: 2018B090904003

Funding source: National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809

Award Identifier / Grant number: Grants No. 12074446

Funding source: Project funded by China Postdoctoral Science Foundation

Award Identifier / Grant number: 2019M652872

Funding source: Guangdong Key Research and Development Program

Award Identifier / Grant number: 2018B090904001

Funding source: NSFC Development of National Major Scientific Research Instrument

Award Identifier / Grant number: 61927816

Funding source: National Natural Science Foundation of China (NSFC)

Award Identifier / Grant number: U1609219

Funding source: Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program

Award Identifier / Grant number: 2017BT01X137

Funding source: Fundamental Research Funds for the Central Universities

Award Identifier / Grant number: 2018ZD01

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors gratefully acknowledge financial support from NSFC Development of National Major Scientific Research Instrument (61927816), Guangdong Key Research and Development Program (2018B090904001, 2018B090904003), National Natural Science Foundation of China (NSFC) (U1609219, Grants No. 12074446), Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X137); Project funded by China Postdoctoral Science Foundation (2019M652872), and the Fundamental Research Funds for the Central Universities (2018ZD01).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/nanoph-2021-0395).

Received: 2021-07-22
Accepted: 2021-09-16
Published Online: 2021-09-29

© 2021 Zhishen Zhang et al., published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

Artikel in diesem Heft

  1. Frontmatter
  2. Reviews
  3. Spin photonics: from transverse spin to photonic skyrmions
  4. Multiple excitons dynamics of lead halide perovskite
  5. Recent advances in bianisotropic boundary conditions: theory, capabilities, realizations, and applications
  6. Research Articles
  7. All-optical modulation based on MoS2-Plasmonic nanoslit hybrid structures
  8. Graphdiyne-decorated microfiber based soliton and noise-like pulse generation
  9. True- and quasi-bound states in the continuum in one-dimensional gratings with broken up-down mirror symmetry
  10. Toward white light emission from plasmonic-luminescent hybrid nanostructures
  11. Observation of elastic heterogeneity and phase evolution in 2D layered perovskites using coherent acoustic phonons
  12. Topological protection of continuous frequency entangled biphoton states
  13. Emission kinetics of HITC laser dye on top of arrays of Ag nanowires
  14. Ultra-narrowband and highly-directional THz thermal emitters based on the bound state in the continuum
  15. High-performance flexible surface-enhanced Raman scattering substrate based on the particle-in-multiscale 3D structure
  16. A mixture-density-based tandem optimization network for on-demand inverse design of thin-film high reflectors
  17. Azimuthally and radially polarized orbital angular momentum modes in valley topological photonic crystal fiber
  18. Plasmonic interference modulation for broadband nanofocusing
  19. Grayscale-patterned metal-hydrogel-metal microscavity for dynamic multi-color display
  20. Waveguide Schottky photodetector with tunable barrier based on Ti3C2T x /p-Si van der Waals heterojunction
  21. Linear-polarized terahertz isolator by breaking the gyro-mirror symmetry in cascaded magneto-optical metagrating
  22. Nonlinear plasmonic response in atomically thin metal films
  23. Thermal near-field tuning of silicon Mie nanoparticles
https://doi.org/10.1515/nanoph-2021-0395
Schlagwörter für diesen Artikel
azimuthally and radially polarized modes; orbital angular momentum fiber; valley topological photonic crystal
Creative Commons
BY 4.0

Artikel in diesem Heft

  1. Frontmatter
  2. Reviews
  3. Spin photonics: from transverse spin to photonic skyrmions
  4. Multiple excitons dynamics of lead halide perovskite
  5. Recent advances in bianisotropic boundary conditions: theory, capabilities, realizations, and applications
  6. Research Articles
  7. All-optical modulation based on MoS2-Plasmonic nanoslit hybrid structures
  8. Graphdiyne-decorated microfiber based soliton and noise-like pulse generation
  9. True- and quasi-bound states in the continuum in one-dimensional gratings with broken up-down mirror symmetry
  10. Toward white light emission from plasmonic-luminescent hybrid nanostructures
  11. Observation of elastic heterogeneity and phase evolution in 2D layered perovskites using coherent acoustic phonons
  12. Topological protection of continuous frequency entangled biphoton states
  13. Emission kinetics of HITC laser dye on top of arrays of Ag nanowires
  14. Ultra-narrowband and highly-directional THz thermal emitters based on the bound state in the continuum
  15. High-performance flexible surface-enhanced Raman scattering substrate based on the particle-in-multiscale 3D structure
  16. A mixture-density-based tandem optimization network for on-demand inverse design of thin-film high reflectors
  17. Azimuthally and radially polarized orbital angular momentum modes in valley topological photonic crystal fiber
  18. Plasmonic interference modulation for broadband nanofocusing
  19. Grayscale-patterned metal-hydrogel-metal microscavity for dynamic multi-color display
  20. Waveguide Schottky photodetector with tunable barrier based on Ti3C2T x /p-Si van der Waals heterojunction
  21. Linear-polarized terahertz isolator by breaking the gyro-mirror symmetry in cascaded magneto-optical metagrating
  22. Nonlinear plasmonic response in atomically thin metal films
  23. Thermal near-field tuning of silicon Mie nanoparticles
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