Single-mode Graded-index Fibers Research Articles

Optical Fiber Communication System and Nonlinear Effects: A Brief Insight

In the modern scenario, optical fiber communication technology has rapidly progressed with continuous exploration of emerging technologies to support more amount of bandwidth, higher data rate and improved security along with reduction in losses and electromagnetic immunity. Optical fiber communication system has remarkably low loss and is reliably capable of meeting the demand of massively increased information traffic employing a minimum number of repeaters in its performance link. In this paper, we discuss broadly optical fiber technology theory, types, working principle with its various merits and demerits in the application scenario. Single-mode graded index fiber has been analyzed in comparison to multi-mode fibers and it has emerged as the most efficient means of broad band signal transmission offering many distinct advantages. The possible consequences of both linear and nonlinear effects of the optical fiber and other limiting factors that influence the performance of propagation characteristics have been discussed which are reasonably relevant to the emerging areas of optical engineering ,photonics and related fiber optic devices.

Nearly 70 Gbit/s NRZ-OOK encoding of a dual-mode 850 nm VCSEL with a highly In-doped and small Zn-diffused emission area

By pre-emphasized encoding of a dual-mode 850 nm vertical-cavity surface-emitting laser (VCSEL), the nearly 70 Gbit/s on–off keying (OOK) transmission performance is performed for the ultrafast data link. This VCSEL is designed with a new structural configuration, including 6 μm oxidized aperture and 4 μm Zn-diffused emission aperture, which exhibits dual-mode lasing with a threshold current of 0.75 mA, a nonsaturated power of 2.2 mW at 8 mA, and a differential quantum efficiency of 0.38 under a lensed OM4 multimode fiber (MMF) coupling scheme. In particular, the high indium (In) dopant density in the quantum well increases its differential gain coefficient to upshift the relaxation oscillation frequency, which effectively broadens the modulation bandwidth to high-speed data transmission. For the back-to-back transmission, the VCSEL coupled with a lensed OM4-MMF (1 m) for short-reach link reveals an NRZ-OOK transmission at 66 and 69 Gbit/s with a corresponding bit-error ratio (BER) of 5.9 × 10 − 10 and 10 − 5 for error-free decoding after forward-error correction. When employing graded-index single-mode fiber (GI-SMF) with 100 m length as the transmission segment, the VCSEL linked to the GI-SMF connected with a lensed OM4-MMF (1 m) collimator can provide the pre-emphasized NRZ-OOK transmission at 51 Gbit/s with a BER of 4.5 × 10 − 10 and SNR of 14.1 dB.

Comparing the Dual-Mode VCSEL in OM4-MMF and GI-SMF Links for NRZ-OOK and 16-QAM-OFDM Transmissions

A dual-mode (DM) vertical-cavity surface-emitting laser (VCSEL) is investigated for carrying high-speed data transmission with either the non-return-zero on-off keying (NRZ-OOK) or the quadrature amplitude modulation-orthogonal frequency division multiplexing (QAM-OFDM) format. In both the back-to-back (BtB) and the 100-m transmission cases with using either the OM4 multimode fiber (OM4-MMF) or the graded-index single-mode fiber (GI-SMF), the mismatch between the core diameter of the lensed MMF pick-up head and the mode field of the DM-VCSEL output controls the coupled transverse mode number and decrease the modal dispersion effect. Using pre-emphasized NRZ-OOK data can compensate the SNR degradation to improve the BER to 5.6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−12</sup> under BtB and 6.9 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−10</sup> after 100-m GI-SMF for the DM-VCSEL delivered NRZ-OOK data at 53 Gbit/s. For 16-QAM OFDM transmission, the pre-leveling algorithm shows better data compensation than the pre-emphasis algorithm in both BtB and the 100-m GI-SMF cases. With the pre-leveling compensation of the 16-QAM OFDM data encoded to the DM-VCSEL with a 0.4-dB/GHz slope, the DM-VCSEL allows 136 Gbit/s for BtB, 112 Gbit/s for 100-m OM4-MMF, and 92 Gbit/s for 100-m GI-SMF transmissions. The pre-emphasis NRZ-OOK and the pre-leveling 16-QAM OFDM data carried by the DM-VCSEL can be used in ultrahigh-speed intra-data-center links in the future.

Coupling angle tolerance of the 850-nm single-mode VCSEL output collimated by lensed OM4-MMF or GI-SMF for a NRZ-OOK link.

By collimating the single-mode (SM) vertical-cavity surface-emitting laser (VCSEL) at 850 nm with either the OM4 multi-mode fiber (OM4-MMF) or the graded-index single-mode fiber (GI-SMF) with lensed end-face, the directly encoded non-return-to-zero on-off keying (NRZ-OOK) data transmission performance is characterized when tilting the coupling angle with respect to the surface normal of the SM-VCSEL. In comparison with the lensed OM4-MMF and lensed SMF coupling, the lensed OM4-MMF collimator shows a large coupling angle tolerance with the coupling efficiency only degraded by 5% when enlarging the tilted angle from 0° to 10°. In contrast, the lensed GI-SMF collimator attenuates the coupled SM-VCSEL output by more than 50% when tilting the coupling angle up to 10°. For the lensed OM4-MMF coupling, the receivable NRZ-OOK data rate in BtB and after 100-m OM4-MMF cases can achieve 50 Gbit/s with its corresponding BER degraded from 6.5 × 10-10 to 8.8 × 10-10 when enlarging its tilting angle ranged from 0° to 10°. By changing the collimator to the lensed SMF, the decoded BER significantly degrades from 5.8 × 10-5 to 1.2 × 10-1 when coupling and transmitting the NRZ-OOK data at 50 Gbit/s. Owing to the low coupling efficiency via the lensed SMF collimator, the error-free NRZ-OOK data rate under the lensed SMF coupling somewhat decreases to 35 Gbit/s in the BtB link and to 32 Gbit/s after the 100-m GI-SMF link with allowable coupling angle tilted from 0° to 4°. This work confirms the applicability of the lensed MMF or SMF collimator for coupling the SM-VCSEL output with a relatively large tolerance on the tilting angle with respect to the surface normal of the SM-VCSEL.

Effect of misalignment on coupling efficiency in laser diode to single-mode circular core graded-index fiber coupling via cylindrical microlens on the fiber tip

Abstract We report here the first theoretical prediction of coupling efficiency of the laser diode to single-mode graded-index fiber coupling via cylindrical microlens on the tip of the fiber in presence of possible transverse and angular mismatches. Moderately efficient cylindrical microlens on the fiber is easily fabricable and graded-index fiber has less sensitivity to macro as well as micro bending. Thus this coupling device emerges as a potential candidate in the field of coupling optics. The analysis takes into consideration the allowable aperture provided by cylindrical microlens. Further, we shall consider here the coupling in the vertical plane only since the coupling in the horizontal plane has poor performance. Using the relevant ABCD matrix of refraction for a cylindrical lens in the vertical plane, we prescribe analytical expressions of the coupling efficiencies in presence of said kinds of misalignments. In our analysis, we use Gaussian field distribution for both the laser and fiber fields. We carry on our investigation for two commonly used wavelengths namely 1.3 and 1.5 µm. As an example of graded-index fiber, we use some typical step, parabolic, and triangular index fibers in our study. The execution of the prescribed formulations involves little computation. Thus the evaluation of the concerned coupling efficiencies is very much user friendly. The present analysis surfaces the tolerance factors of the coupling devices. Accordingly, the results will prove beneficial to designers and packagers in respect of the design of such coupler involving cylindrical microlens in the field of optimum launch optics.

Single-Mode VCSEL Transmission for Short Reach Communications

Single-mode VCSEL technology has advanced significantly in the past few years. The advantages of single-mode VCSELs lie primarily on the narrower linewidth, lower numerical aperture, and smaller spot size compared to multimode VCSELs. They are suitable for transmitting over both multimode fibers and few-mode fibers. For multimode fiber systems, the narrow linewidth can reduce the chromatic dispersion penalty and increase the system reach. A single-mode VCSEL also allows the coupling into graded-index single-mode fiber, which is few-mode around 850 nm with high bandwidth, for few-mode transmission. We review recent progress and present new experimental results and modeling analyses of single-mode VCSEL transmission over both types of fibers. The experiments and analyses shed new light on how single-mode VCSELs can be used with multimode fibers and graded-index single-mode fibers and relative merits between 850 nm single-mode VCSELs versus 980 nm and 1060 nm single-mode VCSELs to address the needs of various applications.

Influence of Kerr nonlinearity on group delay and modal dispersion parameters of single-mode graded index fibers: evaluation by a simple but accurate method

Abstract This paper reports simple but accurate analytical expressions of group delay and modal dispersion parameters for single-mode graded index fibers over a wide range of V numbers. The formulation employs power series expression for the fundamental modal field of graded index fiber derived by Chebyshev formalism. Choosing some typical step, parabolic and triangular index fibers as examples in our present study, we use the prescribed formulations to estimate group delay and modal dispersion parameters of those fibers both in presence and absence of Kerr nonlinearity. Iterative technique is applied for prediction of concerned propagation parameters in presence of Kerr nonlinearity. Our results show excellent agreement with the numerical exact ones both in absence and presence of Kerr nonlinearity. The exact results in case of Kerr nonlinearity are obtained using cumbersome finite element method. The execution of our accurate formalism involves little computation and is thus user friendly for technologists and researchers working in the field of nonlinear optical engineering.

A Simple but Accurate Method for Estimation of the Effect of Kerr Nonlinearity on Confinement and Excitation of the Fundamental Mode in Single Mode Graded Index Fiber

This paper presents prediction of the fractional modal power and excitation of the fundamental mode inside the core of a single-mode graded index fiber, both in presence and absence of Kerr nonlinearity. Our analysis is based on simple power series expression for fundamental mode of graded index fiber, which has been formulated by applying Chebyshev technique. In absence of nonlinearity, analytical expressions for the concerned propagation parameters are prescribed. Employing these analytical expressions, method of iteration is applied for evaluation of the said parameters in presence of Kerr nonlinearity. In this context, some typical step, parabolic and triangular index fibers are used for our study. In absence of nonlinearity, our results show excellent match with the exact results available in literature. In presence of nonlinearity, the results found by our formalism also agree excellently with the exact results which can be obtained by application of rigorous finite element technique. Thus, this simple but accurate method will prove extremely useful for the system users.

A simple but accurate formalism for study of single-mode graded index fiber directional coupler in presence of Kerr nonlinearity

This paper presents performance of directional coupler consisting of two identical single-mode graded index fibers in presence as well as in absence of Kerr type nonlinearity. In this context, parabolic and step index fibers of some typical V numbers are used. Here, we employ a simple series expression for fundamental modal field for such fibers prescribed by Chebyshev formalism. Analytical expression of the coupling length of the directional coupler is formulated. Here, we apply method of iteration in order to take care of nonlinearity. The concerned evaluation involves little computation. Thus, the formalism developed for study of nonlinear directional coupler can be treated as an accurate but simple alternative to the existing complicated methods available in literature. This user friendly method will prove beneficial to the scientists and technologists working in the field of nonlinear optics.

Evaluation of Splice Loss of Single-Mode Graded Index Fiber in Presence of Kerr Nonlinearity

We present here evaluation of splice loss of single-mode graded index fiber in presence of Kerr type nonlinearity by a simple iterative method involving Chebyshev technique. We restrict our analysis to two different cases of splice losses involving angular and transverse offsets because splices are highly tolerant for longitudinal separation. Our analysis by the said power series for two typical graded index fibers namely step index and parabolic index fibers provide excellent results. The evaluation of concerned parameters by our technique requires very little computations. Thus our formalism will prove user friendly to system engineers. Accordingly, this formalism may prove useful in many applications in optical technology involving graded index fibers.

Study of coupling optics involving graded index fiber excitation via upside down tapered parabolic microlens on the fiber tip

Based on the prescribed ABCD matrix for the transmission of paraxial rays, we analyze theoretically laser diode to single mode graded index fiber excitation via an upside-down tapered parabolic microlens on the fiber tip. In this context, we use some typical step, parabolic and triangular index fibers. The ABCD transformation matrices for upside down tapered parabolic microlens on the tips of step-index, triangular-index and parabolic-index fibers are employed in our analysis. In this formalism, we employ Gaussian field distributions for both the source and the fiber. In our study, we use here two different laser diodes emitting wavelengths 1.3 μm and 1.5 μm respectively. The execution of the prescribed formalism requires little computation. Such formalism is expected to generate tremendous interest for study of coupling optics related to such kind of coupler.

High data rate few-mode transmission over graded-index single-mode fiber using 850 nm single-mode VCSEL.

A few-mode transmission system is proposed using 850 nm single-mode VCSEL based transceivers over graded-index single-mode fibers for high data rate data center applications. A graded-index single-mode fiber that supports two mode groups at 850 nm window with a high modal bandwidth of 48.3 GHz·km is realized for the first time. 25 Gb/s transmission experiments using a 850 nm single-mode VCSEL over such fiber demonstrate that the system can support a link distance up to 1.5 km. Additionally, link model analysis provides more insights on how fiber and single-mode VCSEL parameters impact the system performance.

Prediction of Fundamental Modal Field for Graded Index Fiber in the Presence of Kerr Nonlinearity

Abstract The power series formulation for modal field of single-mode graded index fibers by Chebyshev technique has worked excellently in predicting accurately different propagation characteristics in simple fashion. Here we develop a simple iterative method involving Chebyshev formalism to predict the modal field of single-mode graded index fiber in the presence of Kerr-type nonlinearity. Taking step and parabolic index fibers as typical examples, we show that our results match excellently with the available exact results obtained vigorously. Thus, the reported technique can be considered as an accurate alternative to the existing cumbersome techniques. Accordingly, this formalism will be beneficial to the technologies for evaluation of modal noise in single-mode Kerr-type nonlinear graded index fibers.

Coupling of a laser diode to single mode circular core graded index fiber via parabolic microlens on the fiber tip and identification of the suitable refractive index profile with consideration for possible misalignments

We present a theoretical investigation of coupling optics involving a laser diode and circular core graded index single mode fiber via a parabolic microlens on the fiber tip to predict the nature of suitable refractive index profile for the first time in connection with optimum coupling. The study is carried out in absence and presence of possible transverse and angular misalignments. By employing Gaussian field distributions for both the source and the fiber and also ABCD matrix for parabolic microlens under paraxial approximation, we formulate analytical expressions for the concerned coupling efficiencies. The investigations are performed for two different light-emitting wavelengths of 1.3 μm and 1.5 μm for such fibers with different refractive index profile exponents. Further, it is observed that out of the studied refractive index profiles, triangular index profile having the dispersion-shifted merit comes out to be the most suitable profile to couple laser diode to such abovementioned fiber for two wavelengths of practical interest. The analysis should find use in ongoing investigations for optimum launch optics for the design of parabolic microlens either directly on the circular core graded index single mode fiber tip or such fiber attached to single mode fiber to achieve long working distance.

A simple and elegant technique connecting Marcuse spot size relations to variational formulations in single-mode fiber characterization

Accurate knowledge of spot size, an important criterion in single-mode fiber optics, is obtained by two different optimization techniques, the well-known variational method and Marcuse formulation. The later is more accurate but cannot predict fiber parameters from given spot sizes. In this study, it is shown for the first time to the best of our knowledge that using simultaneously Marcuse relations of fiber spot sizes for single-mode graded index fibers and also variational formulation, we can more accurately and easily determine the fiber parameters for a particular normalized frequency. Then it is shown with typical example of fractional power in the core that in the case of such fibers, this synthesis of these two useful approaches can also more accurately estimate propagation characteristics of practical interest. This equivalence provides an easy and useful connection between two fundamental but disjoint approaches and should find wide use.

A Simple Method for Prediction of Effective Core Area and Index of Refraction of Single-mode Graded Index Fiber in the Low V Region

AbstractBased on the simple power series formulation of fundamental mode developed by Chebyshev formalism in the low V region, we prescribe analytical expression for effective core area of graded index fiber. Taking step and parabolic index fibers as examples, we estimate the effective core areas as well as effective refractive index for different normalized frequencies (V number) having low values. We also show that our estimations match excellently with the available exact results. The concerned predictions by our method require little computation. Thus, this simple but accurate formalism will be user friendly for the system engineers.

Bend loss calculation in single-mode graded-index fibers using variational fields

Calculation of bend loss for single-mode graded-index fibers utilizes the fundamental modal field. Using some of the single and two parameter scalar variational approximations available in the literature for this mode, the bend loss has been computed. The exact results are obtained using a well known numerical method. The accuracies of the results obtained from the use of these variational fields have been compared.

Single parameter scalar variational analysis for single-mode fibers with smoothed-out and composite refractive index profiles: A comparative study

A number of single parameter variational approximations for single-mode graded-index fibers have been reported in the literature. One of these approximations was also proposed by us some time ago which describes the propagation characteristics of such fibers having power-law profile with a high degree of accuracy. Using these approximations we have computed the propagation constant and the normalized dispersion for single-mode fibers with smoothed-out and composite refractive index profiles which are of great current interest. We have shown that the single parameter approximation proposed by us earlier computes these propagation characteristics with a better degree of accuracy than all other single parameter approximations even for these special types of profiles.

Evaluation of dimensionless vector and scalar propagation constants for single-mode graded index fibers by a simple technique

We present simple but accurate analytical expressions for prediction of scalar and vector propagation constants for single-mode graded index fibers. Our formulation is based on the recently developed Chebyshev power series expression for the fundamental mode of graded index fibers. Taking parabolic index fiber as example, we show that our estimations agree excellently with the exact results. The concerned calculations involve very little computations.

Variational Approximations for Single-mode Graded-index Fibers: Some Interesting Applications

A simple analytical formula has been proposed to compute the vector propagation constant of single-mode graded-index fibers utilizing single parameter and two-parameter variational approximations for the LP 01 mode. These approximations have also been utilized to study the effect of on-axis dip in the refractive index profile on the propagation characteristic of the fiber.