Complex Refractive Index Profile Research Articles

Femtosecond Laser Fabrication of Gradient Index Micro-Optics in Chalcogenide Glass

Gradient refractive index (GRIN) lenses have been widely used for many applications. However, the traditional manufacturing methods of GRIN lenses are very time-consuming and only suitable for macro-scale operations. In addition, those methods do not have the ability to produce other GRIN optical components with complex refractive index profiles like aspheric or freeform components. We report here an approach to produce GRIN micro-optical components in chalcogenide glass based on a direct laser writing technique. Using this approach, we are able to locally modulate the refractive index of the glass subtrates and create an arbitrary refractive index profile. To prove the flexibility of the method for the production of GRIN micro-optics, we fabricated GRIN micro-lenses and a micro-Fresnel axicon (Fraxicon). The optical properties of micro-lenses can be controlled by varying the writing parameters or the substrate thickness. As a result, the working distance of the micro-lenses can extend from 0 to more than 1000 μm. Also, the micro-Fraxicon exhibits the ability to convert a Gaussian beam to a Bessel-like beam which concentrates the mid-infrared light into an approximately 1200 μm long confinement zone.

Terahertz refractive index control of 3D printing materials by UV exposure

Recently, significant progress has been made in the development of THz optics based on metamaterials to overcome the limited availability of suitable materials for conventional optics. Although 3D printing technology is a promising method for rapidly fabricating these subwavelength structures, the structural degree of freedom for 3D printed metamaterials is still limited by the optical properties of printing materials. In this study, we controlled the THz refractive index and extinction coefficient of the 3D printing resin by UV exposure doses during the printing process. Samples were fabricated as uniform plates under different curing conditions in printing, and their optical properties were measured in the range between 0.3 THz and 2.0 THz using THz time-domain spectroscopy (THz-TDS). The refractive index and extinction coefficient were changed from 1.65 to 1.80, and from 0.04 to 0.12, respectively, with increasing UV doses from 1 mJ/cm2, which allows resin to solidify and become printable, to 100 mJ/cm2, where the optical changes become almost saturated. The results provide insights into optimizing the fabrication process of THz devices, even those with a gradient and complex refractive index profile, by utilizing 3D printing technology for a broad range of applications.

Evaluation of beam convergence driven by spherical gradient refractive index lenses based on nonparaxial beam propagation.

We utilize a theoretical method based on nonlinear beam propagation and finite difference eigenmode solver methods to precisely simulate Gaussian beam propagation in electrical fields through spherical gradient refractive index lenses. The theoretical computation uses second-order partial differentiation of propagation coordinates to generate microwave field propagation. Consequently, it offers accurate simulation results for any complex refractive index profile. The reliability of the proposed method is verified by comparing it with existing experimental and theoretical results. We employ the theoretical method to assess Gaussian beam convergence in terms of four key parameters: beam waist, maximum intensity, focal position, and Rayleigh range. The results indicate that gradient index spherical lenses have better convergence than convex thin lenses, as evidenced by a significant reduction in beam waist size. However, these lenses prompt an extremely short back focal length. Consequently, we propose a slight shift in the boundary and index distribution of spherical lenses to expand their back focal lengths.

Beam quality prediction for Tm-doped fiber system based on finite-difference beam propagation method

A numerical model is established to predict the beam quality factor M2 of fiber laser for the first time. The finite-difference beam propagation method (FD-BPM) is introduced to simulate the beam propagation of thulium-doped fiber lasers (TDFLs) with given design parameters. The output beam profile can be calculated for an active fiber with complex refractive index profiles and various bending radii. The beam quality factor M2 can be obtained by the calculated beam profile. The numerical simulation results agree with the reported experiment data with a deviation of less than 10%, which validates the accuracy of the model. This model provides a convenient and efficient approach for designing the high-beam-quality TDFLs with reduced experiment efforts.

Two dimensional gradient-index beam shapers fabricated using ultrafast laser inscription.

In this paper gradient-index beam shapers are fabricated using the ultrafast laser inscription method. This method enables the fabrication of two-dimensional refractive index profiles inside silica glass, resulting in highly robust and compact beam shapers. The magnitude of this refractive index change can be tailored by adjusting the laser pulse energy, enabling arbitrary two-dimensional refractive index profiles to be manufactured. The process is then demonstrated by fabricating planar waveguides with quadratic index profiles that predictably resize Gaussian beams. Then a more complex two-dimensional refractive index profile is fabricated to transform an input Gaussian beam into a super-Gaussian (flat-top) beam.

PT-symmetry and supersymmetry: interconnection of broken and unbroken phases

The broken and unbroken phases of P T and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of P T -symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in P T -symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in P T -symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken P T -symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter.

Modeling of a sampled apodized fiber Bragg grating moisture sensor

This study presents a theoretical model that enables a fast and precise calculation of a sampled apodized fiber Bragg grating and the related sensor. Transfer matrix method was used since there is no analytical solution due to the complex refractive index profile. Errors brought by the uniform refractive index profile approximation were compensated, which allows a smaller number of divided segments and therefore a fast and memory efficient simulation. This compensation method realizes a high speed and high precision simulation. The theoretical spectra of both the grating and the sensor agrees well with those given by the experiments. According to the experiment, the sensitivity of the moisture sensor is −0.6165 pm/ppm in mineral oil. This theoretical model provides a new choice for the researchers and developers to design and optimize the sensing structure instead of a blind try and error process.

Femtosecond laser direct-written fiber Bragg gratings with high reflectivity and low loss at wavelengths beyond 4 µm.

We report on the fabrication of, to the best of our knowledge, the first highly reflective fiber Bragg gratings for the 4 µm wavelength range. A second-order grating with a coupling coefficient (κ) of 230m-1, losses <0.25dB/cm, and a bandwidth of approximately 3 nm was inscribed into the core of a passive indium fluoride (InF3) fiber using a femtosecond (fs) laser. Thermal annealing of this grating at a temperature of 150°C for 90 min resulted in the enhancement of κ to 275m-1. Further, we show that InF3 fibers respond very differently to irradiation with fs laser pulses as compared to ZBLAN fibers and that this difference manifests itself in a significantly larger process window for inscription and in the formation of a more complex refractive index profile that is believed to be caused by the larger nonlinearity of InF3. This Letter paves the way to the development of new wavelength stabilized all-fiber mid-infrared lasers beyond 4 µm.

Calculation Method of Brillouin Power and Frequency Coefficients for Fiber Strain and Temperature Based on Multi-Layer Segmentation

A novel theoretical calculation method is proposed to obtain Brillouin power and frequency coefficients for strain and temperature of optical fibers used in Brillouin optical time domain sensors. For a GeO2-doped single mode fiber with any kind of complex refractive index profile, if the profile of refractive index and dopants of the fiber is available, the power-strain and power-temperature coefficients can be, respectively, derived by observing the strain and temperature dependence of Brillouin power through the changes of fiber's effective refractive index, density, sound velocity, and acousto-optic effective area. The frequency-strain and frequency-temperature coefficients can be directly obtained by detecting the strain and temperature dependence of Brillouin frequency. The complex problem of the change of acousto-optic effective area is solved by multi-layer segmentation method. The single mode fiber-28 and large effective area fiber are taken as examples to validate the theoretical derivation. The validity of the proposed method is verified by comparing the calculation results of the Brillouin power and frequency coefficients for strain and temperature with the corresponding experimental results in the literature.

Enhanced Modal Coupling Loss in a Two-Mode SOI Waveguide of Broken Parity-Time Symmetry

Effect of optical loss, presented in a superstructure grating with a complex refractive index profile, on the mode coupling is studied in a two-mode silicon-on-insulator waveguide. In this scheme, both our theory and experimental results indicate that the optical loss not only provides optical absorption of a targeted output mode and thus the corresponding modal coupling loss, but also induces a broken parity-time symmetry phase that strongly prohibits power coupling from the incident mode to the output mode. As a result, the latter can give rise to a much-enhanced modal coupling loss of the targeted output mode. Under a reasonable device length about 37 μ m, the enhancement factor can be as high as ∼20 dB in simulation and ∼17 dB in experiment. This paper may offer a different way to exploit the role of optical loss in boosting modal coupling loss that can directly translate to power extinction ratio. It thus may find potential applications in novel intensity modulator designs.

Design of arbitrary modal electric field in planar waveguides

The purpose of this study is to propose a method for designing planar waveguides of arbitrary modal electric field distribution. Normally, the authors know or specify a waveguide and they solve for the mode propagation constant which allows them to plot the electric field. A novel and efficient algorithm is proposed here for determining arbitrary refractive index profile planar waveguides with a given desired mode field distribution. This inverse problem is generally solved using complex and variable refractive index profile planar waveguides. The authors present a method for determining the required refractive index profile for both real and imaginary parts. This inverse problem is solved via modelling the waveguide transversely as a transmission line and work inversely from the electric field. They offer example reconstructions of refractive index profiles which are useful for high-power lasers, mode matching between planar and circular waveguides and complex conjugate electric fields. The method also has applications in designing optical fibres for sensors, where one may require specific shape electric field from a waveguide, and also in refractive index profiling instrumentation.

Refractive-index measurement and inverse correction using optical coherence tomography.

We describe a novel technique for determination of the refractive index of hard biological tissue as well as nonopaque technical samples based on optical coherence tomography (OCT). Our method relies on an inverse refractive-index correction (I-RIC), which matches a measured feature geometry distorted due to refractive-index boundaries to its real geometry. For known feature geometry, the refractive index can be determined with high precision from the best match between the distorted and corrected images. We provide experimental data for refractive-index measurements on a polymethylmethacrylate (PMMA) and on an ex vivo porcine cranial-bone, which are compared to reference measurements and previously published data. Our method is potentially capable of in vivo measurements on rigid biological tissue such as bone as, for example, is required to improve guidance in robot-aided surgical interventions and also for retrieving complex refractive-index profiles of compound materials.

Gain‐guided optical fibre refractive index synthesis starting from arbitrary modal electric field

Novel results on how to reconstruct gain-guided optical fibres starting from arbitrary modal electric fields are presented. It is known that gain-guided optical fibre refractive index profiles are described in terms of complex numbers. Therefore, to achieve the design of such fibres from a knowledge of modal electric fields one is required to use complex refractive index profile waveguides, where one can determine the required refractive index profile on both real and imaginary parts of the refractive index. The novelty here is that the reconstruction starts by using complex-valued desired electric fields. This inverse problem is solved via modelling the waveguide transversely as a transmission line and working inversely from the electric field. Example reconstructions of refractive index profiles are offered which are useful for high-power lasers, in designing optical fibres for sensors, where one may require specifically shaped electric fields from a waveguide, and also in refractive index profiling instrumentation.

Design of small core tellurite photonic crystal fiber for slow-light-based application using stimulated Brillouin scattering

Stimulated Brillouin scattering (SBS) performances of small core tellurite photonic crystal fibers (PCF) are rigorously studied. We propose a design of tellurite PCF that is used for slow-light-based applications. We developed a two-dimensional finite element mode solver to numerically study the acoustic and optical properties of complex refractive index profiles including tellurite PCF. Our results include the calculation of Brillouin gain spectrum, Brillouin gain coefficient (gB) and Brillouin frequency shift by taking into account the contribution of the higher-order acoustic modes. Several simulations were run by varying the air-filling ratio of various PCF structures to enhance the SBS. The real scanning electron microscope image of a small core of highly nonlinear tellurite fiber is considered. Optimized results show a frequency shift of 8.43 GHz and a Brillouin gain of 9.48×10−11 m/W with a time delay between 21 and 140 ns. Such fibers have drawn much interest because of their capacity for increasing and tailoring the SBS gain.

Design of Arbitrary Modal Electric Field in Cylindrical Waveguides

In this paper, we examine for the first time how to design arbitrary shape modal fields within complex refractive index circular waveguides. In order to achieve this flexibility in field shape, we use complex refractive index profile waveguides, where we determine the required refractive index profile on both real and imaginary refractive index. We develop a technique for calculating directly and accurately the refractive index profiles of cylindrical waveguides from knowledge of the desired modal electric field. The method we use to solve this inverse problem is via modeling the waveguide transversely as a transmission line. We demonstrate this algorithm with a number of example reconstructions of different arbitrary modal electric fields. The refractive index profiles generated supporting the required modal electric fields are complex. We reconstruct complex refractive index profiles which support unusual electric field distributions. We expect this technique to be useful in designing special fibers for mode matching between dissimilar waveguides, in designing sensing optical fibers, in mode division multiplexing, in gain flattening optical fiber amplifiers, and also for high power optical fibers.

Plasmonic Modulators for Near-Infrared Photonics on a Silicon-on-Insulator Platform

A CMOS compatible interference-based Mach-Zehnder modulator with each arm comprising a metal-insulator-silicon-insulator-metal structure and a simpler, single-arm variant is considered for electro-optic and electroabsorption modulation, respectively, using finite-element electromagnetic simulations. In the calculation of electron density profiles in bias-induced accumulation layers, the size-quantization effects at oxide-silicon interfaces are considered. These are then used to find the complex refractive index profiles across the structure, in its biased and unbiased states, and eventually the modulator insertion loss and extinction ratio, as they depend on various structural parameters. Furthermore, an alternative modulator, comprising a metalized stub filled with SiGe/Ge multiple quantum wells or quantum dots in a silicon matrix, coupled to a dielectric waveguide structure is also investigated using 3-D finite-element simulations. The principle behind its modulation is the change of electromagnetic field profile after the stub, relative to the incoming mode, which happens when the absorption of the stub material varies. This affects the field coupling into a single-mode output waveguide, resulting in a controllable transmission.

Analysis of absorption property for pumping laser with double cladding rare earth doped fiber

In this paper, a pump laser absorption model for double cladding rare earth doped optical fiber is established by using the finite difference beam propagation method combined with complex refractive index profile, and the absorption properties are analyzed in detail for some typical inner cladding structures by using this model. The results can be used to design the double cladding rare earth doped optical fiber.

Propagation characteristics of thermally diffused expanded core fibers with complexrefractive index profiles

In this paper, we investigate the propagation characteristics of thermally diffused expandedcore (TEC) fibers with complex refractive index using the numerical Galerkin’s method.Complex modal profiles and propagation constants for TEC fibers of differentexpanded core radii are calculated. The imaginary part of the electric field resultsin wavefront distortion showing that the power flows out of or into the dopedregion according to the sign of the imaginary part of the refractive index. Thegain or loss as a function of both mode field radius and operating wavelength iscalculated numerically. Moreover, an approximate formula for the loss or gaincoefficient of these fibers is given and the obtained approximate results agree wellwith those from Galerkin’s method applied to the complex refractive index fiber.

Hidden Under the Carpet

Transformation optics, combined with the ability to fabricate structures with complex refractive index profiles, allow materials to be formed with fascinating optical properties, such as cloaks where both the object and the cloak concealing the object are rendered invisible. To date, the cloaks have been restricted to two dimensions, which limits realistic applications. Based on a photonic crystal structure with a polymer filling the empty space, Ergin et al. (p. [337][1], published online 18 March) have designed, fabricated, and realized a three-dimensional cloak operating at optical wavelengths. [1]: /lookup/doi/10.1126/science.1186351

Three-Dimensional Invisibility Cloak at Optical Wavelengths

We have designed and realized a three-dimensional invisibility-cloaking structure operating at optical wavelengths based on transformation optics. Our blueprint uses a woodpile photonic crystal with a tailored polymer filling fraction to hide a bump in a gold reflector. We fabricated structures and controls by direct laser writing and characterized them by simultaneous high-numerical-aperture, far-field optical microscopy and spectroscopy. A cloaking operation with a large bandwidth of unpolarized light from 1.4 to 2.7 micrometers in wavelength is demonstrated for viewing angles up to 60 degrees.