Threshold Gain Coefficient Research Articles

Supperssion of higher order modes in gain-guided index-antiguided planar waveguide laser

In order to suppress the higher order modes and improve beam quality in high power waveguide laser, based on gainguided index-antiguided theory, a new symmetric layered waveguide structure is designed, and an interval layer is proposed to be sandwiched between waveguide layer and cladding layer in traditional symmetric GG-IAG waveguide structure. As a result, while reducing the leakage loss of fundamental mode, the threshold gain coefficient differences between fundamental mode and higher order modes will be further increased. When the gain in waveguide layer is between threshold gain coefficient of fundamental mode and that of higher order mode, the fundamental mode will have a greater advantage in mode competition than others, so higher order modes can be suppressed and the laser can obtain a single mode output. In the meantime, the guided-mode principle of this waveguide structure is explained with the theory of wave optics in this paper, the eigen equation of each mode is derived from the wave equation, and the field distributions of fundamental mode and higher order mode are also given. Additionally, in this paper we give the solution process of the threshold gain coefficient of each mode in this waveguide structure. The mode leakage losses of fundamental mode and higher order mode, after adding the interval layer, are numerically calculated, and the parameter optimization process of the interval layer is also given in this paper. In addition, the field distributions of fundamental mode and higher order mode are numerically simulated. The calculation results show that comparing with the traditional symmetric GG-IAG planar waveguide, after adding the interval layer, the loss of fundamental mode can be greatly reduced, while ensuring that the leakage loss of higher order mode reaches a maximum value by reasonably controlling the parameters of interval layer. In this way, we can suppress higher order modes and improve laser efficiency. This paper provides a new idea for improving the beam quality of high power waveguide laser with a large mode area.

Lasing-threshold condition for oblique TE and TM modes, spectral singularities, and coherent perfect absorption

We study spectral singularities and their application in determining the threshold gain coefficient ${g}^{(E/M)}$ for oblique transverse electric or magnetic (TE/TM) modes of an infinite planar slab of homogenous optically active material. We show that ${g}^{(E)}$ is a monotonically decreasing function of the incidence angle $\ensuremath{\theta}$ (measured with respect to the normal direction to the slab), while ${g}^{(M)}$ has a single maximum, ${\ensuremath{\theta}}_{c}$, where it takes an extremely large value. We identify ${\ensuremath{\theta}}_{c}$ with the Brewster's angle and show that ${g}^{(E)}$ and ${g}^{(M)}$ coincide for $\ensuremath{\theta}=0$ (normal incidence), tend to zero as $\ensuremath{\theta}\ensuremath{\rightarrow}{90}^{\ensuremath{\circ}}$, and satisfy ${g}^{(E)}<{g}^{(M)}$ for $0<\ensuremath{\theta}<{90}^{\ensuremath{\circ}}$. We therefore conclude that lasing and coherent perfect absorption are always more difficult to achieve for the oblique TM waves and that they are virtually impossible for the TM waves with $\ensuremath{\theta}\ensuremath{\approx}{\ensuremath{\theta}}_{c}$. We also give a detailed description of the behavior of the energy density and the Poynting vector for spectrally singular oblique TE and TM waves. This provides an explicit demonstration of the parity-invariance of these waves and shows that the energy density of a spectrally singular TM wave with $\ensuremath{\theta}>{\ensuremath{\theta}}_{c}$ is smaller inside the gain region than outside it. The converse is true for the TM waves with $\ensuremath{\theta}<{\ensuremath{\theta}}_{c}$ and all TE waves.

Spectral Singularities and CPA‐Laser Action in a Weakly Nonlinear ‐Symmetric Bilayer Slab

We study optical spectral singularities of a weakly nonlinear ‐symmetric bilinear planar slab of optically active material. In particular, we derive the lasing threshold condition and calculate the laser output intensity. These reveal the following unexpected features of the system: (1) for the case that the real part of the refractive index η of the layers are equal to unity, the presence of the lossy layer decreases the threshold gain; (2) for the more commonly encountered situations when is much larger than the magnitude of the imaginary part of the refractive index, the threshold gain coefficient is a function of η that has a local minimum. The latter is in sharp contrast to the threshold gain coefficient of a homogeneous slab of gain material which is a decreasing function of η. We use these results to comment on the effect of nonlinearity on the prospects of using this system as a coherence perfect absorption‐laser.

Lasing thresholds of helical photonic structures with different positions of a single light-amplifying helix turn

Numerical simulation is used to assess the lasing threshold of helical structures of cholesteric liquid crystals (CLCs) in which only one turn amplifies light. This turn is located either in the centre of symmetric structures of various sizes or in an arbitrary place in asymmetric structures of preset size. In all cases, we find singularities in light amplification by a one-dimensional CLC structure for the most important band-edge modes (m1, m2 and m3) and plot the threshold gain coefficient against the position of the amplifying turn. For the symmetric structures, the lasing threshold of the m1 mode is shown to vary linearly with the inverse of the square of the cavity length. Moreover, modes with a lower density of photonic states (DOS) in the cavity may have a lower lasing threshold. This can be accounted for by the dependence of the density of photonic states on the position of the amplifying turn and, accordingly, by the nonuniform electromagnetic field intensity distribution along the cavity for different modes. In the asymmetric structures, the same field energy distribution is responsible for a correlation between and DOS curves.

Study of an active hybrid gap surface plasmon polariton waveguide with nanoscale confinement size and low compensation gain

A silicon-based hybrid gap surface plasmon polariton (SPP) waveguide consisting of an active InP/GaInAsP/InP double heterostructure layer, a silver cladding with a rectangular bump and a gap between them is presented. Based on this waveguide, all the SPP waveguides and even the SPP components share a common planar active medium layer in the whole photonic integration circuit chip, so not only can both the waveguide structure width and the mode lateral confinement width be of nanoscale simultaneously, but optical pumping can also be easily realized for compensating the propagation loss of all the SPP waveguides and components. By means of thickening the active GaInAsP layer and thinning the gap, the threshold gain coefficient is reduced to an achievable range and the mode confinement size is dropped to the nanoscale. Numerical simulation suggests that when the gap size is 50 nm × 10 nm and the GaInAsP height is 350 nm, by adjusting the metal bump height, the effective mode area is at λ0 = 1550 nm and the full-width at half-maximum of the Poynting vector magnitude is 66 nm and the threshold gain coefficient is 158.5 cm−1 or 850.9 cm−1 for different Ag permittivities coming from two sources.

Efficient optical modelling of VCSELs using a vector mode-matching method

Recent vertical-cavity surface-emitting lasers (VCSELs) include complex features, such as oxide apertures or intracavity index-guides, which complicate the electromagnetic modelling problem. Determining the optical characteristics of the cavity is essential to correctly interpret the physical behaviour of these devices. The authors have developed an efficient vector optical solver combining a mode-matching method and Krylov subspace techniques for a general VCSEL structure with cylindrical geometry. The solver generates accurate results for the cavity-mode profiles, resonant wavelengths, losses and threshold gain coefficients. Comparison with experimental data is shown. Scalar and vector modelling results are directly compared for the first time and the limits of the scalar approximation are investigated. It is found that the scalar approximation leads to large errors for small, strongly index-guiding apertures. The model is applied to both oxide-apertured and implant-apertured index-guided VCSEL structures.

Optics and Photonics: An Introduction

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Calculation of the characteristics of a two-mode laser with weakly coulped anisotropic cavities

On the basis of the method of self-consistent waves in lasers with weakly coupled anisotropic cavities we obtained analytical expressions for the spectrum of radiation frequencies and threshold gain coefficients of orthogonally polarized waves in the active part of a coupled cavity for an arbitrary set of anisotropic and other optical elements in its passive part.