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Polygonal Maxwell's fisheye lens via transformation optics as multimode waveguide crossing
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Abstract
Multimode waveguide crossings are crucial components for novel mode-division-multiplexing systems. One of the challenges of multimode waveguide routing in MDM systems is decreasing the inter-mode crosstalk and mode leakage of waveguide crossings. In this work, we present the intersections of three and four waveguides based on polygonal Maxwell's fisheye lens via transformation optics. The designed lenses are implemented by mapping their refractive index to the thickness of guiding Si layer. The three-dimensional finite-difference time-domain simulations are used to evaluate the performance of the proposed $3\times3$ and $4\times4$ crossings. The footprint of the $3\times3$ and $4\times4$ waveguide star crossings are $18.6\times18.6$ and $27.5\times27.5$ $\mu m^2$, respectively. For both waveguide crossings, the intermodal crosstalk in the output port is lower than -22dB while the crosstalk to other ports is lower than -37dB for TE0, TE1, and TE2 modes. The insertion losses for these modes are lower than 0.5dB in a bandwidth of 415nm covering the whole optical telecommunication bands.
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Waveguide crossings are an essential component for constructing complex and functional on-chip photonic networks. Polarization-insensitive waveguide crossings are desired because photonic networks usually involve light with different polarizations. Here, we propose a polarization-insensitive waveguide crossing on a 250-nm silicon-on-insulator platform by using an inverse design method. In simulation, the designed waveguide crossing can maintain insertion loss below 0.18 (0.25) dB in the wavelength range of 1440–1640 nm for the TE 0 ( TM 0 ) mode and achieve minimal insertion loss as small as 0.08 (0.07) dB at the wavelength of 1550 nm. The cross talk maintains below − 32 dB and − 35 dB for the TE 0 and TM 0 modes, respectively. Experimentally, the fabricated waveguide crossing achieves measured insertion loss less than 0.20 (0.25) dB for the TE 0 ( TM 0 ) mode with minimal insertion loss as small as 0.1 dB. The measured cross talk is below − 28 dB and − 31 dB for the TE 0 and TM 0 modes, respectively. Therefore, our proposed waveguide crossing can be widely applied in photonic integrated circuits to construct photonic systems with the capabilities of polarization control and mode (de)multiplexing.
Mode-division multiplexing is a promising and cost-effective way to increase the communication capability of integrated photonic circuits, for both classical and quantum information processing. To construct large-scale on-chip multimode routing systems, the multimode waveguide crossing is one of the key components. However, there have been only a few dual-mode waveguide crossings reported, which can support merely two waveguide modes or two crossing channels. This severely limits the density and capacity of multimode routing systems. Here we demonstrate for the first time, to the best of our knowledge, a universal multimode waveguide star crossing based on transformation optics, which can handle, in principle, any number of waveguide modes and any number of crossing channels as well. The structure is transformed from a Maxwell fisheye and can realize aberration-free imaging for each waveguide mode. A gray-scale electron-beam lithography is adopted to fabricate it on a commercial silicon-on-insulator wafer. The proposed multimode waveguide star crossing has little loss and low crosstalk throughout an ultra-broad wavelength range of ∼ 400 nm . Our study paves the way for realizing highly integrated and large capacity on-chip multimode routing and communication systems.
In this paper, wide-bandwidth low cross-talk W1 photonic crystal waveguide intersections are proposed based on self-collimation effect. The waveguides are realized using a 2D square lattice of GaAs rods in an air background. A second photonic crystal lattice is inserted in the intersection region which provides the self-collimation effect and eliminates the cross-talk. The region between the two lattices is optimized in this paper to produce the highest transmittance and widest bandwidth. Consequently, several waveguide intersections are designed based on the proposed method. Each has a different bandwidth and central wavelength. Due to their unique features such as the wide bandwidth, the low cross-talk value and having high transmittances, such structures have a variety of applications in highly integrated optical circuits which are realized based on photonic crystals. Plane wave expansion and finite difference time domain methods are used to analyze the structures. Simulation results show that a bandwidth of 124 nm and a maximum transmission value of 99% can be obtained using the proposed method.
Waveguide crossing is an important integrated photonic component that will be routinely used for high-density and large-scale photonic integrated circuits, such as optical switches and routers. Several techniques have been reported in achieving high performance waveguide crossings on a silicon-on-insulator photonic platform, i.e., low-loss and low-crosstalk waveguide crossings based on multimode interference, bi-layer tapering, optical transformation, metamaterials, and subwavelength gratings. Until recently, not much attention has been given to the reduction of the footprint of waveguide crossings. Here we experimentally demonstrate an ultra-compact waveguide crossing on silicon photonic platform with a footprint only ~1 × 1 μm². Our simulations show that it has a low insertion loss (< 0.175 dB) and low crosstalk (< −37dB) across the whole C-band, while the fabricated one has an insertion loss < 0.28 dB and crosstalk around −30 dB for the C-band.
On‐chip multimode transmission has drawn tremendous interest for its ability to expand the link capacity with a single wavelength carrier. The waveguide crossing is a basic component in the on‐chip photonic circuit allowing the routing of a complex network. The situation has arisen where the multimode waveguide crossing is required to achieve the high‐density multimode networks. However, the conventional designs of the waveguide crossing only work for the single‐mode. Some works have been reported which realize the multimode crossing, but all suffer from significant losses. Here a multimode waveguide star‐crossing is proposed using the metamaterial‐based Maxwell's fisheye lens, where four multimode waveguides converge at a single junction. The index‐engineered silicon metamaterial is utilized to obtain the Maxwell's fisheye lens on the silicon‐on‐insulator platform. By combining the Maxwell's fisheye lens and tapered waveguides, both TM0 and TM1 modes propagate through the star‐crossing with low losses and cross talk. The fabricated multimode waveguide star‐crossing shows low losses of <0.3 dB and cross talk of <‐20 dB. A multimode waveguide star‐crossing based on the Maxwell's fisheye lens is proposed and demonstrated. The silicon metamaterial is utilized to obtain the index mapping. The losses can be reduced by optimizing the parameters. The fabricated multimode waveguide star‐crossing shows losses of <0.3 dB and crosstalk of <‐20 dB for both TM0 and TM1 modes.
We propose and experimentally demonstrate a novel ultra-compact multimode waveguide crossing. The compact asymmetric subwavelength Y-junction is introduced to convert the high-order modes into fundamental ones, enabling one to implement three or more modes simultaneously in the subsequent processing. Our proposed device occupied only a compact footprint of 34 $\times$ 34 μm2. The measured results indicate our fabricated device exhibited a high performance with insertion loss less than 0.9 dB, crosstalk lower than $\pm$ 24 dB from 1.52 to 1.60 μm for all the three modes. Moreover, our scheme could be easily expended to implement more modes and will show great potential in dense and large-scale on-chip photonic integration.
We propose and experimentally demonstrate a novel ultra-compact dual waveguide crossing based on subwavelength multimode-interference couplers for densely integrated on-chip mode-division multiplexing system. By engineering lateral-cladding material index and manipulating phase profiles of light at the nanoscale using an improved inverse design method, subwavelength structure could theoretically realize the identical beat length for both TE0 and TE1, which can reduce the scale of the device greatly. The fabricated device occupied a footprint of only 4.8 × 4.8 µm 2. The measured insertion losses and crosstalks were less than 0.6 dB and − 24 dB from 1530 nm to 1590 nm for both TE0 mode and TE1 mode, respectively. Furthermore, our scheme could be also expanded to design waveguide crossing supporting more modes.
Silicon slot waveguide intersections are necessary for photonic integrated circuits based on silicon slot waveguides. We theoretically investigate a compact silicon slot waveguide intersection which consists of mode transformers and a multimode strip waveguide crossing. The mode transformer before the crossing converts the slot waveguide mode into strip waveguide modes with amplitudes and phases appropriate for efficient operation of the crossing which is based on multimode interference. The reverse conversion happens in the mode transformer after the crossing. The investigated intersection has a throughput of -0.078 dB, a crosstalk of -41 dB, and a footprint of 79.2 μm $^2$ . Its properties are better than those of previous silicon slot waveguide intersections, and especially its footprint is less than 33 % of the previous ones. The intersection may be used for matrix switches based on silicon slot waveguides.
A dual-mode waveguide crossing is proposed and realized for the application of on-chip multimode interconnection. The present structure is realized by two 90° crossed multimode-interference (MMI) couplers. By properly choosing the width and length of the MMI section, the self-images for both the incident TM 0 mode and the TM 1 mode could be at the center of the crossing. The characterization results for the fabricated device show that low insertion loss below ∼ 1.5 dB and low crosstalk below ∼ − 18 dB can be achieved over a large bandwidth more than 80 nm for both the TM 0 and TM 1 modes.
Gradient index (GRIN) structures have attracted great interests since their invention. Especially, the recent advance in the fields of transformation optics, plasmonics, and nanofabrication techniques has opened new directions for the applications of GRIN structures in nano-photonic devices. In this paper, we apply Luneburg lens and its transformed counterpart to realize efficient coupling to plasmonic nano-waveguides. We first briefly present the general structures of Luneburg lens and generalized Luneburg lens, as well as the design process of flattened Luneburg lens applying quasi-conformal mapping techniques. After that, we study the performance of these lenses for coupling electromagnetic signals to nano-waveguides (the metal-insulator-metal nano-waveguide). Different coupling schemes are investigated. It is found that the proposed Luneburg lens based optical couplers can be used to provide broadband light couplings to plasmonic nano-waveguides under wide incident angles.
We demonstrated a waveguide crossing for submicron silicon waveguides with average insertion loss of 0.18±0.03 dB and crosstalk of -41±2 dB, uniform across an 8-inch wafer. The device was fabricated in a CMOS-compatible process using 248 nm lithography, with only one patterning step.
In the last decade, a technique termed transformation optics has been developed for the design of novel electromagnetic devices. This method defines the exact modification of magnetic and dielectric constants required, so that the electromagnetic behaviour remains invariant after a transformation to a new coordinate system. Despite the apparently infinite possibilities that this mathematical tool introduces, one restriction has repeatedly recurred since its conception: limited frequency bands of operation. Here we circumvent this problem with the proposal of a full dielectric implementation of a transformed planar hyperbolic lens which retains the same focusing properties of an original curved lens. The redesigned lens demonstrates operation with high directivity and low side lobe levels for an ultra-wide band of frequencies, spanning over three octaves. The methodology proposed in this paper can be applied to revolutionise the design of many electromagnetic devices overcoming bandwidth limitations.
A low crosstalk and wideband photonic crystal (PC) waveguide intersection design based on two orthogonal hybrid waveguides in a crossbar configuration is proposed. The finite-dif-ference time-domain (FDTD) and coupled-mode theory (CMT) methods are used to simulate the hybrid waveguides of square lattice. The bandwidth (BW) and crosstalk of the intersection are investigated for various radii of the coupled cavities. It is shown that simultaneous crossing of the lightwave signals through the intersection with negligible interference is possible. The transmis-sion of a 200-fs pulse at 1550 nm is simulated by using the FDTD method, and the transmitted pulse shows negligible crosstalk and very little distortion. Index Terms—Crosstalk, coupled-mode theory (CMT), finite-difference time-domain (FDTD), orthogonal hybrid waveguides, photonic crystal (PC) intersections.
In this paper, we propose a reconfigurable surface plasmon polariton (SPP) wave adapter designed by transformation optics, which can control the propagation of SPP waves on un-even surfaces. The proposed plasmonic device is constructed using homogeneously tunable materials (e.g. liquid crystals) so that the corresponding SPP wave transmission can be reconfigured by applying different voltages. Additionally, modified designs optimized for practical fabrication parameters are investigated. Their performance is verified by full-wave simulations. The proposed devices will pave the way towards developing tunable plasmonic devices.
We propose and experimentally demonstrate a compact, highly efficient, and negligible cross-talk silicon-on-insulator crossing using a periodic dielectric waveguide. The crossing occupies a footprint of less than 4 μm × 4 μm. Around 0.7 dB insertion loss and lower than -40 dB, cross talk was achieved experimentally over a broad wavelength range.
We report on the design, simulation and experimental demonstration of a new type of waveguide crossing based on subwavelength gratings in silicon waveguides. We used 3D finite-difference time-domain simulations to minimize loss, crosstalk and polarization dependence. Measurement of fabricated devices show that our waveguide crossings have a loss as low as -0.023 dB/crossing, polarization dependent loss of < 0.02 dB and crosstalk <-40 dB.
Topology optimization has been used to design intersections in two-dimensional photonic crystal slab waveguides. We have experimentally confirmed that the optimized intersection displays high-transmittance with low-crosstalk for the straightforward beam-propagation line.
A new type of cloak is discussed: one that gives all cloaked objects the appearance of a flat conducting sheet. It has the advantage that none of the parameters of the cloak is singular and can in fact be made isotropic. It makes broadband cloaking in the optical frequencies one step closer.
We present compact crossings for silicon-on-insulator photonic wires. The waveguides are broadened using a 3 microm parabolic taper in each arm. By locally applying a lower index contrast using a double-etch technique, loss of confinement is reduced and 97.5% transmission (-1.7 dB) is achieved with only -40 dB cross talk.
We propose a new mechanism for constructing waveguide intersections with broad bandwidth and low cross talk in photonic crystal (PC) circuits. The intersections are created by combination of coupled-cavity wave-guides (CCWs) with conventional line-defect waveguides. This mechanism utilizes the strong dependence of the defect coupling on the field pattern in the defects and the alignment of the defects (i.e., the coupling angle) in CCWs. By properly designing the defect mode, we demonstrate through numerical simulation the establishment of such a waveguide intersection in one of the most useful PCs, which is based on a two-dimensional triangular lattice of air holes made in a dielectric material. The transmission of a 500-fs pulse at ~1.3 microm is simulated by use of the finite-difference time-domain method, showing negligible distortion and low cross talk.
We present general criteria for crossing perpendicular waveguides with nearly 100% throughput and 0% cross talk. Our design applies even when the waveguide width is of the order of the wavelength. The theoretical basis for this phenomenon is explained in terms of symmetry considerations and resonant tunneling and is then illustrated with numerical simulations for both a two-dimensional photonic crystal and a conventional high-index-contrast waveguide crossing. Cross-talk reduction by up to 8 orders of magnitude is achieved relative to unmodified crossings.
We employ a novel platform for the realization of tunable photonic crystal (PC) circuits together with a Wannier basis modeling and optimization scheme in order to design a broad-band waveguide crossing. The superior performance characteristics of our design include a high bandwidth (2% of the center frequency) as well as low values for crosstalk (-40 dB) and reflection (-30 dB). In addition, we demonstrate the robustness of the device performance against fabrication disorder. Our novel design paradigm will enable efficient and ultracompact PC-based device designs with complex functionalities.
The imaging properties of the Maxwell's fisheye (MFE) lens makes it a viable candidate to implement power coupling between different types of waveguides. A coupler based on the MFE lens is designed to couple a square lattice photonic crystal to a triangular lattice one. The MFE lens is implemented as ring-based multilayer and graded photonic crystal (GPC) structures. The performance of the ring-based MFE lens is better than the GPC-based one in the C-band of optical communication. The proposed ring-based MFE coupler has a footprint of $3.62\times 3.62\mu m$ and covers the entire C and U bands. The S and L bands are partially covered. The average insertion loss of 0.1dB and the maximum return loss of -11dB in the C-band is achieved.
The Maxwell's fisheye (MFE) lens, due to its focusing properties, is an interesting candidate for implementing the crossing of multiple waveguides. The MFE lens is implemented by two different structures: concentric cylindrical multilayer and radially diverging gourd-shaped rods. Realization of the refractive index profile of the lens is achieved by controlling the thickness ratio of the alternating Si and SiO2 layers determined by effective medium theory. Both structures are optimized to cover the entire C-band in the single mode implementation. The transmission efficiency of the ring-based structure is superior to the radial-based implementation, however, the radial-based structure almost covers the entire U-band as well. Other communication bands are partially covered in both cases.Full-wave simulations prove that the performance of multimode waveguide crossing based on the MFE lens with a radius of 2.23 \mu m is promising with the average insertion loss of 0.17dB and crosstalk levels below -24.2dB in the C-band for TM0 and TM1 modes. The multimode intersection almost covers the entire C, L, and U bands of optical communication.
As the integration level of silicon photonics improves, using a large number of 2 × 2 crossings is seemingly inevitable. However, with the help of a multi-ports crossing, which has low crosstalk and loss, the number of crossings can be greatly reduced, then the integration density and routing flexibility can be enhanced. Here, we propose and demonstrate the novel 3 × 3, 4 × 4, 5 × 5 and 6 × 6 silicon waveguide star-crossings based on self-imaging. The star-crossings are fabrication compatible with 180nm commercial CMOS process. The fabricated devices show ultra-low crosstalk and insertion loss. The crosstalk of those crossings are less than -50 dB, -50dB, -49.2 dB and -48 dB, respectively, in Cband. The corresponding insertion loss are less than 0.067 dB, 0.075 dB, 0.081 dB and 0.133 dB, respectively. We also propose the high performance star-crossings with arbitrary angles, which can reduce the difficulty of the waveguide routing and further improve the integration density of photonics IC. The footprint and minimum angle of the proposed star-crossing are also discussed. The crossings have high fabrication tolerance, and will be widely used in the future integrated photonics.
The number of waveguides crossing an intersection increases with the development of complex photonic integrated circuits. Numerical simulations are presented to demonstrate that Maxwell's fish-eye (MFE) lens can be used as a multiband crossing medium. In previous designs of waveguide intersection, bends are needed before and after the intersection to adjust the crossing angle resulting in a larger footprint. The presented design incorporates the waveguide bends into the intersection which saves footprint. In this paper, 4x4 and 6x6 intersections based on ideal and graded photonic crystal (GPC) MFE lenses are investigated, where 4 and 6 waveguides intersect, respectively. The intersection based on ideal MFE lens partially covers the O, E, S, C, L, and U bands of optical communication, while the intersection based on GPC-MFE lens is optimized to cover the entire C-band. For 4x4 and 6x6 intersections based on GPC-MFE lens, crosstalk levels are below -24dB and -18dB, and the average insertion losses are 0.60dB and 0.85dB in the C-band with lenses' radii of 7xa and 10xa, respectively, where a is the lattice constant of the photonic crystal.
With the development of highly densified photonic integrated circuits, the optical cross nodes number exhibits dramatically increasing. Not only efficient but also ultra-compact waveguide crossings are required to materialize the full potential of silicon photonics for on-chip optical intercross connect. In this work, we proposed several inverse-designed 4 × 4, 5 × 5 and 6 × 6 star-crossings based on the photonic-crystal-like (PhC-like) subwavelength structures, which have ultra-high port density of about 7.1 μm2/port, 5.83 μm2/port and 7.3 μm2/port respectively. Moreover, the star-crossings are practically fabricated and experimentally characterized. The average measured insertion losses (ILs) are less than 0.75, 0.9 dB and 1.5 dB, while the crosstalks are sub-22.5 dB, -20 dB and -18 dB for other output ports over 60 nm bandwidth centered at 1550 nm wavelength.
The field of transformation optics shows that media containing gradients in optical properties are equivalent to curved geometries of spacetime for the propagation of light. Conformal transformation optics - a particular variant of this feature can be used to design devices with novel functionalities from inhomogeneous, isotropic dielectric media.
We report the design and fabrication of a four-port InP photonic crystal cavity-waveguide structure in which two crossing waveguides intersect in a cavity. Transmission measurements show that by exploiting mode-gap effects, high cross-talk suppression between the two waveguides can be obtained. In addition, the waveguides couple to two distinct cavity resonances with different quality-factors as well as small mode volumes. This structure is promising for realizing ultra-fast, low-energy optical switches or memories.
This paper introduces a method of measuring the delta between the effective refractive index of a silicon waveguide and a waveguide with wider dimensions through the constructive and destructive interference in a Mach–Zehnder interferometer (MZI). The method consists of a fixed effective refractive index variation incorporated by tapering one of the arms in the interferometer to a wider waveguide dimension. The MZI consists of a Y-branch splitter and a multimode interference (MMI) coupler. The Y-branch splitter splits the input light 50/50 into the two arms, and the MMI is used for recombination of the two arms. A change in the effective refractive index of one arm in comparison with the other arm in the interferometer will introduce a phase difference on recombination in the MMI. The MMI has the following three ports: the top and bottom output ports, which are the antisymmetric outputs, and the middle port, which is the symmetric output. When the two signals are in phase, all the light is coupled into the symmetric port, and when the two inputs are $\pi$ out of phase, the light is coupled 50/50 into the antisymmetric ports. The interferometer is designed on a silicon-on-insulator (SOI) wafer and fabricated through IMEC Belgium. Theoretical, simulation, and measured results are presented and compared.
We theoretically investigate the transmission properties of a cascade of cavities coupled to waveguide by the time domain coupled-mode theory. Based on the theoretical analysis, broad bandwidth optical waveguide intersections in photonic crystals are modeled and optimized. The transmission properties are simulated by finite-difference time-domain method and transmission coefficients higher than 98% for a wide frequency range between 0.360 (2 pic / a ) and 0.364 (2 pic / a ) are obtained.
This paper describes a waveguide crossing design that uses the wavefront matching (WFM) method. The WFM method enables us to design waveguide crossings with lower loss than simple crossings composed of two straight waveguides, without any crosstalk degradation. We report the procedure for designing waveguide crossings based on the WFM method and some experimental results. For experimental confirmation, we made a waveguide crossing test circuit using silica-based planar lightwave circuit (PLC) technology. By comparing the results obtained with samples constructed with different Delta waveguides, we show that our design method is very efficient for higher Delta waveguides suitable for high-density integration. In addition, we describe an example application of our designed crossings to an integrated PLC device, namely a wavelength multiplexer with a variable optical attenuator. We show that waveguide crossings designed by the WFM method are useful for improving the loss characteristic of highly integrated PLC devices.
We have experimentally demonstrated a very low cross talk in photonic crystal waveguide crossings of any kind. For cross talk reduction, we added a resonant cavity to the waveguide intersection designed to operate in microwave frequencies. The two-dimensional waveguide crossing structure was sandwiched between two parallel metal plates to eliminate radiation loss in the vertical direction. Transmission measurements revealed that when designed properly the cross talk reduction was as large as −30 dB at resonance, which is qualitatively consistent with simulation results. From the experimental results, the detailed resonant mode shape at the waveguide intersection was found to play a key role in relaying the input signal in the forward direction and therefore reducing cross talk.
We propose an approach to construct waveguide intersections with broad bandwidth and low cross-talk for square-lattice photonic crystals, by utilizing a vanishing overlap of the propagation modes in the waveguides created by defects which support dipole-like defect modes. The finite-difference time-domain method is used to simulate the waveguide intersection created in the two-dimensional square-lattice photonic crystals. Over a bandwidth of 30 nm with the center wavelength at 1300 nm, transmission efficiency above 90% is obtained with cross-talk below −30 dB. Especially, we demonstrate the transmission of a 500-fs pulse at 1.3 μm through the intersection, and the pulse after transmission shows very little distortion while the cross-talk remains at low level meantime.
We present a design technique for a compact waveguide crossing by using a 90° multimode-interference (MMI) based waveguide crossing sandwiched by four identical miniaturized tapers where the power of the input guided mode is coupled into even modes of the MMI section at a specific power ratio and with different phases, thereby reducing the dimension of this waveguide crossing with imperceptible loss and crosstalk. Using the finite difference time domain method, we demonstrate that the MMI-based waveguide crossing embedded in short Gaussian tapers has a size 5426 nm × 5426 nm, insertion loss 0.21 dB, and crosstalk -44.4 dB at the wavelength of 1550 nm and broad transmission spectrum ranging from 1500 to 1600 nm.
A method for the generation of orthogonal boundary-fitted curvilinear coordinates for arbitrary simply- and doubly-connected domains is developed on the basis of the theory of quasi-conformal mappings of quadrilaterals and of previous work by Ryskin and Leal. The method has useful applications in orthogonal grid generation in two-dimensional and axi-symmetric domains and in the extension of rapid elliptic solvers and spectral methods to complex geometries. A new technique for the calculation of the conformal module of quadrilaterals is also presented.
We report multimode-interference (MMI)-based crossings in high-index-contrast silicon wire waveguides. Our experiments show an MMI crossing of similar to 0.4-dB insertion loss, which suggests similar to 0.9-dB improvement from a control plain crossing of the same size and refractive index contrast. We also experimentally observe significant crosstalk suppression in our MMI crossing. The MMI crossing transmission exhibits wavelength dependence of less than 0.2 dB within the 1520-1580-nm wavelength range.
For centuries, the conventional approach to lens design has been to grind the surfaces of a uniform material in such a manner as to sculpt the paths that rays of light follow as they transit through the interfaces. Refractive lenses formed by this procedure of bending the surfaces can be of extremely high quality, but are nevertheless limited by geometrical and wave aberrations that are inherent to the manner in which light refracts at the interface between two materials. Conceptually, a more natural--but usually less convenient--approach to lens design would be to vary the refractive index throughout an entire volume of space. In this manner, far greater control can be achieved over the ray trajectories. Here, we demonstrate how powerful emerging techniques in the field of transformation optics can be used to harness the flexibility of gradient index materials for imaging applications. In particular we design and experimentally demonstrate a lens that is broadband (more than a full decade bandwidth), has a field-of-view approaching 180 degrees and zero f-number. Measurements on a metamaterial implementation of the lens illustrate the practicality of transformation optics to achieve a new class of optical devices.
A compact waveguide crossing structure with low transmission losses and negligible crosstalk is demonstrated for silicon-on-insulator circuits. The crossing structure is based on a mode expander optimized by means of a genetic algorithm leading to transmission losses lower than 0.2 dB and crosstalk and reflection losses below 40 dB in a broad bandwidth of 20 nm. Furthermore, the resulting crossing structure has a footprint of only 6x6 microm(2) and does not require any additional fabrication steps.
An intersection based on photonic crystal coupled resonator optical waveguides is proposed and analyzed. The two waveguides are designed to have different transmission bands without overlap, which enables light in the two corresponding bands to propagate through the intersection with no cross talk and with excellent transmission. The MIT Photonic-Bands code is used to calculate the band structures of photonic crystal waveguides. The finite-difference time-domain method is used to simulate the relevant structures.
We have studied the wavefront matching (WFM) method, which synthesizes optimum waveguide patterns from the desired characteristics, and demonstrated its feasibility. In this paper, we expand this method to create optimum waveguide shapes with low-loss and low-wavelength dependence in waveguide lenses, Y-branches, and waveguide crossings. We describe the design procedures for each waveguide element and report the experimental results as proof of concept. The measured results agree well with our design requirements, and the waveguide patterns designed by the WFM method exhibit better characteristics than the reference patterns.
Metamaterials are beginning to transform optics and microwave technology thanks to their versatile properties that, in many cases, can be tailored according to practical needs and desires. Although metamaterials are surely not the answer to all engineering problems, they have inspired a series of significant technological developments and also some imaginative research, because they invite researchers and inventors to dream. Imagine there were no practical limits on the electromagnetic properties of materials. What is possible? And what is not? If there are no practical limits, what are the fundamental limits? Such questions inspire taking a fresh look at the foundations of optics and at connections between optics and other areas of physics. In this article we discuss such a connection, the relationship between optics and general relativity, or, expressed more precisely, between geometrical ideas normally applied in general relativity and the propagation of light, or electromagnetic waves in general, in materials. We also discuss how this connection is applied: in invisibility devices, perfect lenses, the optical Aharonov-Bohm effect of vortices and in analogues of the event horizon. Comment: 72 pages, 18 figures, preprint with low-resolution images. Introduction to transformation optics, to appear in Progress in Optics (edited by Emil Wolf)
- M Mccall
- J B Pendry
- V Galdi
- Y Lai
- S Horsley
- J Li
- J Zhu
- R C Mitchell-Thomas
- O Quevedo-Teruel
- P Tassin
M. McCall, J.B. Pendry, V. Galdi, Y. Lai, S. Horsley, J. Li, J. Zhu, R.C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, Roadmap on transformation optics, Journal of Optics, 20 (2018) 063001.