Mitigating photon escape in thin-film photovoltaic devices via non-reciprocal optical path

Abstract

Breaking the optical symmetry is vital for light-harvesting devices, while the broadband asymmetric light manipulation remains challenging. Herein, optical non-reciprocity with subwavelength pyramid arrays (SPAs) is proposed to synergistically harness the Mie resonance and the multi-order diffraction for blocking light escaping. A forward optical transmittance of over 95% is obtained with an asymmetric ratio of over 2.5 dB in a wide spectral region that fully covers the absorption spectrum of organic solar cells (OSCs). The non-reciprocal optical path in OSCs reduces the threshold thickness of the active layer for efficient light-harvesting as well as the boost in charge extraction. The optimized OSCs achieve an efficiency of 20.70% and a certified value of 19.71%. The versatility of the optical non-reciprocity with SPAs has also been demonstrated for the performance enhancement in perovskite and quantum dot solar cells with different absorption spectra. This strategy surpasses traditional anti-reflective schemes and paves the way for optical manipulation in thin-film optoelectronic devices.

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Broader context

For light-harvesting technologies, the efficient photon management is key to overcoming long-standing efficiency limitations, like thin-film photovoltaics. Conventional anti-reflection coatings enhance light ingress but cannot prevent light from escaping, ultimately limiting device performance. Engineering non-reciprocal optical paths (SPAs) emerges as a transformative approach. This work introduces a paradigm by exploiting high-index subwavelength pyramid arrays to achieve broadband optical non-reciprocity through coupled Mie resonance and diffraction. By enabling strong forward transmission while suppressing backward leakage, this asymmetric design resolves the long-standing dilemma in boosting light-harvesting and charge extraction across organic, perovskite, and quantum dot solar cells. The established framework of non-reciprocal optical paths highlights asymmetric nanophotonic structures as a powerful and generalizable tool for controlling light flow in optoelectronic and energy-conversion systems, gaining opportunities for high-efficiency, compact, and directionally engineered photonic devices.

Introduction

Modern optoelectronics has experienced transformative progress driven by engineered light–matter interactions, where phenomena such as surface plasmon polaritons,^1–3 Mie resonances,^4–6 photonic band gaps,^7–9 and the Purcell effect^10,11 enable unprecedented control over light's amplitude, phase, and polarization. Particularly revolutionary has been the shift from symmetric optical configurations to direction-dependent architectures, facilitating the development of non-reciprocal waveguides, selective mode manipulation, and enhanced nonlinear responses.^12–17 These advancements hold great potential for light-harvesting technologies, where optimized photon management is key to overcoming long-standing efficiency limitations.

The core challenge of asymmetrical optical configuration lies in overcoming Lorentz reciprocity, which governs the symmetry of light propagation.^18–20 While magneto-optic effects^21–23 and nonlinear optics^24,25 have been explored as methods to break reciprocity, they are constrained by intrinsic limitations. For instance, Faraday rotation systems exhibit wavelength-dependent responses, nonlinear approaches are limited by power density thresholds, and the trade-offs between optical performance and electronic functionality pose significant hurdles, particularly in photovoltaic applications. Although geometric asymmetry, such as through metallic gratings or gradient metasurfaces, offers alternative pathways to achieve optical asymmetry, these methods often suffer from considerable transmission losses, a critical drawback for efficiency-driven applications like thin-film photovoltaics.^26–30

The design of thin-film photovoltaics epitomizes the trade-off between optical absorption and charge transport efficiency.^31–33 For instance, the state-of-the-art organic solar cells (OSCs) typically utilize thin (∼100 nm) active layers to minimize carrier recombination, but this also limits light-harvesting capacity due to reduced optical path lengths.^34,35 Conventional enhancement strategies, such as plasmonic nanostructures, photonic crystals, or textured surfaces, can degrade interfacial integrity, leading to charge transport losses.^36–38 Furthermore, symmetric non-invasive strategies like anti-reflective coatings, while improving light ingress, often exacerbate light egress from the device, reducing overall efficiency.^39,40 Therefore, a broadband asymmetric photon management strategy that does not sacrifice electron transport efficiency is a practicable way to resolve this dilemma in thin-film photovoltaic devices, but it has never been reported.

In this work, the trade-off between light absorption and charge transfer in thin-film photovoltaic devices has been addressed by proposing a non-reciprocal optical path. Subwavelength pyramid arrays (SPAs) based on titanium dioxide (TiO₂) were fabricated to excite Mie resonance and multiple-order diffraction for broadband asymmetric light response. The SPAs exhibit exceptional forward optical transmission (>95%) when illuminated from the apex, due to suppression of Fresnel reflections via a gradient refractive index surface. When illuminated from the base, multimode diffraction reduces backward transmission, achieving a 2.5 dB contrast (400–900 nm). By incorporating SPAs into OSCs with a thinned active layer, light-harvesting and charge extraction are simultaneously boosted, yielding a champion PCE of 20.7% and a certified value of 19.71%. The optimized SPAs exhibit robust performance enhancement in flexible OSCs, wide bandgap perovskite solar cells, and PbS quantum dot solar cells.

Results and discussion

Theoretical design of SPAs

To break the symmetry, diffraction is first introduced by constructing periodic cube arrays (Fig. 1a). This periodicity enables angle-dependent manipulation of higher-order diffraction. Diffraction efficiency varies with the incident wave vector, and the diffraction condition is given by

mλ = Λ(sin θ_i + sin θ_m) (1)

where m is the diffraction order, Λ is the period of the array, and θ_i and θ_m represent the incident and diffraction angles, respectively. For two-dimensional pyramid arrays, the geometry involves two-dimensional periodicity. Considering a pyramid with an in-plane period of Λ_x = Λ_y = P, the diffraction-induced vector changes are expressed as

Fig. 1 Theoretical design of SPA. Schematic diagram and simulated transmission spectra of (A) periodic cuble array and (B) single pyramid. (C) Simulated far-field optical field distribution of SPA. (D) Schematic optical path for flat, ME-integrated, and SPA-integrated substrates.

The total diffraction orders are derived from the lattice superposition equation of

G_m,n = ub_x + vb_y (3)

where (u, v) refers to the in-plane diffraction orders. Given that the incident vectors (k_in) and diffraction vectors (k_out) obey the phase-matching condition

k_out = k_in + G_u,v (4)

The components of the two-dimensional vectors are given by

For a periodic structure with a strong phase gradient in the propagation direction, it satisfies the equation of

and maximum diffraction orders (m_max) can be calculated byhere, H is the structural height, and Δn represents the refractive index (n) difference between the structure and the surrounding environment. Consequently, m_max exhibits an inverse relationship with λ. In case of a complicated situation of gradient phase distribution and resonance, m_max needs to be modified by a specific coefficient according to the assistance of optical simulation. Basically, m_max in backward transmission is smaller than that in forward transmission, mainly due to differences in n distribution in the opposite direction. To evaluate the contribution of each diffraction order, the diffraction efficiency (η) is then calculated. Considering the phase difference between forward and backward transmission, the forward diffraction efficiency (η_F) and backward diffraction efficiency (η_B) can be described asherein, the asymmetry factor of diffraction (A_diff) is described as

Fig. 1a plots the simulated forward transmittance (T_F) and backward transmittance (T_B) spectra of periodic cube arrays (P = 600 nm, H = 500 nm) composed of dielectric materials with different refractive indices. For n = 1.5, the array exhibits a high T_F exceeding 97%, accompanied by a small asymmetry. The weak n contrast results in low reflection and limited diffraction-induced asymmetry. As the n increases to 2.0 and 2.5, notable changes in optical behavior emerge. Higher n enhances the asymmetric transmission ratio, which exceeds 9 dB for the array with n = 2.5 (Fig. S1). However, this improvement in asymmetry comes at the cost of reduced T_F, which falls below 87%, primarily due to stronger reflection losses and enhanced diffraction effects.

According to the Lorentz symmetry theory, subwavelength structures with geometrical asymmetry, like pyramids and cones, stimulate multi-order resonance modes by Mie scattering, promoting broadband optical response and optical asymmetry.^41,42 Therefore, to intensify the asymmetric transmission and reduce reflection loss, the squares were replaced by a pyramid. The scattering cross-section (σ_sca) of Mie resonance generated by a pyramid can be simplified as

where α is the polarizability defined by n, geometrical volume (l), and phase difference (µ) of various scattering modes. F(H, L) is the shape factor defined by H and the base length (L) of the pyramid. Φ(n, λ, H) is the phase factor. Without considering light extinction, Clausius–Mossotti equation⁴³ determines the equation for refractive index factor (N(n)) as follows:

Due to geometric asymmetric,⁴⁴F(H, L) has different expressions under forward incidence (F_F) and backward incidence (F_B) as

herein, the shape factor (F(q)) is derived from Fourier transform of geometry:where q is the scattering vector and r is the radius vector. e^iqr represents the phase change of the optical wave. For cylinders or cubes, e^iqr is equal in forward and backward directions, resulting in the same F(q). However, the pyramid provides an inverse phase gradient for forward and backward incidence. Phase gradient is in direct proportion to H/L in forward transmission, while it is in inverse proportion to H/L in backward transmission. Since the structure size is comparable to the wavelength in the visible region, the higher-order term can be ignored, and the shape factors in eqn (12) are obtained.

In addition, the pyramidal geometry not only influences the scattering mode, but also suppresses Fresnel reflection under forward incidence. With gradient refractive index in pyramid, Fresnel reflection can be approximately calculated using Wentzel–Kramers–Brillouin method:

where k₀ is the wave number in vacuum and n_eff is the effective refractive index. Since the equation describes the reflection as superposition of each differential optical wave, larger H/L contributes to lower reflection of pyramid under forward incidence. Additionally, Φ(n, λ, H) under a certain incidence angle (θ) should be taken into consideration aswhere Δφ is the phase difference determined by Δφ = 2πnH/λ, φ₀ is an additional phase related to the additional platform (Fig. 1b), which intensifies the asymmetric effect. The asymmetry factor of scattering (A_sca) is defined as the ratio between the backward scattering cross section (σ_sca-B) and the forward scattering cross section (σ_sca-F)

The formula shows that the asymmetric transmission effect of a single pyramid (L = 600 nm, H = 500 nm) increases with the increase in the n of the material, similar to the trend exhibited by periodic cube arrays. The simulated transmission spectra in Fig. 1b provide direct evidence of the influence of n on asymmetric light transmission. For a pyramid structure with n = 1.5, the T_F exceeds 95% across the entire spectral range (400–1100 nm), while the T_B remains only marginally lower, indicating minimal optical asymmetry. This behavior is attributed to the weak Δn, which limits both reflection and diffraction. As n increases to 2.0, the asymmetry in transmission becomes more pronounced. While T_F decreases slightly to approximately 90%, T_B drops more significantly, falling below 87% across the spectrum. This trend becomes even more prominent at n = 2.5, where T_F reduces to around 82%, accompanied by a marked suppression of T_B to approximately 75%. These results demonstrate that high-n materials enhance asymmetric optical manipulation, primarily by strengthening Mie scattering and diffraction effects.

It is noteworthy that, despite the overall decrease in T_F with increasing n, the pyramid structure still offers a transmission enhancement compared to a flat surface due to its graded n profile, which suppresses Fresnel reflection (Fig. S2). The reduction in T_F mainly arises from reflection losses associated with low-duty-cycle flat regions. Replacing flat regions or simple cube arrays with subwavelength pyramids is thus expected to simultaneously enhance T_F and asymmetric transmission performance. Based on these findings, we designed subwavelength pyramid arrays (SPAs) that combine periodicity, geometric asymmetry, and high-n material to achieve both high T_F and low T_B through the interplay of diffraction and Mie scattering (Fig. 1c). For photovoltaic applications, the chosen material must also exhibit high transparency in the visible to near-infrared range to maximize light coupling and suppress escape losses (Fig. 1d). Considering optical properties and fabrication feasibility, titanium dioxide (TiO₂) was selected as the structural material (Fig. S3).

To systematically optimize the asymmetric optical performance, we conducted finite-difference time-domain (FDTD) simulations to explore the influence of structural parameters. As shown in Fig. S4, increasing the P of the SPAs results in a clear redshift of the transmission spectra, with peak and valley transmittance values remaining largely stable. Correspondingly, the peak asymmetric ratio also shifts toward longer wavelengths. Taking into account both the broadband high transmittance under forward illumination and the suppression of backward transmission, a P = 600 nm was determined to be optimal for high-efficiency photovoltaic applications. Further analysis of H and L reveals that these parameters primarily influence transmittance magnitudes rather than peak wavelengths (Fig. S5 and S6). Taller pyramids generate stronger diffraction and scattering, which enhances T_F and suppresses T_B, whereas reducing H causes the SPA to approach the behavior of a planar film, resulting in higher reflection losses and weakened asymmetric transmission. Similarly, reducing L lowers the duty cycle, exposing more flat regions and diminishing the interaction between adjacent pyramids, ultimately weakening the asymmetric effect. Considering these tradeoffs, the optimized structural parameters for the TiO₂-based SPA were set as L = 600 nm, H = 500 nm, and P = 600 nm. The simulated transmission spectra for this optimized design (Fig. 2a) demonstrate pronounced asymmetric transmission across a broad spectral range (400–1000 nm). Notably, T_B drops below 7% at 600 nm, corresponding to an asymmetric transmission ratio exceeding 10 dB (Fig. S7). Compared to flat glass and flat TiO₂ films, the SPA further contributes to anti-reflection performance, boosting T_F to nearly 100% with an average value exceeding 98% (Fig. S8).

Fig. 2 Optical dynamics in SPA. (A) Simulated transmission spectra of SPA. (B) Calculated diffraction orders of SPA. (C) Calculated diffraction efficiency of SPA. Near-field energy flux distribution profiles of a single pyramid under (D) forward illumination (600 nm) and (E) backward illumination (600 nm). Electric field distribution profiles of SPA under (F) forward illumination (600 nm), and (G) backward illumination (600 nm). The arrows represent the direction of illumination. (H) Simulated far-field distribution of forward and backward transmission.

The underlying optical mechanisms responsible for the observed asymmetry were elucidated through diffraction and scattering analyses. As shown in Fig. 2b, forward and backward incidence exhibit markedly different diffraction orders. Under forward illumination, the total number of diffraction orders exceeds 45 at wavelengths below 400 nm and gradually decreases with increasing wavelength, consistent with diffraction angle constraints.

At 600 nm, forward transmission maintains 21 diffraction orders, while backward transmission is limited to only 5 orders, highlighting the directional manipulation of diffractive pathways. To further dissect the contribution of specific diffraction orders, diffraction efficiency simulations were performed (Fig. 2c). The nearly identical efficiency of the zeroth-order (0,0) diffraction under both forward and backward incidence indicates that asymmetry primarily arises from higher-order diffraction channels. While low-order diffraction contributes minimally to transmittance, T_F exceeds 99% in the broadband region via constructive interference from higher-order diffractions, especially from the (±1,0) and (±2,0) orders. The (±1,0) diffraction plays a dominant role in enhancing transmission between 500–1000 nm, while higher orders shift toward shorter wavelengths, with third-order contributions confined to below 500 nm. In contrast, backward transmission exhibits significant order-selective suppression. Only seven diffraction orders remain active between 400–1000 nm. Although the (0, ±1) orders show a 12% higher efficiency below 600 nm compared to forward incidence, the dominant (±1,0) orders display a 47% narrower bandwidth and a 68% reduction in peak efficiency. These results demonstrate that SPA effectively suppresses high-order diffraction above 600 nm and significantly attenuates diffraction channels below 600 nm under backward illumination. The energy from suppressed diffraction orders is redirected into reflections, contributing to the observed asymmetric transmission.

Photon flux distribution simulations further reveal the distinct scattering behaviors of a single pyramid under forward and backward incidence (Fig. 2d and e). Under forward illumination, incident light experiences retardation at the exposed flat surfaces due to Fresnel reflection. It is also effectively concentrated and transmitted by the pyramidal structure, as indicated by the strong red regions within the substrate. In contrast, backward illumination results in significant reflection, as evidenced by diminished wave patterns in the air region and enhanced periodic patterns within the substrate. Electric field distributions provide further insight into light–matter interactions in Fig. 2f–h. Under forward illumination, the electric field is primarily confined within the structure, enabling efficient light transmission with minimal Fresnel reflection (as illustrated by eqn (14)). In the case of backward illumination, the low-order diffractions dominate the transmission. The high reflection in backward incidence is related to the propagation mode of high-order diffraction. Because of the decreasing lateral length, waveguide propagation reduces in backward incidence, resulting in high-order mode cut-off. As a result, high-order diffraction exists in the form of reflection.

Therefore, backward incidence produces distinct field enhancement along the reflection direction, with minimal field intensity near the pyramid apex, corroborating the suppressed backward transmission. Finally, far-field angular scattering patterns in Fig. 2h reveal that forward illumination produces a symmetric scattering profile spanning from −45° to +45°, with minimal backscattering losses. In contrast, backward incidence results in modal coupling and energy redistribution along propagation-aligned wavevectors, significantly suppressing transmitted intensity.

Fabrication and characterization of SPA

The fabrication process of the TiO₂ pyramid array, schematically illustrated in Fig. 3a, consists of three sequential steps. Scanning electron microscopy (SEM) images of the samples in each stage are shown in Fig. S9. Initially, polystyrene (PS) spheres (600 nm in diameter) were assembled on a silicon wafer and reduced by reactive ion etching to function as an etching mask. Subsequent anisotropic etching using potassium hydroxide produced a silicon pyramid array as indicated by the insert top-view and cross-sectional SEM images. The fabricated pyramids exhibit a period of 600 nm, a base width of 500 nm, a spacing of 100 nm, and a height of 450 nm. The topography was then replicated using polydimethylsiloxane (PDMS), followed by pattern transfer to a TiO₂ layer on a glass substrate via soft nanoimprint lithography (Fig. 3b). Corresponding SEM images confirm the successful replication of the pyramid array on TiO₂, albeit with a reduced height. This geometric deviation for pyramids plays a crucial role in modulating the optical asymmetry, as corroborated by numerical simulations. To improve clarity and reproducibility of SPA, imprint pressure was varied during nanoimprinting to mitigate structural distortion during nanoimprinting from 3 bar to 6 bar. The height of pyramids rose as imprint pressure increased (Fig. S10). As described in eqn 14, larger H/L contributes to lower reflection of pyramid under forward incidence, which is in favor of forward transmittance. As the SEM images show in Fig. 3b, the optimized pyramid has a height of 450 nm.

Fig. 3 Processing and optical properties of SPAs. (A) Schematic fabrication and (B) transfer process of SPAs. (C) Ray tracing diagram of glass/SPA under forward and backward illumination. (D) Transmission spectra, (E) derived transmission difference, and asymmetric ratio of SPAs. Angle-resolved transmittance of SPAs under (F) 405 nm, (G) 520 nm, and (H) 780 nm illumination.

Based on the setup displayed in Fig. 3c, optical characterization of SPA was performed (Fig. 3d). The dependence of T_B on the pyramid height and the almost constant T_F are all consistent with simulation results (Fig. S11). The effect arises from the gradual refractive index transition at the air/TiO₂ interface, enabling T_F as high as 96% across the visible spectrum, surpassing that of bare glass that features Fresnel reflection losses (Fig. S12). In contrast, SPAs exhibit significantly reduced T_B from 91% to 54% at 600 nm as pyramid height increases, evidencing strong wavelength-selective attenuation. Notably, the characteristic peaks in the simulated transmission spectra are not found in the measured results. We attribute this discrepancy to the fact that prepared SPAs are arranged in a hexagonal periodicity, which provides different periodicity under varied polarizations. To explore the influence of structural deviation on optical manipulation of SPAs, optical simulations were conducted based on the experimentally realized morphology. The fabricated SPA exhibits a compactly hexagonal periodic arrangement with a rectangular, rather than square, pyramid base (Fig. 3b). As shown in Fig. S13a, such multi-periodic and anisotropic features resulted in smoother transmission spectra, where the secondary peaks become less pronounced. Moreover, SPA with a duty cycle below 100% slightly reduced the asymmetry effect (Fig. S13b). The updated simulated results are consistent with the experimental measurements and confirm that the morphological variations mainly lead to spectral smoothing without altering the fundamental asymmetric optical behavior of the SPA. To evidence the asymmetric optical behavior, SPA with a smaller period was fabricated using PS spheres with a diameter of 400 nm. From the transmission spectra plotted in Fig. S14, the mismatch between T_F and T_B is only found in the spectral region at wavelengths below 850 nm. This is consistent with the simulation results that the asymmetric transmission effect is highly dependent on the wavelength. For illumination from backward and forward directions, the transmission space presents a huge difference that results in different Δn in each situation. According to the calculation, forward diffraction has 45 diffraction orders owing to m_max up to 4. Meanwhile, backward diffraction has only 9 diffraction orders since m_max is limited below 2. Additionally, the equation shows a reverse relation between m_max and λ. For backward diffraction, m_max is limited to 0 when the wavelength is larger than 600 nm, resulting in only one diffraction order. For forward diffraction, the number of diffraction orders decreases significantly when the wavelength is over 770 nm. As a result, the gap between forward and backward diffraction is lessened. The larger proportion of (0,0) diffraction efficiency in the large wavelength region further weakens the difference. The non-reciprocal optical dynamics in SPA are not supported because scattering and diffraction play a very limited role at longer wavelengths. Furthermore, the non-ideal duty cycle of SPA leads to limited asymmetric optical manipulation as demonstrated in Fig. S6. The backward reflectance (R_B) and calculated 1-R-T spectra presented in Fig. S15 demonstrate that R_B reaches 54% and gradually decreases with wavelength, mirroring the inverse trend in T_B. The near-complementary relationship between reflectance and transmittance under forward/backward incidence confirms minimal absorption losses of TiO₂ (Fig. S16), highlighting the suitability of SPA for light harvesting in thin-film photovoltaic devices. The optical asymmetry is further quantified by calculating (T_F − T_B)/100 and the asymmetric ratio (Fig. 3e). More than 50% of backward incidence is blocked. The SPA with broadband asymmetric transmission, particularly having an asymmetry ratio exceeding 2.5 dB at 600 nm and maintaining an ultra-high T_F > 96%, has not been reported previously. Meanwhile, forward and backward transmission spectra were measured at multiple regions of SPA. The schematic of the testing area on the SPA is presented in Fig. S17a. The results exhibited that both T_F and T_B remained nearly identical across different regions, confirming the excellent fabrication consistency and structure uniformity of the fabricated SPA. To provide a more quantitative comparison, we have characterized the forward and backward transmission spectra of ME. As depicted in Fig. S18a–c, ME demonstrated high and almost identical T_F and T_B with derived asymmetry ratio and (T_F–T_B)/100 remaining close to zero across the whole spectral range, indicating the reciprocal optical path of ME. To further clarify the performance differences, the key optical metrics of both ME and SPA are summarized in Table S3. Quantitatively, the average T_F and average T_B in the 400–900 nm region are 96.43% and 96.44% for ME, and 94.81% and 55.06% for SPA, respectively. Accordingly, SPA exhibits a significantly larger maximum asymmetry ratio of 2.95 dB compared to only 0.01 dB for ME.

Angle-resolved transmission at 405 nm, 520 nm, and 780 nm was measured to assess the angular stability of SPA (Fig. 3f–h). T_F gradually decreases with increasing angle, yet remains above 50% even at 40°. The wide-angle transmission enhancement is beneficial for the light harvesting of solar cells in a real application scenario. For backward incidence, the SPA maintains robust light-blocking efficiency across a wide angular range. Although the forward incident light changes direction after passing through the SPA due to the high haze of the SPA, resulting in part of the light reflected from the rear electrode no longer propagating in the normal direction of the substrate plane, the wide-angle suppressed T_B suggests that the oblique reflected light can also be effectively trapped in the device. Only at 780 nm and incident angles of over 40°, T_F falls below T_B, a result attributed to angular phase mismatch and structure-induced interference effects. The light trapping efficiency variation with incident angle was also analyzed through the change in asymmetry ratio. As summarized in Table S3, the asymmetry ratio of ME slightly increases from 0.01 dB for normal incidence to 0.21 dB for 50°, due to marginally reduced T_B at higher angles. In contrast, the asymmetry ratio of SPA shows an almost decreasing trend from 2.95 dB to 1.00 dB with increasing incident angles, reflecting the broadband yet angle-dependent asymmetric transmission behavior. Nevertheless, the light trapping efficiency of ME remains constrained by the reciprocal optical path. Overall, the SPA exhibits broadband, wide angular, and high asymmetric transmission than ME, which is particularly advantageous for enhancing photon harvesting in thin film solar cells under diverse illumination conditions.

Non-reciprocal optical path in thin-film photovoltaic devices

To explore the impact of asymmetric transmission, we integrated the SPAs directly onto the glass side of OSCs with the device architecture of glass/ITO/PEDOT:PSS/D18:Y6:Y6-1O/PDINO/Ag. Active layer thicknesses were systematically varied from 70 nm to 110 nm to investigate thickness-dependent optical performance. For comparison, a moth-eye (ME) structured PDMS film was also applied to assess the effectiveness of symmetric antireflective coatings (Fig. 1d). All devices were characterized under AM 1.5G illumination (100 mW cm⁻²). The statistical performance of 30 devices is summarized in Fig. 4a and Fig. S19, with derived detailed parameters in Table 1. The control device with a standard 110 nm-thick active layer yielded a short-circuit current density (J_SC) of 25.98 mA cm⁻², a fill factor (FF) of 79.64%, an open-circuit voltage (V_OC) of 0.89 V, and a power conversion efficiency (PCE) of 18.45%, close to related reported values.^37,45 While thinner active layers enhance charge extraction and suppress non-radiative recombination, the reduction in optical path length compromises light absorption, leading to a decline in J_SC (Fig. 4b). Light intensity-dependent V_OC measurements in Fig. 4c reveal thickness-dependent recombination dynamics. The ideality factors decrease from 1.22kT/q to 1.09kT/q as the active layer becomes thinner, indicating reduced trap-assisted recombination due to shorter carrier transport distances (the left schematic of Fig. 4d). Additionally, the slope of the J_SC–P_light increases from 0.981 to 0.992 with a thinning active layer, confirming suppressed bimolecular recombination in thinner films. However, this electrical benefit is offset by reduced light absorption, ultimately lowering device PCE.

Fig. 4 Non-reciprocal optical path-enhanced OSCs. (a) PCE, J_SC, and FF, and (b) 1-R-T spectra of control, ME-based, and SPA-based OSCs with various active layer thicknesses. (c) Light intensity-dependent J_SC and V_OC. (d) Schematic optical path and carrier extraction in control, ME-based, and SPA-based OSCs with thin or thick active layer. J–V curves of optimized (e) rigid and (f) flexible OSCs. (g) Variation in photocurrent of flexible OSCs under different bending radius.

Table 1 Photovoltaic parameters of OSCs measured under AM 1.5G illumination (100 mW cm⁻²). The average PCE (PCE_ave) for each OSC is a statistic of the performance of 12 devices

Active layer	Optical structure	V OC (V)	J SC (mA cm^−2)	FF (%)	PCE (%)	PCEave (%)
a The device performance certified by CPVT.
D18:Y6:Y6-1O (90 nm)	Control	0.90	25.40	80.30	18.35	18.01
	ME	0.90	26.36	80.16	18.95	18.67
	SPA	0.91	27.68	80.68	20.23	19.95
D18:L8-BO (90 nm)	Control	0.91	25.47	81.93	18.99	18.73
	SPA	0.91	27.72	82.06	20.70	20.45
	SPA^a	0.9068	26.86	80.93	19.71	—

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The application of ME led to modest yet consistent enhancements in light harvesting across all active layer thicknesses. As shown in Fig. 4b, ME integration reduces surface reflection via a graded refractive index profile, leading to about 4.1% increase in J_SC as compared with control counterparts, regardless of active layer thickness. This enhancement stems from uniform optical coupling rather than directional control, as confirmed by the flat, broadband improvement in 1-R-T spectra and the external quantum efficiency (EQE) spectra (Fig. S20). The error between integrated J_SC values and the measured values is within 3%. Internal quantum efficiency (IQE) spectra in Fig. S21 show minimal changes, confirming that carrier dynamics remain unaffected by ME integration. With unchanged FF and V_OC, the PCE of ME-based OSCs increases by over 4%. As J_SC still decreases with decreasing active layer thickness, suggesting that the effect of ME on the optical path elongation is limited (the middle schematic of Fig. 4d). Consequently, although improved charge collection is evident in IQE and light intensity-dependent measurements, thinner ME-OSCs still suffer from optical losses, reducing PCE from 18.87% (110 nm) to 17.70% (70 nm).

By contrast, the SPA demonstrates significantly stronger control over light propagation, particularly in devices with thin active layers. For instance, in 110 nm-thick devices, J_SC increases from 25.98 to 27.44 mA cm⁻² with minimal changes in V_OC and FF, yielding a PCE of 19.42%. The EQE peak improves from 91% to 93%, with the valley at 650 nm rising from 67% to 74%. The improved 1-R-T spectra and barely affected IQE spectra evidence enhanced absorption in weakly absorbing spectral regions. Some absorption gains in the near infrared region do not lead to EQE increases due to parasitic absorption in functional layers. Notably, in 90 nm-thick devices, SPA elevates J_SC from 25.40 mA cm⁻² to 27.19 mA cm⁻² with an enhancement ratio exceeding 7%. The resulting PCE of 19.90% surpasses even the SPA-integrated thicker devices. The J_SC of 70 nm-thick OSC also improves by over 12% following SPA integration, although the PCE is relatively lower. The stronger performance enhancement in thinner devices highlights the SPA's ability to compensate for reduced film thickness by extending the optical path and redistributing light within the absorber.

Mechanistically, SPA integration induces a non-reciprocal optical path, as illustrated in the right schematic in Fig. 4d. Unlike control devices, where unabsorbed photons are mostly lost, and ME-based devices, where transmission is enhanced in both directions, the SPA biases reflected light backwards towards the active layer. This directional light confinement increases the probability of multiple internal reflections and enhances absorption across a broader spectrum. As supported by the absorption spectra and EQE in Fig. 4b and Fig. S20, SPA integration yields pronounced gains, particularly in the spectral regions with initially low EQE values or under thin-film constraints. Specifically, SPA improves the average EQE of OSCs with 110 nm, 90 nm, and 70 nm active layers by 5.9%, 7.8%, and 11.4%, respectively, correlating closely with the J_SC enhancement. Importantly, the IQE spectra remain unaffected (Fig. S19), indicating that charge extraction remains efficient, and the performance gains stem solely from improved light harvesting via a non-reciprocal optical path. The slight change in IQE spectra of devices with the same active layer thickness (Fig. S21) indicates that charge extraction is barely affected by integrating ME or SPA. While the devices with a thinner active layer feature a higher IQE, suggesting boosted charge extraction. This is also demonstrated by transient photovoltage (TPV) and transient photocurrent (TPC) measurements (Fig. S22). With the same active layer, both control and SPA-integrated devices have almost the same carrier lifetime and carrier extraction time. As the active layer thickness decreased from 110 nm to 90 nm, the carrier lifetime increased from 10.11 µs to 13.85 µs, along with carrier extraction time decreasing from 5.25 µs to 4.90 µs. Notably, for SPA-integrated devices, the non-reciprocal optical path reduces the threshold thickness of the active layer from 110 nm to 90 nm for efficient light-harvesting. Therefore, the optimal SPA-integrated device with a 90 nm active layer shows both enhanced light-harvesting and charge extraction as compared to the control device with a 110 nm active layer.

To demonstrate the broad applicability of the SPA strategy, we extended the design to both rigid and flexible OSCs with architectures of glass/ITO or PET/silver nanowires (AgNWs)/PEDOT:PSS/D18:L8-BO/PFN-Br/Ag. As suggested by Fig. 4e and f and Table 1, SPA integration leads to robust J_SC enhancement without compromising V_OC or FF. Rigid OSCs with SPA achieved a PCE of 20.70%, with third-party certification from the National Center of Supervision & Inspection on Solar Photovoltaic Products Quality of China (CPVT) confirming a J_SC of 26.86 mA cm⁻² and a certified PCE of 19.71% (Fig. S23). The PCE of flexible SPA-based OSCs surpassed 19.40%, among the highest reported values for AgNW-based flexible OSCs (Table S1). The enhancement was ascribed to the improved light harvesting as evidenced by Fig. S24. Under mechanical bending, increased angular incidence typically degrades photocurrent (Fig. 4g). However, the wide-angle optical asymmetry of SPA mitigates this effect, preserving device performance in flexible applications. Furthermore, when implemented in other thin-film photovoltaic technologies with different absorption regions, including FA_0.78Cs_0.22Pb(Br_0.3I_0.7)₃ perovskite with an absorption spectrum up to 680 nm and PbS quantum dot with an absorption spectrum up to 1100 nm, SPA consistently outperformed ME in enhancing photocurrent (Fig. S25 and Table S2), reinforcing the robustness and universality of non-reciprocal optical path on light-harvesting.

Conclusions

In this work, we presented an invasive strategy for optical path management via rationally designed SPA exhibiting strong optical asymmetry. Different from previous reports using low-n materials and nanostructures for anti-reflection, we intentionally adopted a high-n TiO₂ pyramid array to leverage both Mie scattering and diffraction, thereby breaking conventional optical reciprocity. By combining anisotropic etching of silicon and soft nanoimprint technique, SPAs were constructed on glass substrates and supporting the interplay of diffraction and Mie scattering that fundamentally alters light–matter interaction.

The optimized SPA achieves T_F exceeding 96% across the visible range, while suppressing T_B to below 50%, leading to asymmetric transmission ratios surpassing 2 dB, which is not achievable by traditional optical symmetric textures. Implementation of SPA in OSCs generates a non-reciprocal optical path, blocking light from escaping. Specifically, the long-standing trade-off between active layer thickness and light absorption is mitigated, resulting in simultaneously enhanced light harvesting and reduced carrier recombination. Both the champion OSCs with PCE of 20.7% and the performance enhancement of flexible OSCs, perovskite solar cells, and PbS quantum dots solar cells evidence the universality of non-reciprocal optical path in thin-film photovoltaic devices.

Advancing non-reciprocity remains challenging, primarily owing to the complexities involved in fabricating tetragonally close-packed pyramid structures. Therefore, the tetragonally close-packed pyramid patterns with 100% duty cycle are expected to generate a stronger asymmetric transmission effect. This enhancement arises from improved optical coupling and more efficient modulation of diffraction and scattering modes, which could further amplify the optical nonreciprocity in future device designs. Beyond immediate performance gains, this work establishes a generalizable framework for asymmetric optical engineering in optoelectronic devices. These findings underscore the potential of directional nanophotonic structures as a transformative tool in next-generation light-harvesting platforms and lay the groundwork for further integration into a wide range of photonic and energy conversion systems. The achieved asymmetry is currently limited by the n of media and the fabrication fidelity of the nanostructure. The development of high-precision processing of ultra-high-n materials will greatly increase the potential of this strategy for applications in asymmetric optics.

Author contributions

J. C., Y. L., and J. T. conceived the idea for the study and designed the experiments. Y. Z. and H. R. performed nanostructure preparation, device fabrication, and characterization. Y. Z. and J. C. performed the theoretical simulation. S. Z. assisted the device fabrication and characterization. J. Z., and Z. D. carried out morphology characterization. J. C., Y. Z. and H. R. analyzed the data and wrote the manuscript. Y. L. and J. T. edited the manuscript. All authors contributed to the manuscript.

Conflicts of interest

The authors declare no competing interests.

Data availability

The data supporting this article have been included as part of the supplementary information (SI), including the experimental methods and related measurments, such as the optical and morphological properties of different structures via theoretical and experimental characterizations, and device performance. See DOI: https://doi.org/10.1039/d5ee05708f.

Acknowledgements

The authors acknowledge the financial support from the National Natural Science Foundation of China (No. U23A20371, T2425024, 62320106004, 62275181), the Science and Technology Development Fund (FDCT), Macau (No. 0030/2025/AIJ), the Bureau of Science and Technology of Suzhou Municipality (No. SYC2022144), the China Postdoctoral Science Foundation (2025M770829), the Postdoctoral Fellowship Program of CPSF (GZC20250561), the Jiangsu Funding Program for Excellent Postdoctoral Talent (2025ZB271), Collaborative Innovation Center of Suzhou Nano Science & Technology, and Fundamental Research Funds for the Central Universities, in the scope of the projects LA/P/0037/2020, UIDP/50025/2020 and UIDB/50025/2020 of the Associate Laboratory Institute of Nanostructures, Nanomodelling and Nanofabrication – i3N of Portugal.

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Footnote

† J.-D. Chen, H. Ren, and Y.-F. Zhang contributed equally to this work.

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