Low-Dimensional Materials in Nonlinear Optics

By Ibtisam AbbasiReviewed by Louis CastelOct 31 2025

Non-linear optical technologies have significantly advanced the photonics industry and the development of integrated photonic devices, enabling a new wave of innovation. Key areas such as advanced non-linear materials, next-generation lasers and light sources, and novel waveguiding structures are helping to create integrated photonic systems with enhanced bandwidth, greater efficiency, and more flexible fabrication processes.¹ In this context, two-dimensional (2D) materials like graphene and MoS2 are gaining attention as promising non-linear optical (NLO) materials, thanks to their exceptional optical properties and favorable electrochemical characteristics.

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The Optical Nonlinearity of Graphene and MoS₂

Why 2D Materials are Preferred Over Traditional Materials

Since the discovery of graphene in 2004, two-dimensional (2D) materials have gained widespread attention for use in optical devices and integrated non-linear photonic systems. Compared to traditional bulk materials, 2D materials offer several key advantages. They exhibit strong optical responses across a broad spectrum, from ultraviolet and terahertz frequencies to the microwave region, making them highly versatile for various applications.

One of their defining features is a high ratio of exposed surface atoms, which allows for precise tuning of their optoelectronic properties. Their atomically thin structure also makes them ideal for seamless integration with other materials, enabling the development of compact, high-performance photonic devices..

Distinct Properties of Graphene and MoS₂ for Photonic Devices

The integration of micro- and nano-scale optical structures, such as plasmonic structures, photonic crystals, and metamaterials, has further enhanced the optoelectronic performance of 2D materials. These engineered structures significantly improve light–matter interactions, giving 2D materials a clear advantage over traditional materials in terms of optical response.

When non-linear optical (NLO) 2D materials are combined with these advanced architectures, the result is a substantial boost in their functional capabilities. This synergy is particularly valuable for a wide range of photonic and non-linear optical applications, including photodetection, optical modulation, surface-enhanced Raman scattering (SERS), and photocatalysis.²

NLO 2D materials are regarded as highly promising materials with substantially high absorption due to the presence of absorber components. The monolayer atomic arrangement of carbon atoms imparts useful attributes to Graphene, making it viable for ultra-broadband and ultra-fast optical applications such as the fabrication of modulators and photodetectors.³

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Non-Linear Effects in 2D Materials

Third-Harmonic Generation (THG) in 2D Materials

Recent studies have unearthed non-linear optical effects in graphene due to inter-band electronic transitions. Despite the monolayer thickness, several 2D materials similar to graphene display a strong nonlinear optical response. Symmetry-allowed third-order non-linear optical effects are quite dominant in graphene, making it a suitable choice for absorption and optical limiting applications. The in-plane isotropy and coherent nature of third-harmonic generation (THG) allow for probing of the physical structure of graphene without the need for crystallographic orientation. THG in graphene allows for its utilization as a nonlinear optical microscopy probe with minimal optical focusing. Furthermore, it allows for the use of graphene and other 2D materials in optical instruments with higher transverse resolution, enhancing the efficiency of integrated photonic devices specifically.⁴

Saturable Absorption Phenomena in 2D Materials

Graphene and other 2D materials have also been shown to demonstrate saturable absorption in various experimental studies. In graphene, this nonperturbative non-linear optical process can emerge at significantly low light intensities, making 2D materials pivotal for the generation of ultrafast light pulses.⁵ The favorable attributes, like broadband operation, range from visible to infrared wavelength, faster modulation times, and lower losses, have made graphene saturable absorbers (GSAs) a popular platform for developing pulsed lasers.⁶ In addition to these attributes, ultrahigh non-linear Kerr optical nonlinearities, material anisotropy, and layer-dependent properties make 2D materials highly promising for novel photonic devices.⁷

A Comparison of Graphene and MoS₂

The electronic band structure directly affects the electronic attributes and alters the performance of the devices fabricated using the concerned material. The electronic band gap is critical for the classification of the material as either a conductor (with zero band gap), a semiconductor (moderate band gap), or an insulator (large band gap).

In graphene, electrons behave like Dirac fermions, meaning their energy dispersion is linear near the corners of the Brillouin zone. This linear dispersion forms what’s known as a Dirac cone, a characteristic feature that gives graphene its intrinsic zero band gap - primarily due to the presence of free, delocalized electrons.

To tailor graphene’s electronic properties for specific applications, particularly those requiring a band gap, researchers have explored several modification techniques. One widely studied approach is strain engineering, where uniaxial strain is applied to alter the material’s electronic structure and induce a tunable band gap.

On the other hand, electrons in MoS₂ are normal fermions with a parabolic energy dispersion, making MoS₂ a semiconductor with a direct energy band gap exceeding 1.8eV. This makes MoS₂ a highly preferred material for transistor applications, as MoS₂ doesn’t require any sort of strain engineering to develop a finite band gap. This attribute makes MoS₂ a better choice when it comes to opto-electronic devices, transistors, and for manufacturing of energy harvesting components.⁸

Ultrafast Optical Switching and Laser Mode-Locking

Graphene and MoS₂ are preferred materials extensively used as saturable absorbers. Mode-locked lasers are pivotal for applications involving ultra-fast telecommunication, biomedical instruments, and spectroscopy applications. In this regard, experts have integrated a single-layer graphene absorber with a commercially available erbium-doped fiber amplifier (EDFA) to be used as a saturable absorber in mode-locked fiber lasers, demonstrating both passive and active mode-locking.

The experimental results demonstrated that a graphene saturable absorber integrated on the 220 nm on the Silicon-on-chip EDFA platform allows for operation in both active and passive mode-locking. During the passive mode-locking, the pulses were produced with a 1.7ps interval, with a repetition rate of 28MHz. Higher harmonics with fundamental repetition rate were achieved during the active mode.⁹ This proves that graphene can act as a saturable absorber for mode-locked fibers used for modern photonic applications.

Similar to graphene, MoS₂-based composite materials have also been used as saturable absorbers in mode-locked fibers. Using the MoS₂ and SiO2-based absorber, a passive mode-locked EDF laser generated stable pulses with a pulse width value of 780 fs at a pump power of 90mW.

Upon raising the pump power between 100 – 600mW, another stable mode-locking operation was obtained with the pulse width just around 1.2ps and a maximum output power of 5.11mW.¹⁰

These results prove that MoS₂ and graphene can be used in mode-locked lasers to reach pulse durations of less than 100 ps and sub-100 femtoseconds. These attributes make these NLO 2D materials highly promising for next-gen intelligent photonics and opto-electronics applications.

Tunable Photonic Devices and Optical Modulators

2D Materials for Electro-Optical Modulators

The layered structure of 2D materials makes them a preferred material for the development of optical modulators operating in a wide range of wavelengths. The electro-optic modulators could be manufactured using 2D materials utilizing the Franz–Keldysh effect and Pauli-blocked Burstein–Moss shift effect.

Experts have developed an exciton-based electro-optic modulator using a MoS₂ monolayer. The surface atomic layer of MoS₂ enables tight spatial overlapping with the surface plasmon. The MoS₂ was exfoliated on a silicon substrate. A gold nano-disk was fabricated on top of MoS₂ using metal deposition. The increase in V_gs to 8V increased the dip of the Fano-resonance line. Around 685 nm, the scattering intensity reduced with the increase in voltage. The response time of the electro-optic modulator was less than 200ms, highlighting its efficient operational capability.

 Furthermore, graphene is a suitable material, particularly for modulation in the telecom band, and allows for faster response time from the visible to the terahertz range. Graphene-based modulators with higher extinction ratios have been developed by researchers. Experts transferred graphene onto a silicon waveguide with 7nm alumina acting as a dielectric spacer. At a V_g value around -4V, the modulation depth was around 0.1dB/µm. The spectral images reveal electrically modulated transmission between 1200 to 1600 nm. The high carrier mobility of the graphene-based modulator has opened up new avenues for its utilization in high-speed telecommunication.¹¹

All optical modulation devices are essential for the development of next-gen intelligent photonic devices. The substantial success in silicon-based-on-chip optical interconnects, particularly, on-chip optical modulators, has been possible due to 2D materials like graphene, topological insulators (TIs), MXenes, Transition Metal Dichalcogenides (TMDs), and Black Phosphorus (BP), etc. In the future, developing new heterostructure hybrid systems involving highly tunable 2D materials will revolutionize the optical modulation sector ¹²

Key Challenges

Despite their promising properties, the development of practical, industrial-scale devices, or even advanced research prototypes, using 2D materials for optoelectronic and integrated photonic applications still faces several critical challenges. One major hurdle is the growth of large-area, high-quality monolayer 2D crystals with strong quantum efficiency. Maintaining uniformity while minimizing defects during fabrication remains a significant technical obstacle. Another key research focus is the direct growth of 2D nanostructures on photonic integrated platforms, which could streamline device integration and improve performance.

Scalability and cost-effectiveness are also major concerns. Developing reliable, cost-efficient manufacturing techniques is essential for translating 2D material-based technologies, such as non-linear optical modulators, from the lab to large-scale industrial applications. Researchers are actively working to address these barriers and move closer to practical implementation.

Future Outlook

2D materials are on the verge of altering the dynamics of non-linear optics. Experts are expecting them to play a vital role in developing hybrid systems for intelligent photonic on-chip devices. Additionally, the non-linear effects in 2D materials are being researched extensively for the development of free-space optical neuromorphic computing systems, making 2D materials like MoS₂ essential for developing programmable computers demonstrating AI capabilities like Optical artificial neural network (ANN) and digital processing.¹⁴

The NLO 2D materials market will grow rapidly if the manufacturing and scalability challenges are addressed properly. The interest of industrial experts and academic research groups in 2D materials for opto-electronic and photonic devices is proof of the transformative potential these low-dimensional materials hold for the optics industry.

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Further Reading

1. Sirleto, L. et. al. (2023). An Introduction to Nonlinear Integrated Photonics Devices: Nonlinear Effects and Materials. Micromachines. 14(3). 604. Available at: https://doi.org/10.3390/mi14030604
2. Tao, Li. et. al. (2020). Enhancing light-matter interaction in 2D materials by optical micro/nano architectures for high-performance optoelectronic devices. InfoMat. 3(1). 36-60. Available at: https://doi.org/10.1002/inf2.12148
3. Heo, H. et. al. (2019). Broadband absorption enhancement of monolayer graphene by prism coupling in the visible range. Carbon. 154. 42-47. Available at: https://doi.org/10.1016/j.carbon.2019.07.089
4. Hong, S. et. al. (2013). Optical Third-Harmonic Generation in Graphene. Physical Review X. American Physical Society. 3(2). 2160-3308. 13. 021014(10). Available at: http://dx.doi.org/10.1103/PhysRevX.3.021014
5. Marini, A. et. al. (2017). Theory of graphene saturable absorption. Physical Review B. 95. 125408. Available at: https://doi.org/10.1103/PhysRevB.95.125408
6. Karankova, S. et. al. (2023). Optical saturable absorption of conformal graphene directly synthesized on nonlinear device surfaces. Applied Surface Science. 611(A). 155641. Available at: https://doi.org/10.1016/j.apsusc.2022.155641
7. Jia, L. et. al. (2020). BiOBr Nanoflakes with Strong Kerr Nonlinearity towards hybrid integrated photonic devices. Proceedings. 11282. 2D Photonic Materials and Devices III. 112820Q. Available at: https://doi.org/10.1117/12.2546243
8. Jiang, J. (2015). Graphene versus MoS2: A short review. Front. Phys. 10. 287–302. Available at: https://doi.org/10.1007/s11467-015-0459-z
9. Reep, T. et al. (2025). Graphene absorber on an SOI chip for active and passive mode locking of lasers. Sci Rep 15. 9399. Available at: https://doi.org/10.1038/s41598-025-93051-z
10. Li, L. et al. (2019). Mode-Locked Er-Doped Fiber Laser by Using MoS2/SiO2 Saturable Absorber. Nanoscale Res Lett 14, 59. Available at: https://doi.org/10.1186/s11671-019-2888-z
11. Gan, X. et. al. (2022). 2D materials-enabled optical modulators: From visible to terahertz spectral range. Applied Physics Reviews. 9. 021302. Available at: https://doi.org/10.1063/5.0078416
12. Yang, H. et. al. (2022). All-Optical Modulation Technology Based on 2D Layered Materials. Micromachines 13(1). 92. Available at: https://doi.org/10.3390/mi13010092
13. Azimi, A. et. al. (2025). Photonics in Flatland: Challenges and Opportunities for Nanophotonics with 2D Semiconductors. Opticia Open. Preprint. Available at: https://doi.org/10.48550/arXiv.2507.00336
14. Tong, L. et al. (2024). Programmable nonlinear optical neuromorphic computing with bare 2D material MoS2. Nat Commun 15. 10290. Available at: https://doi.org/10.1038/s41467-024-54776-z

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