1. Introduction

Vertical arrays of semiconductor nanowires (NWs) have attracted significant attention because of their unique optical and carrier transport properties compared to their bulk counterparts. In NW arrays, the wavelength range and magnitude of the absorption can be tuned by the nanowire dimension and the distance of nanowires in the array [1–8], leading to “light trapping” and “near-unity” absorption [9] despite low filling fractions. Paired with the possibility to fabricate axial and radial p-n junctions in the NWs, highly efficient solar cells [10–16] and light detectors [17–20] can be realized.

When the semiconductor NWs are periodically arranged with distances of the order of the wavelength of light, the arrays form a photonic crystal (PhC) structure. These photonic crystals, which can be synthesized by selective area epitaxy (SAE) [21,22], enable the design of ultra-compact two-dimensional (2D) [23–28] and one-dimensional (1D) [29–31] laser devices of micrometer size. These novel microlasers have the potential to fulfill the demands for an on-chip coherent light source in optoelectronic integrated circuits (OEIC) which offer a significantly enhanced bandwidth and reduced power consumption per generated bit [32,33].

Less attention has been given to the reflection properties of vertical NW arrays [34–36]. Due to their strong intrinsic birefringence, the reflectance of light is highly polarization dependent. This feature makes NW PhC arrays ideal micrometer-sized optical elements like polarizers, analyzers, and mirrors which are important to control the polarization of the laser emission from NW laser arrays or to analyze the polarization of light after a rotation with electro-optical or magneto-optical elements.

In this work, we investigate the reflective properties of SAE grown wurtzite InP NW PhC arrays as a function of incident light wavelengths ranging from 500 to 1000 nm at an incidence angle close to normal incidence (at 15°). Angle-resolved reflection measurements ranging from 12° to 86° are performed at a fixed laser wavelength of 880 nm close to the wurtzite InP band gap. We further coated the NW array with a nominally 10-nm thick gold film to investigate plasmonic effects. The experiments were accompanied by finite-difference time-domain (FDTD) simulations and transfer matrix method (TMM) calculations to support the interpretation of the experimental data. Our results demonstrate that NW arrays can be used as wavelength-dependent polarizers and analyzers. The operational wavelengths of these optical elements can be tuned as a function of the NW array material, its diameter, pitch, and the thickness of the deposited gold film. The gold-coating enhances the reflectance by a factor of 2 to 3 compared to the bare NW array, which is mainly attributed to plasmonic effects. Our experimental and theoretical investigations open new prospects for the on-chip integration of micrometer-sized optical elements essential for photonic integrated circuits (PICs) [37].

2. Methods

A. Experiments

In the spectrally resolved reflection measurements, an incandescent lamp illuminated the bare and gold-coated samples at a 15° incident angle with respect to the normal of the substrate surface (or a 75° glancing angle to the substrate surface). The incident light was polarized by a sheet polarizer in s- (TE wave) and p- (TM wave) orientation. The s- and p-polarization were conventionally defined as perpendicular and parallel to the plane of incidence, respectively (see inset of Fig. 2(a)). The light spot size (∼100 µm diameter) and its position on the NW array were adjusted by a combination of pinholes and a converging lens (f = 55 mm) between the samples and the lamp. Due to the small pitch of p = 500 nm, the NW array only provides the specular reflection in the investigated spectral range from 500 to 1000 nm. The signal of the specular reflection from the bare and gold-coated array as well as from the adjacent uncoated and gold-coated InP substrate was analyzed by a spectrometer. In order to obtain the spectral reflectance of the InP NW array without the lamp spectrum, we first calculated the ratio of the measured array and the substrate reflection. This ratio was then multiplied by the FDTD calculated reflectance from the InP substrate or gold-coated InP substrate, respectively. This evaluation method was experimentally more accurate than dividing the NW array reflectances by the measured lamp spectrum. More details are given in the supplemental document (SD) section 2 and in Fig. S3(a) and (b). A sketch of the experimental setup of the spectrally-resolved reflection measurements is shown in Fig. S1.

During the angle-resolved reflection measurements, the samples were irradiated with laser light at a wavelength of 880 nm (1.408 eV) provided by a Ti-Sapphire laser in the quasi-continuous wave (CW) mode. The incident light energy was chosen to be close to the wurtzite band gap energy of 1.415 eV [28]. The beam diameter of the laser emission was 6 mm, and the power of the laser beam was kept at ∼160 µW using optical density (OD) filters to avoid saturation of the photodiodes. A 45° beam splitter was installed to separate the laser light into a reference beam and an excitation beam. By using a λ/2 retardation waveplate, the incident laser light was rotated into s- or p-polarization. A beam spot of ∼10 µm in diameter (e^-2 diameter) was focused onto the NW arrays by a converging lens (f = 55 mm), and the angle of incidence was adjusted by a rotation stage from 12° to 86° in 2° steps. Movable photodiodes with high photosensitivity in the near-infrared region (800-1000 nm) were positioned to measure the power of the reference source and the specular reflection from the InP arrays, respectively, as shown in Fig. S2. Multimeters digitized the photodiode signals, which were then transferred to a computer-controlled program.

B. Growth and structural characterization of InP nanowire arrays

The wurtzite InP NW arrays were grown by selective area metal-organic vapor-phase epitaxy (SA-MOVPE) on (111) A zincblende InP substrates. Trimethylindium and phosphine were used as the precursors. Prior to growth, a 30-nm thick SiO₂ layer was deposited on the InP substrate and subsequently patterned by electron beam lithography with hexagonal arrays of circles, followed by chemical etching to form arrays of holes with a pitch of 500 nm. The patterned field had a size of 200 × 200 µm². A detailed description of the bottom-up SA-MOVPE growth of the hexagonal InP NW array has been reported in Ref. [21].

The outer diameter of the hexagonally shaped wurtzite InP NWs was ∼210 nm (corresponding to a 104 nm side length of the hexagon or an apothem length of ∼90 nm), and the length (L) of the NWs (parallel to the c-axis) was ∼1.3 µm. The InP NW array was subsequently conformally coated with a 12-nm thick Al₂O₃ film using atomic layer deposition to protect the InP NWs from the atmosphere and to reduce band bending [38–40]. Figure 1(a) shows scanning electron microscopy (SEM) images of the Al₂O₃/InP NW PhC array on the InP substrate.

 

Fig. 1. (a) SEM image of the hexagonal Al₂O₃-coated InP NW array (top view). (b) SEM image of an InP nanowire array nominally coated with a 10 nm thick gold film viewed at an angle of 30°. The image reveals a granular gold film (yellow-colored for better visualization) with gold accumulation on the top and reduced film thickness at the bottom of the nanowires because of shadowing.

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Fig. 2. Spectrally resolved reflectance of an InP NW array for (a) s-polarized (full black squares) and (b) p-polarized light (full red circles) ranging from 500 to 1000 nm. Thick black and red lines show reflectance simulations for s- and p-polarized light, respectively. Integer numbers k at the first and last interference maximum within the spectral range are indicated. The inset in (a) shows a sketch of the NW array with incident s- and p-polarized light. (c) Refractive index for s- (full black squares) and p-polarized light (full red circles) extracted from (a) and (b). The blue line shows the refractive index of the collective HE11a mode of the InP NW array. (d) Reflectance ratio of s/p- (black line) and p/s-polarized light (red line). The inset shows the calculated polar plot of the reflected laser light intensity I_R at ∼795 nm. Full blue squares indicate the measured reflectance values R_s and R_p from (a) and (b). The open black circles are I_R values from FDTD simulations at different polarization angles $\phi$

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In order to study the influence of a thin gold film on the array reflectance, a nominally 10-nm thick gold layer was deposited around the NWs by organic molecular beam deposition (OMBD) at an evaporation temperature of 1050 °C. An SEM image of the InP nanowire array that was coated with the gold film (yellow-colored for better visualization) is shown in Fig. 1(b). The image reveals an accumulation of gold on the top with a thickness of approximately 30 nm (estimated from the gold particle sizes) and an approximately 10-nm thick continuous gold coating around the NW within ∼100 nm measured from the top. With increasing distance from the NW tip towards the substrate, the gold coating becomes granular and discontinuous. The reduced gold coverage is caused by shadowing in the narrowly spaced NW array.

3. Results and discussion

3.1. Uncoated NW array

Figures 2(a) and (b) show the reflectance spectrum of the uncoated NW array for s- (full black squares) and for p-polarized light (full red circles), respectively, with an incidence angle of 15° relative to the normal direction of the array. The inset in Fig. 2(a) shows the polarization directions of s- and p-polarized light with respect to the main NW axis. The reflectance spectra reveal pronounced oscillations, which are slightly redshifted for p-polarization. In order to find the origin of these oscillations and the redshift, we performed FDTD reflectance simulations (see full black and red lines in Fig. 2). In these simulations (for best fit), a hexagonal InP NW cross-section with an outer diameter of 216 nm (corresponding to an apothem length of ∼93 nm) close to the physical dimensions shown in the SEM image in Fig. 1(a) was used. In addition, a 12-nm thick Al₂O₃ coating around the InP NWs and a hexagonal photonic lattice structure with a lattice constant (pitch) of 500 nm were specified. Since the dielectric constant for wurtzite InP has not yet been experimentally measured, the complex refractive index n was approximated by shifting the optically isotropic zincblende dielectric constants [41] by 80 meV to a higher energy corresponding to the larger band gap of wurtzite InP [42].

The oscillations of the calculated reflection spectra are very sensitive to the length L of the NWs. The simulations show the best agreement when L = 1.25 µm was chosen which is close to the measured NW length of 1.3 µm with SEM (see Fig. 1(b)). Longer or shorter NW lengths in the simulations lead to shorter or longer oscillation periods indicating that the reflection oscillations are due to Fabry-Perot interferences along the length of the NWs. The observed redshift is caused by the strong intrinsic positive [36] birefringence of the NW array. The discrepancies of the Fabry-Perot interference amplitudes between simulations and experiment, particularly in the transparent spectral region, are attributed to light scattering due to surface roughness and length deviation of the InP nanowires in the array.

Figure 2(c) shows the NW array effective refractive indices n(λ) for incident s- and p-polarized light. The refractive index values were extracted from the position of interference of spectral maxima and minima according to $k\lambda = 2n(\lambda )d$ and $(k + {1 / 2})\lambda = 2n(\lambda )d$, respectively, with k being an integer indicated in Fig. 2(a) and 2(b). Based on Snell’s Law, the geometric path length $\phi$ is expressed by $d = L/\cos [sin{(\sin \theta /n(\lambda ))^{ - 1}}]$, with $\theta = 15^\circ$ and $L = 1.25\;\mu \textrm{m}$. To remove any ambiguity of the integer values k, the FDTD simulated reflectance spectrum was continued to 2000 nm. The extracted refractive index values for s-polarized light (see Fig. S5 in the supplemental document (SD)) were fed into a transfer matrix method (TMM) calculation [43,44]. The experimentally obtained reflectance spectrum, the FDTD simulation as well as the TMM calculation curves are shown in Fig. S4. They demonstrate that the interference maximum at λ = 950 nm is unambiguously linked to k = 4. The origin of the dispersion in the transparent region (ranging from 830 to 1000 nm) can be clarified with 2D FDTD simulations. The simulated refractive index of the fundamental collective HE11a mode in a NW array containing 61 NWs for normal incidence is shown in Fig. 2(c) as the blue curve. The simulated refractive index of the collective mode agrees well with the experimental values in the transparent region. Therefore, we conclude that the refractive index of the array is determined by the near-field coupling between the leaky HE11a (and HE11b) modes of the individual InP NWs [1]. The $|\textrm{E} |$-field profile of the leaky HE11a mode at 880 nm of a single NW is shown in Fig. S6(a), while the $|\textrm{E} |$-field profile of the collective HE11a array mode at 880 nm is shown in Fig. S7. Below 800 nm, the HE11a/b modes become increasingly more confined (see E-field profile at 550 nm in Fig. S6(b)); In this region, the HE11a/b modes reveal a high refractive index and contribute to the high absorptance in the NW array of ∼70%. A calculated absorptance spectrum of the InP NW array is shown in the SD section 5 in Fig. S8. Due to this high absorption, the Fabry Perot oscillations in the 500 to 830 nm range can no longer be solely attributed to waveguiding via collective HE11a/b mode. Instead, they originate from the propagation of light through near-field coupled higher-order leaky NW modes (TE01, HE12a/b, TM01 modes) with lower refractive index and absorption.

Figure 2(d) shows the experimental p- to s- (red line) and s- to p-reflectance ratio (black line) derived from Figs. 2(a) and 2(b). These reflectance ratios demonstrate that birefringent InP NW arrays can serve as a wavelength-dependent (partial) polarizer for unpolarized light. At high reflectivity ratios, the NW arrays can also be used to analyze the polarization state of coherent light. In Fig. 2(d), this is the case at λ ∼795 and 735 nm, where the ratios of the reflected light intensity reach ${I_p}:{I_s}\sim 11:1$ and ${I_s}:{I_p}\sim 6:1$, respectively. The electric field intensity of the polarized incident light after its reflection from the InP NW array is given by ${I_R} = {R_s}{I_0}{\sin ^2}(\phi ) + {R_p}{I_0}{\cos ^2}(\phi )$. R_s and R_p are the s- and p-polarized reflectance values shown in Figs. 2(a) and 2(b). As an example, a polar plot of I_R for incident linearly polarized light with a wavelength of λ = 795 nm as a function of its polarization orientation $\phi$ is shown as an inset in Fig. 2(d). Full blue squares indicate the measured reflectance values R_s (90 degrees) and R_p (0 degrees) from Figs. 2(a) and 2(b). The open black circles are intensity values I from FDTD simulations at different polarization angles $\phi$. The polar plot shows that the orientation $\phi$ of incident linearly polarized light can be analyzed with high accuracy. High polarization ratios at specified wavelengths can be achieved by modifying the pitch or diameter of the InP NWs or by choosing a different NW material, demonstrating the potential of NW arrays for a few micrometer-sized polarizing or analyzing optical elements on PIC chips.

Figure 3(a) shows results from the angle-resolved reflectance measurements and reflectance simulations with s- and p-polarized CW laser light at λ_L = 880 nm. The reflectance shows Fabry-Perot oscillations, which are shifted for s- and p-polarization for reasons discussed above. The inset in Fig. 3(b) depicts the extracted refractive indices of the NW array from the Fabry-Perot oscillations. With increasing angle of incidence, the oscillations are fading out, which is attributed to an increasing geometrical optical beam path inside the nanowire array causing increasing absorption and loss of coherence. For p-polarized light, the reflectance minimum at ∼65° is caused by the Brewster angle. The total reflectance reaches a high value when the angle of incidence approaches 90°, which is in accordance with the Fresnel equations. Figure 3(b) shows the angle-resolved experimental p- to s- (red line) and s- to p-reflectance ratio (black line). The observed birefringence again indicates that the InP NW array can be utilized as a polarizer for unpolarized light or as an analyzer at the incident angles of 12° and 28°. Interesting are the incident angles at ∼22° and ∼45°, where an interference minimum (k + 1/2 = 5.5 and k +1/2 = 6.5) of the s-polarized light sits on top of the interference maximum (k = 6 and 7) for p-polarized light. Since the reflectance ratios of both polarizations are nearly equal at these angles, the reflection does not change significantly as a function of the light polarization. Despite the NW array birefringence, the array acts like a typical mirror. Modifying the pitch or the diameters of the InP NWs can shift the reflectance to desired wavelengths and incident angles.

 

Fig. 3. (a) Angle-resolved reflectance of s-polarized (black squares) and p-polarized (red dots) 880 nm laser light. Thick solid black and red lines show reflectance simulations for s- and p-polarized light. (b) Reflectance ratio of s/p- (black line) and p/s-polarized light (red line) derived from (a). The inset shows the refractive index for s- and p-polarized light extracted from the Fabry-Perot oscillations in (a).

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3.2 Gold-coated array

Figures 4(a) and 4(b) show the reflectance spectra of the gold-coated NW array for s- (black symbols) and p-polarized (red symbols) light at an incident angle of 15° relative to the normal direction of the array. The simulated reflectance curves are shown as thick black and red lines. As mentioned before, the SEM images (see Fig. 1 (b)) revealed an approximately 30-nm thick gold cap and a ∼10-nm thick continuous gold coating within the first ∼100 nm measured from the NW tip. The gold coating then becomes discontinuous towards the substrate. Accordingly, a solid 30-nm thick gold cap and a continuous gold coating of 12-nm thickness for the top 90 nm NW length (for best fit) were used in the simulations. The granular gold coating below this length was treated as an air/gold effective medium (EM) coating [45,46]. A plasmonic near-field coupling of the gold particles was presumed with a gold filling fraction of 0.35 (for best fit) and a thickness of 12 nm. For the SiO₂/InP substrate, a solid gold layer of 15 and 30 nm thickness was chosen inside and outside the NW array field, respectively. The FDTD simulations reproduce the experimental reflectance spectra well for a length L = 1.28 µm (including the 30 nm high gold cap) of the gold-coated InP NWs. More details are provided in section 6 in the SD. The good agreement validates the treatment of the granular portion of the gold coating as an air-gold EM medium. Importantly, the overall reflectance in the gold-coated InP NW array increases by a factor of 2 to 3 compared to the uncoated array. A portion of the reflection enhancement is attributed to a plasmonic resonance of the gold caps on the tip of the InP NWs. This interpretation is supported by FDTD simulations shown in Fig. S9, which compare the reflectance ratios of arrays with and without a gold-coated substrate and with and without gold caps, respectively. The simulations reveal that the enhancement is not caused by the gold coverage of the InP substrate but is mainly caused by the gold caps. The interpretation is further supported by reflectance simulations of a gold cap array with a pitch of 500 nm and a gold cap apothem of 117 nm and 30 nm height (surrounded by air). The reflectance curves (see SD section 7, Fig. S10) of the gold cap array show a plasmonic resonance in the range between 600 and 900 nm.

 

Fig. 4. Spectrally resolved reflectance of a gold-coated InP NW array for (a) s-polarized (black squares) and (b) p-polarized light (red circles) ranging from 500 to 1000 nm. Thick black and red lines show reflectance simulations for s- and p-polarized light, respectively. Integer numbers k are indicated above the interference maxima. (c) Refractive index for s- (full black squares) and p-polarized light (full red circles) extracted from the interference extrema in (a) and (b). The small open red and black symbols show the extracted refractive indices of the uncoated InP array for comparison. The solid blue line shows the effective refractive index of the HE11 mode of the gold-coated InP array, while the dashed blue line is for the uncoated array. (d) Reflectance ratio of s/p- (black line) and p/s-polarized light (red line).

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The Fabry-Perot oscillations are slightly redshifted compared to those observed in the bare InP NW array indicating a higher refractive index for both s- and p-polarized light in the gold-coated array. Figure 4(c) shows the dispersion curve n(λ), extracted from the spectral position of the interference maxima and minima in the reflectance for s- (full black squares) and p-polarized light (full red circles). As for the bare InP NW array, the interference maximum at λ = 955 nm can be unambiguously assigned to k = 4. Also shown are the refractive indices for the uncoated InP NW array as open black squares (s-polarization) and open red circles (p-polarization) from Fig. 2(c). A comparison of the dispersion curves demonstrates the increase of the refractive indices in the gold-coated array in the transparent region. In the absorptive region, the refractive indices of the uncoated and gold-coated NW arrays become similar. The solid blue curve in Fig. 4(c) shows the 2D simulated effective refractive index of the fundamental collective H11a mode for 61 NWs at normal incidence. The simulation used a 12-nm thick gold-coated NW array with an effective medium gold-to-air ratio of 0.35 and a pitch of 500 nm. The dispersion curve n(λ) of the collective HE11a (from Fig. 2(c)) mode for the uncoated array is also shown as a dashed blue curve. A comparison of the dispersion curves indicates a clear increase of the refractive index when the NWs are gold-coated in the transparent region. Like for the uncoated InP NW array, the refractive index of the fundamental gold-coated NW array mode in the transparent region is dominated by the near-field coupling between the leaky HE11a/b modes of the individual gold-coated InP NWs. The coupling between higher-order leaky modes is again responsible for the refractive index below 830 nm and the occurrence of the Fabry-Perot oscillations.

Figure 4 (d) shows the experimental p- to s- (red line) and s- to p-reflectance ratio (black line) derived from Figs. 4(a) and 4(b). Compared to the uncoated NW array (see Fig. 2(d)), the reflectance ratios with high values are redshifted to ∼752 and 814 nm. The redshift is attributed to higher refractive index values of the gold-coated NW array than in the uncoated NW array.

Figure 5(a) shows the angle-resolved reflectance and the FDTD simulations from the gold-coated array with s-polarized (full black squares) and p-polarized (full red circles) laser light at λ_L = 880 nm. The angle-resolved reflectance for p-polarized light is very high, reaching values of up to 50% at an incidence angle of ∼45°. The reflectance of s-polarized light remains low at small incident angles but increases rapidly for incident angles > 60° according to the Fresnel equations. In addition, the p-polarized reflectance curve shows pronounced k = 6 and k = 7 Fabry-Perot oscillation maxima (the reflectance minimum at 80° is again Brewster angle related), while the oscillations are nearly not noticeable for s-polarized light. These observations indicate a significant light absorption for s-polarized light while the transparency for p-polarized light is high. This high transparency for p-polarized light is attributed to a plasmonic antenna effect [47]. The incident electric field component parallel to the long axis of the NW is directed via surface plasmons around each NW towards the gold-coated substrate, from which it is reflected. Our interpretation is supported by FDTD calculations for the angle-resolved absorption cross-section of a single gold-coated NW (including the 30 nm gold-cap) from s- and p-polarized light, which is shown in Fig. S11. The absorption cross-section for p-polarized light has a minimum at 45° and reaches a value as low as for an uncoated NW despite the gold coating (see Fig. S11). In contrast, the absorption cross-section for s-polarized light is higher by a factor of 2 at 45° than for p-polarized light, explaining the lack of Fabry-Perot oscillations for s-polarized light. The s- to p- and p- to s-polarization ratio in Fig. 5(b) demonstrates the capability of gold-coated NW arrays to be used as micrometer-sized polarizers or analyzers over a wide angular range between 30° and 65° and with a 2 to 3 times higher reflectance than in uncoated arrays. As mentioned before, high reflectance ratios at desired wavelengths can be achieved by changing the dimensions of the NW array, the NW material, and now, in addition, by adjusting the plasmonic antenna. The antenna can be tuned by selecting the NW length and the thickness of the gold coating.

 

Fig. 5. (a) Angle-resolved reflectance of s-polarized (full black squares) and p-polarized (full red circles) laser light at λ_L = 880 nm. Thick black and red solid lines show reflectance simulations for s- and p-polarized light, respectively. (b) Reflectance ratio of s/p- (black line) and p/s-polarized light (red line).

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4. Conclusion

We have investigated the specular reflection from an uncoated and a gold-coated photonic InP NW array for s- and p-polarized incident light. Both array types show pronounced Fabry-Perot oscillations. Because of the significant intrinsic birefringence in the NW array, the spectral position of the interference maxima and minima are shifted for p- and s-polarized light. FDTD simulations indicate that near-field evanescent wave coupling between the leaky HE11a/b NW modes is responsible for the refractive index dispersion of the NW array in the transparent region. Higher-order leaky modes are accountable for the array refractive index in the absorptive region. Gold-coating of the NW array leads to a significant increase of the reflectance which is partially attributed to the plasmon resonance of the gold caps on the tip of the NWs. Furthermore, there is a strong enhancement in the reflectance of p-polarized light (of up to 50% at an incident angle of 45°) when the InP NW array is gold-coated. This enhancement is attributed to a plasmonic antenna effect. The gold-coating further causes the refractive index to increase, which leads to a redshift of the Fabry-Perot oscillations compared to the uncoated NW array.

Since the Fabry-Perot oscillations can be tuned by the NW array and the gold coating dimensions, NW PhC arrays can be tailored to operate as micrometer-sized polarizers or analyzers or as polarization-independent reflection mirrors at desired wavelengths. Our experiments and simulations open new design opportunities for micrometer-sized optical elements, which are important for the realization of photonic integrated optical circuits