Complex Fourier Surfaces by Superposition of Multiple Gratings on Azobenzene Thin Films

Diffractive optical elements (DOE) are integral components for lightweight and ultra‐thin optical elements due to their ability to manipulate light efficiently and accurately. However, conventional DOEs are static and cannot be altered after fabrication, which hinders their adaptability to changing requirements. To overcome this limitation, the potential of surface patterning on azobenzene thin films to fabricate reconfigurable DOEs is investigated. Using holographic lithography, surface topographies with sinusoidal surface relief gratings (SRG) are created and the superposition of up to 80 SRGs with high accuracy and minimal information loss in subsequent inscriptions is demonstrated. This is enabled by a surface patterning tool combining holographic lithography and digital holographic microscopy. Reconfigurable and adaptive optical elements can improve the efficiency of optical coupling and increase the sensitivity and selectivity of sensors, especially in applications such as near‐eye displays and plasmonic sensors. These results demonstrate the ability to create complex azobenzene‐based DOEs for advanced photonic applications, where the ability to alter optical elements is of high importance.

DOEs based on surface relief gratings (SRG) are particularly widely used in photonic applications. [15,16]Periodically corrugated surface diffracts light in a highly controlled manner, playing an important role in spectroscopy, [17] telecommunication, waveguide coupling, [18] sensing, [19] and anti-counterfeiting. [20] SRGs are commonly produced using holographic lithography, [21,22] a direct laser writing process that requires neither photomasks nor complex optics.In this process, two or more laser beams interfere with a lightsensitive material to create a pattern of interference fringes that form the grating structure.This method has the advantage of being fast, accurate, and cost-effective, but it can create only simple periodic structures.Moreover, if used with photoresists, additional development steps are required, which will selectively remove material to reveal the patterns, making the inscribed DOEs permanent and nonreconfigurable.
Azobenzene, an aromatic molecule consisting of two phenyl rings joined by an azo bond (N=N), and its derivatives represent a broad class of synthetic photoisomerizable compounds. [23]ue to their synthetic tunability, reversible photoisomerization, and photostability, the azobenzene photoswitches have been used in a variety of applications. [24,25][28] Despite extensive studies since its discovery in 1995, [29,30] the exact mechanism of SRG formation is still not clear. [31,32]But it has been proven that SRGs can be inscribed onto a myriad of azobenzene-containing materials without the need for additional development steps.
The characteristics of the SRG fabrication process, such as speed, temperature stability, and modulation depth, can be fine-tuned by selecting a suitable azobenzene system.Azobenzene-containing molecular glasses, for example, are characterized by fast inscription speed, excellent surface quality, and reproducibility. [33]Their relatively low glass transition temperatures allow facile erasure of the topographic features upon moderate heating, making these films ideal for applications requiring SRG reconfiguration.Conversely, some azobenzenecontaining polymers, albeit having slower inscription rates, yield high thermal stability and can withstand temperatures up to several hundred degrees Celsius. [34,35]This makes them particularly useful in environments that require long-term stability or are exposed to high temperatures.In general, all azobenzene SRGs exhibit good temporal stability under ambient conditions, and the topographies remain for several years without degrading.
Unlike classical photoresist-based techniques, holographic photopatterning of azobenzene thin films yields sinusoidal surface profiles, which reduces higher-order diffraction and leads to higher diffraction efficiency compared to binary gratings.The height of the profiles can be easily controlled by adjusting the exposure time and the polarization of the inscription pattern.[47][48][49][50][51] More complex patterns can be inscribed in a single exposure step using a spatial light modulator. [44,52,53]patial light modulator-based lithography can expand the range of structures that can be created and provide greater control and flexibility over the patterning process.However, the size of the structural features is limited due to the relatively large pixel size, while with holographic methods, structural features with periodicities in the range of a few hundred nanometers can be obtained over large areas. [54]e have previously developed a digital holographic microscope (DHM)-based two-beam lithography device with real-time monitoring of the sample surface during the surface patterning process. [55]We introduced an active feedback loop to control the phase difference of the two interfering beams, which is critical for stabilizing the grating position when generating SRGs.This allowed us to inscribe relatively complex optical Fourier surfaces by superimposing sinusoidal gratings, and large-area diffractive structures via spatial stitching of pixelated photopatterns.However, we lacked control over grating vector direction, which limited us to 1D gratings, and were not able to precisely control the heights of the gratings in real time.
In this work, we remove these deficiencies and demonstrate full control over the photopatterning process, including real-time control over the grating height and arbitrary control over the grating vector direction in each pixel.With the improved device, we push the limits of azobenzene photopatetring by superposing up to 80 individual gratings and producing reconfigurable DOEs with arbitrarily programmable diffraction patterns without the use of a mask or spatial light modulator.The presented technique holds great promise for the development of compact, efficient, and cost-effective photolithographic techniques.
With the introduction of the DHM-based recording setup and its extensive interference holography capabilities, we obtain full freedom for spatial frequencies, orientation, and grating height.This allows us to superpose a high number of precisely controlled gratings and fabricate complex Fourier surfaces.No longer limited to rigid patterns, it is now possible to inscribe arbitrary diffractive patterns from a design template pixel by pixel, which effectively makes the proposed system a "printer" for DOEs.The system not only provides a flexible and adaptable platform, but we believe it also represents a competitive advantage over traditional photolithographic methods.The real-time feedback mechanism provides reproducibility and compensates for inherent material variations, making the device a viable alternative for a wide range of optical manufacturing applications.

Design and Operation of Modified DHM
We used a modified DHM, [55] combined with a custom-built holographic photolithography setup, as shown in Figure 1a.The DHM operates in an off-axis configuration, allowing real-time reconstruction of the holograms.An external interference setup was added to the internal optical path using a dichroic mirror, allowing simultaneous inscription and measurement of the samples.The XYZ translation stage and motorized XY mounts are controlled by a computer that allows fully programmable operation with LabVIEW.The inscription is done pixel-by-pixel through an objective on the sample by moving the translation stage with the sample (Figure 1b).A pixel is characterized by having one or more gratings with the same grating parameters over the exposed area.The pixel size and shape can be modified with a circular or rectangular aperture put in the beam path, enabling convenient stitching of large-area holograms.
To inscribe SRGs, a glass substrate was coated with Disperse Red 1-containing molecular glass known to undergo efficient SRG formation. [56]We projected two laser beams with a wavelength of 488 nm onto the sample surface and independently controlled their polar and azimuthal angles so that the orientation of the grating could be freely rotated.The pitch of the interference pattern can be adjusted down to 300 nm.The polarization states of the beams are controlled by quarter-and half-wave plates so that both intensity and polarization patterns can be used.The device features a real-time feedback system to control the height, orientation, and period of the gratings with nanometer precision by extracting the Fourier components from the recorded holograms.Imaging is done with diode lasers for high-precision interferometric observation and reconstruction of surface information.The DHM can detect at least the first diffracted orders of the grating at the installed probe wavelengths, corresponding to a grating period of about 1 μm.The maximum angle between the beam and the sample normal is limited by the numerical aperture of the objective (50×, 0.8 NA, Olympus MPLFLN50X), which is about 53°for this setup.As we will demonstrate, the unique capability to simultaneously measure the surface height and project an interference pattern enables the creation of various micro-and nanoscale structures with high accuracy for a range of diffractive optical elements.
Exposure of a thin film of Disperse Red 1 glass to the interference pattern results in mass-migration of the molecules and the resulting surface topography is determined by the pitch and orientation of the pattern (Figure 1c).The interference of two plane waves with suitable polarization [57] leads to the formation of an SRG with controllable orientation and periodicity, allowing the grating vector to be controlled in two dimensions.Most importantly, the height of the SRG is proportional to the exposure time, which can be used for grayscale patterning, a feature that is difficult to achieve with conventional lithographic methods.
Multiple exposures of the same area with different grating parameters allow the combination of simple topographies, resulting in patterns such as 2D gratings or quasicrystals.Control over the height, period, and orientation of the grating is equivalent to having full control of the grating vector in Fourier space (Figure 1f).Vice versa, a linear combination of the grating vectors yields an arbitrary surface topography in the spatial domain (Figure 1e).A movie in the supplementary materials illustrates the inscription process as observed with the DHM (Movie S1, Supporting Information).
The control scheme makes it possible to access the powerful toolkit of optical Fourier surfaces, which are mathematical descriptions of the diffraction patterns produced by gratings and other periodic structures. [12,43]They allow the design of gratings and other optical elements that produce specific diffraction patterns and thus the creation of structures with highly specific and desirable properties to achieve a wide range of functions in photonic applications.However, we have found that the same exposure time does not always give the same height for different grating parameters, which can make accurate superposition difficult.This may depend on the inscription efficiency of different grating periods, which showed the biggest grating amplitudes around 1-1.5 μm and reduces in both higher and lower periods.Also, the thickness of the film influences the grating height, thicker films lead to a faster grating formation. [58]To overcome this problem, real-time feedback from the DHM was used to provide accurate information on the grating period, orientation, and height from the sample surface by analyzing the Fourier components of the hologram.

Fourier Feedback System for Complex Grating Inscriptions
As the complexity of the pattern increases, it becomes increasingly difficult to detect the individual components in the spatial domain.By real-time the Fourier transform of the observed hologram of the sample surface, the instrument enables the inscription and observation of grating in the spatial frequency domain using the Fourier components.This allowed us to study the effect of subsequent inscriptions on the height of the topography.For the inscription, we used a polarization modulation pattern, which has proven efficient for grating formation in some azobenzene-containing materials. [59,60]We found that the combination of gratings was approximately linear.Therefore, it is possible to simulate the resulting topography by adding the individual Fourier components computationally.To illustrate this, a 2D grating was inscribed by changing the pitch and orientation of each inscription pattern, resulting in a spiral pattern in Fourier space.The resulting topography from this combination of gratings was  simulated and is shown in Figure 1e.The combination of many gratings requires precise and repeatable processes.Therefore, a LabVIEW application was developed to control the interference pattern and the exposure time.The program controls (i) the exposure time, and the grating vector in the (ii) x-and (iii) y-directions.This corresponds to the grating period, orientation, and height of the structure.A sequence of these exposures can be programmed and executed over time (Figure 1g).
Using the developed program, we experimentally inscribed superimposed gratings with different grating parameters.Figure 2 shows the topographies, their corresponding Fourier space patterns, and diffraction patterns.In Figure 2a, a pattern was formed by changing the length of the grating vector of each inscription corresponding to 1.5 μm, 2 μm, and 2.5 μm, while the orientation remained fixed, resulting in a "beating" pattern.This pattern can be used to diffract light of different wavelengths at the same angle, allowing, for example, the combination of the three primary colors-red, green, and blue-to a full-color spectrum.In Figure 2b, the constant-length grating vector was rotated about its origin, resulting in a grating period of 1.5 μm rotated between 0°and 180°in 15°increments.In Figure 2c, the inscribed pattern shows a change in the length of the grating vector with simultaneous rotation.Here, the grating period was gradually increased from 1.5 μm to 2.5 μm while varying the rotation between 0°and 180°in 12°steps.The Fourier transform in the top right of each figure clearly shows which components have been inscribed on the surface and predicts the resulting diffraction pattern very well as seen in the bottom.
To explore the limits of the grating superposition method, we inscribed two complex DOEs in which we superimposed gratings with 41 and 80 components, shown in Figure 3a,b, respectively.The gratings are produced with different parameters in order to obtain pre-designed complex diffraction patterns of a pixelated character (Figure 3a) and a smiley face emoticon (Figure 3b).The grating parameters were calculated based on the coordinates in Fourier space and inscribed with an exposure time of 50 ms for each point.A demonstration movie showing the topography and corresponding Fourier space in real-time is included in Section S2, Supporting Information.The results show that this approach can produce complex surface topography on azobenzene by subsequently superimposing simple gratings, as can be seen in the topographic images acquired with the DHM.The results were verified by recording the sample surface in Fourier space and comparing it to the template.The resulting Fourier images, as shown in Figure 3, resembled the original template, indicating that the entire pattern was superimposed point by point without losing information in the process.

Quantitative Analysis of Grating Superposition
The inscription of a large number of gratings raises the question of whether earlier patterns are eventually overwritten and whether the material responds linearly to subsequent exposures.To a first approximation, it was found that the effect of exposing subsequent grating is the same as it would be by exposing a complex pattern at once.
The high degree of linearity can be attributed to the short exposure time, ≈50 ms per grating.This is significantly shorter than the exposure times typically reported in the literature, which are in the range of several minutes or even hours.The relatively high laser intensity (4 Wcm −2 ) is also important for the fast inscription, and we believe the use of small spot size yields good heat dissipation and the lack of any detrimental thermal effects despite the high intensity.
By using the high-intensity, short-exposure approach, we not only maintain the linear response of the material but also expand the range of diffractive patterns that can be achieved in a reasonable time.This exciting finding suggests that complex surface patterns with many diffraction points can be created by superimposing sinusoidal gratings.The clear visibility and overlap of the designed images in Fourier space demonstrate the linear behavior of the material and a high level of control over the grating parameters.To verify the diffraction pattern, we exposed the samples to a 635 nm laser beam and observed the diffraction patterns projected on a screen (Figure 3).Despite some distortions due to the large angle between the screen normal and the diffraction emission direction, the pattern resembles the design pattern very well.Other artifacts such as the bright spots seen outside the zero-order diffraction are due to reflections.Comparison with the pattern in Fourier space, it was again confirmed that the real-time Fourier transform calculated by the DHM provides us with data matching the resulting diffraction pattern.
While analyzing the diffraction patterns, we found that the initial patterns remained relatively stable and were minimally affected by subsequent inscriptions.To quantify this observation, we plotted the diffraction efficiency of the first inscription of the smiley face pattern after each inscription, shown in Figure 4a.The diffraction efficiency was computed by dividing the absolute value of the diffraction signal by the DC signal within the Fourier space.The results show that the diffraction efficiency decreases slightly with exposure to multiple gratings.Specifically, after 41 inscriptions, the diffraction intensity of the initial inscription retained 73% of its original value.Utilizing linear regression, we estimated a 0.01% reduction in diffraction efficiency per exposure.This factor is crucial when crafting complex DOEs and can be easily accommodated by slightly overexposing initial inscriptions to counteract the decrease of diffraction efficiency from subsequent exposures.As we monitor the surface topography during inscription, this can be implemented as a parameter for the feedback system that controls the patterning.It is important to note that despite the degradation, a remarkably high number of successive inscriptions can be made without damaging the azobenzene film or overwriting the existing patterns.This shows that the method is robust for use in patterning complex DOEs by combining simple periodic structures.
The range of possible patterns is constrained by the inscription wavelength and the objective lens.The spacing of interference fringes is given by where "d" represents the spacing, "" is the light wavelength, and "" is the half-angle between the interfering beams.Given an NA of 0.8, "" calculates to 53.13°, resulting in a minimal achievable period of 305 nm.However, in practical terms, our device successfully inscribes high-quality gratings periodicity as low as 360 nm, as shown in Figure 4b.A limitation of the current objective is its resolution threshold of approximately 1 μm for grating periodicity.This impacts the feedback system, which depends on real-time data from the DHM.While there is no theoretical upper limit to periodicity, in practice, gratings exceeding 10 μm display significantly reduced heights due to the inefficient material transport over extended distances.Figure 4c presents the Fourier image of an experimental recording for typical grating periods ranging between 1 μm and 3 μm, highlighting selected periods of 1.2 μm, 1.5 μm, 2 μm, and 3 μm.A comparison of the target and measured gratings is shown in Figure 4d.The orientation shows excellent alignment with an error of less than one percent and the spatial frequency shows an error typically below 5%, which tends to be slightly below the target value.The discrepancy in spatial frequency is likely due to the miscalibration of the xy translation mounts that control the pitch distance of the interfering beams.This is a mechanical problem that can be corrected in the future by thorough calibration.
The real-time feedback also provides precise control over grating inscription height, as demonstrated in Figure 4e for selected grating inscriptions with a period of 1.5 μm.Target heights were 20 nm, 50 nm, 100 nm, and 150 nm.Despite an overshoot in some inscriptions, the system maintains high accuracy regarding the height parameter.
While the stability and flexibility of multiplexed gratings are promising for facile fabrication of complex DOEs, we note that the overall diffraction efficiency of the obtained multiplexed holograms is relatively low, ≈2-3% (Figure 3).This is too low for highfidelity applications that require high light throughput but sufficient for applications such as anti-counterfeit.The diffraction efficiency can be increased by optimizing the material such that it is minimally susceptible to potential heating during prolonged exposure, and by optimizing the parameter space in terms of intensity versus exposure time and the spatial frequencies used.

Conclusion
This research demonstrates the capabilities of the modified digital holographic microscope in producing complex diffractive optical elements on azobenzene-based materials.The method allows for precise manipulation of grating parameters, including period, orientation, and height, which is essential for creating complex surface structures required in photonic applications such as neareye displays, telecommunications, plasmonic sensors, and anticounterfeiting measures.Utilizing a real-time feedback system and LabVIEW application for managing exposure time and grating vector significantly enhances the method's robustness, accuracy, and repeatability.The programmability makes it possible to "print" arbitrary-shaped DOE pixel-by-pixel from an arbitraty design pattern by superimposing gratings with full control over the parameters.Superimposing a large number of gratings leads to new applications that require arbitrary and precise diffraction control.This represents a significant advance in the capabilities of photolithographic techniques based on azobenzene-based materials, offering a potential competitive advantage for this organic, reconfigurable material compared to existing photolithographic techniques.Even though diffraction efficiency decreases slightly with subsequent inscriptions, the technique remains highly promising for fabricating customizable DOE and adaptable optical devices.This research offers not only a viable alternative to conventional fabrication techniques like electron beam lithography and ion beam etching but also has the potential to transform the design process, lower production costs, and optimize optical device performance.Additionally, it presents new possibilities for developing grayscale patterns, which can be challenging with traditional lithographic methods.Our findings also suggest that, in the field of azobenzene photopattering, this approach can be a good alternative to photopatterning complex topographies with a spatial light modulator, while still maintaining the high resolution and precision that holographic lithography offers.Future studies should concentrate on refining the technique further, increasing resolution, speed, and scalability, and investigating its potential in various photonic applications, such as metasurfaces, wavefront shaping, and holographic data storage.Moreover, examining ways to mitigate the reduction in diffraction efficiency during the inscription process could enhance the overall performance of the fabricated DOEs.As innovation continues in the rapidly progressing domain of miniaturized optical devices, we anticipate considerable advancements in technologies like wearables, augmented reality, and mixed reality, leading to groundbreaking solutions and applications.

Experimental Section
Sample Preparation: A small glass-forming molecule containing the azobenzene dye Disperse Red 1 was used as an inscription medium.The molecule was dissolved in chloroform as a 5% (w/v) solution.The solution was filtered through a polytetrafluoroethylene (PTFE) membrane filter with a pore size of 0.2 μm.It was spincoated on a 1 mm thick microscope glass substrate with a thickness of 300 nm as determined by an AFM (Dimension Icon, Bruker).The samples were then dried on a hot plate at 60 °C for 10 min.
Photolithographic Setup: The gratings were inscribed using interference lithography, a two-beam setup integrated with a digital holographic microscope. [55]The setup used a 488 nm single-mode diode-pumped laser source (Coherent Genesis CX-488 2000) for writing the pattern, which was divided by a polarization-maintaining fiber splitter in two beams with equal intensity.The polarization of the writing beams was adjustable with a quarter-wave plate and a half-wave plate and was selected to be left circular polarized for one beam and right circular polarized for the second.Focusing the beams with a microscope objective on a sample, yielded an interference pattern with uniform intensity but periodically varying polarization.The combined intensity of both beams was 4 W cm −2 on the sample.The period and orientation of the interference pattern could be precisely controlled by shifting the position of the fiber ends of the two interfering beams relative to the optical axis.Adjusting the offset of the fiber ends in 1D allowed control of the period of the interference pattern, achieving a range between about 300 nm and 10 μm.For pattern orientation, a full 360°rotation was obtained by offsetting the fiber ends in 2D while keeping their distance to the optical axis constant.This careful positioning of the fiber ends allowed a high degree of control over the interference pattern.
Data Analysis: The DHM (DHM-R2100, Lyncée Tec) was used to reconstruct the real topography of the interference pattern.A 2D Fourier transform of the holographic image was computed and used for extraction of the main Fourier components corresponding to the orientation, pitch, and height of the grating.This data was processed in real time using LabVIEW (National Instruments), which in turn controlled the actuators for the fiber ends and a shutter in the beam path, resulting in a real-time feedback system.For the comparison with the real diffraction pattern, a red diode laser (635 nm, Thorlabs) was used to observe the diffraction from the final DOE on a white screen at a 10 cm distance.The diffraction efficiency of the holograms was measured with a power meter (LabMax, Coherent) by measuring the diffraction of the diffraction orders +1 and −1 and dividing by the power of the laser diode.The diffraction efficiency of the Fourier image was calculated by dividing the first order diffraction by the DC signal.The topography of the submicron grating was measured with the AFM (Dimension Icon, Bruker) in the ScanAasyst mode.

Figure 1 .
Figure 1.a) Schematic representation of the off-axis DHM combined with a holographic photolithography setup.b)The computer-controlled translation stage allows pixel-by-pixel inscription of gratings, with pixel size and shape defined by an aperture and the maximum field of view of the objective.c) Two-beam interference creates a periodic intensity or polarization pattern on a thin film containing azobenzene and the shape can be changed with an aperture.d) Sinusoidal surface relief gratings are formed in response to interference irradiation, with full control over period, height, and orientation allowed by our setup.e,f) Calculated example of the linear combination of sinusoidal gratings with different grating vectors results in arbitrary surface patterns.g) Programmable control of the parameters enables the generation of complex patterns by superposition of multiple gratings.

Figure 2 .
Figure 2. Experimental superposition of multiple gratings.Each panel shows DHM-recorded topography (left), Fourier transform of the hologram (top), and the resulting diffraction pattern (bottom).a) Superposition of three 1D gratings.b) Superposition of 12 gratings with variable orientation and constant period.c) Superposition of 15 gratings with changing orientation and period.Insets in each panel depict the grating vectors k, where the length of the arrow corresponds to the grating period.

Figure 3 .
Figure 3. Characterization of surface topography by holographic measurements with corresponding Fourier transforms (top) and diffraction patterns (bottom).The inset within the Fourier transform images shows the target patterns, where (a) represents a complex figure obtained by superimposing 80 individual patterns, and (b) shows a smiley symbol realized by superimposing 41 individual patterns.The diffraction pattern matches the design very well but appears slightly distorted due to the high angle between the screen normal and the emission direction of the diffraction.The measured diffraction efficiencies are 2.2% and 2.8%, respectively.

Figure 4 .
Figure 4. a) Diffraction efficiency was calculated after each inscription step by dividing the diffraction intensity of the first inscription by the DC signal.b) Atomic force microscope image of a submicron grating inscribed with the instrument.c) Fourier image showing the diffraction pattern of a multiplexed grating with four different grating periods and full orientation control in 10°steps.d) Comparison between the target grating parameters and the measured grating parameters from Fourier space.e) Height accuracy of the grating structures using the feedback system with the target height shown on the right.