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Abstract
We show theoretically and numerically that artificially engineered nanometer metal/semiconductor composite films provide a versatile platform for coherent perfect absorption (CPA) of light. By engineering the effective permittivity of the composite nanofilms and tailoring the angle of incidence, CPA can be realized freely in a wide range from visible to infrared. A proof-of-principle demonstration using Au/Ge composite nanofilms is implemented. The results show that CPA can be achieved at any wavelength within the studied range. By contrast, CPA cannot be achieved for single layer of Au or Ge with the same thickness. The simple approach to obtain CPA provides a great deal of flexibility in selecting absorption materials, preparation technology, illumination configuration, and wavelength range.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Light absorption is crucial for various types of application, including photovoltaic [1,2], detection [3], sensing [4], imaging [5], cloaking [6,7], switching [8] and modulation [9]. Perfect absorption of incident light is not only an interesting research topic itself from the point of view of basic physics, but also important for many device applications because of highly efficient energy conversion. One of the classical perfect absorber concepts is the Salisbury screen, invented by the American engineer Winfield Salisbury in 1952, and is used to prevent enemy radar detection of military vehicles. It consists of three layers: a metallic ground plane, a lossless dielectric, and a thin absorbent material. This type of perfect absorbers has only one port and perfect absorption happens under the incident of one beam [10–16]. Another perfect absorber concept is the coherent perfect absorption (CPA) which was proposed by Y. Chong et al in 2010 [17]. It was first demonstrated in a Fabry-Perot cavity with a silicon slab [18] and then in a planar metamaterials [9]. CPA relies on the coherent interference of two oppositely directed incident beams and provides a highly flexibility to tune the absorption by changing the relative phase of two beams and offers a promising prospect for all-optical switching and modulation [19–38]. In the past decade, conditions to achieve CPA in various geometries have been intensively studied [39–42], such as normal and oblique incidences [24,33,43], symmetric and asymmetric interferometric control [44,45] and so on. The absorption materials and corresponding structures are the key to absorption spectral ranges and performance of CPA. Typically, traditional Ge, Si and III–V semiconductors provide high absorption in the visible to near infrared spectral range by bandgap transition. However, the absorption of noble metal (Au, Ag, Pt) comes mainly from the free carrier absorption, which is relatively weaker than bandgap transition but ultra-broadband in nature and covers from visible to terahertz (THz) region. A great number of CPA utilizing the semiconductors and metals separately as the absorption materials has been proposed and demonstrated, where the absorption spectral ranges and performance of CPA are limited by the corresponding single absorbent material. Meanwhile, composite materials have shown more flexibility in achieving CPA [23].
In this paper, in contrast to using a single type of absorbent materials to realize CPA, we demonstrate theoretically and numerically that CPA can be obtained based on artificially engineered nanometer metal/semiconductor composite films, which combines both the bandgap absorption and the free carrier absorption. In this approach, the effective permittivity and optical responses of the composite nanofilms can be engineered by simply varying the thickness of metal and semiconductor layers. Moreover, additional control over the absorption is achieved by tailoring the angle of incident light. This provides a great deal of flexibility in selecting absorption materials, preparation technology, illumination configuration, and wavelength range.
2. Theoretical model and results
Figure 1 presents a schematic of suspended metal/semiconductor composite nanofilms illuminated by two incident beams of transverse electric (TE) polarized plane waves with the same incident angle $\theta _0$ and intensity. The metal/semiconductor composite nanofilms consist of a metal film with the relative permittivity $\varepsilon _{r1}$ and thickness $d_1$ on the top of a semiconductor film with the relative permittivity $\varepsilon _{r2}$ and thickness $d_2$, and extend infinitely in the $y$ and $z$ directions. $I_1$ and $I_2$ are the incident beams, $S_1$ and $S_2$ are the scattered beams correspondingly. $E$ and $H$ are the electric and magnetic field components of the incident beams.
Fig. 1. Schematic of metal/semiconductor composite nanofilms illuminated by two coherent beams ($I_1$ and $I_2$), $S_1$ and $S_2$ are the scattered beams.
Given that the structure is a multilayer film structure, we can calculate the light coherent absorption of the nanofilms by combining transmission matrix and scattering matrix theory [43,46]. Since both the thickness $d_1$ and $d_2$ are far less than the wavelength of the incident beams, the composite films can be considered as a homogeneous film with an effective relative permittivity $\varepsilon _{reff}$ [47]. By solving Maxwell equations and boundary conditions, we can deduce the effective relative permittivity $\varepsilon _{reff}$ for TE polarized plane waves as
So, the structure of suspended metal/semiconductor composite nanofilms can be equivalent to a three-layered medium comprising a homogeneous layer (medium 1) between two dielectric (air) half-spaces (medium 0 and medium 2). First, we consider the case of a single beam illuminating ($I_1\neq 0$ and $I_2=0$, or $I_1=0$ and $I_2\neq 0$). The transmission matrix for a single beam illuminating on medium 1 from medium 0 is given byAccordingly, the scattering coefficient can be expressed as
Finally, by simple algebra operation, the coherent absorption of the composite films is given as For a proof of principle, we implement demonstration using Au/Ge composite nanofilms and assuming the two dielectric half-spaces to be air. Considering the first bandgap of Ge is about 0.67 eV(i.e., photon wavelength about 1850 nm) and the several typical experimental results of the dielectric permittivity for the ultrathin Au films obtained by Johnson and Christy [48], Theye [49], and Pells and Shiga [50] have significantly differences in the spectral rang from around 2.0 to 5.0 eV (i.e., photon wavelength about 620-250 nm), we limit the operating wavelength in the 700-1800 nm range, where the experimental dielectric permittivities of Ge, especially Au in different relevant references are consistent. The corresponding relative permittivity $\varepsilon _{r1}$ and $\varepsilon _{r2}$ of Au and Ge exhibit strong frequency dispersion and are determined from experimental data [48,51]. Because the composite nanofilms are sandwiched by two symmetrical air half-spaces, we assume the relative amplitude $a$ of the two beams to be 1 (Indeed, CPA can also be realized for composite nanofilms with asymmetric surrounding media, where the relative amplitudes and phases of the two beams may be different). First, we consider the special case of the single Au and Ge films with the thickness 15 nm. By solving Eqs. (1)–(12), we obtain the theoretical coherent absorption of the single Au and Ge films as a function of wavelength and incident angle of two coherent beams ($\phi =0$), as shown in Fig. 2. From Fig. 2, we can see that the single Au and Ge films with a thickness of 15 nm can only provide a maximum coherent absorption of less 15$\%$ and 29$\%$ in the 700-1800 nm range, respectively. This indicates that CPA in the single Au and Ge films with the thickness of 15 nm cannot be achieved in the 700-1800 nm range.Fig. 2. Theoretical coherent absorption of single Au and Ge films as a function of wavelength and incident angle of two coherent beams. (a) Single Au film with a thickness of 15nm. (b)Single Ge film with a thickness of 15nm.
Now we consider the case where the single Au or Ge films are replaced by the Au/Ge composite nanofilms. We fix the thickness $d$ of the Au/Ge composite nanofilms at the same thickness 15 nm with $d_1$=9nm and $d_2$=6nm as that of the single Au and Ge films. Again, by solving Eqs. (1)–(12), we obtain the corresponding coherent absorption as a function of wavelength and incident angle of two coherent beams ($\phi =0$), as shown in Fig. 3(a). From Fig. 3(a), we can see the Au/Ge composite nanofilms with the same thickness 15 nm ($d_1$=9nm and $d_2$=6nm) can provide coherent absorption of more than 99$\%$ at a wavelength of 700 nm, which implies CPA can be obtained by simply replacing a single Au or Ge film with Au/Ge composite nanofilms. The physical mechanism of CPA of the composite film can be understood by comparing its effective relative permittivity to that of Au and Ge. At the wavelength of 700 nm, the relative permittivity of Au and Ge is −15.64+1.27i and 24.97+4.73i, respectively. And the effective relative permittivity of the Au/Ge composite nanofilm is $\varepsilon _{reff}$=0.6+2.65i. For Au or Ge films, the real part of the relative permittivity (corresponding to polarization) is much larger than the imaginary part of the relative permittivity (corresponding to polarization losses). As a result, most of the incident light on the films is either transmitted or reflected rather than absorbed. On the contrast, for the composite film, its imaginary part of the relative permittivity is comparable to that of Au and Ge while its real part is significantly reduced. This makes it possible to achieve strong coherent absorption under oblique incidence. By the way, the so called “Epsilon Near Zero (ENZ)” materials have previously been used to achieve CPA [8,24]. Actually, CPA can always be realized for thin films with ENZ materials regardless of its imaginary part only if it is not zero at suitable oblique incidence [33].
Fig. 3. Theoretical coherent absorption of the Au/Ge composite nanofilms for fixing the thickness $d$ at 15 nm while varing the ratio of $d_1$ to $d_2$ as a function of wavelength and incident angle of two coherent beams. (a) $d_1$=9nm and $d_2$=6 nm (Au/Ge composite nanofilms composed by 9nm Au and 6nm Ge layers). (b) $d_1$=4 nm and $d_2$=11 nm (Au/Ge composite nanofilms composed by 4nm Au and 11 nm Ge layers). (c) $d_1$=1.9 nm and $d_2$=13.1 nm (Au/Ge composite nanofilms composed by 1.9 nm Au and 13.1 nm Ge layers). (d) $d_1$=1.3 nm and $d_2$=13.7 nm (Au/Ge composite nanofilms composed by 1.3 nm Au and 13.7 nm Ge layers).
We can also find that CPA is obtained at an incident angle of 79.6 degrees and the coherent absorption decreases as the incident angle deviates from 79.6 degrees. The reason corresponds to the fact that the CPA of the nanofilms is closely related to destructive interference where the transmission of one beam will cancel with the reflection of the other beam, resulting in total absorption of all incident energy. However, when the incident angle increases (decreases) well over 79.6 degrees, the reflection amplitude of one beam from the nanofilms is much larger (smaller) than the transmission amplitude of the other beam, and the destructive interference condition is destroyed (to determine the exact condition for CPA one may use the Admittance Matching Method [5][8]).
The above discussion is based on a fixed wavelength of 700 nm. However, in fact, one of the main advantages of the metal/semiconductor composite nanofilms as a platform for CPA is that the wavelength of CPA of the composite nanofilms can be engineered in a very wide range by simply varying the thickness ratio of metal and semiconductor layers. Figures 3(b)–3(d) shows the theoretical coherent absorption of the Au/Ge composite nanofilms with the same thickness 15 nm while changing the ratio of $d_1$ to $d_2$ from 9 nm to 6 nm, to 4 nm to 11 nm, 1.9 nm to 13.1 nm, and 1.3 nm to 13.7 nm. From Figs. 3(a)–3(d), we find that the operation wavelength of CPA of the Au/Ge composite nanofilms is shifted to 1033, 1500 and 1800 nm from 700 nm, respectively, which shows the operation wavelength of CPA of the Au/Ge composite nanofilms is significantly related to and determined by the thickness ratio of $d_1$ to $d_2$. In fact, additional research (not shown here) shows that CPA can be obtained at any wavelength in the 700-1800 nm range by designing the appropriate thickness ratio of $d_1$ to $d_2$ while fixing $d$=15 nm.
Because the coherent absorption of the nanofilms is closely related to destructive interference, the coherent absorption is expected to be periodic sensitive to the relative phase $\phi$ of the two beams. Therefore, we will next examine the coherent absorption sensitivity to the relative phase $\phi$. Figure 4(a) shows the theoretical coherent absorption as a function of the relative phase $\phi$ while fixing the wavelength of incident wave at 700 nm, the incident angle at 79.6 degrees, $d_1$=9nm and $d_2$=6 nm. It can be observed that the coherent absorption can be tuned from 0 to 100$\%$ and has a periodic relationship with the relative phase $\phi$, which is consistent with theoretical expectation. In the following discussion in this paper, we only consider the case where the relative phase $\phi$ of two coherent beams is zero. Next, we consider the situation where the wavelength of two coherent beams is fixed at 700 nm, and the thickness $d$ of the nanofilms varies from 15 nm to 5 nm while fixing the ratio of $d_1$ to $d_2$ at 3/2. The corresponding coherent absorption of the composite films as a function of incident angle of two coherent beams for the different $d$ is theoretically calculated and shown in Fig. 4(b). From Fig. 4(b) , we can see that the perfect absorption angle changes from 45 to 86.5 degrees when the thickness $d$ varies from 55 nm to 5 nm, which implies that the coherent absorption is sensitive to $d$ and the CPA shifts to the larger incident angle as $d$ decreases. This can be understood through the following qualitative analysis. The decreased $d$ leads to an increased transmission amplitude of one beam but has less effect on the reflection amplitude of the other beam. So, the destructive interference condition where the transmission of one beam will cancel with the reflection of the other beam is destroyed. In order to satisfy the destructive interference condition, the corresponding incident angle of two coherent beams needs to be increased to improve the reflection amplitude of the other beam. So, an increase of perfect absorption angle with decreased $d$ occurs. By the way, CPA cannot be realized here in the composite nanofilms even at large incident angles if we replace the transverse electric (TE) polarized plane waves with transverse magnetic (TM) polarized plane waves. For example, the maximum absorption can only reach 54$\%$ and perfect absorption is not achieved for a 15 nm thick composite film (9nm Au and 6 nm Ge) under the illumination of two coherent TM waves with equal phase at the wavelength of 700nm. And the absorption goes down gradually as the incident angle increases from 0 to 90 degree (data not shown here). This is because the increase of the incident angle for TM wave leads to a decrease of the component of electric field parallel to the Au-Ge interface (film plane).
Fig. 4. (a) Theoretical coherent absorption of the composite nanofilms consisting of 9nm Au and 6nm Ge as a function of relative phase $\phi$ of two coherent beams at a wavelength of 700nm and an incident angle of 79.6 degrees.(b) Theoretical coherent absorption as a function of incident angle of two coherent beams at a wavelength of 700nm for the different $d$ while fixing the ratio of $d_1$ to $d_2$ at 3/2 and $\phi$ at 0.
3. Numerical simulation and discussion
To verify the theoretical model and results, we next performed full-wave numerical simulations using the commercial finite element package Comsol MultiPhysics to investigate the proposed Au/Ge composite nanofilm based on coherent perfect absorption. The periodic boundary condition is used in the $x$ direction to describe equivalently an infinite continuation in the $x$ direction of the composite nanofilms and port boundary conditions with plane waves are adopted in the $z$ direction as the two incident coherent beams to shine the Au/Ge composite nanofilms, as shown in Fig. 1. It should be stressed that, in this numerical simulation, the Au/Ge composite films are not regarded as a homogeneous film with an effective relative permittivity, but as two separate layers. In our proposed Au/Ge composite nanofilms, some portion of the energy of the two incident coherent beams will be absorbed by Ge and some lost to Au. So, in the numerical simulation, we use a separate computational method to calculate the absorption fractions in Ge and Au. The average time-harmonic electromagnetic power absorbed in Ge or Au depends on the divergence of the Poynting vector and can be obtained as
where $\omega$ is the frequency of the incident coherent beams, $\varepsilon ''$ is the imaginary part of the permittivity of Ge or Au, and $|E|^2$ is the corresponding magnitude of the electric fields. Figure 5 shows the simulated (blue dotted line) and the corresponding theoretical (red solid line) coherent absorption of the Au/Ge composite nanofilms with different $d_1$ and $d_2$ as a function of incident angle of two coherent beams. From Fig. 5, although based on a completely different absorption calculation method (see Eqs. (12) and (13)), we can see that the simulated coherent absorption is in good agreement with the theoretical results, which shows the correctness of the theoretical model. By the way, we can see from Fig. 5 that the smaller the fill factor of metal, the longer the CPA wavelength. This can be understood qualitatively. As we mentioned above, in order to reach CPA, the real part of the effective permittity should be small. As the fill factor of metal becomes small, its real part of permittivity (absolute value as it is negative) needs to become larger and the working wavelength needs to be longer [the permittivity of Ge changes much smaller as wavelength increases compared to Au].Fig. 5. Simulated (blue dotted line) and theoretical (red solid line) coherent absorption of the Au/Ge composite nanofilms with different $d_1$ and $d_2$ as a function of incident angle of two coherent beams at different wavelengths. (a) Au/Ge composite nanofilms composed by 9 nm Au and 6 nm Ge layers at the wavelength of 700 nm. (b) Au/Ge composite nanofilms composed by 4 nm Au and 11 nm Ge layers at the wavelength of 1033 nm. (c) Au/Ge composite nanofilms composed by 1.9 nm Au and 13.1 nm Ge layers at the wavelength of 1500 nm. (d) Au/Ge composite nanofilms composed by 1.3 nm Au and 13.7 nm Ge layers at the wavelength of 1800 nm.
In order to further investigate the coherent absorption characteristics of the Au/Ge composite nanofilms, we compare the proportion absorbed by Au and Ge layers of the Au/Ge composite films. Figure 6 shows the simulated total coherent absorption and the proportion absorbed by Au and Ge layers of the Au/Ge composite films for fixing the thickness $d$ at the 15nm while varying the ratio of $d_1$ to $d_2$ as a function of the incident angle at different wavelengths. From Fig. 6, we see that the Ge layer absorption contributes more than 74$\%$ while Au layer absorption contributes less than 26$\%$ at the wavelength of 700 nm when CPA occurs. As the wavelength of CPA increases, the proportion absorbed by Au layer increases and that of Ge layer decreases gradually. When the wavelength is larger than 1127nm, the absorption ratio of the Au layer is greater than that of the Ge layer. This is mainly because in the visible range such as 700nm, Ge provides higher absorption by bandgap transition and contributes most of the coherent absorption. As the wavelength increases, the photon energy becomes smaller and the bandgap absorption of Ge decreases. However, the absorption of Au comes mainly from the free carrier absorption, which is less affected by the wavelength. Thus as the wavelength increases, the absorption contributed by Ge layer decreases gradually. By contrast, Au layer becomes the main absorption component. So, the Au/Ge composite nanofilms introducing both the bandgap absorption and the free carrier absorption can be proposed as a platform for engineering coherent perfect absorption in a very wide wavelength range. We have taken Au/Ge composite film as a proof of principle demonstration. The results of this manuscript could indeed be generalized to other material configurations such as Au/Si, Al/SiO$_2$ and so on.
Fig. 6. The simulated total coherent absorption and the proportion absorbed by Au and Ge layers of the Au/Ge composite films for fixing the thickness $d$ at 15 nm while varying the ratio of $d_1$ to $d_2$ as a function of incident angle at different wavelengths. (a) Au/Ge composite films composed by 9 nm Au and 6 nm Ge at the wavelength of 700 nm. (b) Au/Ge composite films composed by 5.4 nm Au and 9.6 nm Ge at the wavelength of 900 nm. (c) Au/Ge composite films composed by 3.4 nm Au and 11.6 nm Ge at the wavelength of 1127 nm. (d) Au/Ge composite films composed by 1.9 nm Au and 13.1 nm Ge at the wavelength of 1500 nm.
4. Conclusion
In summary, we have presented a type of artificially engineered nanometer metal/semiconductor composite films for realizing coherent perfect absorption at oblique incidence. We implemented a proof-of-principle demonstration using Au/Ge composite nanofilms. The results show CPA can be achieved at any wavelength within the studied range (700-1800 nm) by simply varying the thickness ratio of Au and Ge layers and the incidence angles. The proposed composite films with nanometer thickness could be fabricated with the recent progress in deposition technique for ultrathin and ultrasmooth metal films [52–54]. Our work proposes a simple way to engineer coherent perfect absorption and provides a great deal of flexibility in selecting absorption materials, preparation technology, illumination configuration, and wavelength range.
Funding
National Natural Science Foundation of China (11304389, 11674396); Hunan Provincial Science and Technology Department (2017RS3039, 2018JJ1033).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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