One-dimensional photonic crystals (PhCs) are electromagnetic media in which materials are periodically arranged in a certain direction. The periodicity is proportional to the wavelength of light that lies in its photonic bandgap (PBG) . The presence of the PBG and the potential ability to tune its position to match specific frequencies is perhaps the most attractive quality of PhC . The specific properties of a 1D photonic crystal or distributed Bragg reflector (DBR), such as its reflectivity and bandwidth, can be tailored by adjusting the thickness and refractive index of each layer . Distributed Bragg reflectors can achieve near-unity reflectivity within specific wavelength ranges, enhancing light–matter interactions and enabling precise control over quantum states . Attaining optimal light confinement represents a crucial goal in photonics, given that the inherent constraints on light confinement in conventional optical media or devices hinder the miniaturization and integration of photonic devices. Moreover, the enhancement of typically feeble light–matter interaction is enabled by robust light confinement. These characteristics can be exploited to mitigate the intrinsic limitations of photonics technologies compared to electronic and optoelectronic technologies . Distributed Bragg reflectors can be miniaturized onto photonic chips, facilitating the development of integrated and scalable classical and quantum circuits, and they can be fabricated from various materials, allowing for integration with different platforms and functionalities within quantum information processing (QIP) systems. Despite the challenges such as fabrication complexity and loss mitigation scalability to complex circuits , the potential benefits of DBRs for QIP applications continue to drive research and development in this field . As fabrication techniques and material systems develop, DBRs are expected to play an increasingly important role in realizing the promise of quantum technologies.

Lithium niobate (LN) is a compelling choice for DBRs due to its unique combination of material properties as it has a high refractive index and exhibits unique optical and electro-optic properties. The large refractive index (indices of refraction of ordinary and extraordinary waves no = 2.21 and ne = 2.14, respectively, at 1550 nm) contrast between ordinary rays and extraordinary waves enables strong reflections in DBR structures, leading to high extinction ratios . LiNbO3 exhibits strong second-order nonlinearity, allowing for frequency conversion via processes such as second-harmonic generation (SHG) and difference-frequency generation (DFG) . This enables DBRs to manipulate light in additional ways beyond simple reflection. Additionally, its pronounced electro-optic effect (largest electro-optic coefficient r33 = 27 pm/V at 1500 nm) , enables dynamic control of the reflection spectrum of DBR through applied electric fields, unlocking functionalities such as wavelength filtering and modulation . LiNbO3 is transparent across a broad spectrum, spanning from the visible to the infrared (400–5000 nm) . The high degree of flexibility in fabrication created functional photonic nanostructures such as microring, periodically poled lithium niobate, and photonic crystals . This versatility makes it suitable for DBRs to be used in various applications. Moreover, its platform with established fabrication techniques guarantees consistent device performance. Finally, the potential for integration with other photonic components on a single chip, coupled with its CMOS compatibility, paves the way for highly sophisticated photonic integrated circuits and hybrid devices with combined functionalities . We focus on the DBR structure out of lithium niobate. To achieve PhC effects, one of the ways is creating alternating layers of LN and another material with a contrasting refractive index. We chose TiO2 and SiO2 as it has a considerable difference in refractive index which is crucial for the creation of photonic bandgap . In addition, these two materials are highly used in the photonics industry due to their easy availability and low cost. Moreover, both TiO2 and SiO2 can be integrated with various materials. The precise choice of periodicity and layer thickness is important for a photonic crystal. SiO2 exhibits a wide transparency range, enabling its application across diverse wavelengths, including both the visible and near-infrared spectra . TiO2 is a frequently utilized material in photonic crystals, owing to its elevated refractive index and thermal stability, they are suitable for applications at high temperatures. Additionally, TiO2 exhibits a wide bandgap, making it conducive for incorporation into photonic crystals designed to operate within the ultraviolet and visible spectra. Moreover, its high dielectric constant enables the fabrication of photonic crystals characterized by high-quality factors and minimal losses .

The combination of LiNbO3 and TiO2 in multi-stacked 1D PhC holds promise for optical applications . The birefringence and electro-optic modulation capabilities of lithium niobate coupled with transparency and high refractive index of titanium dioxide, offer a versatile platform for designing devices with controlled polarization, tunable modulation, and well-defined photonic bandgaps . The complementary nonlinear optical properties of these materials further enhance the potential for applications such as frequency conversion and signal processing. However, successful implementation requires addressing fabrication challenges to ensure precise layer deposition and interface quality. Overall, combining lithium niobate and titanium dioxide in multi-stacked structures provides a pathway for tailoring optical functionalities in various photonic applications.

While LiNbO3 offers strong light–matter interaction properties, nonlinearity, and tunability for 1D photonic crystals in the 1550 nm regime for quantum information processing (due to its high refractive index, second/third-order nonlinearities, electro-optic effect, and mature platform), its optical losses and birefringence pose limitations . Combining LiNbO3 with TiO2 in a multi-stack can offer advantages such as tighter confinement, tailored dispersion, and complementary functionalities. However, it introduces challenges in fabrication complexity, interface effects, and material compatibility . Lithium niobate film on insulator (LNOI) is a promising photonic platform due to its large transparency window, strong second-order nonlinear optical properties, and ultralow-loss switching through the electro-optic effect . The LNOI enables low-loss waveguides, efficient photon pair sources, and fast low-voltage switches for the successful implementation of quantum circuits . There have been advancements in the successful realization of fabrication methods of LN integration with SiO2. The ion-slicing method has enabled the production of large-scale, high-quality, and submicron-thick crystalline LN films. First, a lithium niobate wafer undergoes ion implantation, typically using hydrogen or helium ions, to create a weakened layer at a controlled depth . After the implantation, the wafer is bonded to a SiO2 (or TiO2) substrate using direct bonding techniques, which involves bringing the surfaces into close contact and applying pressure or heat to form a strong bond. The wafer is then subjected to thermal annealing, which activates the splitting process along the implanted layer. This results in the transfer of a thin LN layer onto the SiO2 (or TiO2) substrate, leaving behind a smooth surface that can be further polished if necessary .

Overall, LiNbO3/TiO2 multi-stacks hold promise for specific applications; however, careful design, advanced fabrication, and interface engineering are crucial for success . The primary motivation for choosing lithium niobate is to utilize materials whose optical properties are sensitive to one or more externally controllable factors, such as electric or magnetic fields, enabling the manipulation of the structure. Jamshidi-Ghaleh et al. investigated the behavior of the LN defect layer in MgF2/Ag/TiO2-based one-dimensional ternary photonic crystal (1DTPC). A voltage-dependent defect mode, arising from the electro-optic characteristics of LN, emerges inside the bandgap of the ternary photonic crystal. The localized wavelength can be tuned by changing the electric field without altering the reflectance values . Shuai et al. introduce a bulk acoustic resonator (BAW) comprised of a sandwich-like structure with an LN film positioned between two aluminum electrodes. In this setup, acoustic waves are generated and transferred onto a DBR structure consisting of 11 layers of SiO2/Ta2O5. The optimized design of the DBR effectively suppresses the leakage of acoustic energy . Superradiance describes a collective effect where excited atoms or molecules emit light much faster than they would individually . This "super-emission" scales with the system size, meaning larger systems shine brighter. The reverse phenomenon (i.e., superabsorption ) enhances light absorption for larger systems and holds promise for creating high-performance quantum batteries. However, directly observing superabsorption is challenging due to its ultrafast nature. In 2022, Quach et al. presented an innovative model of a quantum battery . This device comprises a DBR structure-based microcavity that encloses an organic semiconductor molecular dye, named Lumogen-Forange (LFO). The DBRs comprised 10 bilayers of SiO2/Nb2O5 in the lower region of the microcavity and an additional eight bilayers in the upper area. The bottom DBR was coated with LFO using the spin-coating technique. Ultrafast transient-absorption spectroscopy was used to measure charging dynamics by exciting the microcavity with a pump pulse and observing the evolution of stored energy with a probe pulse. The study demonstrated superextensive charging dynamics, where the rise time decreases as the stored energy density increases. The DBRs in the structure play a crucial role in the experimental setup. Firstly, allowing for the confinement of the optical field and driving coherent interactions with the organic semiconductor molecules. Secondly, enabling the measurement of the evolution of stored energy and the differential reflectivity induced by the pump pulse, which is essential for monitoring the charging dynamics at a femtosecond resolution.

The wavelength-selective nature of DBRs makes them particularly attractive for solar cell applications, where the ability to control the absorption spectrum can lead to significant performance improvements . Colloidal quantum dot (CQD) solar cells are attracting significant research due to their potential as a next-generation photovoltaic technology . These cells offer a compelling alternative to traditional silicon solar cells because of the low manufacturing cost. Additionally, CQDs possess a unique property – their bandgap can be tuned by adjusting the size of the dots. This allows them to capture a wider range of sunlight compared to traditional materials, potentially leading to higher solar energy conversion efficiency . Bae et al. focussed on lead sulfide (PbS) CQDs solar cells where they addressed the major challenge of charge carrier recombination which limits the conversion of absorbed light into electricity . The carrier diffusion length within PbS CQD solar cells aligns closely with the thickness of the CQD films. This correlation introduces a tradeoff between light absorption and charge transport. As the thickness of the CQD film increases to enhance light absorption, it simultaneously elevates the possibility of carrier recombination. Bae et al. incorporated Ag-coated five SiO2/TiO2 bilayered DBRs in combination with Fabry–Pérot (FP) resonators to address this trade-off and enhance the performance of PbS CQD solar cells. Hence, the light absorption near the resonant wavelength of the DBR can be selectively enhanced without increasing the CQD film thickness, thereby overcoming the inherent tradeoff in these devices. The combination of FP resonance and DBR increases the power conversion efficiency (PCE) of PbS CQD solar cells by 54% and enables a very thin PbS layer to absorb four times more near-infrared light .

Flip-chip micro light-emitting diodes (micro-LEDs) are a revolutionary technology with the potential to create next-generation HDR displays due to their tiny size, exceptional brightness, wide color gamut, and energy efficiency . However, a major challenge in their development is maximizing the light that escapes the micro-LED. By incorporating a DBR onto the bottom of a flip-chip micro-LED, engineers can capture light that would normally be lost downward and redirect it upwards, significantly improving the overall light output and efficiency of the device . Chen et al. explored a novel DBR design, the wide reflected angle DBR (WRA-DBR), specifically aimed at overcoming the limitations of conventional double-stack DBRs used in flip-chip micro-LEDs and further enhancing the light extraction capabilities . The proposed wide reflected angle Ti3O5/SiO2 DBR (WRA-DBR) comprises six sub-DBRs tailored for various central wavelengths spanning from blue to red light. With superior reflectivity across the visible light spectrum and reduced angular dependency, the WRA-DBR achieves an average reflectivity of up to 99.73% for light incident at a normal angle within the 400 to 700 nm wavelength range .

Shaaban et al. focus on the theoretical investigation of green light (at a wavelength of 550 nm) emission of microcavity inorganic/organic light-emitting devices based on Zn (Te, Se) . Incorporating DBR as a bottom mirror of the microcavity improved the green light emission intensity of LEDs. The wide application of DBR also extends to laser devices in which DBR acts as a highly selective mirror within the laser cavity. By reflecting a narrow wavelength range, the DBR enables single-mode operation, resulting in a laser emitting light with a precise, pure wavelength and high stability . Yu et al. demonstrated a tunable InGaAs quantum well DBR laser which provides a larger tuning range, single-longitudinal-mode operation, and narrow spectral linewidth, finding it suitable for multiple gas-sensing systems. The research output gives a wide tuning range of 10.7 nm with 19 consecutive channels obtained with a single tuning current at room temperature, expanding to 16 nm with the help of heat sink temperature .

Our focus material, LN, possessing a large electromechanical coupling coefficient (Kt), enables a high bandwidth . In short, LN emerges as an optimal candidate material for one-dimensional photonic crystal design due to its superior optical properties, robust electro-optic effect, and compatibility with integrated optical systems. Leveraging these attributes holds promise for advancing telecommunications, sensing, and quantum optics applications, driving innovation in photonic technologies. We designed one-dimensional photonic crystals (1D PCs) made of lithium niobate with titanium dioxide and silicon dioxide using electromagenetic simulations. Our goal was to maximize reflectivity in the infrared regime (around 1550 nm) by optimizing parameters such as the number of bilayers and thickness. Here, we achieved highly reflective lithium-niobate-based photonic crystals with a reflectance of 99.9% and a photonic band around 1550 nm. Additionally, by exploiting the electro-optic properties of LN, the photonic band could be tuned for specific for real applications.

where λ is the desired central wavelength and ni is the index of the corresponding layer.

Figure 1: The diagrammatic view of the PhC structure with 10 bilayers surrounded by air boundaries.

The value ‘D’ is the combined thickness of the repeating stack, which has been repeated 10 times (D = 321.3 nm for TiO2/LN and D = 443.6 nm for SiO2/LN).

The simulations were done in the wave optics module in COMSOL Multiphysics . The model-building process involved defining parameters and values, creating the geometry, assigning the materials to the created domains, setting boundary conditions, and implementing appropriate meshing. COMSOL Multiphysics utilizes a finite element analysis (FEM method) approach to simulate physical phenomena involving coupled multi-physics problems. Configuring solvers, running simulations, and the software iteratively solves the coupled system of equations numerically.

For a linear media, the relations become:

where D = εE and B = µH.

For a time-harmonic wave and linear media, the two equations can be combined to give:

Using the finite element method (FEM), the relevant partial differential equations will be solved on each discretized spatial element and finally give rise to the collective E field solution. Similarly, for the reflectance calculation on the structure, COMSOL utilizes the transfer matrix method (TMM). The analytical expression for reflectance at the desired wavelength for a lossless even-number-layered 1D PhC is the following :

where nH and nL are the high and low refractive indices of material layers, n1 is the refractive index of the surrounding medium, and N is the number of bilayers.

The simulation was done in the electromagnetic waves-frequency domain in the wave optics module to generate the electric field profile, and TMM helps to calculate the dispersion relation of transmission and reflection spectra of such structure. The simulation was executed on a computer with AMD Ryzen 5-5600H (3.30 GHz base frequency, up to 4.20 GHz maximum boost clock, 16 MB cache, and 6 cores). The simulation ran for an average time of 1 minute 28 seconds.

To obtain highly reflective 1D PhC over a wide range of wavelengths, the material in the alternating layers should have a significant difference in refractive indices. We chose LN-TiO2 and LN-SiO2 structures which have 0.398 and 1.06 of refractive contrast, respectively.

Figure 2: (a) Reflectance spectra of TiO2/LN PhC structures as a function of number of bilayers. (b) Reflectance spectra of TiO2/LN PhC structures with 99.99% reflectance around 1550 nm.

Figure 3: (a) Reflectance spectra of SiO2/LN PhC structures as a function of number of bilayers. (b) Reflectance spectra of SiO2/LN PhC structures with 99.99% reflectance around 1550 nm.

Figure 4: (a) Surface plot of E-field across the of TiO2/LN ten bilayered PhC. (b) Surface plot of E-field with height as the magnitude across TiO2/LN ten bilayered PhC. (c) Surface plot of E-field across the of SiO2/LN ten bilayered PhC. (d) Surface plot of E-field with height as the magnitude across SiO2/LN ten bilayered PhC.

Figure 5: Photonic band diagram of TiO2/LN: (a) 1st Brillouin zone of PhC under floquet periodic condition. (b) Surface electric field distribution on a bilayer of PhC at the value of upper band (band-2) edge at normalized wavevector k = 1. (c) Surface electric field distribution on a bilayer of PhC at the value of lower band (band-1) edge at normalized wavevector k = 1.

Figure 6: Photonic band diagram of SiO2/LN: (a) 1st Brillouin zone of PhC under floquet periodic condition. (b) Surface electric field distribution on a bilayer of PhC at the value of upper band (band-2) edge at normalized wavevector k = 1. (c) Surface electric field distribution on a bilayer of PhC at the value of lower band (band-1) edge at normalized wavevector k = 1.

Table 1: The reflectance of various promising distributed Bragg reflectors.

Lithium niobate is well-known for its strong nonlinear-optical and electro-optical properties. A DBR with LN could enhance nonlinear optical effects such as second-harmonic generation or optical parametric oscillation. Both the proposed LN-based PhCs can be easily integrated with other electro-optic devices, enabling dynamic tuning of the photonic bandgap through an applied electric field. This could be useful for creating tunable filters or modulators for high-power applications. However, successful implementation relies on advanced fabrication techniques, interface engineering, and material selection . If these challenges can be overcome, such structures could offer unique advantages for specific applications compared to using LiNbO3 alone. Overall, LiNbO3/SiO2 multi-stacks hold promise for more specific applications, but careful design, advanced fabrication, and interface engineering are crucial for success.

One-dimensional photonic crystals with lithium niobate (LN) were demonstrated using COMSOL simulation. The LN-SiO2 structure is suitable as a bandpass filter in the microwave regime. The reflectance of the structure in the desired wavelength range was improved by optimizing the number of layers. A 99.99% reflectance was observed for 17 and eight bilayers in LN-TiO2 and LN-SiO2 photonic structures. It can be concluded that our proposed 1D PhC design is viable for practical applications in photonics. The reflectance from the simulated data aligns well with the value calculated using the analytical formula. Our proposed PhC has the upper hand in terms of highly reflective surface, and tunability because of the non-linear optical and electro-optical effects of LN in it. The high reflectivity of DBRs helps in confining and controlling photons within a specific region. The refractive index contrast (RIC) is a crucial factor in the design and performance of one-dimensional (1D) photonic crystals (PCs). A higher RIC, as observed in structures incorporating TiO2 and SiO2, leads to the formation of stronger photonic bandgaps (PBGs) and enhanced light confinement. This confinement is essential for applications such as nonlinear optical processes and high-Q cavities, as it increases the interaction time between light and the material, thereby improving the efficiency of non-linear processes such as second-harmonic generation and modulation. This confinement is also crucial in reducing the impact of environmental noise on quantum systems, providing a more stable and controlled environment for quantum computing experiments. Achieving phase matching is crucial for various quantum processes, such as parametric down-conversion and four-wave mixing.

Recent research explores LiNbO3 as a defect layer in 1D PhC for manipulating quantum light in integrated photonic circuits , opening up potential applications in quantum computing, quantum photonics, and quantum communication . In certain quantum computing architectures, it is desirable to store and retrieve photons on demand. DBRs can be incorporated into the design of optical cavities to facilitate the storage of photons for longer durations, allowing for more complex quantum information processing tasks.

This file contains supplementary materials related to the COMSOL simulation model builder and essential mesh parameters. It includes images of the hierarchical tree of the COMSOL model builder and mesh discretization of the PhC geometry, a table of optimized mesh parameter values used, which are not shown in the main text.

The authors would like to thank TCG CREST for allowing the work to be carried out.

The authors received partial financial support for the research from TCG CREST. This research is partially supported by the Device Development Programme (DST/TDT/DDP-38/2021), by the Department of Science Technology, Ministry of Science and Technology, Government of India.

Midhun Murali: data curation; formal analysis; investigation; methodology; software; validation; writing – original draft. Amit Banerjee: funding acquisition; resources; software; writing – review & editing. Tanmoy Basu: conceptualization; data curation; formal analysis; funding acquisition; investigation; methodology; project administration; resources; software; supervision; validation; visualization; writing – review & editing.

The data generated and analyzed during this study will be avaibale under valid request.