Theory for optimum design and analysis of distributed-feedback lasers

In this paper, we present the theoretical investigation of index-coupled distributed feedback (DFB) laser with tilted single mode ridge waveguides. By tilting part of the ridge waveguide in various degrees, DFB laser with manifold effective grating periods can be realized. The structure is analyzed using couple mode theory in matrix form based on threshold analysis. Important parameters of DFB laser like resonant frequency and threshold gains are obtained by solving the eigen-equation. The results indicate not only that the lasing frequency is modulated by the waveguide titling angle, but also large Gain Margin (GM) can be achieved at the threshold condition which enhance the stable single mode operation in index-coupled DFB laser.

External optical feedback sensitivity in distributed feedback (DFB) semiconductor lasers is analyzed in this paper with special attention to phase-shifted and complex-coupled lasers. The effects of variations of structural parameters such as index and/or gain coupling strengths, facet reflectivities, and corrugation phase angles on external optical feedback sensitivity are studied. Quarter-wave-shifted index-coupled DFB lasers exhibit low external optical feedback sensitivity for large index coupling coefficients and high facet reflectivities. Pure gain-coupled DFB lasers perform better than the uniform index-coupled DFB lasers without any phase-shifting structure but worse than /spl lambda//4 phase-shifted index-coupled lasers with high coupling strengths. External optical feedback sensitivity of complex-coupled lasers is a sensitive function of the structural parameters and varies significantly with the index-to-gain coupling ratio and the total coupling. Presence of a small amount of index coupling relative to the gain coupling in a gain-coupled laser improves the external optical feedback sensitivity.

Mirrorless, distributed-feedback (DFB) laser action has previously been demonstrated in high gain media such as dyes and color center lasers. The feedback mechanism, which is associated with spatial modulation of the gain and refractive index, results in narrow linewidth oscillation within the DFB laser structure. In this paper, we describe DFB laser action in Ce:doped LiCAF and LiSAF gain media for the first time. Laser action for both hosts occurs near 290 nm.

The dynamic linewidth enhancement factor, (alpha) , and damping rate, (Gamma) , for distributed feedback (DFB) lasers are obtained at various bias levels by measuring the frequency modulation and amplitude modulation indices of the lasers simultaneously. The (alpha) -value of a DFB lasers is generally reduced with increasing output power except at low bias, and the (Gamma) -value typically increases with output power. The measured results show that ninety percent of the 1.3-micrometers capped-mesa buried heterostructure DFB lasers have (alpha) -values in the range 4 to 7 and (Gamma) -values below 4 X 10<SUP>10</SUP> s<SUP>-1</SUP>. The 1.3-micrometers lasers have smaller damping rates than the 1.5- micrometers lasers of the same DFB laser structure. Compared with buried heterostructure DFB lasers, multiquantum well (MQW) DFB lasers exhibit a much smaller (alpha) -value and a larger damping rate. For both unstrained and strained 1.5-micrometers MQW-DFB lasers, (alpha) -values as low as 1.5 can be easily realized for these lasers at high output power (&gt;= 10 mW).

In this paper we present an experimental analysis of the effect of RF modulation injection current in DFB and FP lasers nearthe first period doubling bifurcation (PDB). By increasing the amplitude of the modulation frequency at the onset of PDB thefirst results of a virtual Hopf phenomenon like behavior has been observed in both types of lasers. We characterized thisobservation by increasing the amplitude of the current modulation where two peaks appear in the spectrum, approaching oneto the other until fmally merging the onset of period doubling bifurcation as predicted by theory. The same virtual Hopfbehavior was observed when we set the amplitude modulation at a fixed value and we sweep the frequency modulation at theonset of the PDB point.Keywords: Laser Diode, Nonlinear Dynamics, Period Doubling Bifurcations. 1. INTRODUCTION Nonlinear dynamics in diode lasers has been the subject of many theoretical and experimental investigations in the lastdecade as they show a rich variety of irregular behavior in their route to chaos1. A single frequency diode laser is commonlystudied by a rate equation model which describes the time evolution of the photon and carrier densities. In these equations,the inclusion of an additional degree of freedom as modulation of the injection current, external light injection or opticalfeedback is needed for nonlinear dynamics to appear2.To our knowledge, the nonlinear behavior in semiconductor diode lasers has been extensively studied by many authors usingdelayed optical feedback and strong current modulation. In the former, the observed route to chaos was through successivesubharmonic bifurcations or by quasi periodic route3'4. In the strong current modulation case the period sequence wastruncated by period tripling before the onset of chaos5'6.On the other hand, the onset of a period doubling bifurcation point in many physical systems brings to nonlinear phenomenasuch as: 1) small signal amplification, 2) shift and suppression of the bifurcation point and 3) the emergence of a closelyspaced set of peaks in the frequency response7.In semiconductor lasers the parametric amplification was observed by Harth and co-workers8'9 which was analyzed byWiesenfeld few years after'°. In the study developed by Wiesenfeld in ref. 10, semiconductor lasers were proposed as goodcandidate to study the rich variety of nonlinear phenomena near period doubling bifurcations. A recent study has shown thatthe effect of Langevin noise in period doubling semiconductor lasers has a virtual Hopf ur12 previously predicted byWiesenfeld'34 as a virtual Hopf phenomenon in systems undergoing a period doubling bifurcations in the presence ofexternal noise.In the present study we have experimentally investigated the nonlinear dynamics of diode lasers in the period doublingbifurcation point. We study the influence of the amplitude modulation in Distributed Feedback (DFB) lasers near perioddoubling bifurcations. In Fabry-Perot (FP) lasers we performed as well the same study as DFB lasers and the analysis of thefrequency modulation near period doubling bifurcation. So in section II we described the experimental procedure for theonset of the first period doubling bifurcation performed in commercial DFB and FP InGaAsP diode lasers at 1,3 tm emission

591-Mb/s noncoherent FSK 2/sup 23/-1 PRBS transmission experiments using two different commercial standard DFB (distributed feedback) lasers and a phase-tunable DFB laser have been carried out. The commercial DFB lasers are modulated with an AMI (alternated mark inversion) code and the phase-tunable DFB laser with a NRZ (nonreturn to zero) code. With an optical filter bandwidth of 2.7 GHz, receiver sensitivities (for a 10/sup -10/ BER) of -38 dBm for the phase-tunable DFB laser and -36 dBm for both standard DFB lasers are achieved. The influence of optical filter bandwidth and modulation index on the BER is also evaluated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A statistical yield analysis is presented for gain- and index-coupled distributed feedback (DFB) laser structures, allowing a comparison of their single longitudinal mode (SLM) yield capabilities. For the yield calculations, the threshold gain difference and the longitudinal spatial hole burning (SHB) are taken into account. By comparing the experimental and theoretical yield of index-coupled DFB lasers, the significance of SHB for correct yield predictions is illustrated. For the purpose of comparison, yield calculations for various lambda /4-shifted DFB lasers (with low facet reflectivities) are presented. The most emphasis, however, is on partly gain-coupled DFB lasers. Estimations of practical gain coupling coefficient values for gain and for loss gratings are discussed. >

A great improvement in the high-speed characteristics for compressively strained multi-quantum-well (MQW) distributed-feedback (DFB) lasers with self-aligned constricted mesa structures is described. Negative wavelength detuning is an important factor in making possible the extraction of potential advantages for the compressively strained MQW DFB lasers. A 17-GHz bandwidth, which is the highest among the 1.5- mu m MQW DFB lasers, is demonstrated. A wavelength chirp width of 0.42 nm at 10 Gb/s is obtained due to a reduced linewidth enhancement factor that has a magnitude of less than 2. Nonlinear damping K factor in a DFB laser with 45-nm negative detuning has drastically decreased to 0.13 ns, about half of that for unstrained MQW lasers. This is mainly due to an enhanced differential gain as large as 6.9*10/sup -12/ m/sup 3//s. The estimated intrinsic maximum bandwidth is 68 GHz. >

Single longitudinal mode (SLM) lasers are important tools for many scientific and commercial applications. SLM operation can be achieved in distributed-feedback (DFB) lasers based on Bragg structures. Semiconductor waveguide DFB lasers are well-established devices, but their output power is limited to a few hundred milliwatts. DFB lasers have also been demonstrated in dielectric waveguides. However, in this case the output power was even lower. Here we present the first monolithic Yb:YAG DFB laser. The waveguide and the DFB structure were fabricated in the volume of an Yb:YAG crystal by ultrafast laser inscription. The DFB laser delivered 2W of output power at a slope efficiency of 61% in SLM operation under pumping with an optically pumped semiconductor laser. This power level outperforms previously demonstrated dielectric DFB waveguide lasers by nearly an order of magnitude. Our approach paves the way for compact, robust, and highly efficient high-power SLM laser sources.

We report on high-power operation of a fiber distributed-feedback (DFB) laser fabricated from Tm-doped photosensitive alumino-silicate fiber and in-band pumped by an Er/Yb fiber laser at 1565 nm. The fiber DFB laser yielded up to 875 mW of single-ended output at 1943 nm on two orthogonally polarized modes for 3.5 W of absorbed pump power. Further scaling of the DFB laser output power was achieved with the aid of a simple Tm-doped fiber amplifier stage spliced directly to the DFB fiber without the need of an optical isolator. The maximum output power from the DFB laser and fiber amplifier was >3 W for a combined absorbed pump power of 8.1 W. The influence of thermal loading, owing to quantum defect heating in the Tm-doped core, on the output power and longitudinal mode behavior is discussed, and the prospects for further improvement in performance are considered.

Distributed feedback (DFB) lasers are used extensively as optical sources within fiber optic telecommunications systems. These semiconductor lasers are valued for their single optical mode operation which enables their use in high bit rate digital and broadband analog transmission systems. We discuss requirements imposed upon DFB lasers used in such applications. We briefly review and illustrate general techniques for modeling DFB laser operation by comparison of measured and modeled device characteristics below and above lasing threshold. We focus on the phenomenon of spatial hole burning which substantially affects operation of all DFB lasers, especially those tailored to produce high fiber coupled power from a single mirror facet. We illustrate insights gained by measurement and modeling of DFB lasers using as an example the particular case of analog transmission of multichannel video signals.

The effects of radiation mode on the oscillating properties of distributed feedback (DFB) lasers with second-order corrugations are analyzed for designing a new type of DFB laser. A formulation based on the transfer matrix technique is applied to calculating Streifer's /spl zeta/-terms added to the coupled-wave equations. These terms represent the effects of radiation and evanescent modes. This formulation greatly simplifies the analysis of distributed resonance along multilayered waveguide structures with arbitrary-shaped second-order corrugations. The effects of vertical resonance are also incorporated into the formulation. Various types of DFB lasers with phase-shifted second-order corrugations are analyzed using this method. It is found that the phase shift and the blaze of the corrugations greatly affect the longitudinal mode selectivity. A new phase-shift DFB laser structure with two complementary blazing regions connected at the shift is proposed. It is demonstrated that this structure has small radiation loss resulting in low-threshold performance despite employing second-order corrugations.

An analytic expression for the linewidth of distributed-feedback (DFB) lasers is derived. Local fluctuations in carrier density are shown to provide a significant contribution to laser linewidth in the presence of spatial holeburning. In a single-electrode DFB laser the effect can be avoided by careful optimization of the kl-product, but for a multielectrode DFB laser the linewidth can also be reduced by adjusting the injected current profile to compensate for spatial holeburning. Numerical results for a three-electrode lambda /4-shifted DFB laser are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We report high slope efficiency and low noise characteristics in a distributed feedback (DFB) laser lasing at 1.3 /spl mu/m with narrow beam divergence by employment of a laterally tapered active stripe over the whole cavity. This tapered structure is designed to realize narrow beam divergence, low threshold current, and high longitudinal mode selectivity. The fabricated tapered-active-stripe DFB lasers demonstrated of 9.20/spl times/13.40 and a record slope efficiency, for a narrow beam DFB laser, of 0.59 mW/mA. The temperature characteristics from -10/spl deg/C to 85/spl deg/C shows high output power at high temperature, stable single longitudinal mode oscillation and stable far-field patterns. Furthermore, for the first time ever, a low relative intensity noise characteristic of under -155 dB/Hz has been realized when butt-coupling into a single-mode fiber.

While low loss and large bandwidth have allowed optical fibers to become essential in a large amount of telecommunication systems, this has not yet been true for video distribution systems where the cost per subscriber must be as low as possible. First optical video distribution systems have been developped using 1.3 pm distributed-feedback (DFB) lasers. Up to now, the modulation format used in such systems is analog amplitude-modulation vestigial-sideband (AM-VSB) scheme since it provides direct compatibility with cable TV industry and present television sets. However, this modulation scheme requires a very high signal-to-noise ratio on the receiver side so that it is necessary to detect large optical powers (above -10 dBm) to ensure good picture quality. This means that the power budget (budget one can afford for optical fibers and splitters losses) for 1.3 im systems, even with powerful optical sources, is not very important; in turn, this means that it seems difficult to cut the cost per subscriber with this technology. With optical Erbium-Doped Fiber Amplifier (EDFA) breakthrough, many suppliers of cable TV transmission systems moved to 1.5 .tm technology. Whereas this new component is revolutionizing most of the telecommunication systems as optical fiber did 20 years ago, the use of optical amplifiers for analog systems is not so impressive as for robust digital transmission systems. This is due to the fragility of analog signal in respect with noise and distortion. Because of the noise generated by an optical amplifier, it is not possible to cascade a large number of them while reaching a realistic signalto-noise ratio at the network termination. Optical amplifiers may also distort the analog signal when the transmitter consists of a directly-modulated semiconductor laser, suffering from chirp (unwanted wavelength modulation when power modulation is achieved through current modulation). Moreover, shifting from 1 .3 .tm to 1 .5 pm wavelength brings new problems : 1 .5 tm DFB lasers are not yet as linear as 1.3 im DFB lasers and analog system designers have to cope with chromatic dispersion at 1 .5 .tm in standard fibers (i.e. non dispersion-shifted fibers). It is clear that many of the technical issues for 1.5 im analog systems are far from being resolved. In this paper, we investigate the way, and to what extent, erbium-doped fiber amplifiers may improve analog systems power budget. The organization of the paper is as follows. In Section 2, we discuss what is the relevant noise parameter for optical amplifiers to predict the signal-to-noise degradation they cause. We also show that the same overall noise performance can be reached with amplifiers featuring different noise parameter and output power combinations. This section is completed with experimental measurements. Linearity definitions and requirements for AM-VSB systems are presented in Section 3. Included is a discussion of some specific factors that degrade the signal linearity within an optical amplifier in respect with optical source characteristics. Finally, the still opened technical matters and potential evolution for 1.5 jim analog systems are briefly summarized in Section 4