Hankel transform-domain analysis of scattered fields in multilayer planar waveguides and lasers with circular gratings

Radiation patterns of scattered fields with arbitrary azimuthal orders in multilayer planar waveguides and laser cavities with circularly symmetric gratings are formulated based on the volume current method. Full-wave Green's function analysis based on the integral transform method lies at the heart of this approach. Unlike the conventional approach, the dyadic Green's function relates some auxiliary fields to some auxiliary sources in the spectral domain. These auxiliary functions are defined to facilitate the spectral domain formulation in the cylindrical coordinate system and the use of transfer matrix method for obtaining a closed-form solution of the spectral Green's function in multilayer planar structures. More importantly, it is shown that the far-field pattern of the scattered field can be expressed directly in terms of the auxiliary fields in the Hankel transform domain.     

Amplified-spontaneous-emission spectrum of the radiation field in surface-emitting DFB lasers

In this paper, the authors calculate the amplified-spontaneous-emission spectrum of the radiation field in surface-emitting distributed feedback (DFB) lasers. The response of the laser cavity to the Langevin noise source in the frequency domain is obtained using the newly developed Green's functions for the slowly varying amplitudes of the guided waves. The authors show that the power spectra from the surface and the edge are different, and this discrepancy is due to excitation of the radiation field by the interference between the counter-propagating waves inside the cavity. This feature can be properly exploited in the design of surface-emitting DFB lasers for optical communications.     

Above-threshold analysis of second-order circular-grating DFBlasers

The behavior of second-order circular-grating DFB lasers in the above-threshold regime are analyzed. The formulation uses the standing wave method for treating lasers with second-order gratings. The effects of spontaneous emission and the variation of carrier and photon densities in the radial direction are included in a self-consistent fashion in the model. In particular, we examine the output power emitted from the surface of the laser, the near-field, and the far-field pattern of the laser as a function of the injected current     

Second- and higher order resonant gratings with gain or loss-PartII: designing complex-coupled DFB lasers with second-order gratings

For part I see, ibid., p. 1421, (2000). This paper deals with the investigation of second-order DFB lasers with a gain grating. It is shown that by proper choice of the duty cycle, one may take advantage of the different radiation losses between the mode with the lowest threshold gain and the second mode to increase the single-mode yield and also obtain a strong complex-coupling with high external efficiency. The impact of the random phase of high-reflection (HR)-coated facet on modal properties in an anti-reflection and HR combination is also investigated     

Generalized reaction and unrestricted variational formulation of cavity resonators. I. basic theory

Based on the reciprocity theorem, the reaction concept in electromagnetic theory is generalized to the cases where both surface electric and magnetic currents overlap across boundaries, i.e., neither the E-field, nor H-field meets the continuity conditions. An improved systematic method is then developed to obtain unrestricted variational expressions in a cavity resonator for which the tangential components of the trial fields can be discontinuous across its interior boundaries.     

Generalized reaction and unrestricted variational formulation of cavity resonators. II. Nonorthogonal and free-boundary mode-matching method

For pt. I see ibid., vol. 50, no. 11, p. 2480-90 (2002). This paper addresses a systematic method whereby the conventional mode-matching method is generalized to the cases where the set of modes used for the field expansion within a cavity resonator are relaxed to be orthogonal or satisfy any specific boundary conditions. It is shown that this approach is based on the unrestricted variational formulation of a cavity resonator. Reciprocity theorem and generalized reaction are the mathematical foundations of this new formulation. We have shown that the conventional mode-matching method is a special case of this generalized formulation and indeed is variational in nature. More precisely, we have proven that, if the field distribution obtained based on the conventional mode-matching method is used as a trial one in some variational formulas, the resonant frequency will be the same as the one obtained by the mode-matching method.     

Second- and higher-order resonant gratings with gain or loss-Part1: Green's function analysis

We describe a systematic method for obtaining the coupling coefficients due to diffraction orders less than the grating order of second- and higher order resonant complex gratings in a multilayer structure. This method is based on an improved Green's function, and its distinguishing feature is its use of the transfer matrix method to simplify the theoretical analysis for obtaining the Green's function in multilayer structures. More importantly, it is also shown that by introducing gain or loss in second- and higher order resonant gratings, the range of controlling the total coupling coefficient becomes wider than those in first-order complex gratings or second order index gratings. Concepts like in-phase and anti-phase gratings are generalized in this type of grating. Finally, guidelines for designing complex-coupled DFB lasers with second- and third-order grating are also presented     

Above-Threshold Spectrum of the Radiation Field in Surface-Emitting DFB Lasers

This paper addresses the above-threshold analysis of the amplified spontaneous emission spectrum of the radiation field in surface-emitting distributed feedback (DFB) lasers with a second-order grating. To the best of the authors' knowledge, this paper is the first report in this regard. The analysis takes advantage of the time- and frequency-domain approaches. The essence of this method is obtaining the spectrum of the laser power using the fields in the frequency domain, whereas the above-threshold carrier distribution inside the cavity is obtained by the finite-difference time-domain approach. The use of this approach can be justified by the fact that the wave equations in the time and frequency domains are related by the Fourier transform. Applying this method to the surface-emitting DFB lasers with a second-order grating, the authors will demonstrate that excitation of the radiation field by the interference between the counter-propagating waves inside the cavity provides additional filtering mechanism, which makes the side-mode suppression ratio of the power emitted from the surface different than that from the edge. More importantly, it is shown that the interesting features of a properly designed quarter-wave phase-shifted surface-emitting DFB lasers with a second-order grating can be exploited in the design of transmitters for optical communications     

A comparative study of higher order Bragg gratings: coupled-mode theory versus mode expansion modeling

The modal reflectivity and loss of lamellar diffraction gratings to be used in distributed-feedback and distributed-Bragg reflector lasers were computed in dependence of wavelength, duty cycle and Bragg order. Different methods based on the approximate coupled-mode theory and and the exact bidirectional mode expansion modeling were compared and a good mutual agreement was found. The slab Green's function needed to compute the coupling coefficients can be approximated by that of a homogeneous unbounded medium with sufficient accuracy.