It is shown that active-tunable terahertz absorbers can be realized in a sandwich-structured system comprising an ultrathin dielectric film (polyimide) on a temperature-sensitive substrate (InSb) with a metal film on the back by utilizing the intrinsic carrier density (N) variation in InSb. When increasing the temperature from 250 to 320 K, N in InSb varied from ∼ 5.50 × 1015 to ∼ 2.98 × 1016 cm-3. Fixing the thickness of dielectric film with the value of 1.37 μm, the absorption peak shifted from 1.41 to 3.29 THz while keeping absorption higher than 99%. This active tunability can respond to even a slight temperature perturbation, and shows polarization insensitivity as well as high tolerance of incidence-angle (absorption peak can still exceed 90% even the incidence angle reaches 60°). Besides, the refractive index of polyimide (PI) has thermal stability at the terahertz range and the merit of good workability. These characteristics guarantee the stability of active-tunable performance. The peculiarities and innovations of this proposal promise a wide range of high efficiency terahertz devices, such as thermal sensors, spatial light modulators (SLMs) and so on.

Traditional optical composite systems coated with thin films have been extensively studied on absorbing electromagnetic energy.1–6 When lossy semi-transparent dielectric film is attached to the metal or Bragg reflector, an asymmetric Fabry-Perot cavity can realize absorption through gradual accumulation. However, it is necessary to keep the dielectric film at least a quarter-wave of aim wavelength in thickness. With the rapid development of micro-fabrication, absorbers based on metamaterials tread the board,7–11 whose dimensions are much smaller than traditional thin film systems. The ability of absorption depends on its speciality of creating independent tailored electric12 or magnetic13 responding to the incidence radiation. By matching ε and μ independently and manipulating proper resonances, it is possible to make metamaterials impedance-matched to free space for minimizing reflectivity, and energy attenuation occurrence in the electric as well as magnetic fields at target frequencies.14 

Electromagnetic absorbers are widely applied in various fields. Nevertheless, there still exists an urgent demand for active tunability, broad working-band and feasible fabrication, which have aroused extraordinary attention in the terahertz regime.15–21 Although the design and fabrication of metamaterials have been a proven technique, the drawbacks, such as complex fabrication progress, narrow responding band and difficulty in active tunability, still limit their application under specific conditions. For instance, the working circumstances under extreme temperature and the requirement for external temperature sensitivity are both important issues. The deficiency of rapid spatial light modulators (SLMs) with deep modulation depth prevents researches on compressive sensing (CS)22–24 from developing in the terahertz regime further. If the on-to-off active control of absorption can be realized, the novel sort of absorption SLMs can be utilized to explore high efficiency CS imaging.

Recently, it is demonstrated that perfect absorption can be achieved with one ultrathin dielectric layer applied on an opaque and lossy substrate, whose thickness is much thinner than the incident wavelength.25 By utilizing the nontrivial phase shift at the interface between the lossy media and the thin film, the absorbing resonance can be formed and changed in the ultrathin film. In this system, based on this mechanism, a practical design of ultrathin film absorber which works in the mid-infrared regime was proposed by depositing a vanadium dioxide film on a sapphire substrate. The absorption can be switched from 20% to 99.75% at λ = 11.6 μm. Not long ago, Wu et al.26 proposed a method to realize absorption in the terahertz regime by using a system comprising Ge as lossless dielectric film on a doped GaAs substrate. Nevertheless, the deficiency of active tenability retains room for further exploration.

In this article, an active-controlled terahertz absorber with a sandwich-like system is presented, where a lossless dielectric film is coated on a doped semiconductor substrate with a metal film on the back. Polyimide (PI), n-doped InSb and aluminum (Al) were chosen as options of the dielectric film, the substrate and the metal film, respectively. By theoretical derivation and calculation, the anti-reflection can be accomplished with the dielectric ultrathin film. Based on the effect of temperature variation on the carrier density (N in cm-3) in InSb, the correlation between N in InSb and the external temperature was utilized to analyze the temperature-dependent resonance frequency in this system. A novel method to actively modulate the working frequency of absorption is explored. It is also verified that this active tunability has properties of polarization-insensitive and incidence-angle independence in a wide range. The advantages of responding sensitivity and high compatibility are promising for ambient temperature sensing, active SLMs for CS, which can also fill up the lack of active modulators at the terahertz range.

A 600-μm-thick n-type InSb coated by a PI dielectric film with thickness d was chosen. Besides, a 200-nm-thick Al film was deposited to the reverse side of InSb. The Al on the back contributes to increase the optical path for energy attenuation, in case that the thickness of doped substrate is not enough. The permittivity of PI was assumed as εPI = 2.

To simplify the analysis of anti-reflection, it is assumed that PI with refractive index n1 is coated on the doped InSb with complex refractive index n˜2, as illustrated in Fig. 1. The simplified multiple beam interference is schematically shown for clear comprehension. Using the multiple beam interference method,27 the reflection of this hypothetical system can be deduced:

r=r01+r˜12ejδ1+r01+r˜12ejδ
(1)

where r01 is the reflection coefficient for the incident wave from air to lossless dielectric layer, and r˜12 represents the complex reflection coefficient for the incident wave from lossless dielectric layer to substrate. Both r01 and r˜12 can be deduced from the incident condition of the Fresnel equations. The phase changes when the incident wave propagates through the dielectric layer with δ = (4πdn1 cos θ)/λ, where θ is the incident angle in the substrate. To realize anti-reflection, it can be easily acquired that two conditions should be satisfied simultaneously:

|r01|=|r˜12|
(2)
2mπ=δ+φ(r˜12)
(3)

where m is a non-negative integer. When m = 0, the minimal thickness of the lossless dielectric layer to realize anti-reflection is d=φ(r˜12)πλ4n1cθ. The magnitude is related to the thickness of a traditional quarter-wave film with a coefficient φ(r˜12)π (when the angle of the incident light remains unchanged). It can be observed that the thickness of the dielectric layer is sensitive to the value of φ(r˜12) represents the phase angle of r˜12=r˜12=ejφ(r˜12). Therefore, to obtain the minimal value of d, φ(r˜12)0 should be satisfied.

Fig. 1.

Schematic of the designed composite system.

Fig. 1.

Schematic of the designed composite system.

Close modal

The complex conductivity (σ˜s) of InSb can be expressed by the simple Drude model and the complex permittivity (ε˜s) obeys the Debye model,28 

σ˜s=ε0ωp2Yjω
(4)
ε˜s=ε+jσ˜sε0ω
(5)

where ε0 and ε represent the free-space permittivity and the high-frequency dielectric constant of InSb, respectively. The value of ε in the calculation was taken as 15.7.29 The plasma frequency ωp=N(T)e2/ε0m depends on the carrier density N(T), which is strongly related to the temperature. The effective mass m* = 0.015me, where me is the mass of the free electron. γ/2π = 0.05 THz was used in the numerical analysis.29 

2.2.1. Absorption effect

Numerical simulations of the designed structure were performed using the commercial software CST MICROWAVE STUDIO. The sides of the structure were oriented to be parallel to theX^Y^-plane of the Cartesian coordinate system. The designed structure (Fig. 1) was modeled to be a square with l = 10 μm along the x and y axes. Wave-guide ports were chosen as the excitation and reception ports. Fig. 2(a) shows that TE mode (when the electric field is parallel to x axis) and TM mode (when the magnetic field is parallel to x axis) were applied in the range of 0–4 THz for simulations.

Fig. 2.

Numerical calculation results. (a) Schematic of the unit-cell in simulations. (b) Real and imaginary parts of the complex permittivity of InSb, when N = 1.5772 × 1016 cm-3. The refraction index of InSb at the range of 1.5–3 THz is inserted. (c) Illustration graph for solutions of Eqs. (2) and (3) as red solid line, while n2 of InSb plotted as black solid line, where the background color represents φ(r12). (d) Simulated results of reflection and absorption spectra.

Fig. 2.

Numerical calculation results. (a) Schematic of the unit-cell in simulations. (b) Real and imaginary parts of the complex permittivity of InSb, when N = 1.5772 × 1016 cm-3. The refraction index of InSb at the range of 1.5–3 THz is inserted. (c) Illustration graph for solutions of Eqs. (2) and (3) as red solid line, while n2 of InSb plotted as black solid line, where the background color represents φ(r12). (d) Simulated results of reflection and absorption spectra.

Close modal

Firstly, the circumstance was simulated when N = 1.5772 × 1016 cm-3 in InSb. The permittivity of InSb can be calculated from Eq. (5). In Fig. 2(b), the real and imaginary parts of ε˜InSb varied with frequency. The dispersion of the complex index of InSb (n˜2) is shown in the insert of Fig. 2(b). By solving Eqs. (2) and (3) with the above-mentioned parameters, the solutions can be acquired and plotted in Fig. 2(c). Fig. 2(c) demonstrates the relationship among the real part of (as the x axis), the imaginary part of (as the y axis) and the value of φ(r˜12)π (illustrated by the background color). Meanwhile, n˜2 in the range from 0.01 to 3 THz is also plotted for easily finding of the corresponding optimal. As discussed in the previous section, the intersection point of lines in Fig. 2(c) is anti-reflection frequency by simultaneously satisfying Eqs. (2) and (3). In this case, it corresponds to the dispersion of at f0 = 2.4 THz. According to Eq. (3), the value of φ(r˜12) can be deduced at f0 = 2.4 THz. The thickness of PI is calculated approximately to be 1 μm, which is much smaller than the thickness of traditional anti-reflection film and only 1/125 of the incident wavelength at 2.4 THz. The absorption in simulations can be defined as A(ω) = 1 − | R(ω)| − | T(ω)|. Because of the existence of metal film on the back of substrate, the value of | T(ω)| is consistently zero. The reflection and absorption of InSb are plotted in Fig. 2(d). It is obvious that perfect absorption is realized at target frequency and shows strong absorption with some band width.

2.2.2. The influence of film thickness

There always exist some errors of design and fabrication on thickness, which is the magnitude of a few sub-microns even microns. Therefore, it is necessary to take the influence of the dielectric film thickness into account. Moreover, for realizing the function of active modulation rather than passive modulation, it is also essential to fix PI with a predetermined value and keep the absorption conspicuous under different external conditions. Assuming N = 1.5772×1016 cm-3, the cases were simulated when the thickness of PI varied from 0.4 to 2 μm with an interval of 0.2 μm. As shown in Fig. 3, when the thickness deviated from the theoretically designed value, the reflection at target frequency presents a slight increase, i.e., the absorption intensity shows a trend of slight decrease. It can be observed that even though the fabrication thickness doubles the value in theoretical design, the absorption at designed frequency can still be guaranteed to be over 99%.

Fig. 3.

Amplitude of dip reflection at frequency f0 varies with thickness of the dielectric film from 0.4-2 μm.

Fig. 3.

Amplitude of dip reflection at frequency f0 varies with thickness of the dielectric film from 0.4-2 μm.

Close modal

2.2.3. Active thermal tunability

Hereinafter, the thermal tunability of the chosen structure was analyzed. The plasma frequency intensely depends on the temperature. When the temperature varies between 250 and 320 K, the energy gap of InSb changes very little and the intrinsic carrier density can be described by the relation,30 

N=5.76×1014T32e(0.262KBT)
(6)

where KB is the Boltzmann constant, T is the temperature in Kelvin, and the product of two objects is in electron volt. The fluctuation of temperature results in the variation of the carrier density, which consequently brings relative changes to ε˜InSb. Hence, there exist different anti-reflection frequencies according to the deduction in section 2.1 to realize perfect absorption within the terahertz range. Based on the high tolerance of the dielectric film thickness previously studied, this design can achieve the function of active modulation without changing substrates or refreshing correlative structure parameters. By changing T from 250 to 320 K with an interval of 10 K, N varies from ∼ 5.50 × 1015 to ∼ 2.98 × 1016 cm-3. Simultaneously, ωp/2π changes from 5.43 to 12.63 THz. Consequently, the target frequency of perfect absorption is seriously affected by external temperature. Utilizing equations given in section 2.1 and similar processing procedures to N = 1.5772 × 1016 cm-3 in section 2.2.1, the relative thicknesses of PI under different external temperatures (i.e. different N) can be deduced. Fig. 4(a) presents the frequency of peak absorption and the theoretical thickness of PI vary with external temperature. The frequency characterized by absorption peak shows a blue-shift from 1.41 to 3.29 THz, as the temperature increases from 250 to 320 K. Besides, the dielectric film becomes increasingly thinner, even less than 1 μm when the temperature is higher than 290 K. The results prove that the chosen structure can not only realize perfect absorption but also be ultrathin. The absorption spectra are plotted in Fig. 4(b) under various temperatures.

Fig. 4.

(a) Dip frequency and PI thickness vary with external temperature. (b) Simulated temperature-dependent spectra of the absorption.

Fig. 4.

(a) Dip frequency and PI thickness vary with external temperature. (b) Simulated temperature-dependent spectra of the absorption.

Close modal

Next, fixing the thickness of PI at 1.37 μm, the average value of thickness under temperatures varying from 250 to 320 K, simulations were performed to analyze the performance of active tunability. Fig. 5 (a) presents the reflection dip value under different temperatures when the thickness of PI is fixed as a constant. It is apparent that all the amplitudes of dip reflection are lower than 0.1. It means that the absorption at target frequency can be guaranteed to be higher than 99% within the studied temperature range. And the dip frequencies (not shown) present negligible shift compared to the aim frequencies under different temperatures as simulated results in Fig. 4 (b). Therefore, the function of active modulation has been theoretically proved to achieve by this proposed system with changing external temperatures.

Fig. 5.

Simulation results with fixed thickness of PI (a) Amplitude of dip reflection varies with the temperature. (b) The relation between the dip frequency and the incidence angle when temperature changes from 250 to 320 K. (c) The relation between the amplitude of dip reflection and the incidence angle when temperature changes from 250 to 320 K. (d) Reflection spectra near the dip frequency when T = 290 K under TE and TM modes, respectively.

Fig. 5.

Simulation results with fixed thickness of PI (a) Amplitude of dip reflection varies with the temperature. (b) The relation between the dip frequency and the incidence angle when temperature changes from 250 to 320 K. (c) The relation between the amplitude of dip reflection and the incidence angle when temperature changes from 250 to 320 K. (d) Reflection spectra near the dip frequency when T = 290 K under TE and TM modes, respectively.

Close modal

Besides, the effect of the incidence angle and polarization on the performance of active tunability was also investigated. Summarized from Figs. 5(b) and (c), the dip frequency is almost unchanged under different incidence angles, while the amplitude of dip reflection shows more complex changes. The amplitude of dip reflection changes slightly when the incidence angle is under 40°. When the angle increases to 60°, the amplitude is still lower than 0.3. That is, the absorption can still exceed 90% at the working frequency. For the reason that the structure is four-order symmetrical, the characteristic of polarization-insensitivity can be realized. For simplified observation, the simulation when PI fixed at 1.37 μm under 290 K was performed to calculate reflection spectra under TE and TM modes, whose results are shown in Fig. 5(d). For convenience, θ/20 and (θ + 10)/20 are added to the reflection amplitude of TE and TM modes, respectively. It is evidential that the designed absorber can efficiently work under wide-angle incidence and different polarization directions of the electric field, which provides a broad prospect for practical application.

We put forward an active-tunable terahertz absorber comprising a subwavelength ultrathin dielectric film (PI) on a doped semiconductor substrate (InSb) with a metal film on the back, without changing substrates or updating the thickness of dielectric film. The mechanism of active-controlled absorption is based on the tolerance of dielectric film thickness and the tunable carrier density by temperature in InSb. When fixing the thickness at appropriate value, the absorption peak can be actively tuned from 1.41 to 3.29 THz, as the external temperature increases from 250 to 320 K. Simultaneously, the maximal absorption intensity can be guaranteed to be over 99%. Moreover, the structure possesses the advantages of polarization insensitivity and high-compatibility with respect to the variation of incidence angle. This work paves an original path for designing the active-tunable terahertz absorbers. Instead of thermal sensitive InSb, other sorts of materials which are sensitive to external conditions (such as optical pump, bias voltage, surface pressure and so on) can be utilized as the substrate of this proposed system for active-controlled modulation. If the optical control method is applied to this system, the modulation speed can be improved and other semiconductor can be used such as GaAs and Si. In view of the sensitivity to temperature and above-mentioned characteristics, this designed structure can be considered to apply in sensing field and integrate high efficiency SLMs for the development of CS in the terahertz regime.

National Key Basic Research Program of China (Grant No. 2014CB339800); National Science Foundation of China (Grant No.61675145, 61722509, 61422509, 61605143, 61420106006, 61735012, 51677145); Program for Changjiang Scholars and Innovative Research Team in University (IRT) (Grant No. 13033); Hebei Province Science Foundation (Grant No. F2015402156 and F2014402094).

1.
Yan
RH
,
Simes
RJ
,
Coldren
LA
.
Electroabsorptive Fabry-Perot reflection modulators with asymmetric mirrors
.
IEEE Photonics Technol. Lett.
1989
;
1
(
9
):
273
275
.
2.
Chin
A
,
Chang
TY
.
Multilayer reflectors by molecular-beam epitaxy for resonance enhanced absorption in thin high-speed detectors
.
J. Vac. Sci. Technol., B
1990
;
8
(
2
):
339
342
.
3.
Kishino
K
,
Unlu
MS
,
Chyi
JI
, et al 
Resonant cavity-enhanced (RCE) photodetectors
.
IEEE J. Quantum Electron.
1991
;
27
(
8
):
2025
2034
.
4.
Yan
RH
,
Simes
RJ
,
Coldren
LA
.
Surface-normal electroabsorption reflection modulators using asymmetric Fabry-Perot structures
.
IEEE J. Quantum Electron.
1991
;
27
(
7
):
1922
1931
.
5.
Law
KK
,
Yan
RH
,
Coldren
LA
, et al 
Self-electro-optic device based on a superlattice asymmetric Fabry-Perot modulator with an on/off ratio > 100:1
.
Appl. Phys. Lett.
1990
;
57
(
13
):
1345
1347
.
6.
Tischler
YR
,
Bradley
MS
,
Bulović
V
.
Critically coupled resonators in vertical geometry using a planar mirror and a 5 nm thick absorbing film
.
Opt. Lett.
2006
;
31
(
13
):
2045
2047
.
7.
Schurig
D
,
Mock
JJ
,
Justice
BJ
, et al 
Metamaterial electromagnetic cloak at microwave frequencies
.
Science
2006
;
314
(
5801
):
977
980
.
8.
Liu
XL
,
Starr
T
,
Starr
AF
, et al 
Infrared spatial and frequency selective metamaterial with near-unity absorbance
.
Phys. Rev. Lett.
2010
;
104
(
20
):
207403
.
9.
Hao
JM
,
Wang
J
,
Liu
XL
, et al 
High performance optical absorber based on a plasmonic metamaterial
.
Appl. Phys. Lett.
2010
;
96
(
25
):
251104
.
10.
Watts
CM
,
Liu
XL
,
Padilla
WJ
.
Metamaterial electromagnetic wave absorbers
.
Adv. Mater.
2012
;
24
(
23
):
98
120
.
11.
Avitzour
Y
,
Urzhumov
YA
,
Shvets
G
.
Wide-angle infrared absorber based on negative index plasmonic metamaterial
.
Phys. Rev. B
2008
;
79
(
4
):
045131
.
12.
Pendry
JB
,
Holben
AJ
,
Stewart
WJ
, et al 
Extremely low frequency plasmons in metallic mesostructures
.
Phys. Rev. Lett.
1996
;
76
(
25
):
4773
4776
.
13.
Pendry
JB
,
Holden
AJ
,
Robbins
DJ
, et al 
Magnetism from conductors and enhanced nonlinear phenomena
.
IEEE Trans. Microwave Theory Tech.
1999
;
47
(
11
):
2075
2084
.
14.
Landy
NI
,
Sajuyigbe
S
,
Mock
JJ
, et al 
Perfect metamaterial absorber
.
Phys. Rev. Lett.
2008
;
100
(
20
):
207402
.
15.
Alves
F
,
Kearney
B
,
Grbovic
D
, et al 
Strong terahertz absorption using SiO2/Al based metamaterial structures
.
Appl. Phys. Lett.
2012
;
100
(
11
):
111104
.
16.
Tao
H
,
Landy
NI
,
Bingham
CM
, et al 
A metamaterial absorber for the terahertz regime: Design, fabrication and characterization
.
Opt. Express
2008
;
16
(
10
):
7181
7188
.
17.
Padilla
WJ
,
Taylor
AJ
,
Highstrete
C
, et al 
Dynamical electric and magnetic metamaterial response at terahertz frequencies
.
Phys. Rev. Lett.
2006
;
96
(
10
):
107401
.
18.
Bhattacharyya
S
,
Ghosh
S
,
Chaurasiya
D
, et al 
Bandwidth-enhanced dual-band dual-layer polarization-independent ultra-thin metamaterial absorber
.
Appl. Phys. A
2014
;
118
(
1
):
207
215
.
19.
Wang
BX
,
Zhai
X
,
Wang
GZ
, et al 
A novel dual-band terahertz metamaterial absorber for a sensor application
.
J. Appl. Phys.
2015
;
117
(
1
):
014504
.
20.
Li
XW
,
Liu
HJ
,
Sun
QB
, et al 
Ultra-broadband and polarization-insensitive wide-angle terahertz metamaterial absorber
.
Photonics Nanostruct.
2015
;
15
(
4
):
81
88
.
21.
Grant
J
,
Ma
Y
,
Saha
SC
, et al 
Polarization insensitive, broadband terahertz metamaterial absorber
.
Opt. Lett.
2011
;
36
(
17
):
3476
3478
.
22.
Watts
CM
,
Shrekenhamer
D
,
Montoya
J
, et al 
Terahertz compressive imaging with metamaterial spatial light modulators
.
Nat. Photonics
2014
;
8
(
8
):
605
609
.
23.
Withayachumnankul
W
,
Abbott
D
.
Terahertz imaging: Compressing onto a single pixel
.
Nat. Photonics
2014
;
8
(
8
):
593
594
.
24.
Liutkus
A
,
Martina
D
,
Popoff
SM
, et al 
Imaging with nature: Compressive imaging using a multiply scattering medium
.
Sci. Rep.
2014
;
4
(
4
):
5552
.
25.
Kats
MA
,
Sharma
D
,
Lin
J
, et al 
Ultra-thin perfect absorber employing a tunable phase change material
.
Appl. Phys. Lett.
2012
;
101
(
22
):
221101
.
26.
Wu
HX
,
Shi
FH
,
Chen
YH
.
Broadband terahertz absorption enabled by coating an ultrathin antireflection film on doped semiconductor
.
Opt. Express
2016
;
24
(
18
):
20663
20671
.
27.
Born
M
,
Wolf
E
,
Hecht
E
.
Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light
. 7 ed.
NY
:
Pergamon
;
1999
.
28.
Howells
SC
,
Schlie
LA
.
Transient terahertz reflection spectroscopy of undoped InSb from 0.1 to 1.1 THz
.
Appl. Phys. Lett.
1996
;
69
(
4
):
550
552
.
29.
Han
JG
,
Lakhtakia
A
,
Tian
Z
, et al 
Magnetic and magnetothermal tunabilities of subwavelength-hole arrays in a semiconductor sheet
.
Opt. Lett.
2009
;
34
(
9
):
1465
1467
.
30.
Han
JG
,
Lakhtakia
A
.
Semiconductor split-ring resonators for thermally tunable terahertz metamaterials
.
J. Mod. Opt.
2008
;
56
(
4
):
554
557
.