Mach-Zehnder Interferometer Configuration Research Articles

Regeneration of 200 Gbit/s PAM4 Signal Produced by Silicon Microring Modulator (SiMRM) Using Mach–Zehnder Interferometer (MZI)-Based Optical Neural Network (ONN)

We propose and demonstrate a Mach–Zehnder Interferometer (MZI)-based optical neural network (ONN) to classify and regenerate a four-level pulse-amplitude modulation (PAM4) signal with high inter-symbol interference (ISI) generated experimentally by a silicon microing modulator (SiMRM). The proposed ONN has a multiple MZI configuration achieving a transmission matrix that resembles a fully connected (FC) layer in a neural network. The PAM4 signals at data rates from 160 Gbit/s to 240 Gbit/s (i.e., 80 GBaud to 120 GBaud) were experimentally generated by a SiMRM. As the SiMRM has a limited 3-dB modulation bandwidth of ~67 GHz, the generated PAM4 optical signal suffers from severe ISI. The results show that soft-decision (SD) forward-error-correction (FEC) requirement (i.e., bit error rate, BER < 2.4 × 10−2) can be achieved at 200 Gbit/s transmission, and the proposed ONN has nearly the same performance as an artificial neural network (ANN) implemented using traditional computer simulation.

Reconfigurable all-optical logic device based on cross-phase modulation across highly non-linear fiber

All-optical logic gates are the basic building blocks of photonic integrated circuits to be used for signal processing, to ensure high speed signal processing and decreasing complexity of network. In this paper, reconfigurable all-optical logic gate has been proposed and numerical simulations are analysed at a bit rate of 120 Gb/s. Wavelength Converter, NOT, NOR, AND, XOR, XNOR, A¯.B and OR are the all-optical logic gates that has been designed and implemented using single circuit and has minimum quality factor of 27 dB. All the signal processing operations have been implemented by the exploitation of cross-phase modulation in two parallelly placed (Mach-Zehnder Interferometric configuration) highly nonlinear fibers (HNLF). The influence of variation in input power, at different length of HNLF determines that the quality factor increases for increase in power or length of highly nonlinear fiber up to a certain limit. Quality factor increases for decrease in effective area of the highly nonlinear fiber for a certain range of input power and saturates for further increase in input power. Also, the quality factor is not directly affected with increase in bit rate but adversely affected by increase in dispersion.

Design and analysis of SOA-MZI based optical digital circuits for high speed optical networks

This paper explores using Semiconductor Optical Amplifier assisted Mach-Zehnder Interferometer (SOA-MZI) configuration for designing various all-optical digital circuits. A specific focus on the design and analysis of all-optical inverters, decimal-to-binary code converters, and hexa decimal-to-binary code converters operating at a speed of 10 Gbps is given. These circuits employ OR, XOR, and NOR gates. The SOA-MZI configuration capitalizes on the nonlinear properties of the SOA to achieve all-optical logic functions. Phase modulation can be transformed into intensity modulation by incorporating the SOA within an interferometer setup and using 3-dB couplers. The Cross-Phase Modulation (XPM) technique, which offers superior performance compared to other types of SOA non-linearity, is employed to make the incoming signal insensitive to polarization. The system was analyzed using an optisystem. The performance achieved was 0.0109 in terms of Eye height, 3.45 e−70 in terms of Bit Error Rate (BER), and 17.66 in terms of Q-factor.

Simultaneous Generation of Two Negatively Correlated Linearly Frequency-Modulated Pulses Based on an Integrated Anti-Reflection Spectral Shaper

Grating-based spectral shaping (SS) combined with wavelength-to-time (WTT) mapping has proved to be an essential approach to the photonic generation of linearly frequency-modulated (LFM) pulses due to its potential to yield the large time-bandwidth product (TBWP) and to be fully integrated. One of the most challenging issues of chip-level integration is the grating-induced reflection which may significantly impact the laser source. Since the on-chip nonreciprocal devices such as optical isolators and circulators remain difficult to realize, a silicon-integrated anti-reflection spectral shaper based on a Mach–Zehnder interferometer (MZI) comprising two linearly chirped grating-assisted contra-directional couplers (LCGA-CDCs) has been proposed and demonstrated. Thanks to the isolation between the input and output ports of the contra-directional couplers, the reported shaper presents an effective suppression of the reflecting power returned to its input port with a measured rejection ratio of around −10 dB covering the entire C-band. To predict the instantaneous frequency responses of the generated microwave pulses, an equivalent asymmetric MZI configuration with wavelength-dependent length difference has also been introduced to explain the mechanism of SS. Two negatively correlated LFM waveforms with up-chirped profiles and large TBWPs of 45.60 and 53.52 are simultaneously generated using a fabricated sample. Our work paves the way for an all-optical integration of the photonic-assisted isolator-free LFM pulse generation, presenting great potential for multiple application scenarios in pulsed radar systems.

Design and simulation of a dynamically tunable 1× 2 power splitter using MZI configuration in the telecom regime

We propose an ultra-broadband, ultra-compact and a dynamically tunable power splitter on a silicon on Insulator (SOI) platform with a 220 nm thick silicon light-guiding layer, using two multimode interference (MMI) couplers connected with graphene-based waveguides as the phase-tuning section through a Mach-Zehnder Interferometer (MZI) configuration. First, we theoretically present and demonstrate a novel design for the MMI couplers by combining the plane wave expansion method (PWEM) and the mode expansion conjecture concept. To verify the proposed theory, a center-fed MMI coupler and a MMI coupler, respectively, as the input and output sections of our proposed device, are designed and simulated. The simulation results achieved by Lumerical FDTD show good agreement with the design theory. Then, a highly tunable graphene-embedded silicon waveguide, for the highly efficient modulation of the effective mod index (EMI), is duly designed using Lumerical Mode Solutions. As the two MZI arms, a pair of the proposed waveguides is introduced into the middle of the cascaded MMI couplers. Accordingly, the integration properties of the analytically designed MMI couplers and the numerically designed waveguide is demonstrated through our proposed device for the aim of achieving any wanted power splitting ratio. To this end, we consider the case that the real part of the EMI of the waveguide in the lower MZI arm is modulated by varying the graphene Fermi level values, being the same for all the layers belonging to the same waveguide, while that of the upper arm is constant. The corresponding power splitting ratio can be dynamically tuned in the range of All reported results assume TE polarization. The designed MZI-based splitter possesses a bandwidth of over the wavelength range from to for various power splitting ratios, maintaining the averaged insertion loss and the averaged power imbalance, respectively, below as low as and The overall footprint of the proposed device is also highly small, i.e., about

Mathematical modeling of the parameters of an electro-optic modulator in the Mach–Zehnder interferometer configuration based on thin lithium niobate films

Subject of study. An electro-optic modulator in a Mach–Zehnder interferometer configuration based on ridge waveguides made of a thin lithium niobate film was studied. Aim of study. The study aimed to mathematically model the parameters of an electro-optic modulator in a Mach–Zehnder interferometer configuration based on ridge waveguides made of a thin lithium niobate film. Method. The dependence of the optical losses introduced by a Y-branch splitter on the angle of the splitter was investigated using a beam propagation method based on the fast Fourier transform. Main results. The results of mathematical simulation of the parameters of the electro-optic modulator in the Mach–Zehnder interferometer configuration based on thin lithium niobate films were presented. The dependence of the optical losses, introduced by the Y-splitter, on the waveguide separation angle was obtained. Images of interference patterns occurring in the output waveguide were examined. A comparison revealed that the effectiveness of the proposed interferometer configuration was higher than that of the alternative solutions available in the literature. The novelty of the results is that the configuration of the electro-optic modulator investigated in this study was fabricated in the form of an integrated optical circuit based on ridge waveguides of thin-film lithium niobate. Such a solution enables a reduction in the dimensions of the final device and increases the sensitivity compared with that of existing analogs based on bulk electro-optic crystals. Additionally, owing to the use of a semiconductor substrate, an electronic circuit can possibly be integrated into the substrate, which enables the implementation of an electro-optic sensor system on a single chip. Practical significance. The method for interference pattern analysis proposed in this study provides information on the magnitude of the voltage applied to the arm of the interferometer and enables the development of requirements for its further modernization for increasing the accuracy of measurements and developing optoelectronic devices based on thin lithium niobate films, including integrated optical electric-field sensors.

All-Optical Regeneration and Format Conversion for 4APSK Signals Based on Nonlinear Effects in HNLF

An all-optical format conversion and regeneration scheme about 4-ary amplitude and phase shift keying (4APSK) signals is proposed and numerically simulated based on nonlinear effects in the high nonlinear fiber (HNLF). The input 4APSK signal is firstly converted into a regular quadrature phase shift keying (QPSK) signal by the nonlinear Mach-Zehnder interferometer (MZI) based on the self-phase modulation (SPM). Secondly, a degenerate phase-sensitive amplification (PSA) based on the four-wave mixing (FWM) is utilized to convert the regular-QPSK into two binary phase shift keying (BPSK) signals. The nonlinear MZI configuration is also used to compress the amplitude noise of BPSK. Thirdly, one phase shifter and one variable optical attenuator (VOA) are used to adjust the relative phase and power relationships of the two amplitude-regenerated BPSK signals. The regenerated 4APSK and converted QPSK signals can be generated in one 3-dB optical coupler through coherent addition of the two regenerated BPSK signals. The error-vector-magnitude (EVM) and the bit-error-rate (BER) are calculated and compared to evaluate the scheme performance. The proposed scheme can be applied as an optical regenerator or format convertor at the network gateway to increase the transmission distance or connect optical networks with different modulation formats.

Asymmetric, non-uniform 3-dB directional coupler with 300-nm bandwidth and a small footprint.

Here we demonstrate a new, to the best of our knowledge, type of 3-dB coupler that has an ultra-broadband operational range from 1300 to 1600 nm with low fabrication sensitivity. The overall device size is 800 µm including in/out S-bend waveguides. The coupler is an asymmetric non-uniform directional coupler that consists of two tapered waveguides. One of the coupler arms is shifted by 100 µm in the propagation direction, which results in a more wavelength-insensitive 3-dB response compared to a standard (not shifted) coupler. Moreover, compared to a long adiabatic coupler, we achieved a similar wavelength response at a 16-times-smaller device length. The couplers were fabricated using the silicon nitride platform of Lionix International. We also experimentally demonstrated an optical switch that is made by using two of these couplers in a Mach-Zehnder interferometer configuration. According to experimental results, this optical switch exhibits -10 dB of extinction ratio over the 1500-1600 nm wavelength range. Our results indicate that this new type of coupler holds great promise for various applications, including optical imaging, telecommunications, and reconfigurable photonic processors where compact, fabrication-tolerant, and wavelength-insensitive couplers are essential.

A New Design for Enhancing Highly Sensitive Interferometer Biosensor Using a Silicon Rib Waveguide

In this paper, we have proposed a new design, to enhance and simulate a Highly Sensitive Mach-Zehnder Interferometer (MZI) Biochemical sensing platform using a Silicon Rib Waveguide. We considered two different MZI configurations: the first one with an S-bend & Y-junction and the second with an angular Y-junction. We determined the critical cut-off radius and the critical cut-off angle for the S-bend & Y-junction and the angular Y-junction configurations respectively. Based on the analyses of the evanescent field intensity, the mode polarization and cross section dimensions of the Silicon Rib waveguide are optimized using beam propagation method. The critical parameters of the design are calculated to ensure minimal optical losses and a new sensitivity value of 308 dB/RIU with a detection limit of 10-7, which shows the ability of the structure to produce biosensor.

All-Optical Format Conversion of 2-Dimensional MQAM to MPSK Based on Nonlinear Mach-Zehnder Interferometer With Wavelength Preservation

An all-optical format conversion scheme of 2-dimensional multiple-quadrature amplitude modulation (MQAM) to multiple-phase shift keying (MPSK) signals is proposed and numerically simulated by using the nonlinear Mach-Zehnder interferometer (MZI) configuration with wavelength preservation. The input octal-quadrature amplitude modulation (8QAM) signal is generated through the phase modulator (PM) and amplitude modulator (AM) and injected into the nonlinear MZI configuration. The designed nonlinear MZI configuration includes two 3 dB optical couplers (OCs), a piece of high nonlinear fiber (HNLF) and a variable optical attenuator (VOA) in the upper interfering arm and a piece of standard single mode fiber (SSMF) or tunable optical delay line (TODL) and a variable phase shifter (VPS) in the lower interfering arm. The converted octal-phase shift keying (8PSK) signal can be obtained from the nonlinear MZI configuration through vector superposition between the input optical signal and itself with some nonlinear phase shift. The needed asymmetric nonlinear phase shift is mainly induced by the big nonlinear index difference between HNLF and SSMF. The error vector magnitude (EVM) and bit error rate (BER) performance of the scheme are calculated before and after format conversion with the different input and receiver optical-signal-noise-ratios (OSNRs). The scheme can be used in the intermediate node to connect the different networks which adopt 8QAM and 8PSK signals, respectively.

Ultra-high-linearity integrated lithium niobate electro-optic modulators

Integrated lithium niobate (LN) photonics is a promising platform for future chip-scale microwave photonics systems owing to its unique electro-optic properties, low optical loss, and excellent scalability. A key enabler for such systems is a highly linear electro-optic modulator that could faithfully convert analog electrical signals into optical signals. In this work, we demonstrate a monolithic integrated LN modulator with an ultra-high spurious-free dynamic range (SFDR) of 120.04 dB · Hz 4 / 5 at 1 GHz, using a ring-assisted Mach–Zehnder interferometer configuration. The excellent synergy between the intrinsically linear electro-optic response of LN and an optimized linearization strategy allows us to fully suppress the cubic terms of third-order intermodulation distortions (IMD3) without active feedback controls, leading to ∼ 20 dB improvement over previous results in the thin-film LN platform. Our ultra-high-linearity LN modulators could become a core building block for future large-scale functional microwave photonic integrated circuits by further integration with other high-performance components like low-loss delay lines, tunable filters, and phase shifters available on the LN platform.

Refractive index sensitivity enhancement of SF-MZI through metal film deposition

A simple and unique methodology predicting the influence of metal film coating, on non-adiabatic tapered fibers constituting single-fiber Mach-Zehnder interferometer (SF-MZI) configuration, on output fringe pattern of the interferometer, without inducing surface plasma resonance, has been proposed. The suggested approach reveals increase in losses and degree of fringe shift in the output wavelength spectrum of the SF-MZI depending on the properties and thickness of the metal deposited on fiber tapers. In order to substantiate the theoretical findings, layers of aluminium (Al) metal of different thicknesses are deposited on tapered regions of the SF-MZI and refractive index sensing experiments for identifying the presence and concentration of Fluoride ions and Sucrose in water are conducted. The impression of metal coating envisaged by the proposed methodology in terms of sensitivity enhancement (from 291.43 nm/RIU to 368.57 nm/RIU for Fluoride ion and 33.85 nm/RIU to 77.89 nm/RIU, for Sucrose solution), exponential decay of extinction ratio (with attenuation parameter of 0.05 nm−1 and 0.037 nm−1 for Fluoride ion and Sucrose sensing, respectively), fluctuations in free spectral range (FSR) (from 0.6 to 1.3 nm) at the output port of the interferometer have been quantified and validated by the experimental findings.

Silica-based Photonic Crystal Fiber for Supercontinuum Generation in the Anomalous Dispersion Region: Measurement and Simulation

We report on numerical simulation and experimental study of the supercontinuum (SC) generation in the anomalous dispersion region of photonic crystal fiber (PCF). The results show that a flat and stable spectrum with bandwidth of 130 nm around the central pump wavelength was achieved with an input power of 4.0 W. Although the measured spectrum is slightly different from the numerical ones, a good consistency can be recognized in the major sideband positions and spectral width. In addition, the chromatic dispersion of air silica PCF was measured at visible and near-infrared wavelengths using the Mach-Zehnder interferometer configuration and then verified by comparison with simulated results.

Electrical control of surface acoustic waves

Acoustic waves at microwave frequencies are widely used in wireless communication and are potential information carriers in quantum applications. However, most acoustic devices are passive components, and the development of phononic integrated circuits is limited by the inability to control acoustic waves in a low-loss, scalable manner. Here we report the electrical control of gigahertz travelling acoustic waves at room temperature and millikelvin temperatures. We achieve phase modulation by tuning the elasticity of a lithium niobate acoustic waveguide via the electro-acoustic effect. This phase modulator is then used to build an acoustic frequency shifter based on serrodyne phase modulation, and phase modulators in a Mach–Zehnder interferometer configuration are used to create an electro-acoustic amplitude modulator. By tailoring the phase matching between acoustic and quasi-travelling electric fields, we achieve reconfigurable non-reciprocal modulation with a non-reciprocity of over 40 dB. To illustrate the potential of the approach in quantum applications, we show that our electro-acoustic modulator can provide coherent modulation of single-phonon-level acoustic waves at 50 mK. The electro-acoustic effect can be used to electrically control the phase velocity of travelling acoustic waves in a lithium niobate waveguide, and to construct devices that can modulate the phase, frequency and amplitude of acoustic waves, even at the limit of single phonons.

Photonic crystal based interferometric design for label-free all-optical sensing applications.

Optical sensing devices has a great potential in both industrial and biomedical applications for the detection of biochemicals, toxic substances or hazardous gases thanks to their sustainability and high-selectivity characteristics. Among different kinds of optical sensors based on such as fibers, surface plasmons and resonators; photonic crystal (PC) based optical sensors enable the realization of more compact and highly efficient on-chip sensing platforms due to their intriguing dispersive relations. Interferometric devices based on PCs render possible the creation of biochemical sensors with high sensitivity since a slight change of sensor path length caused by the captured biochemicals could be detected at the output of the interferometer via the interferences of separated beams. In this study, a new type of Mach-Zehnder Interferometer (MZI) using low-symmetric Si PCs is proposed, which is compatible with available CMOS technology. Intended optical path difference between the two MZI channels is provided by the periodic alignments of symmetry-reduced PC unit cells in the MZI arms. Unlike the conventional symmetrical PC based MZIs, Fano resonances exist for the proposed MZI design, i.e. transmission dips and peaks appear in the output spectrum, and the location of dip and peak frequencies in transmission spectra can be efficiently controlled by utilizing interference phenomenon. Exploiting this effect, any refractive index change at the surrounding medium could be distinctly observed at the transmission spectra. In the view of such results, it is convenient to say that the proposed MZI configuration is suitable for efficient optical sensing of toxic gases as well as liquids. The designed all-dielectric MZI system is numerically investigated in both spectral and spatial domains to analyze its interferometric tunability: an optical sensitivity of about 300 nm/RIU is calculated for gaseous analytes whereas that sensitivity value is around 263.2 nm/RIU in the case of liquid analytes. Furthermore, high quality factor of Q > 45000 is obtained at Fano resonances with Figure-of-Merit (FoM) value of FoM ∼ 8950 RIU-1(7690 RIU-1) in the case of gas analytes (liquid analytes), which is the indication of enhanced optical sensing performance of the proposed MZI design. Considering all the above-mentioned advantages, the proposed interferometric configurations based on low-symmetric PCs could be utilized for efficient photonic sensor applications that require controllable output power or sensing of gaseous and liquid substances.

Mach-Zehnder interferometer comb filter for multi-wavelength mode-locked generation from erbium-doped fiber laser.

A picosecond pulse multi-wavelength erbium-doped fiber ring laser based on an optically switchable/tunable Mach-Zehnder interferometer (MZI) filter is proposed and experimentally demonstrated. The MZI configuration is constructed with two 3 dB couplers and two short pieces of endlessly single-mode photonic crystal fiber with different lengths in each arm. The combination of the MZI and a polarization controller (PC) acts as a selective comb filter and a mode-locking device. By adjusting the pump power or the first PC (PC1) state, the laser can emit up to 10 channels with a 20 nm tuning range (1530 to 1550 nm). Furthermore, by changing the PC1 condition, stable picosecond mode-locking generation with a repetition rate of 13.5 MHz is realized. To achieve wavelength spacing tunable multiple-channel laser emissions, the MZI is configured by incorporating a second PC (PC2) in one arm of the conventional MZI. Four channels of picosecond mode-locking pulses with a repetition rate of 11.6 MHz in the range of 1530-1550 nm are realized by carefully controlling the pump power and/or PC2 state. With the manipulation of intracavity birefringence through PCs with comb filtering via MZI, the proposed structure may be a potential tool in various photonics applications.

Athermal echelle grating and tunable echelle grating demultiplexers using a Mach-Zehnder interferometer launch structure.

We present a comparative experimental study of three silicon photonic echelle grating demultiplexers that are integrated with a Mach-Zehnder interferometer (MZI) launch structure. By appropriate choice of the MZI configuration, the temperature induced shift of the demultiplexer channel wavelengths can be suppressed (athermal) or enhanced (super-thermal) or be controlled by an on-chip micro-heater. The latter two configurations allow the channel wavelengths to be actively tuned using lower power than possible by temperature tuning a conventional echelle demultiplexer. In the athermal configuration, the measured channel spectral shift is reduced to less than 10 pm/°C, compared to the 83 pm/°C shift for an unmodified echelle device. In super-thermal operation an enhanced channel temperature tuning rate of 170 pm/°C is achieved. Finally, by modulating the MZI phase with an on-chip heater, the demultiplexer channels can be actively tuned to correct for ambient temperature fluctuations up to 20 °C, using a drive current of less than 20 mA.

Design and development of integrated TIRF and common-path quantitative phase microscopic health care system with high stability

We demonstrate a compact microscopy system that enables simultaneous cell imaging in both digital holographic and fluorescence mode thus providing valuable multi-modal information for biosciences applications. The digital holographic imaging system uses a speckle free illumination by employing a rotating diffuser. Further a compact shear plate based interferometer arrangement is used to significantly reduce the system size and increase its robustness when compared with Michelson or Mach-Zehnder interferometer configurations. The overall reduction in form factor of the system is achieved since we employ the shear plate configuration additionally as a beam-splitter for the fluorescence imaging part of the system. We have fabricated a compact total internal reflection fluorescence (TIRF) unit which is combined with the common path sheared interferometer for this purpose. Our experiments with this compact system show excellent temporal phase stability. The working of the system is illustrated with imaging of polystyrene beads and MG63 osteosarcoma cell line sample. The fluorescence image of MG63 cell shows high expression of vinculin protein around the nuclei when compared with the expression in the cell's filopodia. These proteins are among the major molecular markers for cell adhesion and play a vital role in sensing the mechanical stimulus of the microenvironment. Further the quantitative phase information about the cell also provides its optical thickness information that is spatially aligned with the fluorescence signal. The proposed system can find applications in bioscience laboratories as well as in diagnostics.

Optical modulator using ultra-thin silicon waveguide in SOI hybrid technology

We propose a detailed study of an on-chip optical modulator using a non-conventional silicon-based platform. This platform is based on the optimum design of ultra-thin silicon on insulator waveguide. This platform is characterized by low field confinement inside the core waveguide and high sensitivity to the cladding index. Accordingly, it lends itself to a wide range of applications, such as sensing and optical modulation. By employing this waveguide into the Mach–Zehnder interferometer configuration, an efficient optical modulator is reported using an organic polymer as an active material for the electro-optic effect. An extinction ratio of more than 20 dB is achieved with energy per bit of 13.21 fJ/bit for 0.5 V applied voltage. This studied platform shows promising and adequate performance for modulation applications. It is cheap and easy to fabricate.

Optimization of Silicon Nitride Waveguide Platform for On-Chip Virus Detection.

This work presents a rigorous and generic sensitivity analysis of silicon nitride on silicon dioxide strip waveguide for virus detection. In general, by functionalizing the waveguide surface with a specific antibodies layer, we make the optical sensor sensitive only to a particular virus. Unlike conventional virus detection methods such as polymerase chain reaction (PCR), integrated refractive index (RI) optical sensors offer cheap and mass-scale fabrication of compact devices for fast and straightforward detection with high sensitivity and selectivity. Our numerical analysis includes a wide range of wavelengths from visible to mid-infrared. We determined the strip waveguide’s single-mode dimensions and the optimum dimensions that maximize the sensitivity to the virus layer attached to its surface at each wavelength using finite difference eigenmode (FDE) solver. We also compared the strip waveguide with the widely used slot waveguide. Our theoretical study shows that silicon nitride strip waveguide working at lower wavelengths is the optimum choice for virus detection as it maximizes both the waveguide sensitivity (Swg) and the figure of merit (FOM) of the sensor. The optimized waveguides are well suited for a range of viruses with different sizes and refractive indices. Balanced Mach–Zehnder interferometer (MZI) sensors were designed using FDE solver and photonic circuit simulator at different wavelengths. The designed sensors show high FOM at λ = 450 nm ranging from 500 RIU−1 up to 1231 RIU−1 with LMZI = 500 µm. Different MZI configurations were also studied and compared. Finally, edge coupling from the fiber to the sensor was designed, showing insertion loss (IL) at λ = 450 nm of 4.1 dB for the design with FOM = 500 RIU−1. The obtained coupling efficiencies are higher than recently proposed fiber couplers.