[INVITED] Coherent perfect absorption of electromagnetic wave in subwavelength structures

Optics and Laser Technology 101 (2018) 499–506

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Coherent perfect absorption of electromagnetic wave in subwavelength structures Chao Yan a,b, Mingbo Pu a,b, Jun Luo a, Yijia Huang a,b, Xiong Li a,b, Xiaoliang Ma a,b, Xiangang Luo a,b,⇑ a State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, P.O. Box 350, Chengdu 610209, PR China b University of Chinese Academy of Sciences, Beijing 100049, PR China

a r t i c l e

i n f o

Article history: Received 19 October 2017 Received in revised form 28 November 2017 Accepted 6 December 2017

a b s t r a c t Electromagnetic (EM) absorption is a common process by which the EM energy is transformed into other kinds of energy in the absorber, for example heat. Perfect absorption of EM with structures at subwavelength scale is important for many practical applications, such as stealth technology, thermal control and sensing. Coherent perfect absorption arises from the interplay of interference and absorption, which can be interpreted as a time-reversed process of lasing or EM emitting. It provides a promising way for complete absorption in both nanophotonics and electromagnetics. In this review, we discuss basic principles and properties of a coherent perfect absorber (CPA). Various subwavelength structures including thin films, metamaterials and waveguide-based structures to realize CPAs are compared. We also discuss the potential applications of CPAs. Ó 2017 Published by Elsevier Ltd.

1. Introduction Perfect absorption of light is of great importance in a variety of applications ranging from sensing to stealth technologies [1–6]. Achieving perfect absorption at subwavelength scale is particularly important for nanophotonic and electromagnetic applications. In recent years, various approaches of designing ultrathin perfect absorbers have been proposed, including thin films, metamaterials and metasurfaces [7–13]. In a common absorber, the incident energy is delivered to the systems via a single channel, for instance by a plane wave illuminated on one side of the absorber. However, it was found that the incident energy could be perfectly absorbed under incidence on opposite sides of an absorber [14–18]. This interference-assisted absorption is known as ‘‘coherent perfect absorption”, and was experimentally demonstrated in a silicon slab under coherent monochromatic illumination [14,15]. In a coherent perfect absorber (CPA), two counterpropagating input beams of identical amplitudes and phases interfere destructively outside a cavity and dissipate their energy completely by interacting with the intra-cavity losses of the absorber, resulting in perfect absorption. Such a CPA provides a new way for the control of electromagnetic absorption.

In this review, we first discuss the concept and the theoretical basis of a CPA. Then, we outline various subwavelength structures used for coherent perfect absorption. These structures includes thin films, metamaterials and waveguides-based structures. Lastly, we discuss the properties of CPAs and their promising applications in all-optical data processing and photocurrent enhancement, etc. The concept of coherent perfect absorption can also be extended to other contexts apart from classical optics, such as acoustics [19–21], plasmonics [22], and quantum optics [23]. 2. Theoretical analysis Fig. 1(a) shows a typical planar CPA structure. Two coherent beams normally illuminate from two opposite sides. An input beam (A1 or A2 ) of this two-port system is partially transmitted and partially reflected, while an output beam (B1 or B2 ) consists of reflected and transmitted components. To analyze this system, one can solve the Maxwell’s equations by using scattering matrix (S matrix) [24]. In general, the relationship between input and output can be described by




B1 B2

⇑ Corresponding author at: State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, P.O. Box 350, Chengdu 610209, PR China. E-mail address: [email protected] (X. Luo). https://doi.org/10.1016/j.optlastec.2017.12.004 0030-3992/Ó 2017 Published by Elsevier Ltd.




¼S

A1 A2




¼

r11

t 12

t21

r 22




A1 A2

 ;

ð1Þ

where r ij and tij are the reflection and transmission coefficients of an input beam (A1 or A2 ), respectively. The scattering matrix S depends on operating wavelength, geometry of the structure and material properties. For simplicity, we consider a two-port structure which

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Fig. 1. Concept of coherent perfect absorption. (a) Sketch of a coherent perfect absorber. A1 and A2 represent the amplitudes of the input waves, while B1 and B2 represent the amplitudes of the output waves. The output beams consist of reflected and transmitted components. The thickness of the slab is d and refractive index is n. When d and n are properly designed, the output waves can destructively interfere on each side, resulting in perfect absorption. (b) Refractive index of doped silicon described by Drude model and the absorption curves for different thicknesses. The two absorption regions are highlighted as Zone I and Zone II. The theoretical refractive indexes are calculated using Eqs. (11) and (13) for 5THz and 27THz, respectively [17].

is symmetric under a mirror reflection, i.e., r 12 ¼ r 21 ¼ r. If the system is in steady-state and linear regime and exclusive of magneto-optically gyrotropic medium, S matrix will be constrained by optical reciprocity [25,26], which suggests that S is symmetric. For the two-port cases, this constraint implies that t 12 ¼ t 21 ¼ t. In the following part, we will discuss coherent perfect absorption on the basis of optical reciprocity. Thus, the relationship between input and output beams can be written as




B1






¼S

B2

A1 A2






¼

r

t

t

r




A1 A2

 ;

ð2Þ

The reflection and transmission coefficients can be described by [17]

r¼

t¼

ðn2  1Þð1 þ ei2nkd Þ ðn þ 1Þ2  ðn  1Þ2 ei2nkd 4neinkd 2

ðn þ 1Þ  ðn  1Þ2 ei2nkd

;

ð3Þ

;

ð4Þ

where k ¼ x=c, d is the thickness of the slab, and n ¼ n0 þ in is the complex refractive index. Coherent perfect absorption occurs when output wave components vanish (B1 ¼ B2 ¼ 0) and corresponding inputs are so-called CPA eigenmodes. Due to the mirror symmetry of the system, coherent perfect absorption can only be achieved for symmetrical inputs (A1 ¼ A2 , r þ t ¼ 0) or anti-symmetrical inputs (A1 ¼ A2 , r  t ¼ 0). In both cases, the magnitude of reflection and transmission are equal, indicating that a CPA can act as a beam splitter when illuminated by a single beam. Using Eqs. (3) and (4), the CPA condition for normal incidence can be obtained 00

n1 : expðinkdÞ ¼  nþ1

ð5Þ

Note that n should be replaced by the impedance Z for materials with magnetic response [27]. The  sign corresponds to the symmetrical or anti-symmetrical inputs. An infinite number of discrete solutions of Eq. (5) has been obtained for kd  1 [14]. The reflection and transmission coefficients for a single input beam can be written as



Apparently, a phase shift of p is added to the reflection wave for both symmetrical and anti-symmetrical CPAs. However, the phase shifts introduced by transmission for these two conditions are distinctive, i.e., either 0 or p. Thus, for two coherent input beams meeting the CPA condition, the transmitted wave of one beam and the reflected wave of the other beam will interfere destructively, resulting in total absorption of incident energy. An important case of the above-mentioned two-port system is a film structure much thinner than the operating wavelength (d  k, jnkdj  1), such as a dielectric or a metal film. In this case, the left and right side of Eq. (5) can be approximated as 1 þ inkd and ð1  2=nÞ. Since jnkdj  1, only plus sign term in the right side should be selected. The real and imaginary parts of the refractive index (n0 and n00 ) in Eq. (5) are approximately equal as

1 n0  n00  pffiffiffiffiffiffi ¼ kd

rffiffiffiffiffiffiffi c : xd

ð8Þ

where c is the speed of light in vacuum. Thus jnkdj  1 becomes pffiffiffiffiffiffiffiffiffi 2kd  1 and the corresponding refractive index should be much larger than unit (jnj  1). Compared with the general CPA condition described by Eq. (5), the CPA condition for ultrathin film is clearer. Specifically, we can discuss the CPA condition for ultrathin film using metals or certain semiconductors (such as doped silicon) materials. Over a broad frequency range, the complex dielectric function can be explained by Drude model [28]

n2 ¼ e1 þ ie2 ¼ e1 

e1 ¼ e1 

x2p ; xðx þ iCÞ

x2p s2 x2p s2 ; e2 ¼ : 2 2 1þx s xð1 þ x2 s2 Þ

ð9Þ

ð10Þ

where e1 is the dielectric constant, C ¼ 1=s is collision frequency, and xp is the plasma frequency. In the very low frequency range, where x  s1 , hence e1  e2 , and the real and imaginary parts of the refractive index are of comparable magnitude with

sffiffiffiffiffiffiffiffiffi

rffiffiffiffiffi

e2

n0  n00 

2

¼

sx2p : 2x

ð11Þ

 1 n 1 rs ¼  ; 2 n2 þ 1

ð6Þ

Inserting Eq. (11) into Eq. (8), the thickness for CPA at this frequency range can be written as

  1 n2  1 : 2 2 n þ1

ð7Þ

dw 

ts ¼ 

2

2c

x2p s

:

ð12Þ

C. Yan et al. / Optics and Laser Technology 101 (2018) 499–506

This characteristic length is so-called Wolterdorff thickness [29]. It quantifies the thickness of a metallic film with maximum absorption for incoherent input in the low frequency range. When the working frequency increases (x  xp ), the absorption at Wolterdorff thickness decrease. However, the absorption can still be nearly perfect by adjusting the thickness. Setting e1 in Eq. (10) to be zero, the real and imaginary parts of the refractive index becomes

rffiffiffiffiffiffiffiffiffiffi

rffiffiffiffiffi n0 ¼ n00 ¼

e2 2

¼

e1

2xs

:

ð13Þ

By combing Eq. (13) with Eq. (8), a second characteristic length called Plasmon thickness can be obtained

dp 

2cs

e1

:

ð14Þ

It should be noted that Eq. (13) is only suitable for frequency at qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 x2p e1 1  s . When xp s ¼ e1 , the Plasmon thickness is equal to the Woltersdorff thickness. Fig. 1(b) shows that the calculated Woltersdorff thickness and Plasmon thickness (150 nm and 450 nm) are in good agreement with the theoretical values (151 nm and 416 nm). Generally, the two characteristic lengths depart from each other due to their different dependences on scattering time. Both of them are in subwavelength scale according to the approximation made in Eq. (8). For a two-port CPA structure, we can define the absorbance [30] as

A1

jB1 j2 þ jB2 j2 jA1 j2 þ jA2 j2

;

ð15Þ

Absorbance of a CPA is highly dependent on the illumination conditions, particularly on the relative phase between the input beams. For a two-port CPA whose thickness is subwavelength, the absorbance can be specifically described using the impedance. For the coherent illumination, all scattered signals are considered as reflection [31]. The corresponding reflectance under normal incidence in free space is

R ¼ j1  ð0:5Z 0 =Rs Þj2 =j1 þ ð0:5Z 0 =Rs Þj2 ;

ð16Þ

where Z 0 is the vacuum impedance, Rs ¼ 1=rd is the film resistance. Thus the absorbance is calculated to be 1  R. The coherent perfect absorption can also be explained as a timereversed process of a laser [14]. According to semiclassical laser theory, the first lasing mode is an eigenvector of S matrix with an infinite eigenvalue. This means that lasing occurs when poles (points at which an eigenvalue of S diverges) of the S matrix move upward to the real axis by adding gains (n00 < 0) [32]. In contrast, a time-reversed process can arise when a specific degree of dissipation is added to the resonator. In this case, the positive imaginary part of the refractive index (n00 > 0) equals in absolute value to that at the lasing threshold. When the system is illuminated coherently by the time reverse of the output of a laser, the coherent perfect absorption occurs. 3. Structures 3.1. Thin films Thin films or slabs are the simplest structures to realize coherent perfect absorption [14,33]. It was demonstrated that a CPA operated at microwave frequencies can be realized using a singlelayer ultrathin conductive film [31]. The CPA experiment was implemented in free space and the complete absorption is nearly frequency-independent, with a relative bandwidth 100%

501

(Fig. 2(a)). If the distances of the sample to the two antennas are nonzero, the absorption approaches zero when the relative phase difference of the two incident beams is p (Fig. 2(a) inset). A thin film CPA can also be realized using a dielectric slab, such as a heavily-doped silicon film [17]. Mach–Zehnder geometry was used to obtain relative phase of input beams. The phase difference between the two arms in air can be denoted as Du ¼ kDl, where Dl is the path difference between the two arms. The absorbance of doped silicon film can be adjusted from unit to near zero at 2.5 THz when Dl increases from 0 to 60 lm (Fig. 2(b)). It was numerically shown that total absorption can be realized using a photonic crystal slab coated with a monolayer graphene [34,35]. The photonic crystal consists of a square lattice of air holes in a high index dielectric. When the leakage rate of a mode out of the slab is equal to the absorption rate of that mode in the graphene, the system is critically coupled, resulting in the complete absorption of the incident beams. This phenomenon is so-called degenerate critical coupling [34,35]. Such a resonant two port mirror-symmetric system supports degenerate resonances with opposite symmetry at a certain frequency (Fig. 2(c)). The absorption under this condition is insensitive to the intensity and the phase difference of the input beams, which is distinct from the structure discussed above. It should be noted that the graphene layer could be modeled as other structure, for instance, a conductive film with complex conductivity [35]. Among various absorbing materials, graphene is usually used to realize CPAs operating at terahertz frequencies [36–38]. A monolayer graphene can be exploited to realize a terahertz CPA with the assistance of suitable phase modulation between two incident beams at the quasi-CPA frequencies [36]. Such a graphene-based CPA holds broadband angular selectivity and the absorbance can be tuned substantially by varying the carrier concentration through chemical doping. Moreover, it was experimentally demonstrated that a graphene-based CPA can operate over the microwave X-band (7–13 GHz) [39]. The absorbance of the unpatterned graphene monolayer is observed to be greater than 94% over the working band (Fig. 2(d)). Besides, graphene-based CPA can be realized in optical frequencies [40–42]. A 30-layer graphene film sandwiched between silica substrates can modulate the absorption between 90% and 10% at 532 nm [41]. Such multilayer graphene may exhibit the remarkable property of a phase-controllable nonlinearity [42]. Several other thin film CPAs have been theoretically or experimentally investigated, including silicon wafer [15], composite metal–dielectric film [43], and single-layer silicon enclosed by dispersive mirrors [44].

3.2. Metamaterials Metamaterials are novel artificial materials engineered by placing a set of subwavelength scatterers or apertures in a regular array throughout a region of space to achieve unique properties that are not normally found in nature [45]. The combination of coherence and metamaterials may provide more freedom for absorption control, and have attracted considerable interest in realization of CPAs [27,46–53]. It was numerically demonstrated that coherent perfect absorption can be achieved by an ultrathin metamaterial film with metal–insulator–metal (MIM) structure through coherently induced plasmon hybridization (Fig. 3(a)) [27]. Single resonance mode will split into symmetrical and anti-symmetrical modes due to plasmon hybridization [54] in the MIM structure. The antsymmetrical absorption is almost independent of polarization and angle of incident light [27]. As the two-dimensional version of metamaterials, metasurfaces can also be used to realize CPAs. A lossy plasmonic metasurface

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Fig. 2. Coherent perfect absorption in thin films. (a) Coherent absorption of an ultrathin conductive film. The measured (open symbols) and calculated (dash lines) results in free space for the cases of L ¼ 0 and L ¼ 14:5 mm (inset), where L represents the difference in the distance of the film to the two horn antennas. The sheet resistance of the sample is 180 X [31]. (b) Coherent absorption of 150 nm thick doped silicon. The path difference between the two arms in Mach-Zehnder geometry varies from 0 to 60 µm. The symmetrical and anti-symmetrical absorption curves are near unit and zero, respectively [17]. (c) Coupled mode theory analysis of enhanced absorption in a photonic crystal slab supporting two resonances with opposite symmetry. The inset displays resonator system consisting of a graphene layer (gray, not to scale) placed on top of a photonic crystal slab (light blue) [34]. (d) The measured (symbols) and calculated (line) coherent absorption of the graphene monolayer with sheet resistance 310 X. The inset shows the optical photo of the graphene monolayer supported by PET substrate [39]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

consisting of asymmetric split ring plasmonic resonators milled through a 50-nm gold film can serve as a CPA at 1550.5 nm, exhibiting single-beam absorption of 50.18% (Fig. 3(b)) [47]. It should be noted that a two-port system aforementioned can function as a CPA if single-beam absorption reaches 50%. The CPA can achieve phase-controlled total absorption between 0.38% and 99.99%. One can modulate the intensity of signal beam via manipulating the phase or intensity of control beam. In this way, the total output intensity can be modulated between levels of 99.62% and 0.01% [47]. Such type of metasurface can also realize ultrafast alloptical switching [51]. The design flexibility of metamaterials provides more opportunities to achieve coherent perfect absorption. Other metamaterial CPAs include a dipole-like metasurface for polarizationindependent performance [48], an all-dielectric fishnet design [50], a bilayer asymmetrically split ring structure for multi-band operation [52] and so on (Fig. 3(c) and (d)).

absorbance so that the combined working bands cover 0.3–0.6 GHz. The theoretical absorbance was calculated using equation [39]

3.3. Waveguide-based structures

3.4. Other structures

Another route to the realization of CPAs is to employ waveguidebased systems, such as metal rectangular waveguides or plasmonic waveguides [55–58]. We recently demonstrate nearly perfect absorption of EM waves using polyimide films in a waveguide system within the microwave UHF-band (0.3–0.6 GHz) (Fig. 4(a)). Two pairs of coax-to-waveguide adapters were used to measure the

CPAs can be realized in other planar structures, like a diffraction grating [59,60]. Two beams are incident on the same side of the silver grating with different incident angles. The silver thin-film grating perfectly absorbs multiple coherent beams under plasmonic resonance. The state of perfect absorption can be switched to a state of nearly perfect scattering by adjusting the relative

A¼4

ðZ 0 =2Þ= cos h0 Rs


2 ðZ 0 =2Þ= cos h0 1þ ; Rs

ð17Þ

where cos h0 ¼ b=k0 , k0 is the wavenumber in vacuum, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 b ¼ k0  ðp=aÞ2 and a is the dimension of the waveguide. An ultra-compact CPA embedded in a plasmonic MIM waveguide was proposed to work in near-infrared band (Fig. 4(b)) [57]. The MIM waveguide with a subwavelength thick dielectric core can forbid the propagation of the photonic modes. The CPA element is composed of two parallel metal strips. When the two strips are close enough, the resonant modes are separated in frequency domain into electric-dipole and magnetic-dipole resonance, respectively. Such structure can perfectly absorb symmetrically incident modes at the resonance frequency of magnetic-dipole resonance.

C. Yan et al. / Optics and Laser Technology 101 (2018) 499–506

503

Fig. 3. Coherent perfect absorption in metamaterials. (a) A metamaterial-based CPA composed of a metal-insulator-metal (MIM) structure. Coherent absorption in the infrared frequency for different phase shifts was evaluated. Such structure can also realize perfect absorption in the microwave frequency [27]. (b) Dispersion of the output intensity modulation contrast (red line) and traveling wave absorption (blue line) of a plasmonic metasurface CPA. The inset depicts the unit cell geometry of the metasurface [47]. (c) An all-dielectric fishnet design, accompanied by coherent absorptivity as a function of frequency and phase modulation [50]. (d) Absorption spectra of the bilayer split ring metamaterials for both x-polarized single beam illumination and two coherent beams case. The inset depicts the unit cell of metamaterials [52]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Coherent perfect absorption in waveguides. (a) Schematic illustration of experimental setup realizing coherent perfect absorption in a waveguide system, accompanied by the measured (red lines) and calculated (blue lines) absorbance of the polyimide film with sheet resistance 200 X. (b) A proposed CPA embedded in an MIM plasmonic waveguide, accompanied by the magnetic field distribution for symmetrically incident waves. Two parallel metal strips absorb input beams via magnetic dipole resonance [57]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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phase of the input beams [60]. Such a CPA can be interpreted as the time-reverse of a spaser [60,61]. Apart from planar structures, CPAs could be possibly achieved in 2D and 3D structures, such as spheres or rods in free space [62,63]. In the case of sphere, the CPA eigenmodes are spherical waves. It was predicted that a metallic nanosphere with radius much shorter than the free-space wavelength can perfectly absorb coherent light by matching the frequency and field pattern of the incident wave to that of a localized surface plasmon resonance [62]. Besides, coherent perfect absorption of a two-layer spherical medium has also been investigated [64]. Parity- and time-reversal (PT) symmetric systems [65–67] can also be used to realize CPAs. In optical systems, PT-symmetry demands that the real part of the refractive index should be an even function of position, whereas the imaginary part should be odd [66]. Recently, it was shown that a PT-symmetric structure can act as a CPA and a laser simultaneously [64,65]. Such PT-symmetric laserabsorbers can also be realized using optical waveguides [68].

4. Discussion and conclusions For a CPA, we can define the bandwidth as the frequency range over which it exhibits nearly perfect absorption. For a two-port system shown in Fig. 1(a), it can be characterized by Df  c=ð2ndÞ [17]. The CPAs based on standard high Q cavities [14,69] are narrow-band devices which might be useful for several applications including sensors, modulators or optical switches [70,71]. Another approach to realizing narrow-band CPA is to utilize photonic crystal cavity system to achieve asymmetric Fano resonance [72,73]. The bandwidth of the designed CPA is about one hundredth of the working frequency [72]. The CPA bandwidth can be broadened utilizing thin films where d ! 0, which has been theoretically given in [17]. It was recently experimentally demonstrated that coherent perfect absorption could be observed realized in microwave ranging from 6 to 18 GHz [31]. Besides the thin film approach, other methods have been proposed to increase the CPA bandwidth. For example, one design employs epsilon-near-zero (ENZ) materials with permittivity close to zero [74]. Following the boundary condition, the normal component of electric filed can become very large in the ENZ films, which results in strong absorption. Another method utilizes white light cavities. The designed CPA consists of an absorbing layer enclosed by two white-light cavities [75] and achieves coherent absorption over a bandwidth of 40 nm [76]. In addition, octave-spanning ( 800–1600 nm) CPA has been realized using thin aperiodic dielectric mirrors [77]. Aside from the bandwidth properties, the polarization effects of a CPA should also be discussed. Generally, many CPAs are polarization insensitive or respond at a fixed linear polarization. However, certain CPA structures may have unusual polarization features. For instance, coherent perfect absorption of circularly polarized beams in isotropic chiral slab is polarization selective [78]. By controlling the relative phases of the two input beams, the absorbance for clockwise and counterclockwise circular polarization can be different [78]. In contrast, the output intensities are equal for each circular polarization in non-chiral cases. Such chiral CPAs can be used to perform coherent polarization control and have potential applications in imaging, polarimetry and spectroscopy [78,79]. Moreover, a CPA-like structure under coherent illumination can generate polarization standing waves [53]. In contrast with conventional energy standing waves, polarization standing waves have constant electric and magnetic energy densities and a periodically modifying polarization state along optical axis. Coherent absorption in an anisotropic sample is strongly dependent on sample’s orientation and is independent of sample’s axial position.

This performance is in strong contrast to absorption of thin film in a conventional energy standing wave, which unvaryingly depends on the sample’s axial position with respect to the nodes and antinodes of the standing wave [53]. The range of incident angles over which a CPA remains nearly perfect absorption should be considered especially when incident light is not plane wave. A device consisting of a negative refraction slab with nanoparticles placed inside it can absorb all energy from two coherent point sources [18]. In addition, a transversely homogeneous multilayer slab can be designed to implement a desired nonlocal response [80]. This structure operates as an omnidirectional CPA which is capable of perfectly absorbing waves illuminated from both sides by two coherent point sources. Coherent absorption effects may be useful in various applications, ranging from photocurrent enhancement to optical data processing [26]. For many photoelectrochemical systems, the enhancement of light absorption is the key to improving efficiency. In a photoelectrochemical system such as a highly-scattering dyesensitized solar cell [81], the light absorption can be controlled using the effects of coherent absorption. The photocurrent can be enhanced or suppressed by tailoring the wave front of an incident beam. The experimental results show the maximal output electrical power can be enhanced by 4.7 times or reduced by 5.7 times [81]. CPAs based on metasurface can also be used to control the nonresonant photoluminescence emission intensity. This can be achieved in an ensemble of dye molecules coupled to a periodic array of aluminum nanopyramids under coherent illumination [82]. From the perspective of optical data processing, a nonlinear relationship between the intensities of the input and output beams is required to realize all-optical gating function. Typically, many all-optical gating designs utilize highly nonlinear media to achieve this function [83–85]. However, the light-matter interaction in a CPA can be used to perform elementary all-optical computations while the material maintains linear optical properties. For a CPA, increasing one input signal will not proportionally increase one or both of the output signals. Consequently, the relationship between one input signal and one output signal can be nonlinear. This fact can be exploited to realize logical operation, pulse restoration, image processing [46,47,86,87]. An absorbing plasmonic metasurface using coherent control can perform 2D all-optical logical operations (AND, XOR and OR) [86]. Different relative phase of two incident coherent beams correspond to different logical operations. Such a device may open powerful opportunities for novel optical data processing architectures, locally coherent networks and photonic oracles—optical networks [46]. Moreover, it was demonstrated that linear coherent control of light can be used for pattern recognition and image processing [86,88]. Image similarities and differences between binary dot patterns are recognized and detected by projecting the test and target images onto opposite sides of lossy metamaterial beam splitter using coherent light [88]. Compared with nonlinear techniques, this approach can be performed at high speed and low intensities. In summary, we have discussed the basic principles and properties of coherent perfect absorption, CPA-based subwavelength structures and several applications. We have seen rapid development in the field of CPAs, and it will continuously progress. The operation frequencies of CPAs have been designed to range from microwave to infrared region. It is also worthy to mention that the concept of CPA can be further extended to coherent perfect rotation and coherent perfect scattering [89–91]. Acknowledgments This work is supported by the 973 Program of China (2013CBA01700); National Natural Science Funds (NNSF) (61622508, 61575201).

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