1 Introduction

Since carbon nanotubes (CNTs) were discovered by Iijima in 1991 [1], carbon materials have attracted worldwide attention due to their unique structure and excellent properties.

CNTs are known as quasi-one-dimensional nanomaterials. CNTs are mainly divided into multi-walled and single-wall carbon nanotubes. The diameter of CNTs ranges from several nanometers to tens of nanometers, and their length can reach several micrometers or even centimeters. Although single CNTs have many unique properties, the overall behavior of macromaterials comprised of carbon nanotubes (CNTs) is often considered in practical applications. Controlling the directional growth of CNTs and preparing various types of CNT arrays are important prerequisites for the application of CNTs. At present, some studies have been carried out on the applications of CNTs in the fields of phototransistors [2,3,4,5], photoconductivity [6,7,8,9,10,11,12,13,14,15,16,17], photodiodes [18,19,20,21,22,23,24,25], radiometers [26, 27] and photothermoelectric detectors [28,29,30,31,32,33,34,35]. The absorption properties of CNTs have also attracted much attention [36,37,38]. CNT arrays with excellent optical absorption properties have been widely used in national defense and military applications, and in anti-microwave radiation technology for civilian use.

A nanotube is hollow, and a nanowire is a linear material with a certain length-to-diameter ratio, whose diameter is on the nanometer scale but it can be quite long. Carbon nanowires (CNWs) are similar to CNTs and can also be used in military and civilian applications. Solid CNWs and their arrays were constructed in our study, and the length-to-diameter ratio of the CNWs was more than 100.

To fully exploit the application potentials and advantages of CNW array absorption characteristics, it is very important to determine the optimal array structure parameters. In this paper, we used finite-difference time-domain (FDTD) technology to explore the influence of CNW array structure parameters, such as the diameter, spacing, length, incident angle of the light source, and polarization, on the array absorption performance, which provides a theoretical reference and technical support for its application in stealth technologies, nanolight-emitting devices, photoelectric sensors and photovoltaic cells.

2 Structural design and simulation method

In the simulation calculation with FDTD technology, we assume that each CNW in the array is cylindrical, and each CNW is parallel to each other. If there is no special explanation, the structural parameters of each CNW array, such as diameter, length and spacing, are equal, as shown in Fig. 1a. The absorption spectra of CNW arrays with different structural parameters were calculated using the FDTD technique. The plane wave was adopted as the light source, which is incident on the array structure along the axis of the CNW. The complex refractive index of carbon used in the calculation was obtained from reference [39], as shown in Fig. 1b. The CNW arrays are in the air. In addition, the observation zenith angle θ and azimuth angle φ are shown in Fig. 1c, and the -z axis is the normal-incidence direction of the light source. The CNWs are uniformly distributed. Each CNW can be regarded as a uniform glossy transmission line under the action of a light wave field, and an equivalent circuit model of oscillating current interaction can be formed in the adjacent carbon nanowires.

Fig. 1
figure 1

Structural design and the complex refractive index of the CNWs. a Structural design; b Complex refractive index; c Observation zenith angle and azimuth angle

Full size image

3 Results and discussion

3.1 Variation in the absorption properties of the CNW array with excitation wavelength

First, we studied the absorption properties of the CNW arrays with the wavelength of the excitation light. In this study, we set the spacing of the nanowire a = 50 nm, the diameter of the nanowire d = 10 nm, the length of the nanowire l = 20 µm, the zenith angle θ and the azimuth angle φ to 0 degrees, the polarization direction of the excitation light to p polarization, and the excitation wavelength range used in the calculation to 350–810 nm, including visible, ultraviolet and near-infrared bands. As shown in Fig. 2, with an increase in the wavelength of the excitation light, all absorption rates of the CNW array are very high and close to 1 with a very small reduction because the complex refractive index of carbon does not change much with the excitation wavelength, as shown in Fig. 1b.

Fig. 2
figure 2

Variation in the absorption properties of the CNW array with the excitation wavelength

Full size image

3.2 Variation in the absorption properties of CNW arrays with nanowire length

We investigated the dependence of the absorption characteristics of the CNW arrays on the length of the nanowires. In this research, we set the spacing of the nanowire a = 50 nm, the diameter of the nanowire d = 5 or 10 nm, the zenith angle θ and the azimuth angle φ to 0 degrees, and the polarization direction of the excitation light to p polarization. The wavelength of the excitation light is.

350 nm (the absorption at the excitation of this wavelength is the strongest as shown in Fig. 2). As shown in Fig. 3, with increasing CNW length, the absorption of the CNW array gradually increases. This is mainly because as the length of the CNWs increases, the resistance of the CNWs increases, and the effective loss increases under the same induction current, and the absorption of the light waves is enhanced. In addition, the longer the nanowire is, the larger the absorption surface, which is also a possible factor for enhanced absorption. For CNWs with a diameter of 5 nm, the absorption rate of the array tends to be stable at 0.99 when the length of the nanowire increases to 12 µm, and for CNWs with a diameter of 10 nm, the absorption rate tends to be stable at 0.99 when the length of the nanowire increases to 4 µm.

Fig. 3
figure 3

Variation in the absorption properties of CNW arrays with nanowire length

Full size image

3.3 Variation in the absorption properties of CNW arrays with nanowire diameter

We investigated the dependence of the absorption properties of nanowire arrays on the diameter of the nanowires. In this research, we set the spacing of the nanowire a = 50 nm, the length of the nanowire l = 20 µm, the observation zenith angle θ and the azimuth angle φ to 0 degrees, the polarization direction of the excitation light to p polarization, and the wavelength of the excitation light used in the calculation to 350 nm. As shown in Fig. 4, with an increasing diameter of the CNWs, the absorption of the CNW array first increases and then decreases. When the diameter of the nanowire is 7 nm, the absorption of the array reaches its maximum value, approaching 1. This is because nanowires with a diameter of 7 nm have a certain capacitance value, the impedance of the nanowire and air is the best match, and the light wave absorption is the largest. The larger the nanowire diameter deviation is, the smaller the energy of the light wave entering the nanowire, so the absorption of the nanowire decreases.

Fig. 4
figure 4

Variation in the absorption properties of CNW arrays with nanowire diameter

Full size image

3.4 Variation in the absorption properties of CNW arrays with nanowire spacing

We investigated the dependence of the absorption properties of nanowire arrays on the spacing of the nanowires. In this research, we set the diameter of the nanowire d = 10 nm, the length of the nanowire l = 20 µm, the observation zenith angle θ and the azimuth angle φ to 0 degrees, the polarization direction of the excitation light to p polarization, and the wavelength of the excitation light used in the calculation to 350 nm. As shown in Fig. 5, with increasing nanowire spacing, the absorption rate of the CNW array increases gradually. This is because as the distance between the nanowires increases, the density decreases, and the interference cancellation of multi-level reflected light between the nanowire surfaces becomes increasingly obvious; thus, the absorption of light increases gradually, weakening the reflection. When the spacing is 10 nm, the nanowires touch each other, and the absorption rate is 0.88; when the spacing is greater than 50 nm, the absorption rate is above 0.99.

Fig. 5
figure 5

Variation in the absorption properties of the CNW array with nanowire spacing. The spacing is the distance between the nanowire axes

Full size image

3.5 Variation in the absorption properties of the CNW array with observation azimuth angle

We investigated the dependence of the absorption properties of the CNW arrays on the incident zenith angle (also known as the observed zenith angle) of the excitation light. In this research, we set the spacing of the nanowire a = 50 nm, the diameter d = 10 nm, the length of the nanowire l = 20 µm, the observation azimuth angle φ = 0 degrees, the polarization direction of the excitation light to p polarization, and the wavelength of the excitation light used in the calculation to 350 nm. As shown in Fig. 6a, the absorption rate of the CNW array is close to 1 at most incident angles but decreases sharply when the incident angle is more than 85 degrees. This is because the reflection is enhanced with the incidence of a high angle, so that the energy of light refracting into the nanowire is weakened. To improve the absorption rate of the array at a high incidence angle, we.

Fig. 6
figure 6

Variation of absorption properties of CNWs array with the observation zenith angle (a), the flatness (b), the azimuth angle (c). All 20 µm: the length of all nanowires are 20 µm; 20 µm-: the length of all nanowires are away from 20 µm; 20 µm--: the length of all nanowires are more away from 20 µm than 20 µm-

Full size image

constructed CNW arrays with different CNW lengths, and the flatness of the arrays varied with the length difference. As shown in Fig. 6b, destroying the flatness can enhance the absorption characteristics of the array under high angle incidence. The larger the length difference of the nanowires in the array, the larger the increase in the absorption. This is mainly because the larger the length difference is, the greater the diffuse reflection, and the more light energy is incident on the surface of the nanowire.

We also studied the dependence of the absorption properties of the CNW array on the observed azimuth angle. In this research, we set the spacing of the nanowires a = 50 nm, the diameter d = 10 nm, the length of the nanowires l = 20 µm, the observation zenith angle θ = 60 degrees, the polarization direction of the excitation light to p polarization, and the wavelength of the excitation light used in the calculation to 350 nm. As shown in Fig. 6c, the variation in the observed azimuth angle has little effect on the absorption of the CNW array. This is because the azimuth angle of the incident light has no effect on the propagation of light waves.

3.6 Variation in the absorption properties of the CNW array with polarization direction of the excitation light

We investigated the dependence of the absorption properties of the CNW array on the polarization direction of the excitation light. In this research, we set the spacing of the nanowire a = 50 nm, the diameter d = 10 nm, the length of the nanowire l = 20 µm, the observation azimuth angle φ = 0°, the observation zenith angles θ = 0°, 60°, and 89°, respectively. The excitation wavelength used in the calculation was 350 nm. As shown in Fig. 7, except for the high angle incidence, the absorption rate of the array.

Fig. 7
figure 7

Variation in the absorption properties of the CNT array with the polarization direction of the excitation light

Full size image

decreases slightly, and the absorption of the CNW arrays is almost independent of the polarization direction at other incident angles. This shows that the constructed nanowires are isotropic in the simulation calculation.

4 Conclusion

In this paper, the influence of the structural parameters in the range of 350–810 nm on the optical absorption properties of a CNW array were studied with the FDTD technique, and the results show that the wavelength of the excitation light has little effect on the absorption of the CNW array. The larger the nanowire is, the stronger the absorption of the array, but when the absorption increases to nearly 1, it tends to stabilize. As the diameter of the nanowire increases, the absorption of the array first increases and then decreases, and the larger the spacing of the nanowires is, the larger the absorption of the array. At high angle incidence, the absorption of the array is greatly weakened. By changing the flatness of the CNW array, the absorption of the array at high angle incidence can be appropriately improved. The azimuth angle and polarization direction of the incident light have little effect on the absorption of the array. Identification of the structural parameters of CNW arrays that lead to strong absorption is essential for the fabrication of CNW arrays and their application in stealth technologies, nanolight-emitting devices, photoelectric sensors and photovoltaic cells.