Delay-bandwidth Product Research Articles

Impact of BER in fragmentation-aware routing and spectrum assignment in elastic optical networks

Routing and spectrum assignment (RSA) in elastic optical network (EON) is a challenging task as an inefficient RSA may result in spectral and spatial fragmentation, leading to under-utilization of spectrum and increased connection blocking. Previous fragmentation-aware RSA algorithms, based on the assumption of an ideal physical layer, are not suitable for the performance evaluation of practical networks, where quality of the optical signal degrades while travelling long distances through the optical fiber links. Therefore, while running a RSA algorithm, it is necessary to consider the impact of all noise components to evaluate receiver bit-error rate (BER) on the fly, so that each connection is setup only when the estimated BER remains below an acceptable limit. This problem, hitherto unexplored in EONs though more significant and complex as compared to the conventional optical networks, is taken into consideration in this paper while framing fragmentation-aware RSA algorithm. In particular, we present a novel BER-cum-fragmentation-aware RSA algorithm, by using online estimates of BER values while executing fragmentation-aware RSA. The simulation results show that awareness of BER increases the connection blocking, which can however be addressed favorably by increasing transmit power, as much as possible from the available transmitter modules. Finally, we present a histogram of number of established connections versus delay-bandwidth product of the connections, leading to an assessment of the proposed algorithm in respect of the ability to allow long-haul connections with large bandwidth requests.

Slow light with high normalized delay-bandwidth product in organic photonic crystal coupled-cavity waveguide.

In this theoretical study, a photonic crystal coupled-cavity waveguide created on polymer substrate was demonstrated to provide high-performance slow light with low group-velocity dispersion and large normalized delay-bandwidth product. Combined with structural-parameter optimization, the normalized delay-bandwidth product was enhanced to a large value of 0.809, and the group-velocity dispersion was on the order of 104(ps2/km). Furthermore, the optimized coupled-cavity waveguide had tunability capabilities by changing the external pump laser power. Importantly, while adjusting the slow light, the normalized delay-bandwidth product values remained above 0.8, which was necessary to maintain the performance of optical buffering devices.

Theoretical study of a memory-based optical converter with degenerate Zeeman states

Coherent optical memory based on electromagnetically induced transparency (EIT) offers a convenient way to convert the frequency or polarization of an optical probe pulse by storing in one $\mathrm{\ensuremath{\Lambda}}$ system and retrieving in another $\mathrm{\ensuremath{\Lambda}}$ system. We present a theoretical study on the efficiency variation of such an EIT-memory-based optical converter in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affect the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficients for the probe and control transition in the reading channel, which results in a nonadiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a ${\ensuremath{\sigma}}^{+}$-polarized pulse and retrieving with ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.

Simulation of dynamically tunable and switchable electromagnetically induced transparency analogue based on metal-graphene hybrid metamaterial

A planar terahertz electromagnetically induced transparency-like (EIT-like) metamaterial, comprising an outer circular ring resonator (CRS) made by graphene, an inner vertical two-gap circular split ring resonator (VSRR) and a smaller horizontal two-gap circular split ring resonator (HSRR), is proposed. A distinct transparency window can be observed in two perpendicular polarization directions, respectively. By tuning the Fermi energy, the maximum modulation depths in two perpendicular polarization directions respectively can reach up to 83.54% and 94.39%. Meanwhile, the EIT-like effect, amplitude of transparency window, group delay and delay bandwidth product (DBP) can be adjusted dynamically without shift of frequency. The surface currents and three-level Λ-type system can explain the physical mechanism of EIT-like effect. The analytical results based on a two-particle model are in good agreement with the numerical results. Our work provides a new method for dynamically adjustable terahertz slow light devices, which makes the graphene more controllable in metal-graphene hybrid structure.

Wideband Slow Light in a Line-defect Annular Photonic-crystal Waveguide

In this theoretical study, a line-defect photonic-crystal waveguide hosted in an annular photonic crystal was demonstrated to provide high-performance slow light with a wide band, low group-velocity dispersion, and a large normalized delay-bandwidth product. Combined with structural-parameter optimization and selective optofluid injection, the normalized delay-bandwidth product could be enhanced to a large value of 0.502 with a wide bandwidth of 58.4 nm in the optical-communication window, for a silicon-on-insulator structure. In addition, the group-velocity dispersion is on the order of 105 (ps2/km) in the slow-light region, which could be neglected while keeping the signal transmission unchanged.

Sub-hertz optomechanically induced transparency with a kilogram-scale mechanical oscillator

Optical interferometers with suspended mirrors are the archetype of all current audio-frequency gravitational-wave detectors. The radiation pressure interaction between the motion of the mirror and the circulating optical field in such interferometers represents a pristine form of light-matter coupling, largely due to 30 years of effort in developing high quality optical materials with low mechanical dissipation. However, in all current suspended interferometers, the radiation pressure interaction is too weak to be useful as a resource, and too strong to be neglected. Here, we demonstrate a meter-long interferometer with suspended mirrors, of effective mass $~ 125$ g, where the radiation pressure interaction is enhanced by strong optical pumping to realize a cooperativity of $50$. We probe this regime by observing optomechanically-induced transparency of a weak on-resonant probe. The low resonant frequency and high-Q of the mechanical oscillator allows us to demonstrate transparency windows barely $100$ mHz wide at room temperature. Together with a near-unity ($\sim 99.9\%$) out-coupling efficiency, our system saturates the theoretical delay-bandwidth product, rendering it an optical buffer capable of seconds-long storage times.

Broadband quantum memory using electromagnetically induced transparency in atomic medium

ABSTRACTIn this paper, we describe a theoretical design for the realization of a high capacity (bandwidth) atomic quantum memory based on wavelength division multiplexing and electromagnetically induced transparency in adjacently placed 87Rb vapour cells. Magnetic fields produced by Helmholtz coils are used to tailor the atomic energy levels in the vapour cells and hence storage of various probe signals of different wavelengths becomes possible. We give a detailed description of the proposed experimental setup. We have estimated a very high bandwidth of 50 MHz for our design with a delay bandwidth product of approximately 530. Our prototype design is for storing five different wavelength probe pulses which could be extended to larger values in principle.

Slow light performance enhancement of graphene-based photonic crystal waveguide

We propose a graphene-based photonic crystal (PC) slow light waveguide, which is realized by creating periodical air holes in a silicon layer to achieve spatially varying chemical potentials of graphene. The structure is optimized around 30 THz, and a large group index of 166.6 is obtained, with a very low propagation loss of −2.1 dB/um. The corresponding normalized delay-bandwidth product reaches as high as 4.00. Furthermore, the slow light performance can be dynamically tuned by changing a bias voltage. The center frequency of the slow light waveguide can be tuned between 19.1 THz and 27.4 THz. Our results suggest that graphene-based PC structures are very promising for slow light devices.

Improved slow light performances using photorefractive two-wave mixing.

We experimentally observe an ultralow effective group velocity of 0.9cm/s of light pulses using the two-wave mixing process in an Sn2P2S6 (SPS):Te crystal at a visible wavelength. The time delay can be controlled through the nonlinear photorefractive gain and the input pulse duration. By optimizing the nonlinearity strength, we achieve a maximum fractional delay of 0.79 for a pulse duration of 100ms. Our photorefractive slow light system allows combining low group velocity with large delay-bandwidth product for pulse durations spanning three orders of magnitude.

Slow light with high normalized delay-bandwidth product in low-dispersion photonic-crystal coupled-cavity waveguide

Slow-light performance based on photonic-crystal coupled-cavity waveguide (PC-CCW) is investigated with low-dispersion pulse transmission. A chain of periodically arranged specific defect cavities of air holes are created along the axis of the waveguide and each of the cavities looks like an irregular hexagon with arrow-like left and right sides to form the PC-CCW. By changing the radius and position of certain defects, slow light modes are achieved. Through optimization, we obtained a highest compromise value for an operating bandwidth of 12.9 nm with an average group index of 70.75 and a normalized delay-bandwidth product (NDBP) of 0.5873. This value of NDBP with low group velocity dispersion is higher than that in other structures based on waveguides or coupled cavities reported previously. The arrow-like shape of the cavity sides is shown to be perfect for reducing the transmission loss of the waveguide. The proposed structure with high NDBP is beneficial for buffering applications and slow light devices.

Tunable Active Inductor-Based Second-Order All-Pass Filter as a Time Delay Cell for Multi-GHz Operation

In this paper, a CMOS wideband second-order voltage-mode all-pass filter as a time delay cell is proposed. The proposed all-pass filter is made up of solely two transistors as active elements and four passive components. This filter demonstrates a group delay of approximately 60 ps within a bandwidth of 5 GHz, achieving maximum delay–bandwidth product. The proposed circuit is highly linear and has an input-referred 1-dB compression point $$P_{1\mathrm{{dB}}}$$ of 2 dBm. The power consumption of the proposed circuit is only 10.3 mW. On the other hand, an active inductor is employed in the all-pass filter instead of a passive RLC tank; therefore, the three passive components are eliminated, in order to tune the time delay and improve the size. In this case, even though the power consumption increases, the time delay can be controlled across an improved bandwidth of approximately 10 GHz. Moreover, the circuit demonstrates a 1-dB compression point $$P_{1\mathrm{{dB}}}$$ of 18 dBm. The proposed all-pass filter is simulated in TSMC 180-nm CMOS process parameters.

Five-Line Photonic Crystal Waveguide for Optical Buffering and Data Interconnection of Picosecond Pulse

A five-line (5L) photonic crystal waveguide (PCW) capable of realizing compact, optical buffering and low-distortion data interconnection of picosecond pulse is presented and studied through plane-wave expansion and finite-difference time-domain methods. By appropriately modifying the radii of defects in the 5L PCW, high buffering performance and low-distortion slow light transmission of picosecond pulses are achieved, which are guaranteed by an optimized value of normalized delay bandwidth product (NDBP) of 0.6811 for the proposed PCW. The largest buffering storage capacity and bandwidth obtained are about 219.73 bit and 19.55 nm, respectively. It is found that the distortion of pulse transmission in a PCW is greatly affected by the waveguide length. With these optimized parameters, a relative pulse distortion per unit length of 1.15×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> is obtained for a 2.19-ps pulse, meaning that for a signal pulse with a dutyfactor of 0.5, the proposed structure can process optical digital pulse signals at the speed of 0.22831 Tb/s. Moreover, the NDBP value of 0.6811 obtained is much higher than that of all other structures based on waveguides reported in the literature previously so that high performance of the proposed PCW can be achieved. The waveguide proposed is suitable for data interconnections among chips or among processing units within a chip in optical signal processing, and computations where the size of the transmission line or interconnector is highly limited.

Ultracold Rydberg atoms for efficient storage of terahertz frequency signals using electromagnetically induced transparency

Quantum communication with terahertz (THz) frequency signals has many advantages like reduced attenuation and scintillation effects in certain atmospheric conditions along with very high level of data security. In this work, we propose a scheme to realize Quantum Memory (QM) for efficient storage of terahertz (THz) frequency signals using Electromagnetically Induced Transparency (EIT) in an ultracold atomic medium of 87Rb Rydberg atoms prepared in a Two Dimensional Magneto Optical Trap (2D-MOT). The uniqueness of our scheme lies in the choice of the energy levels involved in the EIT process, all three of which have been chosen to be the Rydberg levels (enabling signal beam to be in THz) in a lambda type arrangement. This first of its kind proposal reveals that atomic media are a potential candidate for devising QMs which can store THz frequency signals. We have estimated that the Optical Depth (OD) in our scheme can reach a very high value of 690, very high maximum obtainable storage efficiency (η) of ∼99%, the group velocity (vg) can be as low as 5.07 × 103 m/s, and the Delay Bandwidth Product (DBP) can be as high as 9.5. All of these estimates emphasize the feasibility of our scheme as a QM device for efficient storage of THz pulses.

Effect of transmission impairments in CO-OFDM based Elastic Optical Network design

Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) based Elastic Optical Network (EON) is one of the emerging technologies being considered for next generation high data rate optical network systems. Routing and Spectrum Allocation (RSA) is an important aspect of EON. Apart from spectral fragmentation created due to spectrum continuity and contiguity constraints of RSA, transmission impairments such as shot noise, amplified spontaneous emission (ASE), beat noise due to coherent detection, crosstalk in cross-connect (XC), nonlinear interference, and filter narrowing, limit the transmission reach of optical signals in EON. This paper focuses on the off-line joint optimization of delay-bandwidth product, fragmentation and link congestion for RSA in CO-OFDM EON while considering the effect of physical layer impairments. First, we formulate an optimal Mixed Integer Linear Programming (MILP) that achieves load-balancing in presence of transmission impairments and minimizes delay-bandwidth product along with fragmentation. We next propose a heuristic algorithm for large networks with two different demand ordering techniques. We show the benefits of our algorithm compared to the existing load-balancing algorithm.

Dynamic tuning of the Q factor in a photonic crystal nanocavity through photonic transitions.

Photonic devices based on a high-Q cavity are commonly constrained by narrow operation bandwidth, slow charging, and releasing speed. Here, we analytically and numerically demonstrate that this limitation can be broken via dynamically tuning the Q factors of a single nanocavity and driving controllable photonic transitions between a low-Q cavity mode and an ultrahigh-Q mode by temporal refractive index modulations inside a multimode cavity. During this dynamic process, the bandwidth of signal light is also reversibly compressed. As a result, the fundamental link between the photon lifetime and the operation bandwidth is broken, and a delay-bandwidth product of ∼76 is achieved, which is far greater than that of the usual optical resonator systems. This approach may pave the way for dynamic control of on-chip all-optical information processing.

Ultra-wideband slow light transmission with high normalized delay bandwidth product in W3 photonic crystal waveguide

By separating two photonic crystals with a distance of 23a, where a is the lattice constant, shifting the positions of some discriminatory air holes in the upper and lower edges, and inserting a defect central row, a specific waveguide is set up, W3 photonic crystal waveguide (W3 PCW). An equivalent transmission line model is given, giving the theoretical basis of for the proposed waveguide to have a wider transmission bandwidth and thus higher normalized delay bandwidth product (NDBP). Slow-light properties and performance are studied by using plane-wave expansion and finite-difference time-domain methods. We obtained ultra-wideband of 65.70 nm with low group-velocity dispersion and at the same time a high NDBP of 0.496 through optimization which is a worthy indicator for slow light device performance. Wider bandwidth can allow shorter duration of pulse waves, causing higher field intensity and stronger nonlinear effect.

A polarization independent electromagnetically induced transparency-like metamaterial with large group delay and delay-bandwidth product

In this study, a classical analogue of electromagnetically induced transparency (EIT) that is completely independent of the polarization direction of the incident waves is numerically and experimentally demonstrated. The unit cell of the employed planar symmetric metamaterial structure consists of one square ring resonator and four split ring resonators (SRRs). Two different designs are implemented in order to achieve a narrow-band and wide-band EIT-like response. In the unit cell design, a square ring resonator is shown to serve as a bright resonator, whereas the SRRs behave as a quasi-dark resonator, for the narrow-band (0.55 GHz full-width at half-maximum bandwidth around 5 GHz) and wide-band (1.35 GHz full-width at half-maximum bandwidth around 5.7 GHz) EIT-like metamaterials. The observed EIT-like transmission phenomenon is theoretically explained by a coupled-oscillator model. Within the transmission window, steep changes of the phase result in high group delays and the delay-bandwidth products reach 0.45 for the wide-band EIT-like metamaterial. Furthermore, it has been demonstrated that the bandwidth and group delay of the EIT-like band can be controlled by changing the incidence angle of electromagnetic waves. These features enable the proposed metamaterials to achieve potential applications in filtering, switching, data storing, and sensing.

High-performance Raman memory with spatio-temporal reversal.

A number of techniques exist to use an ensemble of atoms as a quantum memory for light. Many of these propose to use backward retrieval as a way to improve the storage and recall efficiency. We report on a demonstration of an off-resonant Raman memory that uses backward retrieval to achieve an efficiency of 65 ± 6% at a storage time of one pulse duration. The memory has a characteristic decay time of 60 μs, corresponding to a delay-bandwidth product of 160.

Ultra-slow light with high NDBP achieved in a modified [formula omitted] photonic crystal waveguide with coupled cavities

Here, a modified W1 photonic crystal waveguide consisting of silicon rods arranged in a hexagonal lattice in the air is investigated for the aim of obtaining highly flattened defect band under the light line. This condition results in achieving ultra-low group velocity and suppresses the out of plane scatterings, simultaneously. The presented waveguide which is composed of the periodic coupled cavities inside the channel, provided high time delay with group index of ng∼647 and improved normalized delay bandwidth product of ∼0.54 for the propagating wave. A group velocity of about ∼0.001545c is achieved by immersing the rods with the optimized radius and periodicity of r=0.2a and 3a into the center of the channel, respectively. The PWE and the FDTD results with slight discrepancy, present the feasibility of ultra-slow light phenomenon in the presented structure.

Slow-light transmission with high group index and large normalized delay bandwidth product through successive defect rods on intrinsic photonic crystal waveguide

We proposed a strategy with successive cavities as energy reservoirs of electromagnetic energy and light-speed reducers introduced in the first and second rows of rods on the walls of an intrinsic photonic crystal waveguide (PCW) for slow-light transmission in the PCW concerning applications for optical communication, optical computation and optical signal processing. Subsequently, plane-wave expansion method (PWE) is used for studying slow-light properties and finite-difference time-domain (FDTD) method to demonstrate the slow-light propagating property of our proposed structure. We obtained group index as exceedingly large as 6123 with normalized delay bandwidth product (NDBP) as high as 0.48. We designed a facile but more generalized structure that may provide a vital theoretical basis for further enhancing the storage capacity properties of slow light with wideband and high NDBP.