• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.283-294
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• 2007

By a near ${\lambda}$-lattice is meant an upper ${\lambda}$-semilattice where is defined a parti binary operation $x{\Lambda}y$ with respect to the induced order whenever $x$, $y$ has a common lower bound. Alternatively, a near ${\lambda}$-lattice can be described as an algebra with one ternary operation satisfying nine simple conditions. Hence, the class of near ${\lambda}$-lattices is a quasivariety. A ${\lambda}$-semilattice $\mathcal{A}=(A;{\vee})$ is said to have sectional (antitone) involutions if for each $a{\in}A$ there exists an (antitone) involution on [$a$, 1], where 1 is the greatest element of $\mathcal{A}$. If this antitone involution is a complementation, $\mathcal{A}$ is called an ortho ${\lambda}$-semilattice. We characterize these near ${\lambda}$-lattices by certain identities.

• Journal of the Optical Society of Korea
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• v.18 no.3
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• pp.207-216
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• 2014

In this work, we report detailed numerical analysis of the near-elliptic core index-guiding triangular-lattice and square-lattice photonic crystal fiber (PCFs); where we numerically characterize the birefringence, single mode, cut-off behavior and group velocity dispersion and effective area properties. By varying geometry and examining the modal field profile we find that for the same relative values of $d/{\Lambda}$, triangular-lattice PCFs show higher birefringence whereas the square-lattice PCFs show a wider range of single-mode operation. Square-lattice PCF was found to be endlessly single-mode for higher air-filling fraction ($d/{\Lambda}$). Dispersion comparison between the two structures reveal that we need smaller lengths of triangular-lattice PCF for dispersion compensation whereas PCFs with square-lattice with nearer relative dispersion slope (RDS) can better compensate the broadband dispersion. Square-lattice PCFs show zero dispersion wavelength (ZDW) red-shifted, making it preferable for mid-IR supercontinuum generation (SCG) with highly non-linear chalcogenide material. Square-lattice PCFs show higher dispersion slope that leads to compression of the broadband, thus accumulating more power in the pulse. On the other hand, triangular-lattice PCF with flat dispersion profile can generate broader SCG. Square-lattice PCF with low Group Velocity Dispersion (GVD) at the anomalous dispersion corresponds to higher dispersion length ($L_D$) and higher degree of solitonic interaction. The effective area of square-lattice PCF is always greater than its triangular-lattice counterpart making it better suited for high power applications. We have also performed a comparison of the dispersion properties of between the symmetric-core and asymmetric-core triangular-lattice PCF. While we need smaller length of symmetric-core PCF for dispersion compensation, broadband dispersion compensation can be performed with asymmetric-core PCF. Mid-Infrared (IR) SCG can be better performed with asymmetric core PCF with compressed and high power pulse, while wider range of SCG can be performed with symmetric core PCF. Thus, this study will be extremely useful for designing/realizing fiber towards a custom application around these characteristics.

• Proceedings of the KIEE Conference
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• 1999.11a
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• pp.10-12
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• 1999

Optical properties of $Zn_2AgGaSe_4$ and $Zn_2AgGaSe_4$:$Co^{2+}$ crystals are investigated in the visible and near-infrared regions at 298K. The direct band gap at 298K is 1.630eV for the $Zn_2AgGaSe_4$ and 1.567eV for the $Zn_2AgGaSe_4$:$Co^{2+}$ crystals, respectively. In the optical absorption and PAS spectrum of the $Zn_2AgGaSe_4$:$Co^{2+}$, we observed five impurity absorption peaks at $4220cm^{-1}$, $5952cm^{-1}$, $12422cm^{-1}$, $12987cm^{-1}$ and $14184cm^{-1}$. These impurity absorption peaks are attributed to the electronic transitions between the split energy levels of $Co^{2+}$ ions with Td symmetry of $Zn_2AgGaSe_4$ host lattice. The crystal field parameter Dq, the Racah parameter B and the spin-orbit coupling parameter $\lambda$ are given by $442cm^{-1}$, $425cm^{-1}$ and $440cm^{-1}$, respectively.

• Journal of the Korean Vacuum Society
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• v.6 no.2
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• pp.129-135
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• 1997

Undoped and Co-doped $ZnIn_2Se_4$ single crystals crystallized in the tetragonal space group 142m, with lattice constants a=5.748 $\AA$ and c=11.475 $\AA$, and a=5.567 $\AA$ and c=11.401 $\AA$. The optical absorption measured near the fundamental band edge showed that the optical energy band structure of these compounds had an indirect band gap, the direct and the indirect energy gaps of these compounds decreased as temperature changed from 10 to 300 K. The temperature coefficients of the direct energy gaps were found to be $\alpha=3.71\times10^{-4}$eV/K and $\beta$=519 K for $\alpha=3.71\times10^{-4}$eV/K and $\beta$=421K for $ZnIn_2Se_4$: Co. The temperature coefficients of the indirect energy gaps were also found to be $\alpha=2.31\times10^{-4}$ eV/K and $\beta$=285 K for $ZnIn_2Se_4$, and $\alpha=3.71\times10^{-4}$eV/K and $\beta$=609 K for $ZnIn_2Se_4$:Co, respectively. Six impurity optical absorption peaks due to cobalt are observed in $ZnIn_2Se_4$:Co single crystal. These impurity optical absorption peaks can be attibuted to the electronic transitions between the split energy levels of$CO^{2+}$ ions located at Td symmetry site of $ZnIn_2Se_4$ host lattice. The 1st order spin-orbit coupling constant ($\lambda$), Racah parameter (B), and crystal field parameter (Dq) ARE GIVEN AS -$243\textrm{cm}^{-1}, 587\textrm{cm}^{-1}, \;and\;327\textrm{cm}^{-1}$, respectively.