Optical Fiber Refractive Index Research Articles

Numerical Analysis of Optical Fiber Refractive Index in the Miniaturized Graded‐Index Fiber Probe

ABSTRACTWe analyze the impact of the refractive index of optical fibers on the focusing properties of a miniaturized graded‐index (GRIN) fiber probe. The ABCD ray transfer matrix and characteristic parameters are employed to characterize the working distance, focusing spot size, and the depth of field effectively. The three‐dimensional (3‐D) function diagrams and two‐dimensional (2‐D) graphs are used to illustrate the impact of the no‐core fiber (NCF) refractive index and the center refractive index of GRIN fiber on the focusing properties. Numerical analysis results show that when the length of the NCF is 0.36 mm and the GRIN fiber is 0.1 mm, the variation of the refractive index of the NCF between 1.44 and 1.52 leads to the variation of the working distance in the range of 0.02 mm, while the focusing spot size varies in the range of 5 μm. A comparison of 12 probe samples reveals that a 0.02 difference in the center refractive index of GRIN fiber could result in a 0.16 mm variation in working distance and a variation in focusing spot size of over 3 μm. The experimental results indicate that alterations in the length of the fibers have a considerable effect on the focusing properties of the probe. In contrast, the range of variation in focusing properties with fiber refractive index is relatively limited.

A fiber optic refractive index sensor with temperature compensation based on cascaded Mach-Zehnder interference and Intermodal interference

Optical fiber refractive index (RI) sensor with temperature (T) compensation has important application values in biomedicine and environmental monitoring. In order to solve the problem that the detection accuracy of liquid RI is affected by T in practical applications, a T-compensated RI fiber sensor based on cascaded Mach-Zehnder interference (MZI) and multimode interference (IMI) is proposed in this paper. Experimental results showed the proposed sensor achieved a sensitivity of 797.41 nm/RIU for the measurement of RI in the range of 1.3333–1.3640, and a sensitivity of 0.120 nm/°C for the measurement of T in the range of 0–60 °C. The resolution (R) of RI and T measurements reached 2.5 × 10−5 RIU and 0.167 °C, respectively. The detection limits (DL) of RI and T measurements are 3.135 × 10−8 RIU and 1.392 °C, respectively. A matrix is obtained to demodulate the cross-sensitivity in RI and T measurements. The proposed sensor shows the advantages of simple structure, low hysteresis, and good stability.

Enhanced Spectrum Resolution of Optical Fiber Refractive Index Sensors Based on Single-Arm Fiber-Optic Tapered Probe

Enhanced Spectrum Resolution of Optical Fiber Refractive Index Sensors Based on Single-Arm Fiber-Optic Tapered Probe

The Truth of the Experiments of Invariable Speed of Light in Special Relativity

It is pointed out that the most experiments on the invariant speed of light in special relativity proves the round-trip invariant speed of light, not one-way invariant. This paper makes a distinction between them. The Michelson-Morley experiment and the experiment of high-energy particles emitting photons and so on are the round-trip experiment of light’s speed, showing that the average speed of light is a constant. But the Sagnac effect experiment, the Michelson-Gale's experiment that the earth's rotation effects the speed of light, and the satellite signal propagation between China and Japan are the one-way experiments of light’s speed, showing that the speed of light is variable, satisfying the Galilean velocity addition rule. The orbit shape changes of binary stars and the phenomenon of charm stars cannot be observed due to that the calculated observing directions are different from the practical observing direction for the observers on the Earth. The Fizeau water flow experiment and the Sagnac experiment are combined to prove that the rotation of optical fiber would affects the speed of light. The problem that the Sagnac effect is independent of the refractive index of optical fiber is explained well. It is proved that the Sagnac effect formula derived from special relativity is consistent with that derived from classical mechanics when the optical fiber’s refractive index . When , there is no the Sagnac effect according to special relativity. While according to classical mechanics, there is the Sagnac effect. The original experiment of Sagnac effect in 1913 was carried out in atmosphere with . Therefore, the original Sagnac experiment became a judgment experiment. It certainly jugated that the velocity of light satisfied the Galilean addition rule rather than the Lorentz transformation formula.

Replica symmetry breaking in a Rayleigh backscattering-based random fiber laser

Replica symmetry breaking (RSB) phase transition is observed in disordered photonics systems. The key requirements to observe RSB are provided by random lasers, i.e., gain and disorder. However, in a random fiber laser (RFL) with scattering provided by Rayleigh scattering of light, the condition of quenched disorder is not established due to environment perturbations. Here, RSB is observed in a Rayleigh backscattering-based RFL, where light scattering is due to the inhomogeneity of the optical fiber refractive index. This is done by using short-cavity erbium-RFL with reduced interaction with the environment. Spectral characterization is made, and narrow mode linewidths are demonstrated. The intensity dynamics and laser mode behavior are analyzed showing the presence of gain competition. The results indicate a connection between the replica symmetry or RSB, Lévy-like behavior of intensities, and the presence or not of correlated laser intensity fluctuations.

A simple refractive index measurement method for step-index fiber based on radial displacement optical power scan

In this paper, a novel method for measuring the refractive index of single-mode step-index fiber based on radial displacement optical power scan is proposed. The radial displacement optical power curves of different fibers have different bending degrees and a r parameter is used to characterize the bending degree of the radial displacement optical power curve. The r–n polynomial formulas of different core diameters are obtained via beam propagation method, which are used for the calculation of the fiber refractive index. As proof of principle, two commercial single-mode step-index fibers were measured experimentally. Simulation results reveal that the refractive index measurement error is within ±0.0003. The measurement formulas of optical fiber refractive index are given by simulation and the measuring range is 6.0 to 10μm with an interval of 0.5μm. This method has the advantages of low cost, convenient operation, and can be used under laboratory conditions.

Distributed Refractive Index Sensing Based on Etched Ge-Doped SMF in Optical Frequency Domain Reflectometry.

A distributed optical fiber refractive index sensor based on etched Ge-doped SMF in optical frequency domain reflection (OFDR) was proposed and demonstrated. The etched Ge-doped SMF was obtained by only using wet-etching, i.e., hydrofluoric acid solution. The distributed refractive index sensing is achieved by measuring the spectral shift of the local RBS spectra using OFDR. The sensing length of 10 cm and the spatial resolution of 5.25 mm are achieved in the experiment. The refractive index sensing range is as wide as 1.33-1.44 refractive index units (RIU), where the average sensitivity was about 757 GHz/RIU. Moreover, the maximum sensitivity of 2396.9 GHZ/RIU is obtained between 1.43 and 1.44 RIU.

Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in optical fibers

In this paper, the bifurcation, stationary optical solitons and exact solutions in optical fiber propagation are studied. The propagation model is described by a generalized nonlinear Schrödinger equation with Kudryashov’s quintuple power law of refractive index. First, the equation is transformed into a second-order nonlinear ordinary differential equation by an appropriate transformation. Then, the bifurcation of the phase diagram of the obtained ordinary differential equation is established using planar dynamic system theory, and the types of optical solitons and exact solutions are determined. What is more, the stationary optical solitons and exact solutions are obtained by the polynomial complete discriminant system, and are demonstrated in 3D and 2D graphics by using the symbolic computation software Maple. Finally, the obtained stationary optical solitons and exact solutions include the Jacobi elliptic function solution, hyperbolic function solution, rational function solution, trigonometric function solution and exponential function solution. Moreover, the results provide a method to further study stationary optical solitons and exact solutions of propagation pulses in optical fibers.

Portable Multihole Plastic Optical Fiber Sensor for Liquid-Level and Refractive Index Monitoring

In this article, we report a low-cost method to fabricate plastic optical fiber (POF) liquid-level and refractive index (RI) sensors integrated with smartphones by molds and drilling microholes in side-growing POFs (SGPOFs) with high-temperature metal wire. These sensors can be used for real-time liquid-level and RI monitoring, especially under situations requiring portability and illumination. When the liquid level changes, the change of the RI around the microholes leads to a change in the light intensity transmitted in the fiber, enabling us to measure the liquid level and RI. Utilizing one sensor with six holes (0.45 mm radius and 15 mm spacing) in 2.0-mm SGPOF, the results of level and RI measuring are in good agreement with the theory. The liquid-level measurement of the sensor is carried out for water with an RI of 1.333, the level sensitivity is 0.29%/cm ± 0.02%/cm. In the RI measurement, the RI sensitivity of the sensor is −22.8%/RIU ± 0.6%/RIU in the measurement range from 1.333 to 1.475.

Refractive index sensor based on a gradually hot-pressed flatted plastic optical fiber

This paper proposes a gradually hot-pressure plastic optical fiber (POF) refractive index (RI) sensor with a flatted structure to detect the glucose concentration, and experimentally investigates the performance of RI sensor with straight and micro-bending POFs. The sensor is fabricated by a temperature-controllable metal rod to form the hot-pressed end face of POF which can increase signal-to-noise ratio (SNR) of the sensor. The experimental results show that the proposed sensor, utilizing a flatted structure POF with thickness of 0.5 mm and diameter of 0.4 cm, achieves maximum intensity sensitivity of up to 1748.91 %/RIU and resolution of up to 5.97 × 10−4 RIU in the RI range of 1.33 to 1.382. Furthermore, its simple design and manufacturing process shows potential for application, especially in biochemistry and environmental safety.

The optical fiber refractive index profile measurement based on phase-correct quantitative phase microscopy

The optical fiber refractive index profile measurement based on phase-correct quantitative phase microscopy

Single-core multi-channel moiré fiber grating and multi-wavelength LMA fiber grating fabricated based on two-dimensional spatially encoded phase mask

A two-dimensional optical fiber grating with multi sub-gratings based on a 2D spatially encoded phase mask is designed in this study. The 2D fiber Bragg grating (FBG) is composed of two non-overlapping sub-FBGs, which are laterally separated along the radial direction of the fiber core. Unlike traditional FBGs, the refractive index of the 2D FBG is modulated both on the axial and radial directions of the fiber core, which are realized by spatially encoded diffraction based on a 2D spatially encoded phase mask. Compared with the overlapping grating, the 2D FBG can be fabricated at one time to achieve multi-wavelength output, and its compact structure provides a new idea for multi-wavelength multiplexing. As examples, a single-core multi-channel moiré fiber grating and 2D FBG with three subgratings are designed and fabricated on a single-mode fiber and LMA fiber, respectively. Using a 2D spatially encoded mask can improve the optical fiber refractive index modulation from one- to two- or even three-dimensions, which is helpful for precise manipulation of the complex optical field of optical fiber.

When to Crossover From Earth to Space for Lower Latency Data Communications?

For data communications over long distances, optical wireless satellite networks (OWSNs) can offer lower latency than optical fiber terrestrial networks (OFTNs). However, when is it beneficial to switch or crossover from an OFTN to an OWSN for lower latency data communications? In this article, we introduce a crossover function that enables to find the crossover distance, i.e., a distance between two points on the surface of the Earth beyond which switching or crossing over from an OFTN to an OWSN for data communications between these points is useful in terms of latency. Numerical results reveal that a higher refractive index of optical fiber (or $i$) in an OFTN and a lower altitude of satellites (or $h$) in an OWSN result in a shorter crossover distance. To account for the variation in the end-to-end propagation distance that occurs over the OWSN, we examine the crossover function in four different scenarios. Numerical results indicate that the crossover distance varies with the end-to-end propagation distance over an OWSN and is different for different scenarios. We calculate the average crossover distance over all scenarios for different $h$ and $i$ and use it to evaluate the simulation results. Furthermore, for a comparative analysis of OFTNs and OWSNs in terms of latency, we study three different OFTNs having different refractive indexes and three different OWSNs having different satellite altitudes in three different scenarios for long-distance intercontinental data communications, including connections between New York and Dublin, Sao Paulo and London, and Toronto and Sydney. All three OWSNs offer better latency than OFTN2 (with $i_{2}$ = 1.3) and OFTN3 (with $i_{3}$ = 1.4675) in all scenarios. For example, for Toronto–Sydney connection, OWSN1 (with $h_{1}$ = 300 km), OWSN2 (with $h_{2}$ = 550 km), and OWSN3 (with $h_{3}$ = 1100 km) perform better than OFTN2 by 18.11%, 16.08%, and 10.30%, respectively, while they provide an improvement in latency of 27.46%, 25.67%, and 20.54%, respectively, compared to OFTN3. OWSN1 performs better than OFTN1 (with $i_{1}$ = 1.1) for Sao Paulo–London and Toronto–Sydney connections by 2.23% and 3.22%, respectively, while OWSN2 outperforms OFTN1 for Toronto–Sydney connection by 0.82%. For New York–Dublin connection, all OWSNs while for Sao Paulo–London connection, OWSN2 and OWSN3 exhibit higher latency than OFTN1 as the corresponding average crossover distances are greater than the shortest terrestrial distances between cities in these scenarios. Multiple satellites (or laser intersatellite links) on its shortest paths drive up the propagation distance to the extent that OWSN3 ends up with a higher latency than OFTN1 for the Toronto–Sydney intercontinental connection scenario although the related average crossover distance is less than the shortest terrestrial distance between Toronto and Sydney. The challenges related to OWSNs and OFTNs that may arise from this work in future are also highlighted.

D-shaped optical fiber refractive index sensor for application in fuel oil mixtures and leakage detection

D-shaped optical fiber refractive index sensor for application in fuel oil mixtures and leakage detection

Stabilized Time Transfer via a 1000-km Optical Fiber Link Using High-Precision Delay Compensation System

Variations in optical fiber length and refractive index are induced by environmental perturbation, resulting in an additional dynamic propagation delay in fiber-based time synchronization systems, which deteriorate their transfer stability. This disadvantage can be significantly reduced by transmitting the time signal in both directions through fiber and constructing a feedback loop to compensate the propagation delay at the remote end of the link. This paper proposes an analog-digital hybrid proportional integral derivative (PID) control compensation system based on the time-frequency phase-locked loop (TF-PLL). The system is designed to keep the merits of wide servo bandwidth, servo accuracy, and a large dynamic delay compensation range up to 1 s, which is much greater than that reported in previous studies. For proving the validity of this proposed scheme, a self-developed optical fiber time synchronization equipment based on the delay compensation system is applied. The delay compensation system is used on a 1100-km long laboratory optical fiber, and the results show that the time synchronization stability in terms of time deviation (TDEV) is less than 5.92 ps/1 s and 2.56 ps/10,000 s. After successful laboratory evaluation, the proposed system is installed on a real 988.48-km line between the Xi’an Lintong branch of the National Time Service Center (NTSC) and Linfen City, Shanxi Province, realizing the time synchronization of 10 stations along the optical fiber link. The experimental results in the 988.48-km link illustrate that the measured time difference with a peak-to-peak value of 176 ps, the standard deviation of 19.3 ps, and a TDEV of less than 10.49 ps/1 s and 2.31 ps/40,000 s is achieved. The high-precision time delay compensation system proposed in this paper is simple, reliable, and accurate; has a wide range of compensation; and opens up a feasible scheme for providing synchronized time signals to multiple users over the long-distance field optical fiber networks.

Ultra-Long Range Refractive Index Fiber Sensor

The dynamic range of optical fiber refractive index sensors is mainly determined by the refractive index (RI) of the sensor surface in contact with the sample under test. In case of the refractive index sensor based on the hybrid fiber Fabry–Perot interferometer (HFFPI), the largest measurable refractive index value is equal to that of the fiber core. In this work, we demonstrate that it is possible to extend the refractive index dynamic range of a HFFPI by simply adjusting the optical path length (OPL) of the air and solid cavity to be equal or differ by just a small amount. Two isometric versions of the HFFPI (i-HFFPI) with a total length of 100 and 172 μm, where the OPL of the air and solid cavity are very similar, were fabricated and tested. The interferometers were immersed in different samples with a refractive index ranging from 1.000 to 1.733. The response of the interferometers was analyzed in the Fourier domain, and it was possible to establish a one-to-one relationship between the refractive index of the liquid sample and the amplitude of one of the peaks in the Fourier spectra. The amplitude of this peak experienced a linear increment when the RI of the surrounding medium was increased. Tracking the amplitude changes of a Fourier spectrum peak is straightforward which simplifies the online monitoring of the sensor. These features make this compact refractive index fiber sensor very appealing for biosensing applications.

Determination of the Mandelstam – Brillouin Scatter Frequency Characteristic in Optical Fibers of Various Types

The results of researches of the Mandelstam – Brillouin scattering frequency characteristics in single-mode optical fibers of various types are presented in this paper. A technique for obtaining the spectral characteristics of Mandelstam – Brillouin scattering for predefined acoustic mode distributions in single-mode optical fibers is considered. The procedure for determining the frequency characteristics of the Mandelstam – Brillouin scattering for a given structure of the radial distribution of the optical fiber refractive index is discussed. The Mandelstam – Brillouin scattering frequency characteristics of single-mode optical fibers obtained by mathematical modeling and experimental studies are presented. A comparative analyze of obtained results is carried out.

A study of highly sensitive D-shaped optical fiber surface plasmon resonance based refractive index sensor using grating structures of Ag-TiO2 and Ag-SnO2

In this study, we propose a design and simulation of a highly sensitive surface plasmon resonance (SPR) based single-mode D-shaped optical fiber refractive index sensor in the near-infrared (NIR) region. It consists grating structure of silver coated with titanium dioxide (TiO2) and Tin dioxide (SnO2) layer on the core-cladding interface. With the help of the finite element method (FEM), the proposed optical fiber sensors are optimized with various geometrical parameters. Proposed optimized structures are investigated and various performance parameters are calculated. It is found that performance parameters enhance with TiO2/SnO2 coated on Ag grating structure at a particular thickness of TiO2/SnO2. Due to this more generations of surface plasmons take place on metal-metal oxide structures. We find the maximum sensitivity of 15.31 μm / RIU and 9.81 μm / RIU for Ag-TiO2 and Ag-SnO2 grating structure respectively which shows a better result in comparison to the other reported work. So proposed structure may have great potential to enhance the sensing ability of optical fiber-based sensors as compared to the other conventional SPR based optical fiber sensors.

Optical fiber refractive index sensor based on the double cladding fiber

An optical fiber sensing structure based on double-cladding fiber (DCF) is described. The core and outer cladding of the DCF both supports more than one guided mode and the cladding mode resonance as well as modal interference in the fiber. Due to the W-type refractive index (RI) distribution, the outer cladding generates a stronger evanescent field to obtain higher sensitivity. In the transmitted spectrum, all three dips shift to the longer wavelength with the external RI changing from 1.33 to 1.43, and the high sensitivities are 595, 741, and 686 nm/RIU, respectively.

Highly sensitive refractive index sensing based on PCF modal interferometer

A high sensitive optical fiber refractive index (RI) sensor based on Mach-Zehnder interferometer (MZI) is proposed. The sensor consists of single mode fiber-multimode fiber-photonic crystal fiber-single mode fiber (SMPS) structure using fusion technology. The experimental results have shown that the RI sensitivity of the SMPS structure is as high as 342.78 nm/RIU in the range of 1.3330–1.3775. Meanwhile, the effects of different length of PCF on the RI are also investigated. It was found that the shorter the length of PCF, the higher the sensitivity. In addition, a temperature sensitivity of 16.37 pm/℃ for the sensor is achieved. The sensor has advantages of high fringe visibility over 20 dB and simple fabrication, which has displayed great potential in the field of RI measurement.