Accurate modeling of photonic devices is essential for the development of new, higher performance optical components required by current and future high-bandwidth communications systems. This paper reviews several key techniques for such modeling, many of which are used in commercial design tools. These include several mode-solving techniques, the beam propagation method, the method of lines, and the finite-difference time-domain technique.

Numerical techniques for modeling guided-wave photonic devices

Preserving energy resp. dissipation in numerical PDEs using the Average Vector Field method

The density-matrix theory of semiconductor lasers with relaxation broadening model is finally established by introducing theoretical dipole moment into previously developed treatments. The dipole moment is given theoretically by the k . p method and is calculated for various semiconductor materials. As a result, gain and gain-suppression for a variety of crystals covering wide wavelength region are calculated. It is found that the linear gain is larger for longer wavelength lasers and that the gain-suppression is much larger for longer wavelength lasers, which results in that single-mode operation is more stable in long-wavelength lasers than in shorter-wavelength lasers, in good agreement with the experiments.

Density-matrix theory of semiconductor lasers with relaxation broadening model - Gain and gain-suppression in semiconductor lasers

Crystal orientation effects on electronic properties of wurtzite InGaN/GaN quantum wells (QWs) with piezoelectric (PZ) and spontaneous (SP) polarization are investigated using the multiband effective-mass theory. With increasing crystal angle, the internal field of the InGaN/GaN QW structure changes its sign near the crystal angle of 55° while that of the GaN/AlGaN QW structure gradually decreases without changing its sign. The interband transition energy is redshifted for crystal angles near θ=0° and gradually increases with the crystal angle due to the reduced SP and PZ polarization effects. The y′-polarized optical matrix element largely increases with increasing crystal angle. This is mainly due to the fact that the states constituting the topmost valence subband near the band edge are predominantly |Y′〉-like for QW structures with larger crystal angle. Also, it is observed that the average hole effective mass is largely reduced with increasing crystal angle. In particular, the average hole effective ...

Crystal orientation effects on electronic properties of wurtzite InGaN/GaN quantum wells

The Lorentzian-shape filter response of a microring resonator filter is not suitable for practical use in wavelength division multiplexing (WDM) systems because of the lack of passband flatness, high crosstalk, and the large wing in the rejection band. Therefore, the tailoring of filter response shape is required to improve the performance. The series coupled microring resonator is one of the solutions. We designed and fabricated vertically triple coupled microring resonator add/drop filters with a stacked configuration. A box-like filter response with a flat passband was successfully obtained, and the free spectral range (FSR) was expanded to 25.8 nm owing to the Vernier effect.

Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter

The perfectly matched layer (PML) boundary condition for the Helmoltz equation is developed and applied to the finite-difference beam propagation method. Its effectiveness is verified by way of examples.

The perfectly matched layer (PML) boundary condition for the beam propagation method

A new explicit fourth-order finite-difference time-domain (FDTD) scheme for three-dimensional electromagnetic field simulation is proposed in this paper. A symplectic integrator propagator, which is also known as a decomposition of the exponential operator or a general propagation technique, is directly applied to Maxwell's equations in the scheme. The scheme is nondissipative and saves memory. The Courant stability limit of the scheme is 30% larger than that of the standard FDTD method. The perfectly matched layer absorbing boundary condition is applicable to the scheme. A specific eigenmode of a waveguide is successfully excited in the scheme. Stable and accurate performance is demonstrated by numerical examples.

A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator

The reflection coefficient at the dielectric interface orthogonal to the Yee-lattice axis in the finite-difference time-domain (FDTD) scheme is explicitly obtained. In the expression, the effective permittivities assigned to the nodes in the vicinity of the interface are included as parameters. The suitable effective permittivities for the accurate modeling of the interface are investigated theoretically based on the reflection coefficient. Regardless of the angular frequency, the incident angle, and the interface position relative to the lattice, second-order accuracy is achieved by the use of effective permittivities based on the weighted harmonic mean and arithmetic mean of the material permittivities. The second-order accuracy is demonstrated by numerical examples.

The second-order condition for the dielectric interface orthogonal to the Yee-lattice axis in the FDTD scheme

Low-chirp lasing operation in semiconductor lasers is addressed in a theoretical investigation of the possibility of reducing the linewidth enhancement factor ( alpha factor) in quantum-well (QW) lasers to zero. It is shown that in reducing the alpha factor it is essential that lasing oscillation be around the peak of the differential gain spectrum, not in the vicinity of the gain peak. The condition for such lasing oscillation is analytically derived. The wavelength dependence of the material gain, the differential gain, and the alpha factor are calculated in detail taking into account the effects of compressive strain and band mixing on the valence subband structure. The effect of p-type modulation doping in compressively strained QWs is discussed. It is shown that the alpha factor, the anomalous dispersion part in the spectrum, crosses zero in the region of positive material gain, which makes is possible to attain virtual chirpless operation by detuning. >

Theoretical study on enhanced differential gain and extremely reduced linewidth enhancement factor in quantum-well lasers

Basic design principles are formulated for increasing the differential gain of 1.55 μm InGaAsP/InP compressive‐strained multiple‐quantum‐well (MQW) lasers. An InGaAsP quaternary active layer can provide more freedom of design compared to an InGaAs ternary active layer since the amount of strain and the quantum‐well thickness can be independently determined in an InGaAsP material system for a given emission wavelength. Compressive strain ranging from 1% to 1.5% is large enough to reduce the density of states below one‐third of that of unstrained wells. No further reduction is expected even if more compressive strain is applied. When the well thickness is, in turn, determined, it is essential to incorporate a trade‐off between the conduction and valence subband energy spacings and the squared optical matrix elements. The extra enhancement of differential gain in MQW structures with a modulation p doping is also studied. By designing MQW structures according to these principles, differential gain can be incr...

Theoretical analysis of differential gain of 1.55 μm InGaAsP/InP compressive‐strained multiple‐quantum‐well lasers

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