Photonic Crystal Waveguide Modes Research Articles

Physical origin of the small modal volume of ultra-high-Q photonic double-heterostructure nanocavities

We have recently demonstrated the fabrication of ultra-high-Q photonic double-heterostructure nanocavities with Q-factors of almost 1 million and ultra-small modal volumes with dimensions of optical wavelengths. Here, we describe the physical origin of the small modal volume by analysing the (imaginary) dispersion relations of the mode-gap of photonic crystal (PC) waveguides, where the mode-gap effect is the fundamental principle by which photons are confined in the nanocavities. By expanding the real dispersion relations of the propagation modes of different PC waveguides into their complex form, we obtain the (imaginary) dispersion relations of the mode-gap. It is shown that the ultra-small modal volume originates from the unusual dispersion relation of the propagation mode of the PC waveguide and that it can be engineered by the geometric parameters of the waveguide. This is demonstrated experimentally by the fabrication of photon tunnelling structures and measurement of their transmission characteristics. These results reported here will be very useful for the realization of high-Q cavities with ultra-small modal volumes and their application to nanophotonics.

Interaction of two different frequency photonic crystal waveguide modes through the resonant excitation of modes on off-channel Kerr nonlinear media

The properties of two photonic crystal waveguide modes at different frequencies that propagate down a straight photonic crystal waveguide are studied for cases in which the two modes interact with off-channel structures composed of Kerr nonlinear dielectric media. The optical nonlinearity of the off-channel structures mediates an interaction between the two modes that allows the modes to modulate the transmission of each other down the waveguide channel. This interaction and mutual modulation is shown to be pronounced in the case when either of the two waveguide modes resonantly excites a localized mode on the off-channel features formed of Kerr nonlinear media. Cases that are considered are a straight linear dielectric media waveguide with off-channel structures formed as: (a) a single off-channel Kerr site that supports a bound localized electromagnetic mode, (b) multiple off-channel Kerr sites that support a bound intrinsic localized electromagnetic mode, and (c) multiple off-channel Kerr sites that support an intrinsic localized mode that in turn interacts with a semi-infinite waveguide of linear dielectric media. In cases (a) and (b) the effects of resonant excitation of single site and intrinsic localized modes in the Kerr medium on the transmission characteristics are determined. In case (c) the effects of resonant excitation of intrinsic localized modes in the Kerr medium on the transmission characteristics of the two waveguide modes into the infinite and semi-infinite waveguides are studied.

Intrinsic localized modes in photonic crystal waveguides composed of a periodic mixed array of linear and Kerr nonlinear dielectric media

A theoretical treatment is given of intrinsic localized modes in waveguides and in junctions of waveguides formed inside two-dimensional photonic crystals. Two-dimensional photonic crystals are periodic arrays of parallel-axed dielectric cylinders, and the electromagnetic modes of interest propagate in the plane perpendicular to the cylinder axes. Waveguides are formed inside the photonic crystal by replacement of a row of cylinders. The replacement cylinders are chosen so that the waveguide channels formed bind and conduct electromagnetic energy along the channel in the plane perpendicular to the cylinder axes. In the systems we study, the waveguide channels are composed of a periodic array of linear and Kerr nonlinear media in which both the linear and nonlinear dielectric materials differ from the linear dielectric materials forming the bulk photonic crystal. These waveguides are shown to support intrinsic localized modes. The intrinsic localized modes are studied by determining their scattering properties in waveguide systems. The transmission characteristics of a waveguide formed of linear dielectric media but containing a barrier that is a periodic array of linear and Kerr nonlinear dielectric is studied. Studies are also made of the transmission characteristics of waveguides of linear dielectric media that are connected at a waveguide junction that is composed of co-joined segments containing a periodic array of linear and Kerr nonlinear dielectric media. Transmission anomalies in these two types of waveguide geometries (i.e., barrier and junction geometries), associated with the development of intrinsic localized modes in the barrier or segments composing the waveguide junctions, are identified. This work is an extension of that presented in A.R. McGurn, G. Birkok. Phys. Rev. B 69 (2004) 235105, which treated the scattering characteristics of intrinsic localized modes in barriers and junctions formed solely of Kerr nonlinear dielectric media to treat other types of waveguides that can support intrinsic localized modes.

Near-field characterization of propagating optical modes in photonic crystal waveguides

We analyze the propagating optical modes in a Silicon membrane photonic crystal waveguide, based on subwavelength-resolution amplitude and phase measurements of the optical fields using a heterodyne near-field scanning optical microscope (H-NSOM). Fourier analysis of the experimentally obtained optical amplitude and phase data permits identification of the propagating waveguide modes, including the direction of propagation (in contrast to intensity-only measurement techniques). This analysis reveals the presence of two superposed propagating modes in the waveguide. The characteristics of each mode are determined and found to be consistent with theoretical predictions within the limits of fabrication tolerances. An analysis of the relative amplitudes of these two modes as a function of wavelength show periodic oscillation with a period of approximately 3.3 nm. The coupling efficiency between the ridge waveguide and the photonic crystal waveguide is also estimated and found to be consistent with the internal propagating mode characteristics. The combination of high-sensitivity amplitude and phase measurements, subwavelength spatial resolution, and appropriate interpretive techniques permits the in-situ observation of the optical properties of the device with an unprecedented level of detail, and facilitates the characterization and optimization of nanostructure-based photonic devices and systems.

Efficient coupling to chalcogenide glass photonic crystal waveguides via silica optical fiber nanowires

We demonstrate highly efficient evanescent coupling between a highly nonlinear chalcogenide glass two dimensional photonic crystal waveguide and a silica fiber nanowire. We achieve 98% insertion efficiency to the fundamental photonic crystal waveguide mode with a 3dB coupling bandwidth of 12nm, in good agreement with theory. This scheme provides a promising platform to realize low power nanocavity based all-optical switching and logic functions.

Horn waveguide couplers for interfacing between two-dimensional photonic crystal and single mode planar dielectric waveguides

We propose and optimize the horn waveguide couplers based on distributed Bragg reflector waveguide for coupling between two-dimensional dielectric cylinder photonic crystal waveguide and single mode planar dielectric waveguide and evaluate their transmission efficiency using the finite difference time domain method. The simulation results show that the power transmission efficiency is over 98% in a large part of the frequency range of the guided mode of photonic crystal waveguide. The highest transmission efficiency is 99.85%.

Discovery of a novel silicon photonic crystal waveguide modulator

Discovery of a novel silicon photonic crystal waveguide modulator

Theoretical investigation of transverse optical modes in photonic-crystal waveguides imbedded into proton-implanted and oxide-confined vertical-cavity surface-emitting lasers

We explain theoretically the influence of a two-dimensional photonic crystal (PC) defect waveguide imbedded in vertical-cavity surface-emitting laser (VCSEL) structures both gain guided and index guided. In particular, we focus in the control of the transverse modes within the VCSEL cavity. As expected in originally gain-guided VCSELs, the index guiding provided by the PC dominated the gain guiding. The single mode defined by a PC waveguide can be obtained in originally index-guided VCSELs as well as a result of depositing the oxide at the node position. It is shown that the thermal lensing effect leads to multimode generation in the VCSEL.

Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides

A device concept for laterally extracting selected wavelengths from an optical signal traveling along a waveguide, for operation in metropolitan area networks, is presented. The signal on the fundamental mode of a multimode photonic crystal waveguide is coupled to a higher-order mode, at a center frequency that spatially depends on the slowly varying guide parameters. The device is compact, intrinsically fault tolerant, and can split any desired fraction of the signal for monitoring purpose. Characterizations by the internal light source technique validate the optical concept whereas an integrated device with four photodiodes qualifies its potential with respect to real-world applications.

Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator

We present a powerful design and optimization method for devices in a photonic crystal. The method is based on a Wannier basis field expansion and efficient matrix analysis techniques for searching through a vast number of designs. The method permits the design of many compact optical devices with complex and novel functions. We present a design example of a very compact mode separator that is 8.2 microm x 13.3 microm in size that demultiplexes the three modes of an input photonic crystal multimode waveguide into three single-mode output waveguides. We verify the method with finite-difference time-domain calculations.

Broadening compensation for ultrashort pulses in photonic crystals

Extremely large group velocity dispersion of both signs can be achieved at the band edges of guided modes in photonic crystal waveguides. The selection of a proper value and sign of this parameter allows the design of short-length waveguides to compensate for pulse broadening. This pulse broadening can be caused, for instance, when a photonic crystal delay line is introduced. We present a theoretical study of the possibilities of using photonic crystal waveguides as intra-circuital dispersion compensation elements for ultrashort pulses, so the width of a transmitted pulse can be reduced. However, we also demonstrate that recovering the original pulse shape is not possible for these large-bandwidth pulses due to higher-order dispersion terms.

Low-loss guided modes in photonic crystal waveguides

We study disorder-induced propagation losses of guided modes in photonic crystal slabs with line-defects. These losses are treated within a theoretical model of size disorder for the etched holes in the otherwise periodic photonic lattice. Comparisons are provided with state-of-the-art experimental data, both in membrane and Silicon-on-Insulator (SOI) structures, in which propagation losses are mainly attributed to fabrication imperfections. The dependence of the losses on the photon group velocity and the useful bandwidth for low-loss propagation are analyzed and discussed for membrane and asymmetric as well as symmetric SOI systems. New designs for further improving device performances are proposed, which employ waveguides with varying channel widths. It is shown that losses in photonic crystal waveguides could be reduced by almost an order of magnitude with respect to latest experimental results. Propagation losses lower than 0.1 dB/mm are predicted for suitably designed structures, by assuming state-of-the-art fabrication accuracy.

Excitation of radiative and evanescent defect modes in linear photonic crystal waveguides

The dispersion of line-defect modes in silicon-on-insulator photonic crystal waveguides is explored by means of angle- and polarization-resolved micro-reflectance measurements. The frequency-wave vector range accessible to the experiments is greatly expanded by the use of attenuated total reflectance, in addition to the standard one, thereby allowing one to study both truly guided (evanescent) and quasi-guided (radiative) photonic modes. The presence of a supercell repetition in the direction perpendicular to the line defect leads to the

Near-field characterization of planar photonic-crystal-waveguide structures.

Characterization of photonic-crystal-waveguide (PCW) structures at telecommunication wavelengths with a collection scanning near-field optical microscope (SNOM) is considered. The propagation of light in silicon-on-insulator PCWs, formed by removing a single row of holes in the triangular lattice and connecting to access ridge waveguides, is imaged with the SNOM. High-contrast and high-resolution SNOM images of PCW structures containing straight PCWs as well as 90 degrees gradual and 60 degrees sharp PCW bends are obtained in the wavelength range of 1520-1570 nm, allowing for the determination of PCW mode characteristics and bend loss. We relate optical-signal variations along straight PCWs to the interference between a quasi-homogeneous background field and Bloch harmonics of the PCW mode, and use spatial-frequency spectra of the intensity variations to determine the dispersion of the PCW mode propagation constant. The bend loss is evaluated using averaged signal cross-sections and taking into account the fact that the signal is proportional to the PCW mode amplitude. It is directly shown that the bend loss for 60 degrees bends is significantly decreased for smoothened bends having one or three holes moved from the inner side of the bend corner to the outer one. The possibilities and limitations of SNOM imaging for the characterization of PCW structures are discussed.

Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode

Coupling characteristics between the single-cell hexapole mode and the triangular-lattice photonic crystal slab waveguide mode is studied by the finite-difference time-domain method. The single-cell hexapole mode has a high quality factor (Q) of 3.3Chi106 and a small modal volume of 1.18(lambda/n)3. Based on the symmetry, three representative types of coupling geometries (shoulder-couple, butt-couple and side-couple structures) are selected and tested. The coupling efficiency shows strong dependence on the transverse overlap of the cavity mode and the waveguide mode over the region of the waveguide. The shoulder-couple structure shows best coupling characteristics among three tested structures. For example, two shouldercouple waveguides and a hexapole cavity result in a high performance resonant-tunneling-filter with Q of 9.7Chi105 and transmittance of 0.48. In the side-couple structure, the coupling strength is much weaker than that of the shoulder-couple structure because of the poor spatial overlap between the mode profiles. In the direct-couple structure, the energy transfer from the cavity to the waveguide is prohibited because of the symmetry mismatch and no coupling is observed.

Accurate modeling of line-defect photonic crystal waveguides

An accurate three-dimensional method to calculate the Bloch modes of photonic crystal (PhC) waveguides is proposed. Good agreement with available experimental and numerical data is obtained. The originality of the method lies in the fact that the Bloch modes are seen as the electromagnetic fields associated to the complex poles of an in-plane transversal scattering matrix. In comparison with previous approaches, the computational domain discretized is smaller and a higher accuracy for the losses of PhC waveguides is achieved.

Inductivity coupled plasma etching to fabricate the nonlinear optical polymer photonic crystal waveguides

To fabricate the photonic crystal (PC) waveguides with large nonlinearity, the inductivity coupled plasma etching characteristics are systematically investigated for the nonlinear optical (NLO) polymer and the fabrication techniques for the NLO polymer PC waveguides are established at the suboptical wavelength scale. We demonstrate the successful fabrication of the NLO polymer PC waveguides with circular holes of diameter 120 nm and very straight sidewalls by using this technique. Moreover, by the examination of the pattern size dependence of etch rates, it is found that rapid reduction of etch rate due to the microloading effect is prevented in the circular hole sizes up to 100 nm at the optimized polymer etching condition. The sharp dip structures originating from resonance coupling to the photonic crystal waveguide modes are clearly observed in the optical reflectance spectra, which exhibits the high-precision feature of this waveguide and the good processability for the material in this technique.

Multiple-scales analysis of photonic crystal waveguides

The multiple-scales method is used to derive a scalar differential equation that describes the envelopes of photonic crystal waveguide modes. For a photonic crystal heterostructure waveguide and an air core photonic crystal waveguide, the mode frequencies calculated from the envelope approximation and full numerical simulations agree to 9% in the worst case when compared to the frequency difference of the band edges. The single-mode and cutoff width conditions for a photonic crystal waveguide are predicted and verified.

Highly-Dispersive Guided Modes of Two-Dimensional Photonic Crystal Waveguides

We present an analysis of highly-dispersive guided modes of two-dimensional photonic crystal waveguides. By the plane ave expansion method, band structures and mode profiles of two-dimensional photonic crystal waveguides are obtained. It is found that guided modes have very small group velocities and very large group velocity dispersions in the region near the f-point and in the region near the Brillouin zone edge. Especially, the group velocity dispersions are found to be millions of times larger than that of a conventional optical fiber. The contributions of the transverse resonance formed by two photonic band gap reflectors and the standing wave mode formed by periodic structures are discussed. We conclude that the highly-dispersive characteristics originate from the resonator-like aspect of the photonic crystal waveguide.

Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane

We have investigated light propagation through a single line-defect photonic crystal waveguide on a InP membrane. Modal analysis was performed using the finite-difference time-domain method. The fundamental mode has been found to be very close to the fundamental mode in a “refractive” waveguide but, in this case, it is inherently leaky. The propagation losses of this mode in the complete three-dimensional structure have been computed and measured to determine if its use could be of interest for practical applications. Propagation losses in the range of 0.1 dB/μm have been found numerically and experimentally for the fundamental mode whereas stronger out-of-plane losses have been observed for the other leaky mode within the band gap. The origins of the out-of-plane losses were then investigated and have clarified the inherent lower leakage of the fundamental mode.