Analysis of distributed feedback semiconductor lasers bytwo-dimensional theory

The two-dimensional theory of distributed feedback (DFB) lasers to take account of the planar waveguide structure which was presented in a previous paper (see ibid., vol.26, no.3, p.467-72, 1990) is applied to the analysis of the DFB laser threshold conditions with respect to the effects of the waveguide structure and the facet reflection. The asymmetric properties of the transverse functions of the coupled modes with respect to the Bragg frequency in the dispersion relations are found to be enhanced by the asymmetric index waveguide structure and by the asymmetric facet reflectivity. Therefore, the resulting confinement factor differences in the grating layer between the two adjacent lasing modes on both sides of the Bragg frequency give large threshold gain differences     

Analysis of TE/TM mode selectivity in DFB lasers with a phase-shift region

In phase-shift distributed feedback (DFB) lasers, there is limited suppression of the TM mode despite extremely large submode suppressibility. The TE/TM mode selectivity of a DFB laser structure with a nonuniform waveguide region as the phase shifter is analyzed. Calculations of the threshold gain difference between the TE and TM modes are performed using the effective index method and the coupled-wave theory. It is found that the TM mode suppressibility can be doubled by optimizing the dimensions of the phase-shift region. This structure overcomes the TM mode problem.<>     

TE- and TM-coupling coefficients in multiquantum well distributed feedback lasers

Transverse-electric (TE)- and transverse-magnetic (TM)-coupling coefficients for typical 1.55- mu m InGaAs/InP buried-heterostructure (BH) multiquantum-well (MQW) distributed-feedback (DFB) lasers are calculated as a function of waveguide and grating parameters using coupled-mode theory. It is shown that the TE- and TM-coupling coefficients become maximum at a certain number of wells; that number is smaller for TE modes than for TM modes, and increases as the BH stripe width decreases. The difference between the TE- and TM-coupling coefficients decreases as the number of wells increases. There exists a value of the thickness of the grating layer which maximizes the coupling coefficient.<>     

Two-dimensional theory of distributed feedback semiconductor lasers

A theory which takes account of the two dimensional waveguide structure of the distributed-feedback (DFB) laser is presented. Laser threshold conditions in the case of no external reflections are calculated for a three-layer model in which one cladding layer has a periodically changing dielectric constant. In contrast with the coupled-wave theory the threshold conditions are found to be asymmetric with respect to the Bragg frequency. The longitudinal mode which lies below and nearest the Bragg frequency has the lowest threshold gain. The difference between the threshold gains of the two adjacent longitudinal modes straddling the Bragg frequency has a maximum as a function of the coupled strength of the grating     

TM mode suppression property of DFB lasers with a narrow striperegion

The TM-mode suppressibility of DFB lasers with a narrow stripe region is investigated. A waveguide is designed to produce different phase shifts between the TE and TM modes. A threshold gain difference between the TE and TM modes is introduced by a phase shift difference of both modes. A TM and side mode suppression ratio of more than 40 dB is obtained under 1.8-Gb/s NRZ pseudorandom pulse modulation     

Gain margin analysis of distributed feedback lasers for bothtransverse electric and magnetic modes

A theoretical analysis of the gain margin with both transverse electric (TE) and transverse magnetic (TM) modes in distributed feedback (DFB) lasers of second-order gratings and various structural parameters is presented. Though the dominant mode is usually a TE mode, one of the TM modes often becomes the secondary mode with the second lowest threshold and seriously affects the single-mode characteristics of DFB lasers. To design DFB lasers with a large gain margin, proper amounts of facet reflectivity for both polarizations and control of the spatial phase of the grating at the facet are required     

Non-polarization and high-coupling-efficiency coupler using multilevel grating structure

A multilevel grating coupler based on silicon-on-insulator (SOI) material structure is proposed to realize the coupling between waveguide and waveguide or waveguide and fiber. This coupler is compatible with the current fabrication facilities for complementary metal oxide semiconductor (CMOS) technology with vertical coupling. This structure can realize coupling when the beams with transverse electric (TE) polarization and transverse magnetic (TM) polarization are incident at the same time. The influences of the grating coupler parameters including wavelength, the thickness of waveguide layer, the thickness of SiO₂ layer and the number of steps on the TE mode and TM mode coupling efficiencies are discussed. Theory researches and simulation results indicate that the wavelength range is from 1533 nm to 1580 nm when the TE mode and TM mode coupling efficiencies are both more than 40% as the grating period is 0.99 μm. The coupling efficiencies of the incident TE and TM modes are 49.9% and 49.5% at the wavelength of 1565 nm, respectively, and the difference between them is only 0.4%.     

Improved coupled mode analysis of corrugated waveguides and lasers--II: TM mode

In the previous paper [1] we proposed an accurate formalism for analyzing corrugated waveguide devices. This formalism, developed for the TE modes, is extended here to TM modes. Characteristics of TM modes in distributed feedback (DFB) lasers, DBR reflectors, and grating beam couplers are investigated with emphasis on the effect of the radiation loss and they are compared with the TE case.     

Deep-ridge distributed feedback waveguide for polarisationindependent all-optical switching

Structural birefringence in a deep-ridge distributed feedback (DFB) waveguide for polarisation independent all-optical switching is investigated. The coupling coefficient of the DFB structure is also polarisation independent between the TE and TM modes     

Circularly symmetric distributed feedback laser: coupled modetreatment of TE vector fields

The vector orientation of transverse electric (TE) fields in deriving coupled mode equations for radially outward- and inward-going modes in a circular waveguide diffraction grating is treated. The equations are derived for cylindrical waves in a system that is translationally invariant along the cylinder axis; the derivation is then extended to the waveguide geometry. The coupled mode equations are used to describe the operation of the circularly symmetric distributed feedback (DFB) laser. While predicting a similar dependence of the laser threshold gain on an azimuthal mode order to that found by a simpler, scalar-field treatment, the vector-field treatment predicts a fundamental difference in the location of the cavity resonances. The circular DFB laser is expected to lase in multiple azimuthal modes but maintain a relatively narrow overall spectral width     

Simplified coupled-wave equations for cylindrical waves in circulargrating planar waveguides

A simplified form of the coupled-wave equations for cylindrical waves in circular grating distributed feedback (DFB) planar waveguides is presented. The coupling coefficients can be expressed as the product of a cylindrical-wave factor and the corresponding coupling coefficient between planar waveguide modes. Under the large radius approximation (βr≫1), which covers most practical cases, the interpolarization coupling between TE and TM cylindrical waves approaches zero. The coupled-wave equations can then be reduced to two independent families, one for TE- and the other for TM-cylindrical waves     

Elusive bit-error-rate floors resulting from transient partitioningin 1.5-μm DFB lasers

Some 1.5-μm distributed feedback (DFB) lasers modulated at 1.7 Gb/s exhibit bit-error rate (BER) floors for certain fiber lengths, and hence these floors are difficult to detect. For example, a laser that does not exhibit a BER floor for 43 km of fiber may exhibit a BER floor after only 27 km. It is shown that the source of such BER floors is a narrow pulse resulting from transient partitioning between the DFB TE and TM modes. The narrow TM pulses cause false bits if the fiber delay between the modes positions the TM energy within a zero time slot. It is shown that for the 11 lasers studied, TM partitioning floors rarely occur in lasers with adequate threshold gain difference. When the duration of the TM partitioning is only a small fraction of a bit period, the BER floor is effectively removed using a polarized film in the transmission path to suppress the TM mode. Similarly, increased suppression of the TM mode has been achieved by changing the laser structure to reduce the TM mode gain     

Analysis of TM-polarized DFB laser structures with metal surfacegratings

An analysis of distributed feedback (DFB) laser structures with metallized surface grating structures in TM polarization is presented. The modal properties of these structures are described using coupled-mode theory where the coupling coefficients are derived from rigorously computed on-resonant Floquet-Bloch solutions of the waveguide grating problem. Based on this theory, first- and second-order DFB quantum cascade laser structures operating at a wavelength of 10 μm are investigated numerically. We show that, utilizing a metal stripe grating structure, second-order laser structures are feasible showing efficient surface emission, whereas radiation into the substrate is strongly suppressed. The fraction of stimulated emission power being emitted via the surface can be as high as 17.5% whereas a low threshold gain of 20 cm^-1 is maintained     

Effect of p-contact metallization on the performance ofgain-coupled DFBs with oxide-defined surface gratings

The effect of p-contact metallization on the performance of a single-growth-step ridge waveguide InGaAs-GaAs distributed feedback (DFB) laser with a silicon dioxide defined titanium surface grating is analyzed. The metallic surface grating introduces a periodic variation of the loss in the cavity to promote single-frequency emission. Device characteristics for DFBs with 50, 150, and 300 Å of titanium are compared. Under continuous-wave (CW) conditions, the devices with a titanium adhesion layer of only 50 Å operate on single-longitudinal and single-lateral modes, with threshold currents of roughly 14 mA, slope efficiencies of 0.16 W/A and sidemode suppression ratios (SMSRs) of greater than 40 dB     

Collinear interaction of light with space-charge waves in a semiconductor waveguide

The dispersion equation for space-charge waves (SCWs) that couples the wave vector of a traveling wave with frequency and the parameters of a semiconductor waveguide layer is obtained. Numerical analysis of the co-and contradirectional SCW-optical interaction for guided TE and TM modes in a waveguide structure based on n-GaAs is performed. It is demonstrated that the power exchange between the TE modes is more effective than the power exchange between the TM modes. The intervals of the waveguide layer thickness with a relatively high efficiency of the mode transformation are determined.     

Improved coupled mode analysis of corrugated waveguides and lasers

Corrugated waveguides and lasers in resonant and non-resonant situations are analyzed by an improved coupled mode theory based on a set of the coupled mode equations for guided modes and radiation continuum. The distributed feedback (DFB) coefficient and the radiation loss coefficient are given in closed forms. The formulation can be applicable to arbitrarily shaped gratings and multilayer waveguide structures. The accuracy of the theory is examined by comparing it with Tamir's exact calculation for a nonresonant situation and also with Streifer's one for a DFB structure. Reasonable accuracy is obtained by the proper choice of the unperturbed waveguide parameter. The dependence of the two coefficients on the grating depth, the grating period, the guide layer thickness, and the refractive index difference between core and cladding layers is obtained for all Bragg orders up to the fourth, and for four typical grating shapes, namely, for rectangular, sinusoidal, symmetric triangular, and sawtooth gratings. Both the threshold gain of DFB lasers utilizing higher order Bragg reflection and the output coupling efficiency of grating beam couplers are also calculated for these parameters. A new multilayer structure for controlling the radiation loss is proposed and analyzed. This structure is suitable for the suppression of the radiation loss in DBR reflectors as well as for the improvement of the output coupling efficiency in grating beam couplers.     

Electrooptic polymer modulators operating in both TE and TM modes incorporating a vertically tapered cladding

We propose a modified electrooptic (EO) PMMA polymer waveguide structure supporting both TE and TM modes in spite of the large birefringence induced by the poling. A vertically tapered structure is employed to connect a single-mode rib waveguide and a confinement-enhanced rectangular buried waveguide. This waveguide structure can be easily fabricated by a two-step reactive ion etching (RIE) process with a shadow mask. To demonstrate TE/TM confinement and single-mode operation, Mach-Zehnder intensity modulators are fabricated by incorporating the proposed waveguide structure. The extinction ratio is better than -15 dB, which proves the single-mode operation. Half-wave voltages for TM and TE modes are 6 and 24 V, respectively.     

Complex-Coupled DFB Laser Using a Buried SiO2 Grating

In this letter, we report a distributed feedback (DFB) laser having a dielectric grating formed by SiO and InP to explore both the large refractive index difference and the partial gain coupling. Epitaxy lateral overgrowth by metal-organic chemical vapor deposition is conducted to grow the top p-type InP waveguide layer in the dielectric grating template. An index coupling coefficient of about 250 cm is estimated on the laser vertical waveguide structure. The insulating nature of the dielectric grating also partially blocks the injection current flow and modulates the optical gain of the active quantum-well region underneath it. A prototype DFB laser was fabricated and showed a stable single-mode operation with a sidemode suppression ratio larger than 47 dB measured at room temperature and continuous-wave operation. The technology developed can also be used for other applications that require high efficiency grating structures.     

Radiation of Millimeter Waves from a Leaky Dielectric Waveguide with a Light-Induced Grating Layer

A theoretical analysis is presented for the radiation characteristics of millimeter waves in a periodic dielectric waveguide having a light-induced grating layer. The waveguide is assumed to be composed of an insulator (sapphire) slab whose one surface is coated with a high-resistivity semiconductor (silicon) film. A boundary-integral-equation formulation is employed to obtain characteristic solutions of the waveguide. Numerical calculations are made at 94 GHz for both TM and TE polarizations. Estimations of the illumination power required to produce the grating are given. The waveguide presented in this paper, in conjunction with a high-power semiconductor diode laser array as a light source, may be developed to operate as an electronically beam-steerable leaky-wave antenna at millimeter-wave frequencies.