Photonic Crystal Waveguide Modes Research Articles

Inverse design of broadband and lossless topological photonic crystal waveguide modes.

Topological photonic crystal waveguides can create edge states that may be more robust against fabrication disorder and can yield propagation modes below the light line. We present a fully three-dimensional method to modify state-of-the-art designs to achieve a significant bandwidth improvement for lossless propagation. Starting from an initial design with a normalized bandwidth of 7.5% (13.4 THz), the modification gives more than 100% bandwidth improvement to 16.2% (28.0 THz). This new design is obtained using an automatic differentiation enabled inverse design and a guided mode expansion technique to efficiently calculate the band structure and edge state modes.

Zero GVD slow-light originating from a strong coupling of one-way modes in double-channel magneto-optical photonic crystal waveguides.

We have studied the coupling effect of topological photonic states in a double-channel magneto-optical photonic crystal waveguide by introducing a two-stranded ordinary Al2O3 photonic crystal as the coupling layer. There exist both M1 (odd) and M2 (even) one-way modes simultaneously in the bandgap. Interestingly, M1 mode is always a fast-light mode with large group velocity (vg) and large group velocity dispersion (GVD) regardless what the radius (RA) of Al2O3 rods is. However, when RA is appropriate, M2 mode becomes a very slow-light mode exhibiting near-zero vg and zero GVD simultaneously. The physical reason of such slow-light is attributed to the strong coupling effect between the one-way edge modes in both sub-waveguides. Furthermore, the simulation results show that the robustness of both the fast- and slow-light modes are extremely strong against perfect electric conductor defect and the one-way transmittance is close to 100%. Besides, the PEC defect can cause significant phase delay. These results hold promise for many fields such as signal processing, optical modulation, and the design of various topological devices.

Theory of intrinsic propagation losses in topological edge states of planar photonic crystals

Using a semi-analytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular holes. Although conventional photonic crystal waveguide structures, such as the W1 waveguide, have been designed to have lossless propagation modes, they are prone to disorder-induced losses and backscattering. Topological structures have been proposed to help mitigate this effect as their photonic edge states may allow for topological protection. However, the intrinsic propagation losses of these structures are not well understood and the concept of the light line can become blurred. For four example topological edge state structures, photonic band diagrams, loss parameters, and electromagnetic fields of the guided modes are computed. Two of these structures, based on armchair edge states, are found to have significant intrinsic losses for modes inside the photonic band gap, more than 100 dB/cm, which is comparable to or larger than typical disorder-induced losses using slow-light modes in conventional photonic crystal waveguides, while the other two structures, using the valley Hall effect and inversion symmetry, are found to have a good bandwidth for exploiting lossless propagation modes below the light line.

The Integration of Photonic Crystal Waveguides with Atom Arrays in Optical Tweezers

AbstractIntegrating nanophotonics and cold atoms has drawn increasing interest in recent years due to diverse applications in quantum information science and the exploration of quantum many‐body physics. For example, dispersion‐engineered photonic crystal waveguides (PCWs) permit not only stable trapping and probing of ultracold neutral atoms via interactions with guided‐mode light, but also the possibility to explore the physics of strong, photon‐mediated interactions between atoms, as well as atom‐mediated interactions between photons. While diverse theoretical opportunities involving atoms and photons in 1D and 2D nanophotonic lattices have been analyzed, a grand challenge remains the experimental integration of PCWs with ultracold atoms. Here, an advanced apparatus that overcomes several significant barriers to current experimental progress is described, with the goal of achieving strong quantum interactions of light and matter by way of single‐atom tweezer arrays strongly coupled to photons in 1D and 2D PCWs. Principal technical advances relate to efficient free‐space coupling of light to and from guided modes of PCWs, silicate bonding of silicon chips within small glass vacuum cells, and deterministic, mechanical delivery of single‐atom tweezer arrays to the near fields of photonic crystal waveguides.

Coupling of a whispering gallery mode to a silicon chip with photonic crystal.

We demonstrate the efficient coupling (99.5%) of a silica whispering gallery mode microresonator directly with a silicon chip by using a silicon photonic crystal waveguide as a coupler. The efficient coupling is attributed to the small effective refractive index difference between the two devices. The large group index of the photonic crystal waveguide mode also contributes to the efficient coupling. A coupling Q of 2.68×106 is obtained, which allows us to achieve the critical coupling of a silica whispering gallery mode with an intrinsic Q of close to 107 with a Si chip.

Nanolayer-embedded pseudo-photonic crystals

In recent years, novel high-performance nanophotonic devices have been realized by applying ultrathin two-dimensional nanolayer materials to nanophotonics. In this paper, we propose nanolayer-embedded compact pseudo-photonic crystals (PPCs) that enable strong interaction between ultrathin nanolayers and photonic crystal modes. In typical two-dimensional slab photonic crystals, the transverse-magnetic (TM) photonic crystal bandgap is not well formed, making it difficult to operate the TM photonic crystal waveguide modes. However, by utilizing the low-frequency TM PPC bands, a long propagation TM waveguide mode, a slow TM waveguide mode, and a TM photonic bandgap are all readily available. In particular, the insertion of a nanometer-thick low-refractive-index layer in the vertical center of TM PPC waveguide can localize the electric fields tightly in nanometer space, causing strong field interaction with the inserted nanolayer material. Using the TM slow light near PPC band edges, field interaction with the nanolayer is significantly enhanced. We can also realize nanolayer-embedded high-quality-factor (Q-factor > 104) PPC cavities using the TM PPC bandgap. We believe that the proposed TM PPCs will play an important role in the strong interaction of ultrathin nanolayer materials with photonic crystal modes.

Surface modes in photonic crystal waveguides coated with a layer of dispersive left-handed material

In this work, we study the presence of surface modes in two different photonic crystal waveguides characterized by the presence of layers of a dispersive left-handed material. The periodicity required to have a photonic crystal waveguide is considered in two distinct ways. One of them is composed of two perfect electrical conducting rippled surfaces, and the other consists of two at infinite surfaces that surround a periodic one-dimensional array of circular cylindrical inclusions of a perfect electrical conductor, coated with a layer of left-handed material. To study these systems, integral numerical methods were applied to determine their band structures and the electromagnetic field distribution, under the TE and TM polarizations. Numerical results show the presence of surface modes for several frequencies with certain geometric configurations. One of these frequencies is known in the literature and corresponds to the frequency of a Surface Plasmon-Polariton.

Free space excitation of coupled Anderson-localized modes in photonic crystal waveguides with polarization tailored beam

We experimentally demonstrate free space excitation of coupled Anderson-localized modes in photonic crystal (PhC) line-defect waveguides (W1) with polarization tailored beams. The corresponding light beam is tightly focused on a pristine W1, and out-of-plane scattering is imaged. By integrating the scattering spectra along the guide, at the W1 modal cut-off, Anderson-localized cavities are observed due to residual W1 fabrication-disorder. Their spectral lines exhibit high quality Q factors up to 2 × 105. The incident beam polarization and scattering intensities of the localized modes characterize the efficiency of free-space coupling. The coupling is studied for linearly and radially polarized input beams and for different input coupling locations along the W1 guide. The proposed coupling scheme is particularly attractive for excitation of PhC waveguide modes and Anderson-localized cavities by beam steering and scanning microscopy for sensing applications.

Optical pulling using evanescent mode in sub-wavelength channels

Optical evanescent wave in total internal reflection has been widely used in efficient optical manipulation, where the object is trapped by the intrinsic intensity gradient of the evanescent wave while transported by the scattering force along the orthogonal direction. Here, we propose a distinct optical manipulation scheme using the attenuated modes in subwavelength optical channels, where both the trapping and transportation forces are along the channel direction. We create such a mode in a sub-wavelength photonic crystal waveguide and quantitatively obtain the net pushing and pulling forces, which can overcome the Brownian motion within a critical length. Due to the presence of the physical channel, subwavelength trapping on the transverse direction is natural, and manipulation along bend trajectories is also possible without the assistance of the self-acceleration beams provided a channel is adopted. This optical manipulation method can be extended to any other channels that support attenuation mode, and may provide an alternate way for flexible optical manipulation.

Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections.

Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness (~1/1000 of a wavelength) of the fabrication imperfections.

Photonic-crystal-based all-optical NOT logic gate.

In the present paper, we have utilized the concept of photonic crystals for the implementation of an optical NOT gate inverter. The designed structure has a hexagonal arrangement of silicon rods in air substrate. The logic function is based on the phenomenon of the existence of the photonic bandgap and resulting guided modes in defect photonic crystal waveguides. We have plotted the transmission, extinction ratio, and tolerance analysis graphs for the structure, and it has been observed that the maximum output is obtained for a telecom wavelength of 1.554μm. Dispersion curves are obtained using the plane wave expansion method, and the transmission is simulated using the finite element method. The proposed structure is applicable for photonic integrated circuits due to its simple structure and clear operating principle.

Polarization Engineering in Photonic Crystal Waveguides for Spin-Photon Entanglers

By performing a full analysis of the projected local density of states (LDOS) in a photonic crystal waveguide, we show that phase plays a crucial role in the symmetry of the light-matter interaction. By considering a quantum dot (QD) spin coupled to a photonic crystal waveguide (PCW) mode, we demonstrate that the light-matter interaction can be asymmetric, leading to unidirectional emission and a deterministic entangled photon source. Further we show that understanding the phase associated with both the LDOS and the QD spin is essential for a range of devices that can be realized with a QD in a PCW. We also show how suppression of quantum interference prevents dipole induced reflection in the waveguide, and highlight a fundamental breakdown of the semiclassical dipole approximation for describing light-matter interactions in these spin dependent systems.

Coupling of photonic crystal–photonic crystal interface and guided modes in two-dimensional heterostructures

In this work, we propose a two-dimensional photonic crystal–photonic crystal heterostructure that possesses the requirements for exciting an electromagnetic interface mode and investigate its interaction with photonic crystal waveguide modes. To study the interaction and coupling of both types of modes, the proper conditions to excite them are analyzed. Photonic crystal guided modes can appear in nearly any band gap when the photonic crystal has a line of defects within its lattice. Photonic crystal–photonic crystal surface modes can be excited at the junction of two different photonic crystals that share translation symmetry along the interface direction and have overlapped frequency band gaps. When this condition is met, dispersion relations of photonic crystal–photonic crystal surface modes will lie in the common region of both band gaps. Once the proper conditions are provided to excite these two modes, an interaction between them is possible. In the resulting calculations, a symmetric supercell and a plane wave basis are defined to numerically solve the wave equation.

Silica-Clad Silicon Photonic Crystal Waveguides for Wideband Dispersion–Free Slow Light

We comprehensively calculated the photonic bands of the waveguide modes in practical lattice-shifted photonic crystal waveguides, which are completely cladded by silica. We assumed various lattice shifts and found that the shift of the second rows and the mixed shift of the first and third rows along the waveguide generate low-dispersion slow light with group indices of 34-36, which is higher than those with a conventional shift of the third rows, maintaining a wide bandwidth over 10 nm at telecom wavelengths. We fabricated the waveguides using a CMOS-compatible process and confirmed correspondence with the calculation results. We also compared 25-Gb/s photonic crystal slow light Mach-Zehnder modulators and confirmed the improvement of the modulation efficiency by second-row shifts.

Highly directed emission from self-assembled quantum dots into guided modes in disordered photonic-crystal waveguides

We explore the dynamics and directionality of spontaneous emission from self-assembled In(Ga)As quantum dots into TE-polarised guided modes in GaAs two-dimensional photonic crystal waveguides. The local group velocity of the guided waveguide mode is probed, with values as low as $\sim 1.5\%\times c$ measured close to the slow-light band edge. By performing complementary continuous wave and time-resolved measurements with detection along, and perpendicular to the waveguide axis we probe the fraction of emission into the waveguide mode ($\beta$-factor). For dots randomly positioned within the unit cell of the photonic crystal waveguide our results show that the emission rate varies from $\geq 1.55$ $ns^{-1}$ close to the slow-light band edge to $\leq 0.25$ $ns^{-1}$ within the two-dimensional photonic bandgap. We measure an average Purcell-factor of $\sim 2\times$ for dots randomly distributed within the waveguide and maximum values of $\beta\sim 90 \%$ close to the slow light band edge. Spatially resolved measurements performed by exciting dots at a well controlled distance $0-45$ {\mu}m from the waveguide facet highlight the impact of disorder on the slow-light dispersion. Although disorder broadens the spectral width of the slow light region of the waveguide dispersion from $\delta E_{d}\leq 0.5$ meV to $>6$ meV, we find that emission is nevertheless primarily directed into propagating waveguide modes. The ability to control the rate and directionality of emission from isolated quantum emitters by placing them in a tailored photonic environment provides much promise for the use of slow-light phenomena to realise efficient single photon sources for quantum optics in a highly integrated setting.

Extreme optical confinement in a slotted photonic crystal waveguide

Using Optical Coherence Tomography, we measure the attenuation of slow light modes in slotted photonic crystal waveguides. When the group index is close to 20, the attenuation is below 300 dB cm−1. Here, the optical confinement in the empty slot is very strong, corresponding to an ultra-small effective cross section of 0.02 μm2. This is nearly 10 times below the diffraction limit at λ = 1.5 μm, and it enables an effective interaction with a very small volume of functionalized matter.

Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides

The efficient and reliable computation of guided modes in photonic crystal wave-guides is of great importance for designing optical devices. Transparent boundary conditions based on Dirichlet-to-Neumann operators allow for an exact computation of well-confined modes and modes close to the band edge in the sense that no modelling error is introduced. The well-known super-cell method, on the other hand, introduces a modelling error which may become prohibitively large for guided modes that are not well-confined. The Dirichlet-to-Neumann transparent boundary conditions are, however, not applicable for all frequencies as they are not uniquely defined and their computation is unstable for a countable set of frequencies that correspond to so called Dirichlet eigenvalues. In this work we describe how to overcome this theoretical difficulty introducing Robin-to-Robin transparent boundary conditions whose construction do not exhibit those forbidden frequencies. They seem, hence, well suited for an exact and reliable computation of guided modes in photonic crystal wave-guides.

High efficiency asymmetric directional coupler for slow light slot photonic crystal waveguides.

An asymmetric directional coupler scheme for the efficient injection of light into slow light slot photonic crystal waveguide modes is proposed and investigated using finite-difference time-domain simulation. Coupling wavelengths can be flexibly controlled by the geometrical parameters of a side-coupled subwavelength corrugated strip waveguide. This approach leads to a ~1dB insertion loss level up to moderately high light group indices (nG≈30) in wavelength ranges of 5-10nm. This work brings new opportunities to inject light into the slow modes of slot photonic crystal waveguides for on-chip communications using hybrid silicon photonics or sensing based on hollow core waveguides.

Coupling of a 2D photonic crystal–metal surface wave to photonic crystal waveguide modes

Photonic crystal waveguides are being used for different applications in sensors, lasers, interferometers, and optical circuits. The process of coupling a light beam to a waveguide presents an inherent loss of energy, particularly for monomode waveguides. In this work, we study the coupling of an interface mode in a metal-2D photonic crystal (2DPC) and a photonic crystal waveguide mode. The coupling produces a hybrid mode that presents an avoided crossing inside the photonic crystal band gap. The avoided crossing produces a mini-stop band whose frequency width is larger when the waveguide is closer to the interface. Using the finite difference time domain method (FDTD) we show that the hybrid mode can be excited by incident light normal to the interface for an appropriate thickness of the metal. For an incident light beam with a given frequency such that two hybrid modes can be excited simultaneously, the energy goes from the interface to the waveguide and vice versa, oscillating with a period given by the coupling distance, as described by coupled mode theory (CMT).

Guided Modes of Positive and Negative Group Index in the Honeycomb Photonic Crystal Waveguides

A guided mode of positive and negative group index structure is essential to quantum optics for design and development of high efficiency optical devices which are useful to security optical communication system and to diverse applications such as Optical Time-Division-Multiplexing, Optical Switch, Laser, LED, Entangled Photon Source and Single Photon Source. Thus, we proposed to develop an efficient photon emission along line defect of two-dimensional honeycomb photonic crystal waveguide in the silicon slab. The honeycomb lattice of circular air holes on a silicon plate is simulated to obtain two nearest guided modes between positive and negative group index regimes. This significant property shows the potential applied guided modes of photonic crystal waveguide enhancing spontaneous emission for controlling photon emission between two resonance frequencies. Significantly, this work is oriented to produce the novel optical devices for control photon emission in the optical communication system. In addition to the honeycomb lattice, it can easily be made on a Si on insulator (SOI) wafer.