Photonic Nanojets: Fundamentals & Applications

• Photonic nanojets are highly localized, intense electromagnetic beams with subwavelength waists formed on the shadow side of dielectric microstructures under optical illumination.
• They are generated via near-field diffraction, resonant mode excitation, and controlled interference, resulting in enhanced, non-conventional focusing behavior.
• Their unique properties enable practical applications in ultramicroscopy, optical trapping, integrated photonics, and nanoscale fabrication by boosting light–matter interactions.

Photonic nanojets are highly localized, intense electromagnetic beams with subwavelength waist that are typically formed on the shadow side of dielectric microstructures under optical illumination. Distinguished from conventional focusing phenomena, their generation relies on the interplay of geometrical optics, near-field diffraction, and resonant mode excitation. Photonic nanojets exhibit properties critical for applications in ultramicroscopy, optical manipulation, high-resolution imaging, and nanofabrication, as well as promoting enhanced light–matter interaction in integrated photonic systems.

1. Generation Mechanisms

Photonic nanojets (PNJs) are produced when electromagnetic waves—usually plane waves or tightly focused Gaussian beams—impinge on mesoscale dielectric particles such as spheres, cylinders, or ellipsoids. The underlying mechanisms include:

• Near-field diffraction: A curved dielectric interface acts as both aperture and focusing element, creating a diffraction pattern whose central bright maxima is the nanojet. The constructive interference of secondary wavelets from the interface, with appropriate phase delays dictated by the Huygens–Fresnel principle, generates a high-intensity focal spot (Salhi et al., 2017). The field at distance $X$ along the optical axis can be expressed as:

$$E_{tot}(X) = E_{0} \int_{-\pi/2}^{\pi/2} \cos([\Delta \phi_1(\alpha) + \Delta \phi_2(X,\alpha)]) \cos \beta(\alpha) d\alpha$$

with phase terms:

$$\Delta \phi_1 = \frac{2\pi n_1}{\lambda} R(1 - \cos \alpha), \qquad \Delta \phi_2 = \frac{2\pi n_2}{\lambda} \sqrt{R^2 + X^2 + 2RX \cos \alpha}$$

• Resonant mode excitation: High-order resonant eigenmodes (whispering gallery modes in dielectrics, localized surface plasmon modes in metals) can further concentrate the near fields, especially when illuminated by structured beams such as Laguerre–Gaussian (LG), resulting in asymmetric multi-peak nanojets or the emergence of optical vortices (Kiselev et al., 2014).
• Destructive interference and evanescent harmonics: Use of diffraction-free beams formed by two interfering plane waves enables destructive cancellation of propagating spatial harmonics, enhancing subwavelength focusing and local field near dielectric microcylinders due to the dominance of evanescent waves (Heydarian et al., 2020).

2. Structural and Wave Parameter Dependence

Nanojet characteristics depend on a synergy between material properties, geometry, and illumination:

• Particle shape and refractive index contrast: The width and intensity of the nanojet are strongly modulated by particle geometry and refractive index (RIC). As RIC increases, the focus becomes tighter and positioned closer to the surface; the jet width is bounded by the diffraction limit, typically $\lambda/(2n)$ (Salhi et al., 2017, Gu et al., 2020).
• Incident wavelength and beam profile: Increasing wavelength ($\lambda$) stretches the nanojet longitudinally, broadening both the length and width; beam profile engineering (e.g., using LG beams) imprints angular momentum onto the nanojet, modulating the far-field symmetry and peak multiplicity (Kiselev et al., 2014, Yousefi et al., 2021).
• Boundary conditions and truncation: For high-index dielectrics ($n > 2$), the focal spot is naturally located inside the microparticle. The retrograde-reflection approach, incorporating a flat mirror adjacent to the particle, doubles the focusing process and shifts the PNJ externally, allowing high-intensity, extended focal spots—a regime unobtainable by conventional methods (Geints et al., 2020, Aljuaid et al., 2022).

3. Modulation and Control Strategies

Advanced control of nanojet morphology and localization is achieved through:

• Particle symmetry breaking: Asymmetric microstructures, such as Janus cylinders with differing refractive indices or geometric deformations, produce photonic hooks—curved light beams with FWHM smaller than straight PNJs, and tunable by material composition, rotation, or deformation (Gu et al., 2019).
• Asymmetric illumination: The use of masks or selective illumination divides the incoming interface into regions of rapid/slow change (RRC/RSC), with an inflection point defined by the zero of the second derivative of the emergent ray slope’s logarithm. By modulating intensity profiles across these regions, one can switch between straight nanojets and curved hooks, tightly controlling working distance, beam waist, and bending angle (Minin et al., 2020, Gu et al., 2020).
• Optical tweezers configuration: Double optical tweezers employing two collinear, co-propagating focused beams allow dynamic switching of nanojet formation via beam positioning, overcoming limitations of standard optical trap equilibrium and enabling intracellular applications (Neves, 2015).

4. Analytical and Computational Models

Accurate description and design of photonic nanojets leverages both analytical and high-fidelity computational frameworks:

• Generalized Lorenz–Mie Theory (GLMT): Decomposition of the incident field into partial waves with beam shape coefficients (BSCs) enables rigorous calculation of the scattered field and nanojet properties for focused beams, including the impact of trap position and equilibrium shifts (Neves, 2015).
• Finite-element/FDTD simulations: Implementation of full-wave numerical methods (FEM, FDTD, COMSOL Multiphysics) reproduces near-field intensity maps and Poynting vector distributions, quantifying enhancements and validating analytical models under realistic conditions (Gu et al., 2019, Minin et al., 2020, Salhi et al., 2017).
• Optimization Under Uncertainty (OUU): Stochastic optimization, including adjoint-based BFGS approaches, incorporates manufacturing errors by modeling the refractive index heterogeneity as a spatial random field and minimizes both mean and variance of nanojet intensity at a target location, yielding designs robust against fabrication uncertainties (Alghamdi et al., 2022).

Parameter	Effect on Nanojet	Note
Refractive Index	Higher $n$: tighter width, higher intensity, focus closer to surface	Bound: $\text{min width} \sim \lambda/(2n)$
Wavelength	Larger $\lambda$: broader and longer nanojet, lower intensity	Linear scaling of jet dimensions
Geometry/Shape	Ellipsoid/triangle: altered intensity distribution, focus location	Engineered asymmetry enables hooks or composite jets

5. Applications and Experimental Observations

Photonic nanojets are foundational for numerous emerging technologies due to their unique spatial and intensity characteristics:

• Super-resolution microscopy and spectroscopy: Nanojets achieve subwavelength resolution in ultramicroscopy, enhance detection thresholds for single-molecule Raman and fluorescence spectroscopy, and promote local field amplification for photoluminescence (Neves, 2015, Kuchmizhak et al., 2015).
• Optical manipulation and trapping: Optical tweezers benefit from nanojet-based enhancements, with measured force amplification by factors of 3–10 compared to Gaussian beams. Position-dependent force modulation enables tractor-like behavior (Valdivia-Valero et al., 2012).
• On-chip integrated photonics: Planar photonic chips utilizing all-dielectric Bloch surface waves facilitate subwavelength focusing with low loss, and engineered geometries such as isosceles triangles permit robust, on-chip manipulation of nanoparticles with spot sizes down to 0.66$\lambda_{BSW}$ (Kim et al., 2017).
• Nanoscale fabrication and sensing: Laser-ablative methods yield periodic nanocrowns and nanojets, offering templates for high-density plasmonic substrates and photoluminescence enhancement in organic dyes (Kuchmizhak et al., 2015). Fiber-integrated high-index dielectrics allow practical endoscopic imaging and remote sensing by generating controllable nanojets at the fiber tip (Aljuaid et al., 2022).

6. Future Research Directions

Advancements in photonic nanojet science and technology depend on several pressing research issues:

• Geometry and material engineering: Exploration of hybrid, reconfigurable structures (Janus, composite, stretchable materials) may expand control over nanojet morphology and curvature, and facilitate dynamic tuning (Gu et al., 2019, Gu et al., 2020).
• Inverse design and topology optimization: Integration of realistic fabrication constraints within topology optimization algorithms enables dielectric cavities with unprecedented subwavelength photon confinement (mode volume $V \sim 3 \times 10^{-4}\lambda^3$, Q ∼ 1100), surpassing conventional designs and advancing nanophotonic device performance (Albrechtsen et al., 2021).
• Robustness to manufacturing uncertainty: Adoption of OUU frameworks yields nanojet designs with reduced sensitivity to spatial random field errors, ensuring reproducibility in manufacturing and long-term device stability (Alghamdi et al., 2022).
• Composite applications: Hybrid schemes combining photonic and plasmonic effects, or integrating nanojet-formed trails/particles as templates for photonic elements, are avenues for synergistic advances in light–matter interaction and nanolithography (Song et al., 2010, Kuchmizhak et al., 2015).

7. Theoretical and Practical Controversies

It is established that photonic nanojets are adequately described within the framework of near-field diffraction, rather than representing fundamentally sub-diffraction optical modes (Salhi et al., 2017). The jet's width is ultimately bounded by ($\lambda/(2n)$), consistent with the Rayleigh criterion modified for refractive enhancements. Tailoring environmental and optogeometric parameters—refractive index, wavelength, interface curvature—provides practical routes for nanojet engineering, but does not overcome physical diffraction limits.

In summary, photonic nanojets constitute a versatile class of near-field optical phenomena with rigorous analytical foundations, robust computational models, and essential roles in cutting-edge applications from optical trapping and microscopy to integrated nanophotonic architectures. Their continued paper, especially in the context of engineered beams, complex geometries, robust optimization, and functional hybridization, stands to further expand both fundamental understanding and technological utility in light-based nanosciences.