Showing papers in "Journal of Lightwave Technology in 2003"

Survivable WDM mesh networks

Abstract: In a wavelength-division-multiplexing (WDM) optical network, the failure of network elements (e.g., fiber links and cross connects) may cause the failure of several optical channels, thereby leading to large data losses. This study examines different approaches to protect a mesh-based WDM optical network from such failures. These approaches are based on two survivability paradigms: 1) path protection/restoration and 2) link protection/restoration. The study examines the wavelength capacity requirements, and routing and wavelength assignment of primary and backup paths for path and link protection and proposes distributed protocols for path and link restoration. The study also examines the protection-switching time and the restoration time for each of these schemes, and the susceptibility of these schemes to multiple link failures. The numerical results obtained for a representative network topology with random traffic demands demonstrate that there is a tradeoff between the capacity utilization and the susceptibility to multiple link failures. We find that, on one hand, path protection provides significant capacity savings over link protection, and shared protection provides significant savings over dedicated protection; while on the other hand, path protection is more susceptible to multiple link failures than link protection, and shared protection is more susceptible to multiple link failures than dedicated protection. We formulate a model of protection-switching times for the different protection schemes based on a fully distributed control network. We propose distributed control protocols for path and link restoration. Numerical results obtained by simulating these protocols indicate that, for a representative network topology, path restoration has a better restoration efficiency than link restoration, and link restoration has a faster restoration time compared with path restoration.

Optimization of the split-step Fourier method in modeling optical-fiber communications systems

Abstract: We studied the efficiency of different implementations of the split-step Fourier method for solving the nonlinear Schro/spl uml/dinger equation that employ different step-size selection criteria. We compared the performance of the different implementations for a variety of pulse formats and systems, including higher order solitons, collisions of soliton pulses, a single-channel periodically stationary dispersion-managed soliton system, and chirped return to zero systems with single and multiple channels. We introduce a globally third-order accurate split-step scheme, in which a bound on the local error is used to select the step size. In many cases, this method is the most efficient when compared with commonly used step-size selection criteria, and it is robust for a wide range of systems providing a system-independent rule for choosing the step sizes. We find that a step-size selection method based on limiting the nonlinear phase rotation of each step is not efficient for many optical-fiber transmission systems, although it works well for solitons. We also tested a method that uses a logarithmic step-size distribution to bound the amount of spurious four-wave mixing. This method is as efficient as other second-order schemes in the single-channel dispersion-managed soliton system, while it is not efficient in other cases including multichannel simulations. We find that in most cases, the simple approach in which the step size is held constant is the least efficient of all the methods. Finally, we implemented a method in which the step size is inversely proportional to the largest group velocity difference between channels. This scheme performs best in multichannel optical communications systems for the values of accuracy typically required in most transmission simulations.

Optical switching: switch fabrics, techniques, and architectures

Abstract: The switching speeds of electronics cannot keep up with the transmission capacity offered by optics. All-optical switch fabrics play a central role in the effort to migrate the switching functions to the optical layer. Optical packet switching provides an almost arbitrary fine granularity but faces significant challenges in the processing and buffering of bits at high speeds. Generalized multiprotocol label switching seeks to eliminate the asynchronous transfer mode and synchronous optical network layers, thus implementing Internet protocol over wavelength-division multiplexing. Optical burst switching attempts to minimize the need for processing and buffering by aggregating flows of data packets into bursts. In this paper, we present an extensive overview of the current technologies and techniques concerning optical switching.

Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations

Abstract: Ultra-wide-band analog-to-digital (A/D) conversion is one of the most critical problems faced in communication, instrumentation, and radar systems. This paper presents a comprehensive analysis of the recently proposed time-stretched A/D converter. By reducing the signal bandwidth prior to digitization, this technique offers revolutionary enhancements in the performance of electronic converters. The paper starts with a fundamental-physics analysis of the time-wavelength transformation and the implication of time dilation on the signal-to-noise ratio. A detailed mathematical description of the time-stretch process is then constructed. It elucidates the influence of linear and nonlinear optical dispersion on the fidelity of the electrical signal. Design issues of a single-sideband time-stretch system, as they relate to broad-band operation, are examined. Problems arising from the nonuniform optical power spectral density are explained, and two methods for overcoming them are described. As proof of the concept, 120 GSa/s real-time digitization of a 20-GHz signal is demonstrated. Finally, design issues and performance features of a continuous-time time-stretch system are discussed.

Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO/sub 2/ laser pulses

Abstract: In this paper, we report a novel long-period fiber grating (LPFG) fabricated by using a new writing technique that is mainly based on the thermal shock effect of focused high-frequency CO/sub 2/ laser pulses at several kilohertz. A number of unique characteristics of such a LPFG, such as bend, torsion, and transverse load, are observed by experiments, for the first time, to our knowledge. Based on these unique features, a novel bend-insensitive LPFG sensor that could solve the problem of cross-sensitivity between bend and other measurands, a novel torsion sensor that can realize absolute measurement of twist rate, and a load sensor that can achieve simultaneous measurement of transverse load and temperature using a single LPFG element are proposed and demonstrated. These unique features of the LPFGs are mainly due to the asymmetrical distribution of the refractive index on the cross section of the LPFG induced by high-frequency CO/sub 2/ laser pulses.

A unified study of contention-resolution schemes in optical packet-switched networks

Abstract: This paper presents a comprehensive study of contention-resolution schemes in a multiwavelength optical packet-switched network. This investigation aims to provide a unified study of a network of optical routers, which include contention resolution in wavelength, time, and space dimensions. Specifically, we show: 1) how to accommodate all three dimensions of contention resolution in an integrated optical router; 2) how the performance of the three dimensions compare with one another; and 3) how various combinational schemes can be designed and how they perform. With the representative architectures and network topologies studied in this paper, the simulation experiment results capture the characteristics of different contention-resolution schemes, and they quantify the upper-bound average offered transmitter load for these schemes. The combinational contention resolution schemes are shown to effectively resolve packet contention and achieve good network performance under light to intermediate load.

Optical packet switching and buffering by using all-optical signal processing methods

Abstract: We present a 1 /spl times/ 2 all-optical packet switch. All the processing of the header information is carried out in the optical domain. The optical headers are recognized by employing the two-pulse correlation principle in a semiconductor laser amplifier in loop optical mirror (SLALOM) configuration. The processed header information is stored in an optical flip-flop memory that is based on a symmetric configuration of two coupled lasers. The optical flip-flop memory drives a wavelength routing switch that is based on cross-gain modulation in a semiconductor optical amplifier. We also present an alternative optical packet routing concept that can be used for all-optical buffering of data packets. In this case, an optical threshold function that is based on a asymmetric configuration of two coupled lasers is used to drive a wavelength routing switch. Experimental results are presented for both the 1 /spl times/ 2 optical packet switch and the optical buffer switch.

Optical intensity modulators for digital and analog applications

Abstract: This tutorial describes the basic principles and performance analysis of optical intensity modulators using electrooptic and electroabsorption effects, for use in analog and digital communication systems. These include lithium niobate modulators, semiconductor electroabsorption modulators, semiconductor Mach-Zehnder modulators, and polymer modulators.

Optical regeneration at 40 Gb/s and beyond

Abstract: As optical amplifiers have opened new perspectives for optical communication systems with ultrahigh capacities and long-haul transmission distances (more than 1 Tb/s over 10 000 km), fundamental limits are being felt. In order to overcome these propagation impairments, another technology revolution is soon required. Promising developments concern in-line all-optical regeneration, which makes it possible to transmit optical data over virtually unlimited distances. In this paper, we recall the basic principles of optical regeneration in optical communication systems and review the current technology alternatives foreseen for future 40-Gb/s transmission system implementation, as investigated in Alcatel Research and Innovation. The alternative offered by optoelectronic regeneration is also discussed, so as to identify and highlight the advantages of the all-optical approach.

Fast optical wavelength interrogator employing arrayed waveguide grating for distributed fiber Bragg grating sensors

Abstract: A new type of interrogator for distributed fiber Bragg grating (FBG) sensors that employs an arrayed waveguide grating (AWG) is proposed and its operating features are in detail investigated both theoretically and experimentally. The remedy for achieving the linear characteristics of wavelength detection as well as for insuring the reliable and environmentally stable operation of interrogation is proposed and its usefulness is demonstrated in good agreement with the experimental results. The developed interrogator consists of a fully passive, small, all-solid, rugged optical IC and can detect wavelengths of a great number of FBG sensors with high precision better than 0.5 pm and high speed.

120-GHz wireless link using photonic techniques for generation, modulation, and emission of millimeter-wave signals

Abstract: We present a wireless link system that uses millimeter-wave (MMW) photonic techniques. The photonic transmitter in the wireless link consists of an optical 120-GHz MMW generator, an optical modulator, and a high-power photonic MMW emitter. A uni-traveling carrier photodiode (UTC-PD) was used as the photonic emitter in order to eliminate electronic MMW amplifiers. We evaluated the dependence of UTC-PD output power on its transit-time limited bandwidth and its CR-time constant limited bandwidth, and employed a UTC-PD with the highest output power for the photonic emitter. As for the MMW generation, we developed a 120-GHz optical MMW generator that generates a pulse train and one that generates a sinusoidal signal. The UTC-PD output power generated by a narrow pulse train was higher than that generated by sinusoidal signals under the same average optical power condition, which contributes to reducing the photocurrent of the photonic emitter. We have experimentally demonstrated that the photonic transmitter can transmit data at up to 3.0 Gb/s. The wireless link using the photonic transmitter can be applied to optical gigabit Ethernet signals.

Fabrication and characterization of photonic devices directly written in glass using femtosecond laser pulses

Abstract: Both straight and curved waveguides are written in a variety of silicate glasses using near-IR femtosecond laser pulses. Writing parameters are identified that produce waveguides that support only a single mode and yield smooth-mode profiles. The laser pulse-induced refractive index change is reconstructed from near-field mode profile data using the scalar wave equation and by refractive near-field profiling. Waveguide propagation losses are determined by throughput and Fabry-Perot resonator measurements. Both coarse and fine period gratings are written and characterized, and the thermal stability of these gratings is investigated. The utility of the femtosecond writing technique is demonstrated by fabricating an optical interleaver.

Electrooptic modulation of silicon-on-insulator submicrometer-size waveguide devices

Abstract: In this paper, we propose and analyze an electrically modulated silicon-on-insulator (SOI) submicrometer-size high-index-contrast waveguide. The geometry of the waveguide provides high lateral optical confinement and defines a lateral p-i-n diode. The electrooptic structure is electrically and optically modeled. The effect of the waveguide geometry on the device performance is studied. Our calculations indicate that this scheme can be used to implement submicrometer high-index-contrast waveguide active devices on SOI. As an example of application, a one-dimensional microcavity intensity modulator is predicted to exhibit a modulation depth as high as 80% by employing a dc power consumption as low as 14 /spl mu/W.

Optical satellite networks

Abstract: With high-speed space optical crosslink being a reality, the construction of an optical satellite network as part of a larger integrated space-terrestrial network is now feasible. This paper explores the architecture implications of the invention of such a radical technology building block. Not only can the satellite network performance and cost undergo quantum-leap improvements but also such a network can have profound transforming effects on space system architectures and data network user applications.

Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor

Abstract: We present a detailed discussion of the three-interface surface plasmon resonance (SPR) geometry with the "angular interrogation" approach, and study the effect of thermal changes on the SPR curve through numerical simulations. An optical temperature sensor based on SPR, which has been shown to be a promising method to be used in the development of chemical, physical, and biomedical sensors, is proposed. The temperature sensor employs a three-interface SPR geometry where the layer making the interface with the environment has a refractive index highly sensitive to the changes in the temperature of the environment. The resolution of the temperature measurement is dependent on the angular resolution of the detection system and the temperature sensitivity of the sensing layer. The comparison of thermal sensitivities of three and two-interface SPR geometries is also presented.

Beam steering in planar-photonic crystals: from superprism to supercollimator

Abstract: We utilize the anomalous dispersion of planar-photonic crystals (PhCs) near the dielectric band edge to control the wavelength-dependent propagation of light. Light beams with up to 20/spl deg/ divergence were collimated over a 25-nm (1285 nm to 1310 nm) bandwidth using a triangular lattice. The "superprism" phenomenon is demonstrated in the same configuration, simply by tuning the wavelength. Sources of loss are discussed. Both the plane-wave expansion calculation and finite-difference time-domain simulation match well with the experimental results. This is the first experimental demonstration of self-collimating phenomena in a PhC configuration.

High-speed electrooptic modulator characterization using optical spectrum analysis

Abstract: This paper presents our latest studies on high-speed electrooptic modulator characterization using the optical spectrum analysis method. Several new characterization techniques are theoretically analyzed and experimentally demonstrated for the measurement of critical device parameters at very high modulation frequencies. Applying this method in our wide-band electrooptic (EO) modulator characterization experiment, we have successfully measured halfwave voltages, frequency responses, and the chirp parameter at frequencies over 10 GHz for several typical high-speed LiNbO/sub 3/ modulators. Our experiment showed that the optical spectrum analysis provides an accurate and convenient platform for ultra-high-speed EO modulator characterization.

Provisioning of survivable multicast sessions against single link failures in optical WDM mesh networks

Abstract: In this paper, we investigate approaches and algorithms for establishing a multicast session in a mesh network while protecting the session against any single link failure, e.g., a fiber cut in an optical network. First, we study these approaches and algorithms to protect a single multicast tree in a mesh network and then extend it to dynamically provision survivable multicast connections (where connections come and go) in an optical wavelength-division multiplexing (WDM) network. We propose two new and efficient approaches for protecting a multicast session: 1) segment protection in which we protect each segment in the primary tree separately (rather than the entire tree) and allow these backup segments to share edges with the other existing primary and backup segments and 2) the path-pair protection in which we find a path-pair (disjoint primary and backup paths) to each destination and allow a new path pair to share edges with already-found path pairs. Unlike previous schemes, such as finding link-disjoint trees and arc-disjoint trees, our new schemes 1) guarantee a solution where previous schemes fail and 2) find an efficient solution requiring less network resources. We study these approaches and algorithms systematically, starting with the existing approaches such as fully link-disjoint and arc-disjoint trees and then presenting our new and efficient proposed approaches, such as segment-disjoint and path-disjoint schemes for protecting multicast connections. Our most efficient algorithm, based on the path-pair protection scheme, called optimal path-pair-based shared disjoint paths (OPP-SDP) algorithm, finds a solution if such a solution exists and outperforms all the other schemes in terms of network cost. We also show that OPP-SDP performs close to the optimal solution obtained by solving a mathematical formulation of the problem expressed as an integer linear program. Building upon the study on protecting a single tree, we perform simulations, employing the above protection schemes, to study dynamic provisioning of survivable multicast sessions (where sessions come and go) in a WDM mesh network. Our simulations show that the most efficient scheme, OPP-SDP, has minimum blocking probability.

Modeling and simulation of next-generation multimode fiber links

Abstract: This paper describes an advanced multimode-fiber-link model that was used to aid the development of Telecommunication Industry Association standard specifications for a next-generation 50-/spl mu/m-core laser-optimized multimode fiber. The multimode-link model takes into account the interactions of the laser, the transmitter optical subassembly, and the fiber, as well as effects of connections and the receiver preamplifier. We present models for each of these components. Based on these models, we also develop an efficient and simple formalism for the calculation of the fiber transfer function and the signal at the link output in any link configuration. We demonstrate how the model may be used to develop specifications on transmitters and fibers that guarantee any desired level of performance.

Wavelength channel data rewrite using saturated SOA modulator for WDM networks with centralized light sources

Abstract: This paper describes a method for realizing the efficient utilization of wavelength resources in wavelength-division multiplexing networks with centralized light sources. Using a deeply saturated semiconductor optical amplifier (SOA) modulator located in a remote node (RN), we erase the data on a downstream signal with a low extinction ratio and modulate it with new data to generate an upstream signal. Thus, we use only one wavelength for bidirectional transmission between a center node and an RN, without placing lasers at the RN. In this paper, we analyze the data suppression characteristic of the SOA using a large signal model. We also estimate the bit error rate degradation in the presence of an unsuppressed downstream bit pattern in an upstream signal. We then report experimental results that confirm the basic characteristics of the wavelength channel data rewriter, which we constructed using a linear amplifier and an SOA. Finally, we provide the results of a data transmission experiment that we undertook using the data rewriter.

A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise

Abstract: We have compared experimentally the transmission performance of return-to-zero differential phase-shift keying (RZ-DPSK) with RZ-ON-OFF keying (OOK), nonreturn-to-zero differential phase-shift keying (NRZ-DPSK), and NRZ-OOK for 100/spl times/10-Gb/s transmission with a spectral efficiency of 0.22 b/s/Hz over transoceanic distances. The Q degradation of the RZ-DPSK after transmission over 9180 km was 3 dB greater than that of RZ-OOK. The experimental results clearly showed the major cause of degradation for DPSK is not cross-phase modulation but self-phase modulation. The calculated nonlinear phase noise, i.e., the Gordon-Mollenauer effect, agreed with the experimental results. A distributed-Raman-amplifier assisted erbium-doped-fiber-amplified transmission line acted well in reducing the nonlinear phase noise.

Low-power-consumption short-length and high-modulation-depth silicon electrooptic modulator

Abstract: We propose and analyze a novel compact electrooptic modulator on a silicon-on-insulator (SOI) rib waveguide. The device confines both optical field and charge carriers in a micron-size region. The optical field is confined by using a planar Fabry-Perot microcavity with deep Si/SiO/sub 2/ Bragg reflectors. Carriers are laterally confined in the cavity region by employing deep-etched trenches. The refractive index of the cavity is varied by using the free-carrier dispersion effect produced by a p-i-n diode. The device has been designed and analyzed using electrical and optical simulations. Our calculations predict, for a 20-/spl mu/m-long device, a modulation depth of around 80% and a transmittance of 86% at an operating wavelength of 1.55 /spl mu/m by using an electrical power under dc conditions on the order of 25 /spl mu/W.

Two-photon laser precision microfabrication and its applications to micro-nano devices and systems

Abstract: Two-photon absorption (TPA) provides the ability to confine photochemical and physical reactions to the order of laser wavelength in three dimensions. For applying TPA to laser precision microfabrication, we proposed a two-photon photopolymerization technique, by which photonic crystals and various micromachines with near-diffraction-limit features have been produced. Here we show that the diffraction limit was exceeded by utilizing nonlinear laser-matter interaction processes, and spatial resolutions far smaller than the diffraction limit were achieved. The super resolution, combined with other technologies newly developed by us including three-dimensional imaging of voxels, rapid surface profile scanning, device functionalization and its mechanical driving with a laser trapping force, and dye-doping polymerization for three-dimensional microdiagnosis, makes the technique quite compelling for nanophotonic and optical microelectromechanical (MEMS) applications.

Beam-steering micromirrors for large optical cross-connects

Abstract: This paper describes Si-micromachined two-axis beam-steering micromirrors and their performance in 256 /spl times/ 256- and 1024 /spl times/ 1024-port large optical cross-connects (OXCs). The high-reflectivity wavelength-independent mirrors are electrostatically actuated; capable of large, continuous, controlled, dc tilt in any direction at moderate actuation voltages; and allow setting times of a few milliseconds. Packaged two-dimensional (2-D) arrays containing independently addressable identical 256 and 1296 mirrors are used to build fully functional bitrate and wavelength-independent single-stage, low-insertion-loss, single-mode fiber OXC fabrics.

Optical carrier supply module using flattened optical multicarrier generation based on sinusoidal amplitude and phase hybrid modulation

Abstract: This paper presents an optical carrier supply module (OCSM) that functions as a common multicarrier light source, a wavelength bank, for superdense wavelength-division multiplexing (SD-WDM) networks that utilize a large number of wavelengths with narrow channel spacing. A novel sideband generator based on a sinusoidal amplitude-phase hybrid modulation scheme is the key technique. The sideband generator generates nine flattened optical sidebands within 3 dB from one seed light source, and the input from wavelength-division multiplexing (WDM) seed carriers expands the number of generated sidebands. Scalability against the number of wavelengths is achieved by increasing the number of seed carriers used. The SD-WDM system employing OCSM reduces the number of laser diodes (LDs) and attendant wavelength monitoring/stabilization circuits. Multiple distributions to SD-WDM networks by splitting the OCSM output can promote this effect. We designed OCSM and experimentally investigated its performance pertaining to the electrical signal-to-noise ratio (SNR) of the OCSM output. The experimental results show the wavelength scalability to 1000 channels. We also developed an OCSM prototype that generated 12.5-GHz-spaced 256-channel WDM carriers. All the generated carriers exhibit the electrical SNR of more than 31.5 dB at 2.5 Gb/s and the power flatness of within 3 dB. The distribution over 100 SD-WDM networks is experimentally confirmed.

Optical switch fabrics for ultra-high-capacity IP routers

Abstract: Next-generation switches and routers may rely on optical switch fabrics to overcome scalability problems that arise in sizing traditional electrical backplanes into the terabit regime. In this paper, we present and discuss several optical switch fabric technologies. We describe a promising approach based on arrayed waveguide gratings and fast wavelength tuning and explain the challenges with respect to technical and commercial viability. Finally, we demonstrate an optical switch fabric capable of 1.2-Tb/s throughput and show packet switching with four ports running at 40 Gb/s each.

Analog laser predistortion for multiservice radio-over-fiber systems

Abstract: We have developed some low-cost predistortion circuits to compensate second- and third-order laser distortions in multiservice radio-over-fiber industrial systems. Depending on the predistorter configuration implemented, average reductions of 10-15 dB and of 8-10 dB have been observed in the laser second- and third-order distortions, respectively, within the cellular bands relevant to the European TETRA, GSM, and DCS standards. In particular, the development of the prototypes here illustrated is based on a new and original procedure that formalizes and suitably integrates in a sinergistic way modeling, design, and experimental activities.

Transmission characteristics of long-period fiber gratings having arbitrary azimuthal/radial refractive index variations

Abstract: A numerical method is presented for determining the transmittance of long-period (LP) fiber-gratings having arbitrary azimuthal/radial refractive index variations. The method uses coupled-mode theory and includes both the sine and cosine character of the LP modes. The model treats interactions between the fundamental LP/sub 01/ mode and high-azimuthal-order cladding modes. The method utilizes the transfer matrix method to model cylindrical layers both in the core and the cladding regions.

Ultra-wide-band tellurite-based fiber Raman amplifier

Abstract: We describe the first wide-band tellurite-based fiber Raman amplifier (T-FRA) for application to seamless ultra-large-capacity dense wavelength-division multiplexing (WDM) systems. First, we confirmed that the Raman scattering characteristics of the tellurite-based fiber has so large a gain coefficient and Stokes shift that we can achieve a wide-band tellurite-based fiber Raman amplifier with a shorter fiber length than when using silica-based fiber. Second, we investigated the small signal gain and the signal transmission characteristics for a high gain and high output power operation with a single-stage amplifier. Focusing on double Rayleigh scattering, we compared the high gain limit of tellurite- and silica-based fibers. We then studied the impact of nonlinear effects by measuring the bit error rate (BER) when using a two-stage amplifier with a high output power of 18.8 dBm in which we simultaneously amplified eight channel signals in the L-band located on the ITU 100-GHz grid. Finally, we designed a wide-band tellurite-based fiber Raman amplifier with a multiwavelength band pumping scheme. We constructed this amplifier with a tellurite-based fiber only 250 m in length pumped by four-wavelength-channel laser diodes, and it provided a 160-nm bandwidth with a gain of over 10 dB and a noise figure below 10 dB from 1490 to 1650 nm. We also measured the BER to confirm the transmission characteristics of the amplifier for single channel operation over the whole signal wavelength range of 160 nm. We thus confirmed that the amplifier could be employed in ultra-high-capacity WDM systems.

Trap avoidance and protection schemes in networks with shared risk link groups

Abstract: Shared risk link group (SRLG) has been widely recognized as an important concept in survivable optical networks. However, there are still several SRLG-related problems of both theoretical interest and practical importance that have not been explored fully. Specifically, there are two major issues that are still open: avoiding failures in path determination caused by "traps" and maximizing bandwidth sharing. These issues are more challenging when considering shared path protection in networks with SRLGs. In this paper, we address the above two open issues, starting with a heuristic approach to avoiding traps. In networks with SRLGs, a simple heuristic may run into traps up to 30% of the time. Integer linear programming (ILP)-based approaches, on the other hand, are not feasible for large SRLG networks. One of the widely used heuristics for trap avoidance is based on K shortest paths (KSP). As an alternative to KSP, we propose an innovative trap avoidance (TA) heuristic that requires much less running time than KSP (and ILP) and yet can effectively avoid almost all the avoidable traps as an ILP-based approach. We also propose an efficient shared SRLG protection scheme based on TA that can achieve a bandwidth efficiency that is nearly as high as other schemes based on ILP or KSP.