1252 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 48, NO. 10, OCTOBER 2012 Dynamic Analysis of High-Order Laterally Coupled DFB Lasers Using Time-Domain Traveling-Wave Model Akram Akrout, Kais Dridi, and Trevor J. Hall, Member, IEEE Abstract— This paper describes the application of a time-domain modeling approach for a laterally coupled dis- tributed feedback (LC-DFB) semiconductor laser for the first time. We numerically study the effect of the radiation modes on LC-DFB laser properties. We integrate the Streifer’s coefficients, which represent the effects of radiation and evanescent modes into the time-domain coupled-wave equations. High-order corru- gated gratings with λ/4 phase-shift are analyzed, where the degree of longitudinal spatial hole burning can be effectively reduced by means of fine tuning of the grating duty cycle. Additionally, we show a remarkably enhanced side-mode suppression ratio (SMSR). For example, for the third-order gratings with a 50% duty cycle, an SMSR as high as 45 dB can be predicted. Index Terms— High-order gratings, laterally coupled distributed feedback (LC-DFB) lasers, longitudinal spatial hole burning, time-domain coupled-wave equations. I. I NTRODUCTION S EMICONDUCTOR distributed feedback (DFB) lasers use buried Bragg gratings to achieve selective optical feedback and, hence, to ensure single mode operation. Such struc- tures usually require at least two epitaxial-growth steps [1]. Regrowth leads to difficulties associated with complicate fab- rication, and ultimately increases the device cost. In laterally- coupled ridge waveguide DFB (LC-DFB) lasers, the gratings are lithographically patterned out of the ridge waveguide sidewalls on the top cladding layer [2], [3] - as shown in our designed laser cavity in Figure 1. The corrugated ridge waveguide induces index modulation, which interacts with the lateral optical fields (i.e. evanescent fields) to provide the optical feedback. Such design allows LC-DFB laser fabrication without any epitaxial regrowth as demanded in conventional DFB lasers and, hence, simplifies the fabrication process, increases the yield and, ultimately, reduces manufacturing cost [4], [5]. Moreover, the surface-gratings structure lends itself to monolithic integration with other optoelectronic devices [6]. Manuscript received March 12, 2012; revised June 8, 2012; accepted June 15, 2012. Date of publication June 28, 2012; date of current version July 30, 2012. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, the Canadian Institute for Photonic Innovation, the Ontario Centers of Excellence, the Canadian Foundation for Innovation, One Chip Photonics Inc., and CMC Microsystems. The authors are with the Center for Research in Photonics, University of Ottawa, Ottawa, ON K1N 6N5, Canada (e-mail: akramakrout0601@gmail.com; k.dridi@uottawa.ca; tjhall@uottawa.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2012.2206570 Using high order-gratings is more suitable from the manufacturing viewpoints. It results in relative ease of mass production with longer pitches, when compared to the first order devices, which offers more relaxed fabrication tolerances [7]. As one of the key design parameters in LC-DFB lasers is the coupling coefficient [8], [9], these devices require deep and finely-etched gratings to maintain acceptable performance whereas with higher orders a better degree of precision is achieved with standard lithographic techniques [10]–[13]. The frequency chirp and mode stability are considered to be the major parameters that reduce the performance of conventional DFB lasers. Considerable development work has been done on standard DFB lasers [14]–[16] and several models have shown - especially when high-order gratings are considered - that the longitudinal spatial hole burning (LSHB) have significant influence on the mode stability as well as the modulation response of devices [17]–[19]. However, for higher orders LC-DFB [20], [21] comparatively little design work exists; especially when considering the transient response of the laser. LC-DFB lasers with high-order gratings have been pre- viously analyzed using the modified coupled-mode (MCM) theory [22]. The MCM theory of Streifer [23] has been extended into two dimensions, taking into account the effect of both radiating partial waves and grating variation in the 2D transverse section [22]. However, this time-independent model did not take into consideration important key parameters such as the LSHB and the side-mode suppression ratio (SMSR). To the best of our knowledge, no time-domain modeling has been yet advanced for DFB lasers with laterally-corrugated gratings. The purpose of this paper is to study the effect of considering high-order grating on the transient performance of LC-DFB lasers. This paper is organized as follows: in section II, we present a relatively simple self-consistent dynamic model based on a direct solution of the time-dependent MCM equations. The model takes into account the spontaneous emission, the longitudinal variations of carrier density, photon distribution, the refractive index and radiating partial waves. In Section III, we present the effect of high order grating in LSHB versus the gratings duty cycles. The steady state spectra for high order grating versus duty cycle will be also discussed. Finally, conclusions are given in section IV. 0018–9197/$31.00 © 2012 IEEE