There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Photonic cavities that strongly confine light are finding applications in many areas of physics and engineering, including coherent electron-photon interactions, ultra-small filters, low-threshold lasers, photonic chips, nonlinear optics and quantum information processing. Critical for these applications is the realization of a cavity with both high quality factor, Q, and small modal volume, V. The ratio Q/V determines the strength of the various cavity interactions, and an ultra-small cavity enables large-scale integration and single-mode operation for a broad range of wavelengths. However, a high-Q cavity of optical wavelength size is difficult to fabricate, as radiation loss increases in inverse proportion to cavity size. With the exception of a few recent theoretical studies, definitive theories and experiments for creating high-Q nanocavities have not been extensively investigated. Here we use a silicon-based two-dimensional photonic-crystal slab to fabricate a nanocavity with Q = 45,000 and V = 7.0 x 10(-14) cm3; the value of Q/V is 10-100 times larger than in previous studies. Underlying this development is the realization that light should be confined gently in order to be confined strongly. Integration with other photonic elements is straightforward, and a large free spectral range of 100 nm has been demonstrated.

High- Q photonic nanocavity in a two-dimensional photonic crystal

An overview is presented of the current state-of-the-art in silicon nanophotonic ring resonators. Basic theory of ring resonators is discussed, and applied to the peculiarities of submicron silicon photonic wire waveguides: the small dimensions and tight bend radii, sensitivity to perturbations and the boundary conditions of the fabrication processes. Theory is compared to quantitative measurements. Finally, several of the more promising applications of silicon ring resonators are discussed: filters and optical delay lines, label-free biosensors, and active rings for efficient modulators and even light sources.

/pdf/silicon-microring-resonators-3fzr4lpxbh.pdf

Silicon microring resonators

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

The design, fabrication, and measurement of photonic-band-gap (PBG) waveguides, resonators and their coupled elements in two-dimensional photonic crystal (PhC) slabs have been investigated. We have studied various loss mechanisms in PBG waveguides and have achieved a very low propagation loss (~1 dB/mm). For these waveguides, we have observed a large group delay (>100 ps) by time-domain measurement. As regards PBG resonators, we realize very high-Q and small volume resonators in PhC slabs by appropriate design. Finally, we demonstrate various forms of coupled elements of waveguides and resonators: 2-port resonant-tunneling transmission devices, 4-port channel-drop devices using the slow light mode, and 3-port channel-drop devices using the resonant-tunneling process.

Waveguides, resonators and their coupled elements in photonic crystal slabs.

Efficiency droop in InGaN light-emitting diodes (LEDs) is analyzed based on the rate equation model. By using the peak point of the efficiency versus current-density relation as the parameters of the rate equation analysis, internal quantum efficiency and each recombination current at arbitrary current density can be unambiguously determined without any knowledge of A, B, and C coefficients. The theoretical analysis is compared with measured efficiency of a LED sample and good agreement between the model and experiment is found. The investigation of recombination coefficients shows that Auger recombination alone is not sufficient to explain the efficiency droop of InGaN LEDs.

Rate equation analysis of efficiency droop in InGaN light-emitting diodes

Using finite-difference time-domain calculations, we investigate the hexapole mode of photonic-crystal-slab modified triangular single-defect cavity structures as a good candidate for a high-quality factor (Q) and small-mode volume (V) resonant mode. Structural parameters are optimized to obtain very large Q of even higher than 2×106 with small effective V of the order of cubic wavelength in material, the record value of theoretical Q/V. It is found, by the Fourier-space investigation of resonant modes, that such a high Q from the hexapole mode is achieved due both to the cancellation mechanism related to hexagonally symmetric whispering-gallery-mode distribution and to the mode delocalization mechanism.

/pdf/high-quality-factor-and-small-mode-volume-hexapole-modes-in-3gmi88qzje.pdf

High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities

Photonic band-edge lasers are realized in the free-standing triangular photonic crystal slab with InGaAsP quantum wells at 80 K. Surface-emitting lasing actions are observed from the samples whose wavelengths correspond to the second or the third photonic band edge near the Γ point of the band structure, which is confirmed by the three-dimensional finite-different time-domain calculation. A very low threshold of 35 μW (incident pump power) is achieved from the laser operating near the third transverse-electric-mode band edge. This low threshold is benefited from low optical losses near the Γ point as well as reduced surface recombination carrier losses and enhanced material gain at low temperature. It is interesting to note that this two-dimensional distributed feedback lasing action is observed from a surprisingly small pump area of 6 μm in diameter.

Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs

Light extraction efficiency (LEE) in AlGaN deep-ultraviolet (DUV) light-emitting diodes (LEDs) is investigated using finite-difference time-domain simulations. For flip-chip and vertical LED structures, LEE is obtained to be <10% due to strong DUV light absorption in the p-GaN layer. In flip-chip LEDs, LEE of transverse-magnetic (TM) modes is found to be more than ten times smaller than that of transverse-electric (TE) modes, which explains the decreasing behavior of external quantum efficiency of DUV LEDs with decreasing wavelength. It is also found that vertical LED structures can have advantages over flip-chip structures for increasing LEE in the TM mode.

https://iopscience.iop.org/article/10.7567/APEX.6.062101/pdf

Han-Youl Ryu

Papers

Waveguides, resonators and their coupled elements in photonic crystal slabs.

Rate equation analysis of efficiency droop in InGaN light-emitting diodes

High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities

Very-low-threshold photonic band-edge lasers from free-standing triangular photonic crystal slabs

Investigation of Light Extraction Efficiency in AlGaN Deep-Ultraviolet Light-Emitting Diodes