Fabrication of Porous Anodic Alumina (PAA) by High-Temperature Pulse-Anodization: Tuning the Optical Characteristics of PAA-Based DBR in the NIR-MIR Region

In this work, the influence of various electrochemical parameters on the production of porous anodic alumina (PAA)-based DBRs (distributed Bragg reflector) during high-temperature-pulse-anodization was studied. It was observed that lowering the temperature from 30 to 27 °C brings about radical changes in the optical performance of the DBRs. The multilayered PAA fabricated at 27 °C did not show optical characteristics typical for DBR. The DBR performance was further tuned at 30 °C. The current recovery (iamax) after application of subsequent UH pulses started to stabilize upon decreasing high (UH) and low (UL) voltage pulses, which was reflected in a smaller difference between initial and final thickness of alternating dH and dL segments (formed under UH and UL, respectively) and a better DBR performance. Shortening UH pulse duration resulted in a progressive shift of photonic stopbands (PSBs) towards the blue part of the spectrum while keeping intensive and symmetric PSBs in the NIR-MIR range. Despite the obvious improvement of the DBR performance by modulation of electrochemical parameters, the problem regarding full control over the homogeneous formation of dH+dL pairs remains. Solving this problem will certainly lead to the production of affordable and efficient PAA-based photonic crystals with tunable photonic properties in the NIR-MIR region.


Introduction
Distributed Bragg reflectors (DBRs) are 1D photonic crystals (PCs) built of alternate low and high refractive index (RI) layers designed to forbid specific light to propagate in the structure. This phenomenon arises from the partial reflection of a wavelength that is close to four times the optical thickness of the layers from each layer boundary. As a consequence of constructive interference of the multiple reflections, DBR demonstrates high reflectance (or low transmittance) of light in a given part of the spectrum, which is called photonic stopband (PSB). DBRs are frequently used in LEDs [1,2], solar cells [3,4], or vertical-cavity surface-emitting lasers [5,6] as important optical components that enhance luminous or light trapping efficacy. Conventional DBRs are made of two different materials that require careful consideration of their optical and mechanical properties, as well as when choosing a reliable/reproducible method to grow the anticipated structure. This approach has many limitations, appeared to be very interesting. It was observed that for the DBR prepared at 25 • C, photonic stopbands (PSBs) were split and hardly distinguishable, whereas the DBR synthesized at 30 • C demonstrated well-resolved and symmetric PSB peaks, shifted towards red part of the spectrum. Hence, the 25 to 30 • C region is further investigated in this work. In Figure 1, current density (i a )-time (t) transients along with the corresponding transmittance spectra of the multilayered PAA prepared during pulse anodization in the temperature range 26-29 • C, are shown (for comparison, the transmission spectrum of the sample anodized at 30 • C is also presented [27]).
Materials 2020, 13, 0 4 of 18 (PSBs) were split and hardly distinguishable, whereas the DBR synthesized at 30 • C demonstrated well-resolved and symmetric PSB peaks, shifted towards red part of the spectrum. Hence, the 25 to 30 • C region is further investigated in this work. In Figure 1, current density (i a )-time (t) transients along with the corresponding transmittance spectra of the multilayered PAA prepared during pulse anodization in the temperature range 26-29 • C, are shown (for comparison, the transmission spectrum of the sample anodized at 30 • C is also presented [27]). As can be seen, up to 27 • C PSBs remain distorted. The peaks start to shape up again at 28 • C. Furthermore, the spectral positions of the bands shift towards the red part of the spectrum as the temperature increases. Although above 6 µm Al 2 O 3 does not transmit light due to absorption by Al-O bond vibrations [28,29], in the sample fabricated at 28 • C, just above the edge of the transmission, a vague first order PSB (λ 1 ) can be also discernable. The resonance peaks were assigned to different orders of a given stop band based on the Bragg-Snell equation [30], assuming the angle of incidence θ 0 (λ i , i = 1-4, correspond to 1-4 orders of PSB). The broad peak at around 3000 nm, present in all spectra and marked by vertical, black, dotted line, originate from the OH group vibrations of adsorbed water [31].
In Figure 2, BSE images of the PAA multilayered structure prepared at 29 (a), 28 (b), 27 (c), and 26 • C (d) are demonstrated, where the material density contrast between alternate and subsequent d H (formed under U H ) and d L (formed under U L ) layers are clearly visible. As can be seen in Figure 1a, the current recovery peak (the i a max was determined as in the work [27]) after application of subsequent U H pulses decreased with the number of cycles, which indicates a decrease of the total amount of charge involved in the anodization reaction. The decreasing amount of the net amount of charge, in turn, means that the thickness of the d H segments grown at the following U H pulses will be gradually reduced. In Figure 2e, the normalized i a max as a function of number of cycles is presented for the As can be seen, up to 27 • C PSBs remain distorted. The peaks start to shape up again at 28 • C. Furthermore, the spectral positions of the bands shift towards the red part of the spectrum as the temperature increases. Although above 6 µm Al 2 O 3 does not transmit light due to absorption by Al-O bond vibrations [28,29], in the sample fabricated at 28 • C, just above the edge of the transmission, a vague first order PSB (λ 1 ) can be also discernable. The resonance peaks were assigned to different orders of a given stop band based on the Bragg-Snell equation [30], assuming the angle of incidence θ~0 (λ i , i = 1-4, correspond to 1-4 orders of PSB). The broad peak at around 3000 nm, present in all spectra and marked by vertical, black, dotted line, originate from the OH group vibrations of adsorbed water [31].
In Figure 2, BSE images of the PAA multilayered structure prepared at 29 (a), 28 (b), 27 (c), and 26 • C (d) are demonstrated, where the material density contrast between alternate and subsequent d H (formed under U H ) and d L (formed under U L ) layers are clearly visible. As can be seen in Figure 1a, the current recovery peak (the i a max was determined as in the work [27]) after application of subsequent U H pulses decreased with the number of cycles, which indicates a decrease of the total amount of charge involved in the anodization reaction. The decreasing amount of the net amount of charge, in turn, means that the thickness of the d H segments grown at the following U H pulses will be gradually reduced. In Figure 2e, the normalized i a max as a function of number of cycles is presented for the samples synthesized at different temperature. The i a max course can be well described by a simple first order exponential decay (y = A 1 exp(−x/d c ) + y 0 , where A 1 is the amplitude, y 0 is the offset term that represents residual i max , and d c is the decay constant). In this particular case, the d c indicates the U H pulse at which the course reaches 1/e or ≈37% of the difference between the initial (y 0 ) and final (y) steady state values. y 0 value was fixed to 0.5 for all samples, to assure the same fitting range from the maximum value up to the point where the i a max reaches the half of its maximum value. The larger the d c value, the more efficient is the current recovery under subsequent U H pulses, and thus a better selection of the electrochemical parameters to maintain a stable pulse anodization is achieved. Based on this analysis, the processes conducted at 27 (d c = 11) and 30 • C (d c = 12) were better designed than the other ones ( Figure 2e). This is, however, not compatible with optical analyses (Figure 1b), where the sample produced at 27 • C did not show features characteristic of the DBR structure. It thus seems that the variability of the d c parameter within the range 6-12 does not significantly affect the optical characteristics of the multilayer PAA structure. The only parameter that matters in this case is the temperature: the multilayered PAA transforms into the DBR only at relatively high temperature (28-30 • C). The statement is also supported by the difference between initial (mean thickness of the first three layers) and final (mean thickness of the last three layers) d H . Figure 2d shows that this difference weakens as the anodizing temperature increases. However, it has to be noticed that starting from 28 • C, the number of d H +d L pairs decreases (the numbers are shown in square frames in Figure 2f). This means that the thickness of initial d H was not determined for exactly the first three (1-3) layers, but for 2-4, or even 6-8 ones, which might have decreased slightly its average value. Consequently, the difference between initial and final d H thickness is a bit underestimated. The lack of several layers may be due to non-equilibrated rate-and diffusion-controlled processes at a high anodization temperature [27]. However, it is also very probable that the first layers are simply falling off from the stack after the synthesis. The BSE image of the sample PAA-26 • C (Figure 2d), for instance, suggests that the first segments are more brittle and vulnerable to exfoliation. The exfoliation may occur during the Al dissolution in the mixture of HCl acid and CuCl 2 or during the preparation of the samples to analysis (the samples have to be broken in order to analyze their cross-sectional). While the thickness of the d H layers increased substantially with the anodizing temperature, the d L for the samples anodized at 26-29 • C apparently stayed on more or less the same level ( Figure 2f). final (y) steady state values. y0 value was fixed to 0.5 for all samples, to assure the same fitting range from the maximum value up to the point where the ia max reaches the half of its maximum value. The larger the dc value, the more efficient is the current recovery under subsequent UH pulses, and thus a better selection of the electrochemical parameters to maintain a stable pulse anodization is achieved. Based on this analysis, the processes conducted at 27 (dc = 11) and 30 °C (dc = 12) were better designed than the other ones ( Figure 2e). This is, however, not compatible with optical analyses (Figure 1b), where the sample produced at 27 °C did not show features characteristic of the DBR structure. It thus seems that the variability of the dc parameter within the range 6-12 does not significantly affect the optical characteristics of the multilayer PAA structure. The only parameter that matters in this case is the temperature: the multilayered PAA transforms into the DBR only at relatively high temperature (28-30 °C). The statement is also supported by the difference between initial (mean thickness of the first three layers) and final (mean thickness of the last three layers) dH. Figure 2d shows that this difference weakens as the anodizing temperature increases. However, it has to be noticed that starting from 28 °C, the number of dH + dL pairs decreases (the numbers are shown in square frames in Figure 2f). This means that the thickness of initial dH was not determined for exactly the first three (1-3) layers, but for 2-4, or even 6-8 ones, which might have decreased slightly its average value. Consequently, the difference between initial and final dH thickness is a bit underestimated. The lack of several layers may be due to non-equilibrated rate-and diffusion-controlled processes at a high anodization temperature [27]. However, it is also very probable that the first layers are simply falling off from the stack after the synthesis. The BSE image of the sample PAA-26 °C (Figure 2d), for instance, suggests that the first segments are more brittle and vulnerable to exfoliation. The exfoliation may occur during the Al dissolution in the mixture of HCl acid and CuCl2 or during the preparation of the samples to analysis (the samples have to be broken in order to analyze their cross-sectional). While the thickness of the dH layers increased substantially with the anodizing temperature, the dL for the samples anodized at 26-29 °C apparently stayed on more or less the same level ( Figure 2f).   [27] are also shown for comparison).
Previously, an improvement of the geometrical and photonic properties of the PAA-based DBR produced at 30 • C upon increasing the U H ->U L rate was observed [27]. The same protocol was applied to the PAA sample anodized at 29 • C. As visible in Figure 3, the increase of this parameter resulted in a complete distortion of the PSBs. Already under application of the U H ->U L = 0.156 V/s, the transmission spectrum lacks the features typical for the DBR structure. This is quite surprising considering the small (only by 1 • C) temperature drop. Figure 4a-c shows typical multilayer structures with an increased number of d H +d L layers as the U H ->U L rate increases. The d c determined for the samples prepared with the increased U H ->U L rates is even larger than the d c determined for the sample anodized with the lowest U H ->U L rate = 0.078 V/s ( Figure 4d). Again, this might suggest that the d c within the 8-13 range does not influence the optical performance of the PAA material. As previously observed [27], the thickness of the initial and final d H layers decreases as the U H ->U L increases (Figure 4e), whereas d L demonstrates a quite stable behavior. Taking into account the possible exfoliation of the first two layers (in the sample anodized under the 0.078 V/s rate) and the first one (in the sample anodized under the 0.156 V/s rate) from the potential 20-layer stack, the difference between the initial and final d H seems to remain stable. What is, therefore, the reason causing the deterioration of the PSBs in these samples? It is possible that the temperature of 29 • C is already too low to maintain good pore reorganization when the change from U H to U L is too fast.   Since lowering the temperature already by 1 • C has such detrimental effect on the optical characteristics of PAA multilayered structures, we decided to analyze the influence of other anodizing parameters on the PAAs prepared at 30 • C using an optimal U H ->U L rate (0.234 V/s), as determined based on the previous investigations [27]. At first, the effect of U H and U L values and U H -U L contrast of the geometrical and optical properties of multilayer PAAs was analyzed. In Figure 5, the i a (t) curves along with the corresponding transmission spectra recorded for PAA anodized under different U H and U L pulses, are shown. As can be seen, the photonic characteristics typical for the DBR structure are maintained for all the studied samples. Upon a decrease of U H from 50 to 40 V and simultaneously a decrease of the U H -U L contrast, the PSB peaks shift towards the blue part of the spectrum, while keeping their intensity and symmetry. Additionally, in the spectrum of the PAA_40-20 sample, a clear λ 1 band is discernable at~5560 nm. Decreasing U L from 20 to 10 V, and at the same time increasing the U H -U L contrast, causes a further shift of the PSB peaks towards shorter wavelengths. In general, the PAA-based DBRs in this batch of the samples preserve their good optical characteristics, which is particularly visible when monitoring the λ 2 mode behavior. It can be stated that the best optical performance demonstrates the PAA_40-15 sample for which both λ 1 and λ 2 bands are symmetric and intensive (T = 0.3 and 0.07, respectively). In the PAA_40-10 sample, the λ 1 and λ 2 peaks appear to weaken and become less symmetric. The intensity of higher photonic modes (e.g., λ 3 and λ 4 ) varies from sample to sample. It is well known that higher interference modes are more sensitive to possible structural imperfections or boundary conditions [32]. Therefore, any deviation from ideal multilayered structure (e.g., irregular layer thickness) or some damages in the structure, is more noticeable in higher modes.  Since lowering the temperature already by 1 °C has such detrimental effect on the optical characteristics of PAA multilayered structures, we decided to analyze the influence of other anodizing parameters on the PAAs prepared at 30 °C using an optimal UH-> UL rate (0.234 V/s), as determined based on the previous investigations [27]. At first, the effect of UH and UL values and UH-UL contrast of the geometrical and optical properties of multilayer PAAs was analyzed. In Figure  5, the ia(t) curves along with the corresponding transmission spectra recorded for PAA anodized under different UH and UL pulses, are shown. As can be seen, the photonic characteristics typical for the DBR structure are maintained for all the studied samples. Upon a decrease of UH from 50 to 40 V and simultaneously a decrease of the UH-UL contrast, the PSB peaks shift towards the blue part of the spectrum, while keeping their intensity and symmetry. Additionally, in the spectrum of the PAA_40-20 sample, a clear λ1 band is discernable at ~5560 nm. Decreasing UL from 20 to 10 V, and at the same time increasing the UH-UL contrast, causes a further shift of the PSB peaks towards shorter wavelengths. In general, the PAA-based DBRs in this batch of the samples preserve their good optical characteristics, which is particularly visible when monitoring the λ2 mode behavior. It can be stated that the best optical performance demonstrates the PAA_40-15 sample for which both λ1 and λ2 bands are symmetric and intensive (T = 0.3 and 0.07, respectively). In the PAA_40-10 sample, the λ1 and λ2 peaks appear to weaken and become less symmetric. The intensity of higher photonic modes (e.g., λ3 and λ4) varies from sample to sample. It is well known that higher interference modes are more sensitive to possible structural imperfections or boundary conditions [32]. Therefore, any deviation from ideal multilayered structure (e.g., irregular layer thickness) or some damages in the structure, is more noticeable in higher modes.   (Figure 6e). This trend is followed by the decrease of the difference between initial and final d H values (Figure 6f). In the PAA_50-20, PAA_45-20, and PAA-40-20 samples, the different decreases are owed to the U H -U L contrast decrease and is the smallest for the PAA_40-20 sample. This sample is also built out of complete 20 d H +d L segments, suggesting that the actual difference between initial and final d H layers in the samples PAA_50-20 and PAA_45-20 (16 d H +d L pairs) is even greater than shown in Figure 6f. The difference seems to decrease as well for the subsequent PAA-40-15 and PAA-40-10 samples, despite the increase of the U H -U L contrast. This is, however, an apparent effect coming from the reduced number of the d H +d L pairs. The sample PAA_40-10 consists of only 13 d H +d L segments, so initial d H value was actually determined for the 8th to 10th layer, not for the first three (1-3) real layers. The BSE image of the PAA_40-10 sample (Figure 6d) strongly indicates that this DBR structure is more susceptible to exfoliation as compared to other samples, which is most likely caused by its higher brittleness. The higher fragility, in turn, may result from relatively low values of potential pulses applied during anodization (U L is only 10 V). Owing to the large structural imperfection, the PAA_40-10 DBR demonstrates also a slightly worse optical characteristics (Figure 5b), as compared to other samples from this batch. Contrary to the d H behavior, both initial and final d L layers are stable in the PAA_50-20, PAA_45-20, and PAA-40-20 samples, and go down in the PAA-40-15 and PAA-40-10 samples due to the U L decrease. λ 1 band is discernable at~5560 nm. Decreasing U L from 20 to 10 V, and at the same time increasing the U H -U L contrast, causes a further shift of the PSB peaks towards shorter wavelengths. In general, the PAA-based DBRs in this batch of the samples preserve their good optical characteristics, which is particularly visible when monitoring the λ 2 mode behavior. It can be stated that the best optical performance demonstrates the PAA_40-15 sample for which both λ 1 and λ 2 bands are symmetric and intensive (T = 0.3 and 0.07, respectively). In the PAA_40-10 sample, the λ 1 and λ 2 peaks appear to weaken and become less symmetric. The intensity of higher photonic modes (e.g., λ 3 and λ 4 ) varies from sample to sample. It is well known that higher interference modes are more sensitive to possible structural imperfections or boundary conditions [32]. Therefore, any deviation from ideal multilayered structure (e.g., irregular layer thickness) or some damages in the structure, is more noticeable in higher modes.  Next, the influence of the UH and UL pulse duration on the multilayer PAA formation and its optical performance was tested. In Figure 7, the ia(t) curves and corresponding transmission spectra of the PAA-based DBRs prepared under UH with decreasing duration (tH) are shown. Owing to the shorter tH, the dH segments become progressively thinner. This results in a blue shift of PSBs. When Next, the influence of the U H and U L pulse duration on the multilayer PAA formation and its optical performance was tested. In Figure 7, the i a (t) curves and corresponding transmission spectra of the PAA-based DBRs prepared under U H with decreasing duration (t H ) are shown. Owing to the shorter t H , the d H segments become progressively thinner. This results in a blue shift of PSBs. When U H pulses with t H = 240 s are applied, a weak outline of the λ 1 peak is already visible in the transmission spectrum. The λ 1 band becomes well-resolved in the PAA-based DBR anodized with t H = 180 s.  The BSE images of the PAA_300-480, PAA_240-480, and PAA_180-480 are shown in Figure 8a, b, and c, respectively. The course of i a max is comparable for all samples from this batch (Figure 8d). The d c parameter is within the range of 5 to 13. The decrease of d H segments upon shortening of the U H duration is well presented in Figure 8d. Moreover, with shorter t H, the number of d H +d L layers increases; the PAA_180-480 DBR is built out of complete 20 d H +d L segments. Taking into account the lower number of the d H +d L pairs in other DBRs (Figure 8e) it can be concluded that the difference between initial and final d H remains pretty stable. Therefore, the analysis presented in Figure 8 confirms similar optical characteristics for all these samples: the PSBs are well-resolved (although some λ 2 bands are overlapped with water peak), symmetric, and intensive ( Figure 7). The BSE images of the PAA_300-480, PAA_240-480, and PAA_180-480 are shown in Figure 8a, b, and c, respectively. The course of i a max is comparable for all samples from this batch (Figure 8d). The d c parameter is within the range of 5 to 13. The decrease of d H segments upon shortening of the U H duration is well presented in Figure 8d. Moreover, with shorter t H, the number of d H +d L layers increases; the PAA_180-480 DBR is built out of complete 20 d H +d L segments. Taking into account the lower number of the d H +d L pairs in other DBRs (Figure 8e) it can be concluded that the difference between initial and final d H remains pretty stable. Therefore, the analysis presented in Figure 8 confirms similar optical characteristics for all these samples: the PSBs are well-resolved (although some λ 2 bands are overlapped with water peak), symmetric, and intensive ( Figure 7).
In Figure 9, the i a (t) curves and corresponding transmission spectra of the PAA-based DBRs fabricated under U L with decreasing duration (t L ) are demonstrated. With decreasing t L , a small blue shift of PSBs is observed. However, these DBRs seem to start losing their good photonic properties: the PSBs are becoming progressively broadened and start to severely split as t L decreases (Figure 9b). The samples PAA_180-480, PAA_180-420, PAA_180-360, and PAA_180-300 consist of full 20 d H +d L pairs (Figure 10a-c) and the d c parameter varies within the range 10-18 ( Figure 10d). Moreover, the difference between initial and final d H appears to be stable for all samples in this series or even slightly decreases when shortening the t L (Figure 10e). The latter observation may indicate more efficient diffusional processes occurring when t L is shortened. Hence, both current behavior and determined geometrical features do not say much about the source of the slight but visible worsening of optical performance. However, the changes are evident upon shortening t L . It can thus be supposed that the resulted thinner d L segments (Figure 10e) somehow affect an overall multilayer structure, which becomes to a certain degree distorted. The distortion can for instance be linked with worse pore arrangement and circularity in the d L layers formed under shorter U L pulses. It was demonstrated that these parameters depend on the anodizing time: the longer the anodization time, the better the pore arrangement and circularity [33]. In Figure 9, the ia(t) curves and corresponding transmission spectra of the PAA-based DBRs fabricated under UL with decreasing duration (tL) are demonstrated. With decreasing tL, a small blue shift of PSBs is observed. However, these DBRs seem to start losing their good photonic properties: the PSBs are becoming progressively broadened and start to severely split as tL decreases (Figure 9b). The samples PAA_180-480, PAA_180-420, PAA_180-360, and PAA_180-300 consist of full 20 dH + dL pairs (Figure 10a-c) and the dc parameter varies within the range 10-18 ( Figure 10d). Moreover, the difference between initial and final dH appears to be stable for all samples in this series or even slightly decreases when shortening the tL (Figure 10e). The latter observation may indicate more efficient diffusional processes occurring when tL is shortened. Hence, both current behavior and determined geometrical features do not say much about the source of the slight but visible worsening of optical performance. However, the changes are evident upon shortening tL. It can thus be supposed that the resulted thinner dL segments (Figure 10e) somehow affect an overall multilayer structure, which becomes to a certain degree distorted. The distortion can for instance be linked with worse pore arrangement and circularity in the dL layers formed under shorter UL pulses. It was demonstrated that these parameters depend on the anodizing time: the longer the anodization time, the better the pore arrangement and circularity [33].     Summarizing, the PAA-based DBR is extremely sensitive to pulse anodization temperature. In the temperature >10 • C and up to 27 • C the typical DBR features are not observed in transmission spectra. Above 27 • C, the PAA multilayer structure transforms into the DBR photonic crystal, which is manifested by the appearance of distinct, well-resolved, and symmetric peaks in the transmission spectra. Within the conditions applied in this study, optimal PAA-based DBRs are produced at 30 • C using a U H ->U L drop rate close to 0.234 V/s. The optical properties of the DBRs formed under the high-temperature pulse-anodization can be tuned by changing other anodization parameters, such as U H , U L , U H -U L contrast, and t H . Decreasing t L causes progressive deterioration of the optical characteristics of the photonic crystals. On the other hand, too low U L voltage contributes to the formation of too much brittleness of the multilayer PAA material and, consequently, harsh exfoliation of initial d H and d L layers.
DBR performance (i.e., transmittance and PSB bandwidth) is determined by the number of pairs as well as the refractive index contrast between low and high RI layers [34]. A larger contrast and higher number of pairs can lead to lower transmittance and wider PSBs. In the electrochemical production of PAA-based DBR at relatively high temperature, the most challenging task is to control a uniform growth of d H +d L pairs, which is directly proportional to the net amount of the charge involved in the anodization reaction. The non-uniform layer formation can be partially counteracted by decreasing U H and U L values and U H -U L contrast. Nevertheless, it is still difficult to maintain a steady current recovery (constant value of i a max ) during the whole process. Therefore, to master the production of PAA-based photonic crystals with the desired photonic properties in NIR-MIR spectral range, this experimental approach will be modified in future studies. The PAA-based DBRs with the best optical properties observed in this work are presented in Table 1 with the anodization parameters used to produce those samples. Table 1. Electrochemical parameters applied during a 20-cycle pulse anodization at relatively high temperatures, which was used to synthesize PAA-based DBRs with the best optical properties along with the observed PSBs (T stands for transmission intensity).

Sample
Temperature The observed optical resonances generated by the samples gathered in the Table 1 were also verified theoretically assuming a DBR structure built of uniform segments that are formed under equilibrated conditions (no rate and diffusion limitations). These conditions are operative during application of the first U H and U L pulses in a given pulse sequence. Accordingly, the thickness of the initial d H and d L layers can be considered as the one that would be repeated in every cycle if no rateand/or diffusion-limited processes occurred, thereby assuring the same amount of charge flowing in each cycle. However, owing to the lack of the first one to three layers in some of the multilayer stacks, the thickness of the initial d H and d L segments (d H init and d L init , respectively) was determined with support of the data established in ref. [35]. In Figure 11a, the growth rate (k PAA ) of PAA layers formed under pulse anodization (this work) is compared with that determined in [35]. It can be seen that owing to the lack of the first layers in the DBR stacks, the k PAA of d H init segments formed at 40 and 45 V were underestimated. However, the k PAA of the d L init segments formed at 15 and 20 V and that of d H init formed at 50 V (the PAA_180-480 sample with the full 20 d H +d L pairs) agreeed very well with the trend established in ref. [35]. The d H init and d L init thicknesses for the DBR produced at 29 • C was measured directly on the sample PAA_29 • C. In order to determine refractive indices of the d H init and d L init layers, porosity of PAA layers was calculated using the following equation [36]: where D p is pore diameter and D c is the interpore distance. To measure D p and D c of d H layers, two-period stacks were synthesized using the following pulse sequence: U H -U L -U H -U L , whereas the U L -U H -U L -U H inverse pulse sequence was used to analyze the d L layers. In Figure 11b Figure 11d). The hexagonal cells form an almost perfect honeycomb structure. Since it was not possible to determine both pore diameter and interpore distance from such complex images using the protocol described in the Section 2, the D d L and D c L were derived from the formulas developed in the work [37]. All geometrical parameters of PAA layers are gathered in Table 2.
Having porosity values, the refractive indices of the d H init and d L init segments (n H and n L , respectively) were determined based on the Bruggeman's effective medium theory [38], and the effective refractive index (n eff ) of each double layer was calculated using the following formula [39]: Bragg-Snell law gives the spectral positions of photonic stop bands (PSBs) [30]: where λ is the wavelength of a photonic stop band (PSB), m is the order of the PSB, d is the periodicity , θ is the angle of incidence (θ~0 in the studied cases), n eff is the effective refractive index, and n air is the refractive index of air. The optical constants and the calculated PSBs are presented in Table 3.
where Dp is pore diameter and Dc is the interpore distance. To measure Dp and Dc of dH layers, two-period stacks were synthesized using the following pulse sequence: UH-UL-UH-UL, whereas the UL-UH-UL-UH inverse pulse sequence was used to analyze the dL layers. In Figure 11b-f, SEM images of dH and dL layers (top views) of the selected samples are shown. It can be seen that the dL layers have a complex structure where a few smaller pores are located within a larger hexagonal cell (about 10 pores per cell; the image showing larger magnification of the dL layer in Figure 11d). The hexagonal cells form an almost perfect honeycomb structure. Since it was not possible to determine both pore diameter and interpore distance from such complex images using the protocol described in the Section 2, the Dd L and Dc L were derived from the formulas developed in the work [37]. All geometrical parameters of PAA layers are gathered in Table 2.     As can be seen, the resulting spectral positions of λ 1 and λ 2 are shifted towards longer wavelengths as compared to the observed ones (λ 1 obs and λ 2 obs ), suggesting that the real n eff and/or d values of the studied DBRs are smaller. Therefore, the PSBs spectral positions were also determined, taking into account the mean values of both initial and final d H and d L layers (d H and d L , respectively, Table 2; d = d H + d L in this case). The corresponding PSBs (λ 1 and λ 2 ) are collected in Table 3. The n eff remained practically stable when d H init and d L init were substituted by the d H and d L in Equation (2): its values changed only in the third decimal place. Now, the λ 1 and λ 2 are much closer the observed ones (λ 1 obs and λ 2 obs ). The match would be even better if an average porosity of all 20 d H and d L pairs was known. The porosity of subsequent segments may also vary: in the 20-period DBR stacks the initial segments most likely have larger pore diameters-and thus porosity-than the final ones due to the prolonged stay in the oxalic solution. Consequently, the average P H and P L would be larger than the ones determined for the two-period stacks. The larger porosity, in turn, contributes to smaller refractive indices of porous layers and thus to smaller n eff . In Table S1 (Supplementary Materials), simulated optical spectra of the PAA-29 • C, PAA_45-20, PAA_40-15, and PAA_180-480 DBRs are demonstrated for d H init , d L init , and the n H and n L determined based on the layer porosities. The optical spectra are compared with those simulated for the d H and d L and for n H and n L chosen to make PSBs match with the the λ 1 obs and λ 2 obs . Based on this analysis it appears that the actual n H and n L of the DBRs are in the ranges 1.28-1.41 and 1.18-1.24, respectively. The effective refractive index, in turn, lies within the range 1.24-1.39.

Conclusions
In this work, the influence of various electrochemical parameters on the production of PAA-based DBRs during high-temperature-pulse anodization was studied. It was observed that the process and resulting DBR properties are very sensitive to anodizing temperature: lowering the temperature from 30 to 27 • C brings about drastic changes in optical performance of the DBRs. The multilayered PAA fabricated at 27 • C did not demonstrate optical properties typical for DBR. Upon decreasing U H and U L potential and U H -U L contrast, the current recovery (i a max ) after application of subsequent U H pulses started to stabilize, which was also manifested by a smaller difference between initial and final d H thickness and a better DBR performance. The optimal U H -U L contrast at 30 • C is 25 V: in the PAA_40-15 sample both λ 1 and λ 2 bands in the transmission spectra are well-resolved, intensive and symmetric. Furthermore, shortening the U H pulse duration results in a progressive shift of PSBs towards blue part of the spectrum without signs of PSB deterioration. The sample PAA_180-480 generates well-developed peaks in the MIR (λ 1 = 5183 nm) and NIR (λ 2 = 2697 nm) region. The effective refractive indices n eff for the best performing samples lie within the range 1.24-1.39 and are smaller than the ones calculated for perfect multilayer structures of uniform thickness and porosity. Despite the obvious improvement of DBR properties in the NIR-MIR region by modulation of electrochemical parameters, there is still a problem with a full control over the homogeneous formation of d H +d L pairs. Since the amount of charge determines the thicknesses of anodized segments at given anodization potentials, the problem with the non-uniform growth of d H +d L pairs can be solved, for instance, by designing potential pulse sequences with a given amount of charge for U H and U L pulses. In this approach, the duration of subsequent U H and U L pulses would be adjusted to the time needed to reach the same amount of charge for each U H and U L pulses-this work is now in progress.