Johannes Skaar

On the synthesis of fiber Bragg gratings by layer peeling

Two methods for grating synthesis which have appeared in the literature recently are compared directly. In particular, we point out the similarity between the two; both algorithms are based on propagation of the fields through the structure with simultaneous evaluation of the coupling coefficient according to simple causality arguments (layer-peeling algorithms). The first published method (the discrete layer-peeling algorithm) is reformulated in a simpler, more efficient way, and it is shown that its implementation can be made exact. For mathematical comparison, a derivation of the second method (the continuous layer-peeling algorithm) is presented. The methods are compared both mathematically and numerically. We find that the discrete layer-peeling algorithm is significantly faster and can be more stable than its continuous counterpart, whereas the continuous algorithm offers some advantages in flexibility.

A genetic algorithm for the inverse problem in synthesis of fiber gratings

A new method for synthesis of fiber gratings with advanced characteristics is proposed. By combining the Runge-Kutta method for calculating the reflection spectrum of a fiber grating and a genetic algorithm, we obtain a promising method for the synthesis. Compared to other methods, the proposed method facilitates the task of weighting the different requirements to the filter spectrum. In addition, the method is general, and would thus be useful for other inverse problems.

Effects of detector efficiency mismatch on security of quantum cryptosystems

We suggest a type of attack on quantum cryptosystems that exploits variations in detector efficiency as a function of a control parameter accessible to an eavesdropper. With gated single-photon detectors, this control parameter can be the timing of the incoming pulse. When the eavesdropper sends short pulses using the appropriate timing so that the two gated detectors in Bobs setup have different efficiencies, the security of quantum key distribution can be compromised. Specifically, we show for the Bennett-Brassard 1984 (BB84) protocol that if the efficiency mismatch between 0 and 1 detectors for some value of the control parameter gets large enough (roughly 15:1 or larger), Eve can construct a successful faked-states attack causing a quantum bit error rate lower than 11%. We also derive a general security bound as a function of the detector sensitivity mismatch for the BB84 protocol. Experimental data for two different detectors are presented, and protection measures against this attack are discussed.

After-gate attack on a quantum cryptosystem

We present a method to control the detection events in quantum key distribution systems that use gated single-photon detectors. We employ bright pulses as faked states, timed to arrive at the avalanche photodiodes outside the activation time. The attack can remain unnoticed, since the faked states do not increase the error rate per se. This allows for an intercept-resend attack, where an eavesdropper transfers her detection events to the legitimate receiver without causing any errors. As a side effect, afterpulses, originating from accumulated charge carriers in the detectors, increase the error rate. We have experimentally tested detectors of the system id3110 (Clavis2) from ID Quantique. We identify the parameter regime in which the attack is feasible despite the side effect. Furthermore, we outline how simple modifications in the implementation can make the device immune to this attack.

Experimentally Faking the Violation of Bell's Inequalities

Entanglement witnesses such as Bell inequalities are frequently used to prove the nonclassicality of a light source and its suitability for further tasks. By demonstrating Bell inequality violations using classical light in common experimental arrangements, we highlight why strict locality and efficiency conditions are not optional, particularly in security-related scenarios.

Thermal blinding of gated detectors in quantum cryptography.

It has previously been shown that the gated detectors of two commercially available quantum key distribution (QKD) systems are blindable and controllable by an eavesdropper using continuous-wave illumination and short bright trigger pulses, manipulating voltages in the circuit [Nat. Photonics 4, 686 (2010)]. This allows for an attack eavesdropping the full raw and secret key without increasing the quantum bit error rate (QBER). Here we show how thermal effects in detectors under bright illumination can lead to the same outcome. We demonstrate that the detectors in a commercial QKD system Clavis2 can be blinded by heating the avalanche photo diodes (APDs) using bright illumination, so-called thermal blinding. Further, the detectors can be triggered using short bright pulses once they are blind. For systems with pauses between packet transmission such as the plug-and-play systems, thermal inertia enables Eve to apply the bright blinding illumination before eavesdropping, making her more difficult to catch.

Reconstruction of gratings from noisy reflection data

The worst-case error amplification factor in reconstructing a grating from its complex reflection spectrum is shown to be of the order 1/T(min), where T(min) is the minimum transmissivity through the grating. For a uniform grating with coupling coefficient-length product kappaL, the error amplification is exp(2kappaL). The exponential dependence on the grating strength shows that spatial characterization of gratings from a measured reflection spectrum is impossible if the grating is sufficiently strong. For moderately strong gratings, a simple regularization technique is proposed to stabilize the solution of the inverse-scattering problem of computing the grating structure from the reflection spectrum.

Design and characterization of finite-length fiber gratings

A rigorous analysis of the response of fiber Bragg gratings of finite length is presented. For the discrete grating model, we find necessary and sufficient conditions for the response to be realizable as a grating of finite length. These conditions are used to develop a general method for designing gratings with a prescribed length. The design process is divided into two parts. First, we find a realizable reflection spectrum which approximates the target spectrum. Once the spectrum is found, one can determine the associated grating profile by straightforward layer-peeling inverse-scattering or transfer matrix factorization methods. As an example, a dispersionless bandpass filter is designed and compared to the results when the layer-peeling algorithm is applied directly to a windowed impulse response. We also discuss potential applications to grating characterization including regularization and finding the absolute reflection spectrum from a measured, normalized version.

Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms

We present a flexible and accurate approach for the design of grating-assisted codirectional couplers. The design method is based on a discrete coupling model. The two spectral responses of the coupler are chosen according to certain physical constraints. We prove necessary and sufficient conditions for realizability and demonstrate how they can be applied for determining an optimal coupler response. The ambiguity when designing a coupler with a specified cross-coupling response is also discussed in detail. Once the realizable responses have been found, they can be applied as input to a layer-peeling inverse-scattering method which computes the required coupler structure. The layer-peeling algorithm is implemented in the time domain for increased efficiency and clarity. Since the algorithm is tailored to the special case of codirectional coupling, divergence problems for strong coupling is avoided. Numerical design examples are shown in order to illustrate the performance of the method. Various realizations of square passband filters with high power transfer and a long-period fiber grating filter for EDFA gain flattening within the entire C-band have been designed.

Controlling an actively-quenched single photon detector with bright light

We control using bright light an actively-quenched avalanche single-photon detector. Actively-quenched detectors are commonly used for quantum key distribution (QKD) in the visible and near-infrared range. This study shows that these detectors are controllable by the same attack used to hack passively-quenched and gated detectors. This demonstrates the generality of our attack and its possible applicability to eavsdropping the full secret key of all QKD systems using avalanche photodiodes (APDs). Moreover, the commercial detector model we tested (PerkinElmer SPCM-AQR) exhibits two new blinding mechanisms in addition to the previously observed thermal blinding of the APD, namely: malfunctioning of the bias voltage control circuit, and overload of the DC/DC converter biasing the APD. These two new technical loopholes found just in one detector model suggest that this problem must be solved in general, by incorporating generally imperfect detectors into the security proof for QKD.