Breaking dense integration limits: inverse-designed lithium niobate multimode photonic circuits

Domain: physics
Published: 2025-12-21
Editorial outcome: minor_revision

Abstract
Despite the growing interest in thin film lithium niobate (TFLN) as a material platform for photonic integrated circuits (PIC), its moderate refractive index, CMOS-incompatible fabrication processes and inherent material anisotropy still raise questions about achieving dense integration comparable to mature platforms like silicon photonics while preserving the superior properties of lithium niobate. Here we show a photonic inverse design method to enable miniaturization and dense integration of lithium niobate PIC components. As proofs-of-concept, we experimentally demonstrate ultra-compact mode-division (de)multiplexer (19×25μm²), multimode waveguide crossing (15×15μm2), and waveguide bends (30μm bending radius). The fabricated components are used to construct multimode photonic circuits for large-capacity data communications, demonstrating dense integration of over 10 waveguide elements within a 0.06mm² chip area. By integrating electro-optic modulators on the same chip, high-speed data modulation is demonstrated with 120 Gbps data rate per channel alongside multimode signal transmission. This work is expected to advance 10-fold higher area density of passive components and optical path design in TFLN.

Introduction
Modern photonic integrated circuits (PICs) are undergoing a paradigm shift toward dense integration, which is essential for scaling bandwidth, minimizing energy per bit, and supporting on-chip convergence of diverse optical functionalities1. Achieving such advancements requires photonic platforms that offer not only high index contrast but also wide spectral transparency, strong nonlinear and electro-optic properties2. Conventional silicon, silicon nitride and III–V platforms, while mature in CMOS-compatible processes, face inherent limitations in nonlinear performance, electro-optic response, or material transparency. In this context, thin-film lithium niobate on insulator (TFLNOI) has emerged as a promising alternative that combines a wide optical transparency window, strong nonlinear optical performance and high-speed electro-optic modulation3,4. Recent advances in TFLNOI-based electro-optic modulators have demonstrated unprecedented 100 GHz bandwidths and near-1V driving voltages at different wavelength ranges5,6, enabling more than a ten fold footprint reduction compared to bulk lithium niobate counterparts. These breakthroughs, driven by applications such as terabit per second optical communications7, precision optical metrology8 and quantum photonic processors9, position TFLNOI as a versatile platform for multifunctional photonic systems. However, the relatively modest refractive index contrast in TFLNOI waveguides, especially those fabricated with partial etching, inherently limits the mode confinement10. Thus, device dimensions such as waveguide bending radius face limitations, which constrain the achievable chip integration density and challenge the scalability demands of large-scale PICs. To bridge the gap between TFLNOI’s exceptional material properties and dense chip integration, advanced photonic design methods are emerging as powerful tools toward compact footprints while maintaining compatibility with fabrication processes.

Inverse design, which leverages intelligent optimization algorithms to explore a vast parameter space, can significantly improve multistage efficiency in device design, simulation and fabrication by enabling fast creation of complex optical structures, e.g., metasurface, with ultra-compact size, unprecedented precision and functionality11,12. Significant breakthroughs have been achieved in silicon photonics during the last few years, with the device footprint scaled down to the micron level, paving the way to densely integrated on-chip optical systems13–16. However, to obtain inverse-designed PIC components and complex optical systems in TFLNOI, the inherent barriers of material, method and fabrication process are particularly intractable. First, an X-cut TFLNOI platform experiences refractive index anisotropy in the y/z plane, and the traditional scalar-based inverse design methods are inappropriate to address the scenarios of anisotropic material. Although a Z-cut TFLNOI platform can avoid the material anisotropy in the plane of lithium niobate thin film17, the access to the strong electro-optic coefficient of lithium niobate (r33) requires laying out electrodes vertically, which is inconvenient for chip integration. Second, a tensor-based inverse design method can be extended to the X-cut TFLNOI platform by considering the impact of material anisotropy of lithium niobate18. However, a computational complexity increase is inevitable compared to that of traditional scalar-based inverse design methods, which brings higher requirements for computing resources and simulation time. Third, the generally used physical direct etching method for TFLNOI can induce a slanted waveguide sidewall, which limits the device feature size19, resulting in significant degradation and variability in device performance. Thus, the inverse designed lithium niobate photonics requires an overall optimization to overcome the material anisotropy and limited device feature size, while reserving the access to excellent material properties of lithium niobate.

In this work, we demonstrate inverse-designed high-density multimode photonic circuits for high-speed and large-capacity data communications in a silicon nitride-TFLNOI (X-cut) hybrid platform. As shown in Fig. 1a, integrated multimode photonics can enable large-scale signal parallelism and enhance the information capacity of PICs by introducing higher-order waveguide modes as data carriers20, which has also attracted attention in optical computing21, sensing22 and spectroscopy23. Unfortunately, the arbitrary routing of multimode signals is usually built in a large chip area, even in a high-indexed material platform, due to the radiation leakage and inter-mode coupling14. As shown in Fig. 1b–d, we design, fabricate and experimentally demonstrate an optical mode-division (de)multiplexer (19×25μm2), a multimode waveguide crossing (15×15μm2) and a multimode waveguide bend (30μm bending radius) for the first three quasi-transverse electrical modes (TE0, TE1 and TE2). The measured insertion losses are lower than 2.5 dB at the wavelength of 1550 nm, while the mode crosstalk stays below −15 dB at a wavelength range from 1530 nm to 1570 nm. These components are used to construct ultra-compact photonic circuits, enabling arbitrary routing of multimode signals through dense integration of more than 10 waveguide elements within a 0.06mm2 (200×300μm²) chip area. To demonstrate the advancement in combination of high integration density with excellent material properties, a high-speed data modulation and transmission system is implemented through the monolithic integration of electro-optical modulators and multimode photonic circuits. The single-channel data modulation and transmission rate for on–off key signal reaches up to 120 Gbps.

Results
Waveguide platform
Silicon nitride is selected as an isotropic optical loading material. Thus, the optical structures in the loading layer can be optimized using a scalar-based inverse design method and fabricated by mature silicon nitride etching processes, enabling improved design efficiency and well-controlled device feature size. There are also other available loading materials, such as silicon, polymers and chalcogenide glasses. Among them, silicon is naturally an attractive loading material for dense integration since its high refractive index (~3.45 at 1550 nm) allows strong mode confinement in the loading rib, which can help to dramatically reduce the device footprint. However, the propagation loss of silicon-TFLNOI hybrid waveguide is relatively high24, the lower mode confinement in lithium niobate thin film may lead to reduced electro-optical modulation and optical nonlinear efficiency25, and the initial optical transparency window of silicon limit the waveguide’s usefulness for nonlinear optical applications across a large wavelength range26. By contrast, silicon nitride can be deposited by different methods with low optical loss, which offers a similar but slightly lower refractive index (~2.0 at 1550 nm) than lithium niobate (ne ~2.14, no ~2.22 at 1550 nm), and similar optical transparency window spanning from visible to mid-infrared wavelengths compared with lithium niobate27. The silicon nitride-TFLNOI (X-cut) hybrid platform is designed to avoid the direct etching of lithium niobate thin film, while providing a high mode confinement factor (~60%) in lithium niobate. The layers from top to bottom are air cladding, silicon nitride loading layer, lithium niobate slab, buried oxide layer and silicon substrate, respectively. A hybrid silicon nitride-TFLNOI ridge waveguide is formed by the deposited and etched silicon nitride loading rib and the unetched lithium niobate slab. Light is coupled to the hybrid ridge waveguide modes without evanescent coupling between different layers (see Supplementary Note 1 for details). The thicknesses of the silicon nitride and lithium niobate layers are both 300nm, which avoids the mode lateral leakage at second-harmonic wavelengths28. The thickness of the buried oxide layer is selected as 4.7μm to ensure index match and a relatively low radio-frequency loss for electro-optic modulation.

Mode (de)multiplexer
Mode (de)multiplexers (MUXs) serve as critical PIC components to enable parallel propagation of multimodal signals in a single waveguide. Previous works in TFLNOI platform are generally based on directional coupler structures by forward design29–32. In this case, the low-loss and low-crosstalk mode coupling relies on strict control of phase and mode field distribution, requiring a large device footprint. In contrast, in this contribution, we employ the inverse design method to implement a three-mode MUX with an ultra-compact effective size of only 19×25μm2.

Figure 2a,b show an illustration and a scanning electron microscope (SEM) image of the device structure, which is designed and fabricated by patterning the silicon nitride layer. By considering the anisotropy of lithium niobate, the device is designed along the crystallographic Z direction to avoid the mode hybridization between TE1 and TM modes33. The widths of the input single-mode waveguides and output multimode waveguide are designed as 1μm and 4.3μm, while the gaps between the adjacent input waveguides are 2μm. Compared with the directly etched TFLNOI waveguide, a near-vertical waveguide sidewall is available when etching silicon nitride, which means a smaller device feature size is allowed. The achievable smaller feature size enables creation of a refined waveguide structure, which is demonstrated to significantly improve the device performance, including insertion losses and mode crosstalk (see Supplementary Note 2 for details). To ensure fabrication reproducibility, we set the minimum feature size to 100 nm in this work.

We use two cascaded devices with the same structural parameters for signal multiplexing and demultiplexing in the experiment, as shown in Fig. 2c. Grating couplers are used as optical interfaces, which are designed with a period of 920 nm (940 nm for Y propagating) and a filling factor of 0.434. The simulated electric field profiles of a single device are monitored by using the three-dimensional finite-difference time-domain (3D-FDTD) method35, at a wavelength of 1550 nm. As shown in Fig. 2d, the input TE0 modes in the middle (I0), upper (I1) and lower (I2) waveguides are coupled to TE0, TE1 and TE2 modes in the output waveguide, respectively. The corresponding transmission spectra at a wavelength range from 1530 nm to 1570 nm are depicted in Fig. 2e–g. The simulated insertion losses of the TE0, TE1 and TE2 modes are 0.52 dB, 0.63 dB, and 0.87 dB at the wavelength of 1550 nm, while the mode crosstalk stays below −20.1 dB across the whole wavelength range. To further characterize the device performance, the transmission spectra of different modes are measured by using the device shown in Fig. 2c. As shown in Fig. 2h–j, the measured insertion losses of TE0, TE1, and TE2 mode channels are 1.05 dB, 1.42 dB, and 2.50 dB at the wavelength of 1550 nm, with the mode crosstalk lower than −15.9 dB across the whole wavelength range, which are in good agreement with the simulation results. The demonstrated MUX exhibits comparable performance with the conventional counterparts based on directional couplers (see Supplementary Note 3 for details), while representing a more than tenfold footprint reduction. Moreover, we have fabricated two other devices in which the widths of the etched waveguide patterns deviate from the optimal design by ±20 nm. The measured results indicate that the fabricated device maintains low insertion loss, low mode crosstalk and wide bandwidth across fabrication variations, demonstrating good fabrication tolerance (see Supplementary Note 4 for details).

Multimode waveguide crossing
Waveguide crossing is another important PIC component for dealing with the cross connect in waveguide routing36. The discontinuities at the intersection can induce mode coupling and interference, presenting inherent challenges for device design.

As shown in Fig. 3a, an ultra-compact three-mode waveguide crossing is designed with a device footprint of only 15×15μm2. The widths of the input and output multimode waveguides are 4.3μm, which are consistent with those of the MUX. As mentioned earlier, the minimum feature size is set to 100 nm, considering the trade-off between device performance and fabrication reproducibility. Figure 3b shows an SEM image of the fabricated device. To ensure the device performance, the electric field profiles of different modes are simulated at a wavelength of 1550 nm by using the 3D-FDTD method. As shown in Fig. 3c, the multimode signals pass through the waveguide crossing with negligible intermodal coupling and radiation loss. We characterize the waveguide crossing by using a pair of auxiliary MUXs based on directional couplers. The microscope image of fabricated devices is shown in Fig. 3d. The input TE0 modes are coupled to different mode channels at the input ports, and then pass through the device. The multimode signals are demultiplexed at the output ports for transmission spectra measurements. The insertion losses of the fabricated waveguide crossing are measured through the cut-back method. As shown in Fig. 3e, the measured and fitted insertion losses of TE0, TE1, and TE2 modes at the wavelength of 1550 nm are 0.16 dB, 0.33 dB, and 0.55 dB, respectively. In addition to the ultra-low insertion losses, the fabricated waveguide crossing is also demonstrated to have low inter-modal crosstalk at a wide wavelength range from 1530 nm to 1570 nm. As shown in Fig. 3f–h, the simulated transmission spectra predict that the inter-modal crosstalk for TE0, TE1 and TE2 mode channels stays below −19.4 dB, −46.2 dB and −18.9 dB. The corresponding measured results are shown in Fig. 3i-k, where the inter-modal crosstalk is lower than −17.7 dB, −15.0 dB and −16.1 dB for TE0, TE1 and TE2 mode channels, respectively. We have noted that the crosstalk for the TE1 mode channel is limited, due to the unexpected mode coupling in the auxiliary MUXs (see Supplementary Note 3 for details).

It should also be noted that the anisotropy of lithium niobate has been included in the device optimization. Thus, the designed and fabricated device has similar performance when light propagates along the crystallographic Z direction of lithium niobate (see Supplementary Note 5 for details).

Multimode waveguide bend
The waveguide bending radius is strongly limited in the TFLNOI platform due to the relatively low refractive index. The single-mode waveguide bending radius in a micro-ring resonator typically reaches up to 80~100μm, to reduce the mode mismatch and radiation losses37,38. The multimode waveguide bends require a larger size, inevitably due to the weaker confinement for higher-order modes. Though shape optimization like Euler bends31, B-spline39 or air grooves40 can significantly reduce the multimode waveguide bending radius to 100~160μm, there is still a gap between the size required for dense integration. Here, we demonstrate an ultra-compact multimode waveguide bend with an effective bending radius of only 30μm, which is equivalent to that of the sharpest single-mode waveguide bend with a partial-etched waveguide cross-section in X-cut TFLNOI platforms41,42, to the best of our knowledge.

The schematic diagram and SEM image of the multimode waveguide bend are shown in Fig. 4a,b. The widths of the input and output multimode waveguides are 4.3μm. Figure 4c shows the electric field profiles of different modes, simulated by using the 3D-FDTD method at a wavelength of 1550 nm. After passing through the topology optimization area, the propagation directions of multimodal signals are turned by 90° with negligible inter-modal coupling. Similarly, we characterize the device by using the directional coupler-based auxiliary MUXs. The microscope image of fabricated devices is shown in Fig. 4d. The insertion losses of the fabricated waveguide bends are measured through the cut-back method. As shown in Fig. 4e, the measured and fitted insertion losses for TE0, TE1, and TE2 modes at the wavelength of 1550 nm are 1.02 dB, 1.96 dB, and 2.17 dB, respectively. The waveguide bend has low inter-modal crosstalk over a wide wavelength range. As shown in Fig. 4f–h, the simulation transmission spectra predict that the inter-modal crosstalk for TE0, TE1 and TE2 mode channels can stay below −20.4 dB, −16.2 dB and −19.8 dB at a wavelength range from 1530 nm to 1570 nm. For the convenience of measurement, the propagation directions of the multimode signals are actually turned by 180° in the experiment (two 90° bends). The corresponding measured results are shown in Fig. 4i–k, where the inter-modal crosstalk for TE0, TE1 and TE2 mode channels is lower than −16.2 dB, −15.1 dB and −15.9 dB, agreeing well with the simulated results. Moreover, we have performed an additional design for a single-mode 90° waveguide bend by using the same method. It is demonstrated that the wide input and output waveguides offering strong mode confinement for the TE0 mode can help to reduce the waveguide bending radius to about 14μm (see Supplementary Note 6 for details).

Multimode photonic circuits
To further demonstrate the device performance in dense integration, we design and fabricate two types of multimode photonic circuits. The first PIC shown in Fig. 5a consists of two independent circuits with path crossing of the two circuits, while the second one shown in Fig. 5b is a single circuit with multipath crossings of the same circuit. The input fundamental modes are first coupled into different mode channels by the mode multiplexer. The multiplexed multimode signals are then routed in the chip plane by using the waveguide crossings and bends, which are finally demultiplexed by another mode demultiplexer. An only a chip area of 200×300μm² is occupied to implement these operations.

The measured transmission spectra of the first PIC are shown in Fig. 5c–e. The insertion losses for TE0, TE1 and TE2 mode channels are 4.2 dB, 7.8 dB and 7.1 dB, while the inter-modal crosstalk stays below −20.3 dB at the wavelength of 1550 nm. Similarly, the measured transmission spectra of the second PIC are shown in Fig. 5f–h. It can be seen that the insertion losses for TE0, TE1 and TE2 mode channels are 6.5 dB, 11.5 dB and 11.9 dB, while the inter-modal crosstalk still stays below −12.5 dB at the wavelength of 1550 nm. The measured insertion losses of PICs are very close to the sums of individual device insertion losses, with the deviations lower than 1 dB, 2.13 dB and 0.74 dB for TE0, TE1 and TE2 modes (see Supplementary Note 7 for details). The deviations can be attributed to the following two aspects. First, the reported insertion losses of waveguide crossing and bends are measured and fitted by using the cut-back method. It can be seen from Figs. 3e, 4e that the measured insertion losses actually vary for different components in the experiment due to the fabrication variations. Second, the PICs and individual components are fabricated in different regions on the same chip. Thus, the fabricated structural parameters for the same device can also be slightly different. Overall, despite a significant increase in the number of waveguide elements, the measured results still indicate good performance, presenting the good system scalability and dense integration capability of the inverse-designed devices.

To demonstrate the advancement in the combination of dense integration capability and excellent material properties, an on-chip data modulation and transmission system is implemented. We design and fabricate three electro-optical modulators based on the micro-ring resonator structure, corresponding to the employed three-mode channels. Light emitted by the lasers is modulated by high-speed radio-frequency signals, then routed in the chip plane by the multimode photonic circuits, and finally detected by photodetectors. A microscope image of the fabricated electro-optical modulator is shown in Fig. 6a. The designed waveguide width and the coupling gap are 1μm and 750 nm, respectively. The radius of the ring waveguide is 300μm, while the length of the straight track is 1.5 mm. The measured transmission spectrum of the micro-ring resonator is shown in Fig. 6b. The insertion loss at a non-resonant wavelength is lower than 0.54 dB, while the extinction ratio is larger than 12.4 dB. A ground-signal-ground (G-S-G) traveling-wave electrode is employed. The width of the signal electrode is designed as 23μm, and the gap between signal and ground electrodes is 6μm. Figure 6c shows the measured eye diagrams for different mode channels with the modulated and transmitted on-off key signal rates of 100 Gbps and 120 Gbps. The measured signal-to-noise ratios are larger than 5.4 dB. The clear and open eyes indicate good system performance.

Methods
Inverse design method
Gradient optimization based on the adjoint method is used to implement topology optimization through iterative material distribution updates. The dielectric permittivity of the design area is initially projected onto a [0,1] space for parametric normalization (Eq. (1)). The material distribution is subsequently smoothed via a convolutional filtering (Eq. (2)) to eliminate subwavelength defects. Finally, an adaptive binarization projection function (Eq. (3)) is used to increase filter sharpness β and obtain a binary distribution of dielectric constants. We only need to optimize the distribution of isotropic silicon nitride loading material. Thus, the scalar-based inverse design method is applicable.

ρ = ε r (ρ)·ε min (1)
0 ε max -ε min

ρ =w(x)⊗ρ (2)
1 0

ρ = tanh(β·η)+tanh(β·(ρ -η))
2 tanh(β·η)+tanh(β·(1-η)) (3)

where ρ0, ρ1 and ρ2 denote the normalized design parameters of the initial, filtered and binary design area, while ε(ρ), εmin and εmax represent the material dielectric constants of the design area, air cladding and silicon nitride load. In addition, w(x) is the convolution kernel, β is the filter sharpness parameter, and η is the design threshold. Device performance is quantified through a broadband figure of merit (FOM, Eq. 4).

FOM= λ 1 λ Z λ 2jT (λ)jpdλ ! 1=p · λ 1 λ Z λ 2jT(λ)·T 0 (λ)jpdλ ! 1=p
2 1 λ 1 2 1 λ 1 (4)

where T0(λ), T(λ) is the target and actual forward transmission at a wavelength of λ, while p is the generalized norm value which can control the optimization preference between transmission and bandwidth (see Supplementary Note 9 for details). In this instance, the effects of lithium niobate birefringence on device performance are included in the simulation.

Fabrication processes
We use an X-cut TFLNOI wafer from NanoLN, China. The silicon nitride thin film is deposited onto the chip by using a reactive sputtering process48. The grating coupler and waveguide structures are patterned by using electron-beam lithography, and then formed by using single-step inductively coupled plasma etching. Finally, the electrodes (500-nm-thick Au) are fabricated by using laser direct writing, e-beam evaporation deposition and lift-off processes. The propagation losses of the fabricated waveguides are measured to be about 0.25 dB/cm by using the cut-back method. The coupling losses of the fabricated grating couplers are measured to be 6 dB/facet, at a peak coupling wavelength of 1560 nm.

Experimental setup
Light is emitted by a tunable laser, followed by a polarization controller used to maintain TE polarization before coupling light into the chip. For static measurements, signals coupled out of the chip are directed to an optical spectrum analyzer for spectral analysis.

For a high-speed data modulation and transmission experiment, the laser light is modulated by the on-chip electro-optical modulator using a 210−1 pseudo-random binary sequence generated by an arbitrary waveform generator. After coupling into and out of the chip, the signals are amplified by an erbium-doped fiber amplifier, followed by an optical tunable filter for reducing background noise. Finally, the signals are received by a digital communication analyzer for eye diagram measurements (see Supplementary Note 10 for details).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manu., the authors demonstrate inverse-designed multimode photonic devices and densely integrated photonic circuits in a lithium niobate on insulator (LNOI) platform. As an emerging integrated photonics material platform, LNOI has driven breakthrough advances in communications, metrology, and quantum optics in recent years, owing to its exceptional material properties. However, compared to silicon photonics, lithium niobate's relatively low refractive index leads to larger device footprints, its optical anisotropy results in propagation-direction-dependent waveguide mode behavior, and its immature fabrication processes impose limitations on the minimum feature size. The above aspects make it difficult to further improve the chip integration density. The authors in this manu. address these challenges and propose a potential solution. In their work, the authors achieve precise control and routing of higher-order modes within ultra-compact chip area, demonstrating that the footprint of passive components and optical path design in LNOI can be comparable to those in silicon photonics. Their heterogeneous integration approach enables flexible control of feature sizes while preserves the high performance of active components such as electro-optic modulators, reflecting a high technical level. Overall, the manuscript is well written, and I would recommend its publication in Nature Communications after the following points are addressed.\n1. If only the device footprint is considered, silicon might be a superior choice as the loading material. However, taking into account other properties in dense integration such as propagation losses, modulation efficiency and optical transparency window, silicon nitride is likely a better option. I suggest that the authors include more comparative discussions on the waveguide platform.\n2. How does the inverse-designed devices perform in fabrication tolerance? If the structural parameters deviate from the central design values due to fabrication variations, can the device functionality still be maintained?\n3. The waveguide bending radius is constrained by the relatively low refractive index of lithium niobate, which constitutes a significant factor limiting the chip integration density. Thus, I am also curious about the minimum achievable bending radius for a single-mode waveguide designed using the inverse method in this platform. It would be highly beneficial to include some results in the Supporting Information.\n4. When multiple multimode devices are interconnected to form a complex photonic circuit, does the total loss correspond to the sum of the losses from the individual components?\n5. I suggest using a darker shade for the LN layer in Figure 1c, to ensure better visual consistency with the representation in Figures 1b and 1d.", "reviewer_2": "The authors demonstrate the use of inverse design for photonic components such as mode crossings and multiplexers. With inverse designed devices, one of the concerns is the loss which they have demonstrated to be relatively low. For example, the simulated mode demultiplexer has a measured loss of 1.05-2.5dB for the mode channels and the waveguide crossing has <1dB loss. The designs are interesting and experimental characterization of the devices show that they perform their function well. I recommend publishing this paper with the following comments for the authors' consideration :\n1) The refractive index of SiN and LiNbO3 while well known, should be stated in the manuscript\n2) The SiN layer is used as a loading layer and LiNbO3 in this case is not etched. It would be useful for readers if the authors describe the pathway of light eg. which layer it is coupled into, whether it undergoes evanescent coupling etc.\n3) Related to the previous point, what percentage of the light resides in the LiNbo3 and SiN layers with this platform? Modal confinement is a metric which impacts a variety of optical phenomena eg. how small of a bending radius ring resonators can have. Is there any future improvements that can be made if the relative quantity of light residing in these two layers is changed?\n4) If low loss LiNbO3 etching is available to the authors, how do you envision that the designs and performance will change? Could eg. the device footprint become even smaller? Please discuss this point.\n5) The authors fabricate a circuit composed of the three inverse designed devices and the results are shown in Fig. 5. The insertion losses for the TE0, TE1 and TE2 mode channels are 4.2 dB, 7.8 dB and 7.1 dB respectively. can the authors analyze this loss and comment on whether it is as expected from the loss for each individual component If it is higher, suggest reasons for it.\n6) Figure 6 shows data modulation and multimode signal transmission. from the experimental results, it looks like the authors used the inverse designed devices prior to the data modulation. The eye diagrams for each of the three modes are shown. I suggest revising the paragraph of text which discusses Fig. 6. This excerpt of text, \" Light emitted by the lasers 'can be' modulated by high-speed radio-frequency signals, then routed in the chip plane by the multimode photonic circuits, finally detected by photodetectors,\" makes it sound like the light can be routed by the multimode photonic circuits, as a possibility and it is ambiguous as to whether this was done. The words, 'can be' may be replaced to is, so it sounds clearer.\n7) The authors include a table of comparison with other TFLN devices. I suggest also including a table and discussion which compares the performance of this work with other work which report inverse designed devices."}, "author_response": "Responses to Reviewer 1’s Comments:\n[... full text of author response to Reviewer 1 ...]\nResponses to Reviewer 2’s Comments:\n[... full text of author response to Reviewer 2 ...]"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I think that the authors have considered my comments seriously, and revised their manuscipt accordingly. I do not have any more concerns for publishing it at Nature Communications.", "reviewer_2": "I have read the revised paper, \"Breaking Dense Integration Limits: Inverse-Designed Lithium Niobate Multimode Photonic Circuits,\" by X. Han et al. The paper is suitably revised and may be published."}, "author_response": ""}]

Decision letter