This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg)Nanyang Technological University, Singapore.

Shaping high‑Q planar fano resonantmetamaterials toward futuristic technologies

Lim, Wen Xiang; Manjappa, Manukumara; Pitchappa, Prakash; Singh, Rajan

2018

Lim, W. X., Manjappa, M., Pitchappa, P., & Singh, R. (2018). Shaping high‑Q planar fanoresonant metamaterials toward futuristic technologies. Advanced Optical Materials, 6(19),1800502‑. doi:10.1002/adom.201800502

https://hdl.handle.net/10356/138748

https://doi.org/10.1002/adom.201800502

© 2018 WILEY‑VCH Verlag GmbH & Co. KGaA, Weinheim. All rights reserved. This paper waspublished in Advanced Optical Materials and is made available with permission ofWILEY‑VCH Verlag GmbH & Co. KGaA, Weinheim.

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Article type: Progress Report

Shaping high-Q planar Fano resonant metamaterials towards futuristic technologies

Wen Xiang Lim, Manukumara Manjappa, Prakash Pitchappa, and Ranjan Singh*

Wen Xiang Lim, Manukumara Manjappa, Dr. Prakash Pitchappa, Prof. Ranjan Singh

Division of Physics and Applied Physics, School of Physical and Mathematical Sciences,

Nanyang Technological University, Singapore 637371, Singapore

Centre for Disruptive Photonic Technologies, The Photonics Institute, Nanyang

Technological University, 50 Nanyang Avenue, Singapore 639798

E-mail: ranjans@ntu.edu.sg

Keywords: Fano resonance, metamaterials, plasmonics, high quality factor, future

applications

2

Abstract: Advances in plasmonic metamaterials have been rapidly evolving with

inventions aimed at developing metadevices with real world applications. In reality,

energy losses in plasmonic systems are prevalent and it is paramount to come up with

solutions that could overcome limitations that impede further advancements towards the

miniaturization of optoelectronics devices. High-Q Fano resonance as a scattering

phenomenon can be triggered easily by introducing asymmetry into plasmonics system,

and thus it offers a simple approach to reduce radiative losses through lineshape

engineering. High-Q Fano resonance possesses narrow linewidth and intensely confined

electromagnetic fields which makes it viable for wide-spread applications. The purpose

of this review is to consolidate the current advances or contributions that high-Q Fano

resonance has made in the metamaterials community. Two general modes of energy loss

including radiative and non-radiative losses are introduced and we examined possible

ways to overcome these challenges. Following which, applications based on high-Q Fano

resonance including sensors, lasing spaser and optical switch are introduced as we

embrace on the future of Fano resonance-based technologies.

3

1. Introduction

In the current era of science and technology, optics and photonics have become an

integral part of core technological platform that has transformed human lives as we know

of today. The researchers are continuously pushing forth the frontiers of modern optics

and photonic devices to achieve higher sensitivity, miniaturization, advancement in

functionality and more novel and intriguing applications. Without doubt, these efforts

have been the driving force towards the revolution in the fields of high speed

telecommunication, enhanced health technology, sensitive spectroscopy system, and

many more. At the backbone of these applications lies a set of unique features offered by

optics and photonics. The ultimate speed limit of photon due to its massless property led

to the telecommunication and internet revolutions as it could transfer huge capacity of

information over long distances with extremely low latency and power.[1, 2] For real

applications into telecommunications, a great deal of interest has been generated on

signal processors,[3] multiple-wavelength source,[4, 5] modulators[6] and frequency

combs[7, 8] to enable the integration of CMOS (complementary metal-oxide-

semiconductor)-compatible platforms. Furthermore, the non-destructive and remote

sensing capabilities of photonics has led to the improvements in health technology which

bring about label-free and non-invasive techniques with advanced sensing modalities that

facilitate early detection of disease-causing molecules.[9, 10, 11] The strong interaction

of materials to the various optical parameter such as amplitude, frequency, phase and

polarization has been instrumental in the development of sensitive spectroscopy system.

This allows for accurate and timely detection of gas molecules that provides several

4

benefits such as real-time monitoring of the environmental air quality, sensing explosive

traces for security and tracking of toxic gas leakage in clinical laboratory to ensure a safe

and healthy workplace.[12, 13, 14, 15] With significant steps taken to boost the quality of

our life, it is hard to imagine living without these technological devices that have

benefited us by contributing to the simplicity and convenience of human mankind in

several ways. More interestingly, the sensitivity, speed and accuracy of these optical

systems can be significantly enhanced through optical resonator cavities that strongly

confine the interacting optical field in an extremely narrow region or increase the

interaction time by trapping the photon in the cavity. The performance of an optical

resonator is determined by its ability to trap the optical energy within the cavity and is

usually characterized by quality (Q) factor.

Q-factor is a dimensionless parameter that quantifies the amount of energy stored as a

ratio to the amount of energy lost per cycle through dissipation in a resonator system. In

other words, a resonator with low-Q loses energy more quickly over time due to stronger

damping. In electronic circuits, this is described by the equation,

𝑄 = 2𝜋𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑

𝐸𝑛𝑒𝑟𝑔𝑦 𝑙𝑜𝑠𝑡 𝑖𝑛 𝑜𝑛𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 (1)

whereby a period has 2π radians. In photonics, likewise the quality factor of a resonator

system is defined as the ratio of the resonant frequency, f0 to the full-width at half

maximum at the resonant position, δf and is written as,

𝑄 =𝑓0

𝛿𝑓 (2)

5

The full-width at half maximum (or resonance line-width) also corresponds to the

bandwidth which dictates the broadness of the resonance. For a less damping system, the

bandwidth is narrower with a higher-Q as compared to a system with higher damping,

and more energy can be stored. However, in all optical systems, energy losses are

unavoidable and they are associated with the radiative and non-radiative scattering of

charge carriers. The situation worsens and becomes more apparent as the overall size of

the system reduces from micro- to nanoscale dimensions.

As technology progresses, scaling down of devices becomes even more attractive with

customizable novel optical properties, hence pushing us to venture into another field of

research. Metamaterials is one such field that has gained huge research interests over the

past two decades, owing to the extreme spectral scalability, designed optical properties

and ease of realization and integration. Metamaterials are periodic arrangement of meta-

atoms which have been engineered to exhibit material properties not available in nature.

Their properties are mainly dependent on the size, shape, geometry and arrangements of

the meta-atoms. Futhermore, the meta-atoms are so small that miniaturization of future

devices look possible. By going smaller, we increase the portability of the device, allow

more components to be packed together, and in doing so, the operational efficiency will

be higher.[16, 17, 18, 19] However, advancements in technology are not always smooth-

sailing with several setbacks and challenges faced ahead. Energy losses remain one of the

critical issues for implementing feasible metamaterial-based devices, as it affects the

speed, efficiency and reliability of devices.

6

Radiative loss is inherent in metamaterials at lower frequencies, while energy loss at

higher frequencies is largely dominated by a non-radiative process (ohmic loss) owing to

the subwavelength nature of the resonators. Nevertheless, radiative loss remains present

in metamaterials across the electromagnetic spectrum. As an approach, without

significantly redesigning the architecture of the device, radiative loss can be reduced by

breaking the symmetry of the metamaterial which in turn induces a trapped mode

resonance termed as Fano resonance. Fano resonance does not interact directly with the

propagating electromagnetic wave and so radiative loss is suppressed. It is an extremely

peculiar dark resonance mode with very sharp asymmetric lineshape and high-Q factor.

Such high-Q resonance mode possesses a strong confinement of electric or magnetic field

which is imperative for useful applications. The Q-factor of a Fano lineshape can be

derived from the Fano fitting equation written as below,

𝑅 (𝜔) = 𝐴0 + 𝐹0

[𝑞+2(𝜔−𝜔0)

Γ]

2

1+[2(𝜔−𝜔0)

Γ]

2 (3)

whereby A0 and F0 are constant factors, q is the asymmetry parameter of the system

defined as the ratio between resonant and non-resonant state, ω0 is the resonance

frequency and Γ is the full-width at half maximum of the resonance frequency. Thereafter,

the Q-factor is calculated by 𝑄 =𝜔0

𝛤.[20, 21, 22, 23]

A higher Q-factor is evidently desirable in most metamaterial devices. Therefore, an

understanding on the behaviour of Q-factor is paramount to realizing scalable and

functional metamaterial devices across the electromagnetic spectrum. Appropriate loss-

7

engineering solution can be implemented to suit different situations (different frequency

regimes or geometrical parameters) so that an optimal high Q-factor can be obtained. It

has been reported that with a decreasing asymmetry, α (shape ratio parameter) or at lower

frequency regime, the Q-factor increases exponentially.[23] The increase in the Q-factor

can be attributed to the linewidth narrowing of the Fano resonance. However, the larger

Q-factor comes at the expense of a weaker resonance mode. This suggests that while a

maximum field confinement can be attained at the lowest asymmetry parameter, the

resonance has a low intensity, which is undesirable as high resolution and signal-to-noise

ratio are extremely critical for any sensor device. Hence, the Figure of Merit (FoM)

defined as the product of the Q-factor and the peak-to-dip intensity of the resonance

mode was devised to determine the optimized condition of the high-Q resonance which

considers the trade-off between the linewidth and resonance strength.[24] As compared to

other resonance modes in metamaterials, Fano resonance as a high-Q mode has great

potentials in many domains of technology [25].

In this review, we aim to present the latest developments of high-Q reports with emphasis

on Fano resonant metamaterials. We will introduce the models that have been used to

describe the origin of the resonance mode, types of system based on a variety of unit cell

designs to excite Fano resonance in the contemporary metamaterial society and their

application to current state-of-the-art devices. In addition, we will also introduce

superconductors as an alternative to metallic structures to lower non-radiative losses in

metamaterials. Our future outlook presents different loss-engineering schemes such as

8

unit cells arrangement or changing the material properties to all-dielectrics which also

offer solutions for reducing energy losses in subwavelength systems.

2. Characterization of Fano resonance

(a) Hybridization model

In recent years, E. Prodan et al.[26] has proposed a hybridization model, an

electromagnetic analogy to the orbital hybridization theory, which can be used to

visualize the plasmonic interactions between two or more metallic bodies. From this

model, nanostructure with complex geometry is decomposed into several components

that make up the design. Interpretations based on the spectral distributions of the

individual bodies in the coupled and uncoupled states are utilized to further modify the

state of the plasmonic system to suit different situations. As an example, when an

electromagnetic wave is incident onto the metal nanoshell, surface charges are induced

along the inner radius a and outer radius b of the metal shell whereby the modes of the

sphere and the cavity interact with each other and hybridize. Using spherical harmonics,

the plasmon frequencies of these modes are:[27]

𝜔𝑙±2 =

𝜔𝐵2

2[1 ±

1

2𝑙+1√1 + 4𝑙(𝑙 + 1) (

𝑎

𝑏)

2𝑙+1

] (4)

9

where 𝜔𝐵 = √2𝜋𝑒2𝑛0

𝑚 is the surface plasmon frequency (n0 is the electron density, e is the

electronic charge and m is the effective mass of electron) and l > 1 is the degree of the

associated plasmon mode.

For a dipolar mode (l = 1), and in the limit of the inner radius approaching zero, the

plasmon frequencies of the cavity 𝜔𝑐 and sphere 𝜔𝑠𝑝 modes are respectively,

lim𝑎→0

𝜔+ = 𝜔𝑐 = √2

3𝜔𝐵, (5)

lim𝑎→0

𝜔− = 𝜔𝑠𝑝 = √1

3𝜔𝐵, (6)

The hybridization of the sphere and cavity modes generate two nanoshell resonances

which in the energy-level diagram is categorized as longitudinal coupling whereby the

higher energy plasmon mode |𝜔+⟩ is anti-symmetric or antibonding and the lower energy

plasmon mode |𝜔−⟩ is symmetric or bonding (Figure 1a). The other form of

hybridization is a transverse coupling, in which the higher energy plasmon mode is

symmetric and the lower energy plasmon mode is anti-symmetric.[28] In addition, the

strength of the coupling between the sphere and cavity modes is determined by the

thickness of the shell that possesses a finite penetration depth. The coupling is stronger

for thinner shell, and the resonance frequency blueshifts. In the more complicated case of

a "nano-matryushka" structure, there are four linearly independent plasmon modes which

split into other four hybridized plasmon resonances. The coulombic interactions between

the four linearly independent plasmon modes are dependent on the thickness of the

10

dielectric spacer layer that separates the inner and outer metal shells. Therefore, as the

thickness of the dielectric spacer layer reduces, the coupling strength shifts from strong to

weak, and finally to an uncoupled case. Ever since the establishment of the model, it has

been applied as a simple and intuitive tool to understand the plasmonic resonances, which

include Fano resonance of complex nanostructures in several demonstrations.[29, 30, 31,

32, 33, 34, 35, 36].

(b) Coupled oscillator model

The origin of Fano resonances in the classical systems is theoretically modeled using the

coupled oscillators, [20, 24, 37, 38, 39, 40, 41, 42] where one of the oscillator is strongly

driven by the external field that is termed as the 'bright mode' while the other oscillator

termed as 'dark mode' is not coupled to the free space field. Equations of motion

determining the coupling between the bright and the dark modes, are described by the

following set of coupled equations,

0)()()()(

)()()()(

22

22

=+++

=+++

txtxtxtx

Eftxtxtxtx

bddddd

bdbbbbb

. (7)

Where, (xb, xd), (ωb, ωd) and (γb, γd) are the scattering amplitudes, angular resonance

frequencies and the linewidths of the bright and dark modes, respectively. Ω defines the

coupling strength between the bright and dark modes. fb = qb/mb quantify the free space

coupling strength of bright mode with the incident light, where qb and mb are the effective

charge and mass of the oscillator, respectively. The dark mode oscillator is completely

decoupled from the incident driving field. The coupled equations provide the insight on

11

the interactions that leads to the Fano type of destructive interference in the amplitudes xb

and xd for contrasting linewidths b and d of bright and the dark modes. After solving for

the scattering amplitudes xb and xd in the coupled Eqn. 7, one can arrive at the

susceptibility expression for light-matter interactions given by,

+−+−−

+−=

))((

)(22224

22

bbdd

dd

ii

iK

(8)

The real part (Re[]) of the susceptibility expression in Eqn. 8 represents the dispersion

and the imaginary part (Im[]) gives the absorption losses in the system, where K is the

normalizing constant. 1-Im[] represents the transmission response of the system for the

appropriate fitting parameters of ωb, ωd, γb, γd and . The strength of the Fano resonance

depends on the coupling strength Ω which in turn relates to the asymmetry parameter α in

the metamaterial structures.

(c) Babinet's Principle for Electromagnetic Fields

Fano resonance has also been studied in complementary counterparts which are the

inverse design of positive metamaterial structures. As dictated by the Babinet's principle,

the transmission spectra of the positive structures and complementary structures should

sum up to the initial intensity of the electromagnetic wave that passes through as if

nothing existed.[43] In complementary structures, contrary to positive structures, the

electric field component should be interchanged with the magnetic field component of the

same electromagnetic wave. Hence, the transmission spectrum of the complementary

structure corresponds to a mirror-image of the the transmission spectrum of the positive

12

structure in a way that the peaks and dips are interchanged.[44, 45] Complementary split

ring resonators (CSRR) and positive split ring resonators (SRR) were first reported for

this phenomenon in metamaterials as shown in Figure 1b.[46] Near-field microscopy was

performed by A. Bitzer et. al and agreement between the theoretical, simulation and

experimental results fully validate the Babinet's principle.[47] The concentration of the

electric field in positive asymmetric split ring (ASR) relates to the accumulation of

surface current in complementary asymmetric split ring (CASR), and the surface current

accumulates at a region in positive ASR which relates to the concentration of the electric

field in CASR as shown in Figure 1c.[48] Subsequently, complementary structures of

various designs could be promising as polarization-sensitive graphene modulator,[49]

high-Q chiral metasurface for circular polarizers,[50] and directional filters.[51] In a

recent work, by strategically positioning dust particle along the nanoslit, the phononic

mode of the particle is detected as seen from the Fano lineshape, with maximum signal

towards the middle of the nanoslit. The presence of the dust particle breaks the symmetry

of the nanoslit, hence inducing a Fano signal on the plasmonic background. Narrower

nanoslits are beneficial for the detection of ultra fine dust particle via surface-enhanced

infrared absorption.[52] Thus, in many possible ways, Fano resonance is manifested in a

variety of systems composed of positive or complementary geometries.

13

Figure 1. a) The energy-level diagram of the hybridization between the sphere and cavity

modes. b) Measured transmission coefficient of a unit cell of SRR and CSRR, spectra

showing mirror-image of each other. c) Simulated surface current and electric field

distributions of the ASR and CASR, illustrating the Babinet's principle.

3. Classification of planar metallic Fano system

14

Planar metasurfaces are by far the easiest electromagnetic metamaterials to study light-

matter interactions in Fano resonant plasmonic systems due to the simplicity of the

fabrication process as compared to 3D metamaterials. In addition, due to the ease of

modifying the spectral response of the plasmon resonance, a plethora of unit cell designs

based on symmetry-broken configurations have been conceptualized to observe the Fano

resonant scattering phenomenon across a broad frequency (optical to terahertz) spectrum.

These planar Fano metamaterials can be broadly categorized into single-particle, dual-

particle or multi-particle systems based on the number of physical resonators present in a

single unit cell. In all of these systems, the contrast in the electromagnetic field

distribution among the sub-unit cells leads to the resonant coupling of the bright and dark

hybridized plasmon modes, which give rise to Fano resonance.[53] Bright mode is often

associated with the finite dipole mode of the metamaterial structure which is radiative in

nature and can interact with the far-field of the propagating electromagnetic wave in free

space. The spectrum of a bright mode is broadened due to radiative damping. Intuitively,

dark mode is non-radiative and prohibited in perfectly symmetric system. It is

represented by higher order mode that exhibit weak dipole moment and can only be

excited through near-field coupling with the radiative mode, hence making it accesible in

the spectroscopy (transmission, reflection or absorption) spectrum. Thus, Fano resonance

is also termed as "trapped-mode" resonance when first discovered in planar

metamaterials.[54] It is evident that symmetry breaking of the geometry of a unit cell,

permits the excitation of high-Q Fano resonance.

15

Single-particle

Nanodisk on its own, is one of the simplest geometrical structure that requires only one

particle in the unit cell to generate Fano resonance. The shape of the nanodisk is circular

and it possesses a 2 rotational symmetry. Therefore, to break the symmetry of the

nanodisk, a defect is introduced into the structure as a wedge which is angle controllable

(Figure 2a).[32] According to the hybridized model, the nanodisk contributes to the

broad dipole plasmon mode whereas the cut-out wedge contributes to the narrow

quadrupole plasmon mode. As a result, the spectral overlap of the two plasmon modes

lead to the effective generation of high-Q Fano resonance. Upon symmetry breaking (by

increasing the angle of the wedge), the intensity of the Fano resonance increases with a

distinct appearance of an asymmetric lineshape. However, further increasing the angle of

the wedge beyond the range of 90˚ to 105˚ weakens the resonance due to a reduction in

the edge charge density at the wedge. In addition, the radial size of the symmetry broken

nanodisks ranges from 140 to 200 nm where Fano resonance in the visible spectrum can

be easily achieved. Closely related is a distorted nanodisk, shaped in the form of an

ellipse. The elliptical disk fabricated on top of the Mylar film (membrane substrate) is

etched with double gaps along the long axis of the ellipse and separated by a rectangular

bar, whose position along the long axis determines the asymmetry of the system.[55] The

presence of the Fano resonance is illustrated clearly from the antiparallel surface currents

flowing on each side of the long axis. Further studies conducted on the properties of

membrane substrate reveal that membranes with small dielectric loss tangent and

thicknesses in the range of 10 to 50 µm are essential to achieving high-Q Fano resonance

16

at terahertz (THz) frequencies. This is attributed to a reduction in the amount of energy

dissipated through a less lossy substrate membrane, and so it interacts effectively with the

electromagnetic field, hence improving the sensitivity of THz membrane devices.

Dual-particle

Fano resonance in metamaterials was first reported in asymmetric split ring resonators

(ASRRs) in the microwave region that are composed of two arms with different

lengths.[54] Metallic resonators in the microwave region behave as almost perfect

conductors in which the main dissipative losses are attributed to absorption in substrates.

Despite of that, metallic resonators still losses energy radiatively. In ASRRs, the unit cell

is designed such that antisymmetric surface currents are excited on each arm with

unequal amplitude. The induced surface currents at the arms of each neighbouring unit

cell cancel with each other leaving only the peripheral surface currents at the edge of the

array, and the overall dipole moment is reduced greatly.[56] Furthermore, the magnetic

dipole of the excited Fano resonance does not interact with the propagating fields of the

electromagnetic wave and radiative losses to free space are significantly suppressed. An

experimentally measured high-Q of ~200 for Fano resonance has been obtained.[57] This

effect is more strongly observed in coherent arrays comprising of larger number of unit

cells, and the Q-factor of the Fano resonance can be improved.[56]

Other dual-particle unit cell systems that have been successful in their demonstrations of

high-Q Fano resonance include nanocross-bar,[33] asymmetric double bars,[58, 59, 60,

17

61, 62, 63, 64] ring-disk[31, 34] and concentric rings.[65] By employing the plasmon

hybridization model, the evolution of Fano resonance in nanocross-bar configuration was

elegantly pictured with the help of charge density distributions as depicted in Figure 2b.

For this instance, the excitation of the Fano resonance is only achievable for light

incident at grazing angle. This is because it introduces a field gradient along the surface

of the nanocross and results in a quadrupole mode (grey dot - forbidden for normal

incidence) appearing at the broad spectrum of the dipole nanocross (blue dot). As a result,

the quadrupole of the nanocross couples strongly with the dipole of the bar (black dot) to

form a hybridized mode, whose resonance mode spectrally overlaps with the broad dipole

spectrum of the bar. The destructive interference of both modes suppresses the radiative

dipole mode, hence creating a high-Q Fano resonance (green dot) at the optical

region.[33]

Thus far, the simplest asymmetric geometry model used for excitation of Fano resonance

at optical frequency is the asymmetric double bars.[58] Fano resonance originates from

the destructive interference between the bright mode of the double bars and the dark

mode of the asymmetric double bars which is indirectly excited through near-field

coupling. Electric field distributions attribute the bright mode to two in-phase dipoles

(parallel currents) that interfere constructively while the dark mode is due to destructive

interference of out-of-phase dipole oscillation (antiparallel currents).[59, 62] It was

further reported that at a certain length displacement for one of the double bar, the

plasmonic system is optimized and a high-Q Fano resonance can be obtained in the

infrared region.[59]

18

The geometrical structures reviewed so far are composed of elements whose strong field

enhancements are located near the sharp edges. Besides, circular or round geometrical

structures such as a ring-disk[29, 31, 34] or concentric rings have also been fabricated.

For a non-concentric ring-disk configuration, the inner dipole disk is either displaced

from the central position in the quadrupolar/higher order ring, or placed alongside the

ring. In a similar way to other configurations, the plasmon hybridization model provides

a visual interpretation to describe the nature of the plasmon modes. Here, Fano resonance

arises from the destructive interference between the dark quadrupolar ring plasmon mode

and bright dipole disk plasmon mode. Angle dependence of the incident light was also

performed on non-concentric ring-disk configuration which reveals the spectral shaping

of Fano resonance between asymmetric and symmetric shape, at which higher order

modes start appearing. Therefore, these higher order dark modes hybridize with the broad

continuum to form higher order Fano resonance modes. A relatively high-Q factor of 5.2

is obtained in the optical region.[29, 34] Concentric rings configuration has been

demonstrated across a wide electromagnetic spectrum which includes infrared,[65]

terahertz[66, 67] and microwave[68]. The benefit of concentric rings is that it is

independent of polarization, and so symmetry breaking is achieved without breaking the

geometry of the structure, but instead achieved through variation in the electromagnetic

field of the two rings. The difference in the circumference of the inner and outer rings

leads to induced currents which flow opposite to one another in both rings. Such current

configurations cancel each other, leaving an overall weak magnetic dipole moment which

does not scatter to the free space.[68]. Every unit cell in the metamaterial array does not

19

interact with the surrounding unit cells, hence concentric ring configuration is an

incoherent metamaterial array.[56] Further enhancement (more than 4 times) in the Q-

factor of concentric ring resonators is acheived by adding interdigitated finger pairs

between the inner and the outer rings, illustrated in Figure 2c. Such concept improves the

coupling between both rings so that the induced currents are able to cancel out more

effectively, leading to higher Q-factor.[66] An interception cut created at the minimum

electric field positions of the concentric rings allows the Fano resonance to be switched

on and off, by changing the polarization of light.[65]

Multi-particle

In multi-particle plasmonic systems, more than two sub-unit cells such as dolmen or

heptamers are used to excite Fano resonance. Although not as deeply explored as single

or dual-particle system, the multi-particle system provides more degree of freedom to

break the symmetry of a unit cell since it is composed of several sub-unit cells. Dolmen

structures[31, 69] are composed of three rectangular slabs whose arrangement is depicted

in Figure 2d. Two rectangular slabs are placed parallel to each other to form a dimer and

the third slab is placed perpendicular to them along the shorter edge of the slabs. For

polarization parallel to the symmetry axis of the dolmen, a broad dipole moment is

excited (orange dot), while a perpendicular polarization induces an overall quadrupole

charge distribution in the dimer (blue dot). The spectral overlap between the quadrupole

and dipole modes results in the appearance of a sharp asymmetric Fano lineshape in the

20

optical regime. The evolution of the Fano resonance is also shown clearly in Figure 2d by

rotating from perpendicular to parallel polarization. Multiple Fano resonances can be

induced for dolmen structures with larger dimension. On the other hand, heptamer is a

unit cell composed of seven sub-unit cells which are arranged in a hexagonal shape (6-

sided polygon). In this arrangement, heptamer has six lines of reflection, and so it

possesses a 6-fold rotational symmetry. The bonding bright mode is due to all seven

particles oscillating in-phase, while the antibonding dark mode is due to the out-of-phase

oscillation of the six outer particles with the central particle.[70] Therefore, destructive

interference between the bright and dark modes, create the Fano resonance which is

otherwise forbidden in the quasistatic nonretarded limit. Such system can be expanded to

polygon with n-sides, but dipole moments that are equal and opposite must cancel to

result in a net zero dipole moment to satisfy the criteria for strong Fano resonance.[71]

21

Figure 2. a) Calculated and simulated extinction cross-section spectra of the symmetry-

broken nanodisk with increasing angle of wedge. Middle portion shows the SEM images

of fabricated nanodisk with varying wedge size. b) Experimental extinction spectra of the

nanocross, nanocross-bar and bar structures with their simulated charge density

22

distributions in the inset. c) Simulated and measured transmission spectra of the

interdigitated concentric ring resonators that are independent of p- and s- polarization. d)

Experimental and simulated extinction spectra of the single dolmen structure. Top right

shows the measured extinction spectra by rotating from perpendicular to parallel

polarization. Bottom shows the surface charge distributions at different position of the

spectra in top left.

Across the electromagnetic spectrum, higher Q-factor is most easily achievable at longer

wavelengths, especially from the THz to microwave region due to the higher conductivity

of metals. Furthermore, among all designs materialized, split ring resonators (SRRs)

remain quintessential for developing THz metamaterials.[48, 72, 73] THz radiation spans

the region in the electromagnetic spectrum that possesses unique properties shared

between infrared radiation and microwave radiation. It is non-ionizing with low photon

energies, hence very suitable for medical imaging purposes. Besides, THz radiation is

transparent to a wide range of non-conducting materials, which allows for the detection

of explosive traces and defects in commerical products. Therefore, THz metamaterials

are especially enticing because of their ability to effectively manipulate THz wave at the

microscale level and also enhance the THz signal, which provides useful information

such as THz spectral fingerprint of biological cells or explosive materials.

Fano resonance in THz metamaterials is advantageous in THz regime and different

strategies have been proposed to fully harness the strength of Fano resonance by

widening its applicability, and also to further boost the high-Q of THz Fano

23

resonance.[55, 56] Lattices composed of two different sizes of SRRs placed in the

diagonal and anti-diagonal axis of the unit cell have shown to excite multiple Fano

resonances in a single plasmonic system at THz frequencies.[72] This is also applicable

to Fano resonators at other regimes of the electromagnetic spectrum.[63] Based on the

quantitative analysis of surface currents (Figure 3a), the Fano-like asymmetric lineshape

of trapped mode f1 and f2 correspond to the resonance mode driven in the larger SRRs

and smaller SRRs respectively. At resonance f3, it is a Fano-like lattice mode derived

from collective excitation of both SRRs at the lattice mode. The coupling of the

resonance f3 with lattice mode brings about the third sharp asymmetric lineshape which

has a high-Q double that of resonance f1 and f2.[74] Mirrored configuration of

asymmetric SRRs could also lead to an excitation of a higher-Q subradiant resonance

mode. In a super cell composed of 4 unit cells, antiparallel surface currents that flow

opposite to each other in the neighbouring SRRs lead to effective cancellation of dipole

moment and reduces the scattered field as illustrated in Figure 3b, c. A narrow full-width

at half maximum (FWHM) bandwidth of 29 GHz was obtained in the THz range, which

gives a Q-factor that is 3 times more than the non-mirrored configurations.[75] Along

with considering the orientation or positioning of the unit cells arranged in a lattice, the

geometrical aspect of the SRRs was also explored. As it has been proven, when the gap

width decreases, it results in a narrower and sharper asymmetric linewidth where the Q-

factors obtained both theoretically and experimentally are 106 and 51 (improved by a

factor of about 3 when the gap width is reduced by a factor of 2), respectively.

24

Nonetheless, the extent of decreasing the gap width still has to be within the resolution

limits of the fabrication and measurement technique.[76]

Figure 3. a) Simulated surface current distributions of resonances f1 to f4, with their

steady state currents calculated to attribute the origin of the high-Q resonances. b)

25

Measured and simulated transmission spectra of the non-mirrored and mirrored

configuration. c) Simulated surface current distributions for both configurations, with

stronger distribution in the non-mirrored configuration.

4. Applications

Fano resonance as a type of resonant scattering phenomenon is ideal for preserving

energy in the plasmonic system since self-cancellation of dipole moments caused by

antiparallel induced currents dramatically reduce the radiative losses. Consequently,

several of the proposed unit cell designs have been adopted as part of the strategies for

the realization of a wide variety of applications that can provide solutions to overcome

challenges and limitations in the current technologies. They have been developed in

passive or active control applications such as sensors, surface-enhanced infrared

absorption, lasing spaser and optical switch, which will be reviewed accordingly.

Sensing based on Fano Resonant Metamaterials

In plasmonic sensors, detection of weak signals coming from the analyte is strongly

elevated due to the presence of electromagnetic field enhancement which is supported by

surface plasmon resonance located at the interface of metal and dielectric.[77, 78]

However, another class of sensors based on Fano resonances in plasmonics has also seen

an impressive rise in the sensing community. At Fano resonance frequency, high resonant

26

field can be confined at regions of gaps or along the edges of the planar structures. Any

pertubations that are introduced into their local environment disturbs the sensitive nature

of the resonant field. This enables the slightest detection or sensing of the variations near

the vicinity of the field. As such, Fano sensors utilize the unique scattering phenomenon

of Fano resonance that possesses not only intense confinement of electromagnetic field,

but also the high Q asymmetric lineshapes that are pivotal in making sensors with better

sensitivity and selectivity.

As one of the prominent structure that was conceived in the early stage of metamaterials,

[79] SRRs have played significant role in THz sensing. For an asymmetric THz SRRs

that is equipped with a relatively high-Q of 65 for quadrupole and 28 for Fano resonances,

a superior analyte sensitivity of 5.7 × 104 nm/refractive index unit (RIU) was achieved

for Fano resonance compared to the quadrupole resonance with sensitivity of 7.75 × 103

nm/RIU.[80] Hypothetically, the higher the Q factor of the metamaterial, the longer the

photon lifetime and light-matter interactions should be greatly enhanced. Simulated

electric field distributions of the quadrupole, dipoles and Fano resonances reveal that the

tightly confined fields at the Fano resonance frequency is much stronger than the

quadrupole and dipole resonances whose electric field enhancements are spread across

four nodes at the arms and two nodes in each arm of the SRRs respectively, as shown in

Figure 4a-d. Therefore, given the high field confinement in the small spatial volume of

the capacitive split gaps, Fano resonance has the upper hand and a significantly higher

analyte thickness sensitivity as compared to the quadrupole resonance is obtained. In

addition, when the refractive index of the analyte is varied from n =1 to n = 1.6, the Fano

27

resonance shows a sensitivity of 4.23 × 104 nm/RIU while the quadrupole resonance had

a sensitivity of 5.62 × 103 nm/RIU. The results affirm Fano resonance as a good

candidate for achieving highly sensitive refractive index sensing capabilities, even at

other regimes of the electromagnetic spectrum.[33, 34, 62] It was further reported that a

thinner substrate would promote a greater sensitivity using such high-Q resonances as it

allows for a stronger interaction between the intense field and the analyte.[55, 80, 81]

With another two split gaps imposed onto the adjacent arms of the already asymmetric

SRRs, Fano resonance and quadrupole resonance can be excited simultaneously which

could be utilised for thickness sensing and also serves as a double referencing for

increasing the accuracy of the sensitivity results.[81] Recently, Y. K. Srivastava et. al

have demonstrated dual-surface sensing based on a flexible platform suggesting the

possibilities of incorporating sensor devices onto non-uniform surfaces.[82] The results

presented is consistent with the use of an ultrathin substrate for improved sensing

capabilities[55] and to increase the amount of fringing electromagnetic fields accessible

on either sides of the substrate. Compared to previous works,[80] the use of the underside

of the substrate for sensing contributes to an additional red shift of the Fano resonance

frequency by 6 GHz, which amounts to a total red shift of Fano resonance frequency by

89 GHz for a 100 nm thick germanium deposited onto a low refractive index substrate of

25 µm thickness. These results clearly demonstrate the advantages of using dual surfaces

of the substrate as the overall sensitivity of the analyte can be increased. In addition, a

thin substrate with low refractive index also shows enhancement in thin-film sensitivity

when it comes to detecting small volume of biomolecules.

28

So far, Fano sensors have been explored for its improved sensitivity towards different

refractive indices of analytes. In a more advanced senario, these sensors can be used to

differentiate between a target molecule and its group of molecules.[83, 84] Such Fano

sensors have been achieved in the mid-infrared regime, whereby a modified dolmen

structure comprised of the monomer adjoined to one slab of the dimer is used as

illustrated in Figure 4e.[69] In this system, Fano resonance is excited for electric field

polarized parallel to the dimers. When the Fano resonance is far from the vibrational

modes of the amide, it yields information about the thickness of the protein molecules

with an accuracy difference of 0.1 nm between theoretical and experimental results. If the

Fano resonance matches with the vibrational modes of the proteins, strong interaction

between the proteins and the asymmetric dolemen structure enhances the amplitude of the

vibrational modes which provides indications of the protein's secondary structure and

orientation. This is important because ascertaining the orientation or conformational state

of the protein molecules helps to find suitable biotarget for functional availability.

Complementary Fano resonant structures of coupled annular and rectangular aperture

have shown tremendous high-Q Fano resonance of 79 (simulated) and 38 (experimental),

which were excited based on whispering gallery approach in the near-infrared

frequencies.[85] The high-Q Fano resonators exhibit spectrally tunable single and

multiple Fano resonances by changing the polarization of the incident light. The

realization of such high-Q Fano resonance is a feat, and as a proof-of-concept, the Fano

resonators (with a modified geometrical structure – inclusion of multiple concentric ring

apertures) as shown in Figure 4f have demonstrated ultrasensitive detection of molecular

29

vibrational modes of poly(methyl methacrylate) (PMMA) using surface-enhanced

infrared absorption spectroscopy (SEIRA).[86] When the position of the Fano resonance

spectrally aligns with the vibrational modes of C-O-C and C-H; -CH2 and -CH3; and

C=O; spectral fingerprints that were absent in the reference spectra are precisely

identified from the amplified spectra. By using the whispering-gallery-mode-based Fano

resonators, weak signals of ultrathin PMMA (50 nm thickness) are enhanced, overcoming

the limitation imposed by the exponentially decreasing absorption as thickness decreases.

Figure 4. Simulated electric field distribution of a) quadrupole and b,c) two different

dipoles under horizontal polarization, d) Fano resonance under vertical polarization,

without and with an analyte above the asymmetric THz SRRs. Schematic diagrams of the

e) modified dolmen structure used in the identification of vibrational modes of protein

30

molecules and f) coupled annular and rectangular apertures used in the SEIRA of PMMA

(inset shows the different metasurfaces used to excite multiple Fano resonances).

Lasing spaser

Light amplification by stimulated emission of radiation (LASER), has been widely used

in optical systems for broad applications in telecommunications, health technology,

military defence, research industry and other commercial purposes. With miniaturization

of devices being a trend in the modern world, it is a challenge to fit a laser into nanoscale

devices. Bergman and Stockman first proposed the concept of surface plasmon

amplification by stimulated emission of radiation (SPASER) in 2003, which suggests that

surface plasmons can be used to confine and concentrate optical energy into dimensions

smaller than a wavelength, beating the diffraction limit of light.[87] A spaser works on

the principle similar to a laser, but with a resonant cavity made up of its nanoparticle and

emits surface plasmons. By introducing a gain medium into the spaser, self-sustaining

stimulated amplification occurs within whereby energy is transferred between the

luminescence resonance of the gain medium and the surface plasmon modes, thus

stimulating more identical surface plasmons as illustrated in Figure 5a.[88] A high-Q

resonance is preferred for its ability to sustain both phase and energy when subjected to

external electromagnetic field, in which an ideal choice would be Fano resonance. N.

Zheludev and his group proposed the combination of strong coherent planar

metastructures with a gain material to generate spatially and temporally confined

31

coherent electromagnetic radiation (Figure 5b).[89] It was theorectically demonstrated

using asymmetric SRRs which exhibits reduction of radiation losses in an infinite

periodic array.[56] Therefore, if a high-Q Fano resonance is employed with a gain

material, losses can be sufficiently overcome to the extent that the minimum condition set

by the lasing threshold of the plasmonic system can be met for lasing action to occur,

hence successfully realising a lasing spaser at nanoscale dimensions. As a first step, lead

sulphide (PbS) semiconductor quantum dots were spin coated onto asymmetric SRRs

array. The Fano resonance was designed such that it matches exactly at the luminescence

resonance of the quantum dots and strong coupling between the excitons and plasmon

modes leads to multifold enhancement of the quantum dot luminescence and spectral

narrowing of the linewidth as shown in Figure 5c,d.[64, 90] Till date, there is no

demonstration of a planar lasing spaser based on Fano resonance due to the requirement

of high pumping power which generates excessive heat losses in plasmonic

metamaterials.

32

Figure 5. a) Schematic of energy transfer between excitons of nanocrystal quantum dots

(gain medium) and surface plasmon modes of metallic nanoshell. b) Lasing spaser with

planar metastructures on a gain medium slab (green). Enhanced fluorescence intensity

spectra of PbS quantum dots on c) asymmetric double bars and d) complementary

asymmetric SRRs, when the luminescence resonance are matched to the Fano resonance

frequency. Bottom of Figure 6d shows the trade-off between intensity enhancement and

FWHM as the luminescence resonance are tuned from the Fano resonance frequency.

Optical Switch

33

One of the key strengths of Fano resonance is the sensitive nature of the intense

electromagnetic field present in the planar structures. As a result, it could be used for

purposes where external influences can be introduced to realise more functionalities of

the Fano devices. Active photoswitching of Fano resonance has been demonstrated by R.

Singh and his group using optically active medium such as solution-processed

perovskites,[91, 92] silicon,[93] germanium,[94] and MoS2[95] in asymmetric SRRs. An

ultralow fluence of <7 µJ cm-2 of the optical pump beam is required for resonant

switching behaviour in organic-inorganic lead halide perovskites as shown in Figure 6a.

Upon increasing optical excitation fluence, the metadevice manifests phonon-Fano

coupling which shows the sensitive nature of Fano resonance to detection of the phonon

modes.[92] By evaporating a single-element germanium onto the asymmetric SRRs, an

ultrafast full recovery time of 17 ps was achieved (Figure 6b), comparable to the

switching time of inductive-capactive (LC) resonance using ErAs/GaAs superlattice

structures.[96, 97] Such approach is simple and universally applicable to other

metadevices, and the results also show that Fano resonance as compared to other

resonances is more sensitive to optical switching.[94] Another approach to active

switching is via applying a voltage onto a liquid crystal to change the phase of the

medium, which alters the polarization of the incident light propagating through and

excites the symmetry-broken octamer structure to reveal the Fano resonance. Hence, the

switching on and off of the voltage indirectly excites the octamer structure with different

polarization of incident light, realizing an electrically switchable Fano switch in the

visible spectrum as shown in Figure 6c.[98] In addition, phase-transition metal oxide

34

such as VO2 undergoes an insulator-to-metal transition (IMT) at 68˚C and have shown

active switching of THz transmission in the THz band,[99] which also can be

implemented into Fano resonance system. Numerically simulated results show that

hybrid VO2/Au asymmetric double bars induces a relatively high-Q Fano resonance when

the dipole resonance that arises from VO2 bar in its metallic state interferes with the

dipole resonance of Au bar. In its insulator phase, Fano resonance disappears and a dipole

resonance solely contributed by the Au bar appears around 0.95 THz.[100]

35

Figure 6. a) Low power dependence THz transmission spectrum of organic-inorganic

lead halide perovskites for resonant switching behaviour. b) Measured THz transmission

spectra under various time delays, with a complete recovery of 17 ps. Bottom to figure

illustrates the color map of the whole ultrafast switching behaviour. c) A plasmonic Fano

switch whose Fano resonance is actively modulated via voltage control under different

polarization.

For other active control applications, patterned graphene of SRRs has also been

considered in THz metamaterials. Graphene is a material with rich optical and electronic

properties which has shown great prospects due to its wide operating spectral range and

its role for active control in optoelectronic devices.[101] Graphene has a high electron

mobility and its electrical properties are easily tunable by modifying the Fermi level

relative to the Dirac points through introducing external stimuli such as electric or

magnetic field, and chemical doping.[102] Patterned graphene of symmetric SRRs were

theoretically investigated for possible applications such as sensing and slow light devices.

The results show that as the Fermi level increases, carrier concentration also increases

which transits graphene from a semi-metallic into a metallic state, and so increases

reflection and decreases transmission of the incident terahertz radiation.[73] In a similar

work, for an asymmetric SRRs, when the Fermi level increases, the plasmonic system

recognises an asymmetric environment caused by the metallic-state resonators, and hence

the Fano resonance (polarization of electric field perpendicular to the gap) or quadrupole

resonance (polarization of electric field parallel to the gap) is excited. The sensitivity of

the graphene-based SRRs also performs better than metallic SRRs when there is a

36

variation of refractive index or thickness of analyte.[80] For both resonances excited, the

effective group index is at least 30 times larger than a metal plasmonic system, promising

as a potential candidate for slow light applications.[73] In the infrared regime, by

combining single-layer graphene (SLG) with high-Q Fano metasurfaces made up of an

array of wire and SRR structures, two Fano resonances with a reflectivity dips were

observed in the spectrum. An electrostatic potential applied between the SLG and Si

backgate controls the free carrier density in graphene which can potentially blue-shift the

Fano resonance spectrum with increasing Fermi energy. Similar observation was seen in

another numerical study of a hybrid graphene disk and metallic ring system which has

been proposed to realise tunable terahertz sensor.[103] Overall, the change in the free

carrier density results in a modulation depth of about 10 dB, thus achieving an

electrically controlled IR modulator.[104] However, dissipation losses remain a cause for

concern even if graphene is to replace metals in metamaterials.[105]

5. Perspectives to Loss-Engineering

Superconductors as resonator material

In the THz regime, non-radiative losses are reduced due to the higher conductivity of

metals, making radiative losses as the dominant loss mechanism. Therefore, Fano

resonance provides a means of reducing the losses contributed by radiation to free space.

However, to push beyond the limits of reducing non-radiative losses in planar

metastructures, superconductors as an alternative to metal permits the existence of Fano

37

resonance beyond a critical point of asymmetry parameter with an even higher Q-

factor.[106] As shown in Figure 7a, the linewidth of superconducting Fano resonators is

narrower than metallic Fano resonators. A high Q-factor of 167 was obtained using

YBCO-THz ASRRs, which is about two times the Q-factor (84) obtained using Al-THz

asymmetric SRRs. In fact, if a material such as perfect electric conductor (PEC) with zero

resistivity could exist, the ohmic losses will undoubtedly disappear, and a higher Q-factor

can be obtained as compared to metal or superconductor, as depicted in Figure 7b. This

suggests that for an entirely hypothetical material, the maximum value of attainable Q-

factor for Fano resonance is purely restricted by radiative losses.[107] Nevertheless, the

use of superconductors is a more practical solution and would suffice for accessing the

high Q-factor Fano resonance at low asymmetry regimes.

Unfortunately, superconductors are only accessible at the terahertz or lower frequency

regime because at higher frequencies, the incident photon could break the binding energy

of Cooper pairs in superconductors, hence disabling the superconductivity

properties.[108] As a consequence, there have to be other alternatives to further increase

the Q-factor of Fano resonance. We look at possible alternatives to reduce radiative

losses in planar metallic metamaterials.

Manipulating configuration

Realistically, metals are still the preferred choice of material for exciting Fano resonance

in metamaterials as superconductivity only works under low temperature condition.

38

Therefore, alternative solution to enhance the Q-factor of Fano resonance has to be

established. An approach would be to manipulate the configuration of unit cells in the

metamaterial array to mitigate radiative losses. It was reported that by alternating[109] or

inverting[110] an asymmetric dipole bars (which constitute to one of two sub-unit cells)

and placing it adjacent to neighbouring asymmetric dipole bars, an enhancement in the

Q-factor of Fano resonance can be achieved. Based on the schematic of dipole-dipole

interference, an enhancement in the Q-factor of Fano resonance in an alternating unit cell

configuration was ascribed to destructive interference of dipole moments contributed by

neighbouring sub-unit cells as illustrated in Figure 7c. As a result, the net dipole moment

of the alternating unit cell configuration is smaller than the non-alternating unit cell

configuration. Therefore, the radiative loss in an alternating unit cell configuration is

much lower which establishes a higher Q-factor.[109] Quantitative analysis of

complementary asymmetric double bars using multipole decomposition reveals that the

linewidth narrowing of resonance in an inverted unit cell configurations is due to the

competition between magnetic quadrupole and toroidol dipole. In this case, the magnetic

quadrupole serves to narrow the resonance linewidth, while the toroidal dipole broadens

the resonance linewidth.[110]

Toroidal dipole has been actively studied using planar asymmetric SRRs, whereby two

asymmetric SRRs that individually produces Fano resonance are placed in a mirroring

configuration.[111, 112, 113, 114, 115] Each Fano resonance in an asymmetric SRRs has

a magnetic dipole moment that points perpendicular to the plane of the metasurface. In a

mirrored configuration, the anti-parallel magnetic dipole moments of both asymmetric

39

SRRs form a head-to-tail alignment, hence introducing a magnetic toroidal dipole into the

Fano system (Figure 7d). A comparison between the toroidal and Fano resonances shows

that a higher Q-factor can be obtained in a mirroring configuration of asymmetric SRRs.

In this instance, multipole analysis further affirms that the narrow linewidth and

enhanced Q-factor in the planar metamaterial system is attributed to the newly generated

toroidal dipole resonance.[113, 114] Toroidal resonance boasts a stronger localization of

electromagnetic fields and lesser radiative loss as compared to Fano resonance. Thus, it

has already shown substantial promises in future applications such as sensor,[116]

photoswitch[117] and lasing[118] devices.

Dielectrics as resonator material

All-dielectric planar Fano structures represent a highly feasible and efficient way of

reducing both radiative and non-radiative losses. In particular, low-loss and high

refractive index dielectric materials can address the problems of non-radiative losses

faced in most metallic planar metamaterials as absorption in metallic systems is

unavoidable. The huge dissipation loss is inherent in metals,[119] especially at visible

and infrared regimes.[120] Fano resonance in all-dielectrics have been demonstrated in

asymmetric double bars,[121, 122] oligomers,[123] dolmen structures,[124] and coupled

rectangular and ring resonators.[125] Furthermore, the suppression of radiative losses is

also reliant on the collective and coherent oscillations of the resonators in the array.[125,

126] In contrast, electromagnetic fields are concentrated within the dielectric

40

nanostructures, whereas in plasmonic nanostructures the separation between the

resonators reduces the localized field confinement at the gaps, which suggests that

dielectric metamaterials are insensitive to geometrical imperfections in the unit cell.[122]

All-dielectrics offer other advantages over plasmonic metamaterials such as lower ohmic

losses, robustness in the position of the Fano resonance frequency (Figure 7e),[123] and

larger damage threshold for nonlinear effects. [127] Using Si-based metasurfaces, EIT

effects with high Q-factor of 483 has been realized for refractive index sensing, hence

achieving a high figure-of-merit of 103.[125] Fano resonance in chiral Si metasurfaces

(Q > 100) has achieved high (50%) linear-to-circular polarization conversion efficiency

and shown great potential in spectroscopic characterization of single-layer graphene or

protein monolayers (with at least 40% transmission change) without the need of highly

focused infrared light source. [124] An array of coupled rectangular and nanodisk

resonators with a high Q-factor of 466 has demonstrated third harmonic generation

(THG) enhancement of at least 105 owing to the good modal overlap with Si medium,

hence achieving a conversion efficiency of 10-6 using a peak pump intensity of 3.2 GW

cm-2 (Figure 7f).[127] Recently, a record high Q-factor of 1011 has enabled

photoluminscence enhancement of 103 at the peak MM1 position in an asymmetric air hole

configuration that is composed of semicircle and semiellipse, embedded with germanium

(Ge) quantum dots (Figure 7g).[128] All-dielectrics is a feasible replacement to the

plasmonics counterpart as it offers low-loss high-Q Fano resonances, that can be realized

for similar metamaterials-based applications. To summarize the perspectives to loss-

41

engineering, we have put together in Table 1 which details the advantageous and

disadvantages of the loss-engineering schemes.

Table 1. Advantageous and disadvantageous of different loss-engineering schemes to

achieve high-Q Fano resonance.

Loss-Engineering

Schemes Advantages Disadvantages

Superconductor

Enhan

ces

Q-f

acto

r ef

fect

ivel

y

• Reduces non-radiative

losses (ohmic losses).

• Accessible only at THz or

lower frequencies.

• Low temperature condition is

required.

Manipulating

configuration

(Metallic)

• Mitigates radiative losses.

• Strong field enhancement.

• Approach is relevant to entire

electromagnetic spectrum.

• Dissipative losses at visible

and infrared frequencies is

still present.

• Thermal heating effect.

All-dielectrics

• Suppresses both radiative

and non-radiative losses

(ohmic losses).

• Insensitive to geometrical

imperfections in the unit

cell.

• High optical damage

threshold for nonlinear

effects.

42

Figure 7. a) Simulated and measured transmission spectra showing comparison between

metallic and superconducting Fano resonators. b) Calculated Q-factor of PEC,

superconductor and metal. c) Scheme of dipole-dipole interference, where situations of

constructive and destructive interferences are presented. The electric fields of the

alternately (alt)-flipped configuration shows more cancellation as compared to the non

(N)-flipped configuration, which results in a smaller net dipole moment and a higher Q-

43

factor. d) Illustration of the Fano and Toroid configurations with their surface currents

inducing magnetic dipole moments that does not couple in the Fano configuration but

couple in a head-to-tail configuration (Toroid). A higher Q-factor is seen in the Toroid

configuration as compared to the Fano configuration. e) Simulated scattering cross-

section of all-dielectric (Si) oligomers and metallic (Au) oligomers, in which the Fano

resonance continues to persist despite widening the separation between the particles. (f)

Simulated electric field strength of the all-dielectric (Si) Fano resonators and the THG

intensity spectra of metasurface or unpatterned bare Si film on the bare quartz substrate.

(g) Measured transmission (dark cyan) and photoluminescence spectra of the metasurface

embedded with Ge quantum dots at 295K (blue) and 5K (magenta).

Future outlook and conclusion

In summary, we have reviewed an extensive but not exhaustive list of unit cell designs

that are suitable for lineshape engineering of Fano resonance. Fano resonance in planar

metallic structures provide an effective approach to mitigate radiative losses. Fano

resonance possesses a sharp asymmetric lineshape and an intense electromagnetic field

confinement exists at the resonance frequency. With these two distinct characteristics,

Fano resonance has caught a significant amount of attention in the metamaterial

community and enabled metadevices with remarkable functionalities to be developed.

However, non-radiative losses such as ohmic and absorption losses continue to hinder

practical applications of plasmonic metamaterials. Superconductors may be a good

44

alternative but its operating condition exists only at low temperature which makes it not

as feasible for facile applications. As the innovations in plasmonic metamaterials

continue to be explored, exploiting low-loss, high-refractive index dielectric materials is

the next viable option to consider reducing non-radiative losses. Indeed, several

applications similar to plasmonic counterparts can be realized using all-dielectrics.[53,

129] Without doubt, high-Q Fano resonance promises wide applicability in

miniaturization of a variety of optoelectronics devices including sensors, photoswitch,

and active control devices. Thus, it is not surprising to envision that Fano resonance-

based metadevices could be at the forefront of modern technologies and devices.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgement

This work is supported by research grants from Singapore Ministry of Education No.

MOE2016-T3-1-006(S) and MOE2015-T2-2-103.

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff))

Published online: ((will be filled in by the editorial staff))

45

46

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