High-efficiency femtosecond Raman soliton generation with a tunable wavelength beyond 2 µm.

We report an efficient Raman soliton laser system by optimizing the chirp of input pulses. The highest efficiency of energy transferred to a Raman soliton is up to 97%, and the tunable range is from 1.98 to 2.31 µm. The pulse width of these tunable Raman solitons remains below 200 fs. The efficiency and the wavelength range are mainly limited by the background loss of the silica fiber.

Mid-IR supercontinuum pumped by femtosecond pulses from thulium doped all-fiber amplifier.

We present a mid-infrared (mid-IR) supercontinuum (SC) light source pumped by femtosecond pulses from a thulium doped fiber amplifier (TDFA) at 2 µm. An octave-spanning spectrum from 1.1 to 3.7 µm with an average power of 253 mW has been obtained from a single mode ZBLAN fiber. Spectral flatness of 10 dB over a 1390 nm range has been obtained in the mid-IR region from 1940 - 3330 nm. It is resulted from the enhanced self phase modulation process in femtosecond regime. The all-fiber configuration makes such broadband coherent source a compact candidate for various applications.

Split-step finite-difference time-domain method with perfectly matched layers for efficient analysis of two-dimensional photonic crystals with anisotropic media.

This Letter presents a split-step (SS) finite-difference time-domain (FDTD) method for the efficient analysis of two-dimensional (2-D) photonic crystals (PhCs) with anisotropic media. The proposed SS FDTD method is formulated with perfectly matched layer boundary conditions and caters for inhomogeneous anisotropic media. Furthermore, the proposed method is derived using the efficient SS1 splitting formulas with simpler right-hand sides that are more efficient and easier to implement. A 2-D PhC cavity with anisotropic media is used as an example to validate the efficiency of the proposed method.

Investigation and suppression of the pump-to-Stokes relative intensity noise transfer in chalcogenide waveguide Raman laser.

The characteristic of pump-to-Stokes relative intensity noise (RIN) transfer is comprehensively investigated for integrated As2Se3 waveguide Raman laser (As2Se3-WRL). It is found that, compared to its silicon counterpart, the RIN transfer is 5 dB lower across all frequencies for As2Se3-WRL, mainly due to its relatively smaller Raman gain coefficient. A bidirectional pumping scheme is proposed and verified as an effective configuration to suppress RIN transfer because doubling of the inverse round trip time eliminates the RIN transfer peak at the odd multiples of the resonance frequency. The optimization of waveguide length on RIN transfer is also performed, in which two distinct regions are identified due to different dominant physical processes. In addition, we show that RIN transfer in As2Se3-WRL can be further reduced by using a high cavity for both pump and Stokes waves.

Modeling hemoglobin at optical frequency using the unconditionally stable fundamental ADI-FDTD method.

This paper presents the modeling of hemoglobin at optical frequency (250 nm - 1000 nm) using the unconditionally stable fundamental alternating-direction-implicit finite-difference time-domain (FADI-FDTD) method. An accurate model based on complex conjugate pole-residue pairs is proposed to model the complex permittivity of hemoglobin at optical frequency. Two hemoglobin concentrations at 15 g/dL and 33 g/dL are considered. The model is then incorporated into the FADI-FDTD method for solving electromagnetic problems involving interaction of light with hemoglobin. The computation of transmission and reflection coefficients of a half space hemoglobin medium using the FADI-FDTD validates the accuracy of our model and method. The specific absorption rate (SAR) distribution of human capillary at optical frequency is also shown. While maintaining accuracy, the unconditionally stable FADI-FDTD method exhibits high efficiency in modeling hemoglobin.

Modeling magnetic photonic crystals with lossy ferrites using an efficient complex envelope alternating-direction-implicit finite-difference time-domain method.

In this Letter, we present an efficient complex-envelope alternating-direction-implicit finite-difference time-domain (CE-ADI-FDTD) method for the transient analysis of magnetic photonic crystals with lossy ferrites. The proposed CE-ADI-FDTD method is generally formulated for a saturated ferrite with anisotropic permittivity tensor and ferrite loss. Auxiliary differential equations for modeling saturated ferrite and Maxwell's curl equations are first cast into a first-order differential system in a CE form. Then, by using an efficient ADI splitting formulas, the proposed CE-ADI-FDTD method is attained in a very concise form with few and simple right-hand side terms. The performance of the proposed method is validated and compared with the explicit FDTD method.

Generalized eigenproblem of hybrid matrix for Floquet wave propagation in one-dimensional phononic crystals with solids and fluids.

A method based on the solution to a generalized eigenproblem of hybrid matrix is presented for stable analysis of Floquet wave propagation in one-dimensional phononic crystals with solids and fluids. The method overcomes the numerical instability in the standard eigenproblem of transfer matrix, thus enabling Floquet waves to be determined reliably. The recursion relations of hybrid matrix for periodic multilayered structure of various solid and/or fluid phases are formulated. Dispersion relation and omnidirectional reflection for one-dimensional phononic crystals with solids and fluids are discussed. The frequency-thickness range of phononic bandgap is determined conveniently based on the Floquet wavenumbers.

Matrix algorithms for modeling acoustic waves in piezoelectric multilayers.

Matrix algorithms for modeling acoustic waves in piezoelectric multilayers are presented. All the algorithms considered are capable of resolving the numerical instability of transfer matrix at high frequency-thickness product. The formulation of basic matrices for the algorithm building blocks, and the development of recursive algorithms for the stack matrices, are systematically presented for both the conventional scattering and impedance matrices as well as the more recent hybrid matrix. Many variants of the algorithms are discussed, along with their respective usefulness and deficiency. Comparisons are made in their computational efficiency and numerical stability. For unconditional stability throughout large and small thicknesses, both scattering and hybrid matrix algorithms are applicable. For most efficiency, the algorithms that synergize both scattering and hybrid or impedance submatrices are superior, using surface matrix approach. Other aspects of algorithms such as formula conciseness, physical insight, versatility in incorporating boundary conditions, etc., are also noted.

Enhanced R-matrix algorithms for multilayered diffraction gratings.

I present enhanced R-matrix algorithms for analysis of general multilayered diffraction gratings. The previous R-matrix algorithms are enhanced in three aspects: computational efficiency, numerical stability, and application of half R-matrix in addition to full and quarter R-matrix recursions. On the basis of the eigensolutions of rigorous coupled-wave analysis, the enhanced R-matrix algorithms deal with eigen-submatrices directly and bypass the auxiliary layer R matrix. Such exclusion of a layer matrix leads to improvements in efficiency and algorithm robustness particularly for zero or small layer thickness relative to wavelength. Application of the enhanced algorithms to grating diffraction is exploited especially for the half and quarter R-matrix recursions. Comparison of various R-matrix algorithms via a table of flop counts shows that the enhanced algorithms are more efficient apart from being well conditioned.

Hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media.

This paper presents the hybrid compliance-stiffness matrix method for stable analysis of elastic wave propagation in multilayered anisotropic media. The method utilizes the hybrid matrix of each layer in a recursive algorithm to deduce the stack hybrid matrix for a multilayered structure. Like the stiffness matrix method, the hybrid matrix method is able to eliminate the numerical instability of transfer matrix method. By operating with total stresses and displacements, it also preserves the convenience for incorporating imperfect or perfect interfaces. However, unlike the stiffness matrix, the hybrid matrix remains to be well-conditioned and accurate even for zero or small thicknesses. The stability of hybrid matrix method has been demonstrated by the numerical results of reflection and transmission coefficients. These results have been determined efficiently based on the surface hybrid matrix method involving only a subset of hybrid submatrices. In conjunction with the recursive asymptotic method, the hybrid matrix method is self-sufficient without hybrid asymptotic method and may achieve low error level over a wide range of sublayer thickness or the number of recursive operations.

A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids.

This paper presents a concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids. The formalism is capable of resolving completely the numerical instability problems associated with transfer matrix method, thereby obviating the extensive reformulation in its modified versions based on delta operator technique. In contrast to the earlier reflection matrix formalisms, all scattering matrices are obtained in a direct manner without invoking wave-propagator or scatterer operator concepts. Both local and global reflection and transmission matrices corresponding to scatterings in two and more layers are derived. The derivation of global scattering matrices in terms of the local ones is carried out concisely based on physical arguments to provide better insights into scattering mechanism. Another formulation which is even more succinct is also devised for obtaining the global scattering matrices directly from eigensolutions. The resultant expressions and algorithm are terse, efficient and convenient for implementation.

A robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies.

This paper presents a robust formulation of SAW Green's functions for arbitrarily thick multilayers at high frequencies. The formulation is an alternative to that based on the transfer matrix method, which suffers from numerical instabilities when the frequency and/or thickness parameters become large. This numerical difficulty can be attributed to the mixture of exponentially growing and decaying terms during the transfer matrix calculations. To be more instructive, the numerical instability is delineated in terms of upward-bounded and downward-bounded waves within each layer. In accordance with such boundedness association, a recursive scheme not involving any growing terms is developed based on the scattering matrices to eliminate the instability. The resulting reflection matrix method is extremely concise and preserves the simplicity and convenience of the transfer matrix method. Using the reflection matrices, the generalized Green's functions that relate the particle velocity and the rate of electric potential change to the surface stress and charge are formulated succinctly. These Green's functions are useful for having incorporated the electrical properties of the vacuum above the surface. Numerical computations are exemplified to demonstrate the instabilities of the transfer matrix method and to justify the robustness of the reflection matrix formula.

Note on formulation of the enhanced scattering- (transmittance-) matrix approach.

The enhanced transmittance matrix approach developed by Moharam et al. [J. Opt. Soc. Am. A 12, 1077 (1995)] is reformulated in a concise and illuminating form in terms of scattering (reflection and transmission) matrices directly. Two equivalent recursive formulations, corresponding to their full- and partial-solution approaches, are presented and extended to allow simultaneous determination of both reflected and transmitted amplitudes. The relationships between these formulations and the S-matrix algorithm, together with their relative efficiencies and usefulness, are ascertained and compared by means of compact formulas featuring parallel algebraic structures. It is made evident that given the eigenmode solutions, the enhanced approach is the most direct and efficient way for deducing global scattering matrices.