Luigi Zeni

@unicampania.it

Professor - Department of Engineering
University of Campania Luigi Vanvitelli



              

https://researchid.co/lzeni

Luigi Zeni is full professor in electronics & photonics at University of Campania Luigi Vanvitelli, president of the Research Consortium on Advanced Remote Sensing Systems – . and Rector’s delegate for technology transfer activities. He has been, from 2001 to 2012, vice-director of the Department of Information Engineering and, from 2013 to 2021, member of the Board of Directors of University of Campania Luigi Vanvitelli. He took his degree in Electronic Engineering, summa cum laude, from University of Naples in 1988 and his Ph.D. in Electronics and Computer Science, from Italian Ministry of University in 1992. He has been research assistant at the University of Naples "Federico II" and, from 1998 to 2006, he has been associate professor of Electronics at the Second University of Naples. He worked at TU-DELFT (The Netherlands) as a visiting scientist. He has been visiting professor at the University of Cluj-Napoca (Romania).
Founder of the Spin-off company OPTOSENSING

EDUCATION

Degree in Electronic Engineering
PhD in Electronics and Computer Science

RESEARCH INTERESTS

Optoelectronics and Photonics

429

Scopus Publications

Scopus Publications

  • Plasmonic immunosensors based on spoon-shaped waveguides for fast and on-site ultra-low detection of ochratoxin A in coffee samples
    Thais de Andrade Silva, Francesco Arcadio, Luigi Zeni, Roberto Martins, Jairo Pinto de Oliveira, Carlos Marques, and Nunzio Cennamo

    Elsevier BV

  • Distributed Temperature Sensing through Network Analysis Frequency-Domain Reflectometry
    Rizwan Zahoor, Raffaele Vallifuoco, Luigi Zeni, and Aldo Minardo

    MDPI AG
    In this paper, we propose and demonstrate a network analysis optical frequency domain reflectometer (NA-OFDR) for distributed temperature measurements at high spatial (down to ≈3 cm) and temperature resolution. The system makes use of a frequency-stepped, continuous-wave (cw) laser whose output light is modulated using a vector network analyzer. The latter is also used to demodulate the amplitude of the beat signal formed by coherently mixing the Rayleigh backscattered light with a local oscillator. The system is capable of attaining high measurand resolution (≈50 mK at 3-cm spatial resolution) thanks to the high sensitivity of coherent Rayleigh scattering to temperature. Furthermore, unlike the conventional optical-frequency domain reflectometry (OFDR), the proposed system does not rely on the use of a tunable laser and therefore is less prone to limitations related to the laser coherence or sweep nonlinearity. Two configurations are analyzed, both numerically and experimentally, based on either a double-sideband or single-sideband modulated probe light. The results confirm the validity of the proposed approach.

  • Innovative optical pH sensors for the aquaculture sector: Comprehensive characterization of a cost-effective solution
    Guilherme Lopes, Nunzio Cennamo, Luigi Zeni, Ragini Singh, Santosh Kumar, António J.S. Fernandes, Florinda Costa, Sónia O. Pereira, and Carlos Marques

    Elsevier BV

  • 3D-printed biosensors in biomedical applications exploiting plasmonic phenomena and antibody self-assembled monolayers
    Francesco Arcadio, Waqar Ali, Debora Bencivenga, Domenico Del Prete, Chiara Marzano, Lorena Saitta, Emanuela Stampone, Rosario Cennamo, Vincenzo Carafa, Lucia Altucci,et al.

    Optica Publishing Group
    In this work, a 3D-printed plasmonic chip based on a silver-gold bilayer was developed in order to enhance the optical response of the surface plasmon resonance (SPR) probe. More specifically, numerical and experimental results were obtained on the 3D-printed SPR platform based on a silver-gold bilayer. Then, the optimized probe's gold plasmonic interface was functionalized with a specific antibody directed against the p27Kip1 protein (p27), an important cell cycle regulator. The 3D-printed plasmonic biosensor was tested for p27 detection with good selectivity and a detection limit of 55 pM. The biosensor system demonstrated performance similar to commercially available ELISA (enzyme-linked immunoassay) kits, with several advantages, such as a wide detection range and a modular and simple-based architecture. The proposed biosensing technology offers flexible deployment options that are useful in disposable, low-cost, small-size, and simple-to-use biochips, envisaging future applications in experimental and biomedical research.

  • Distributed Vibration Sensing Through a Network Analysis Optical Frequency-Domain Reflectometer
    Rizwan Zahoor, Raffaele Vallifuoco, Ester Catalano, Romeo Bernini, Luigi Zeni, and Aldo Minardo

    Institute of Electrical and Electronics Engineers (IEEE)
    In this article, we demonstrate the use of a network analysis optical frequency domain reflectometer (NA-OFDR) for distributed vibration sensing at a spatial resolution of ≈3 cm and an acquisition rate up to ≈80 Hz. The system makes use of a continuous-wave (CW) laser, whose amplitude is modulated using a vector network analyzer. The latter is also used to demodulate the amplitude and phase of the beat signal obtained by coherently mixing the backscattered light with a local oscillator. Two configurations are considered, based on either double sideband or single sideband modulation of the probe light. The single sideband modulation is shown to possess superior performance in terms of localization capabilities of the applied perturbation.

  • Plasmon resonance biosensor for interleukin-1β point-of-care determination: A tool for early periodontitis diagnosis
    Nunzio Cennamo, Debora Bencivenga, Marco Annunziata, Francesco Arcadio, Emanuela Stampone, Angelantonio Piccirillo, Fulvio Della Ragione, Luigi Zeni, Luigi Guida, and Adriana Borriello

    Elsevier BV

  • Hotspot Detection by Phase-Modulated Pump-Based Brillouin Scattering
    R. Vallifuoco, E. Catalano, L. Zeni, and A. Minardo

    Institute of Electrical and Electronics Engineers (IEEE)
    In this letter, we present an optimized configuration for high-spatial resolution hotspot detection based on stimulated Brillouin scattering. The method makes use of a Brillouin optical frequency-domain analysis (BOFDA) configuration with a phase-modulated pump. Experiments show that the proposed method provides an average SNR enhancement of <inline-formula> <tex-math notation="LaTeX">$\\approx ~3$ </tex-math></inline-formula> dB compared to a conventional BOFDA scheme making use of an intensity-modulated pump. In detail, we demonstrate hotspot detection with a temperature standard deviation of <inline-formula> <tex-math notation="LaTeX">$\\approx ~0.15~^{\\circ }\\text{C}$ </tex-math></inline-formula>, a spatial resolution of 8 mm, a measurement range of 50 m, and an acquisition rate of 0.49 Hz. We believe that the proposed method can be usefully applied for quench detection in superconducting magnet systems, where sufficient spatial and temporal resolution are required to detect incipient quenches.

  • A plasmonic gold nano-surface functionalized with the estrogen receptor for fast and highly sensitive detection of nanoplastics
    Mimimorena Seggio, Francesco Arcadio, Nunzio Cennamo, Luigi Zeni, and Alessandra Maria Bossi

    Elsevier BV

  • A novel plasmonic optical-fiber-based point-of-care test for periodontal MIP-1α detection
    Marco Annunziata, Francesco Arcadio, Adriana Borriello, Debora Bencivenga, Angelantonio Piccirillo, Emanuela Stampone, Luigi Zeni, Nunzio Cennamo, Fulvio Della Ragione, and Luigi Guida

    Elsevier BV

  • A Femtomolar Detection Range via Plasmonic Biosensors Based on V-Shaped Optical Adhesives Waveguides
    Domenico Del Prete, Chiara Marzano, Francesco Arcadio, Gianluca Cicala, Lorena Saitta, Luigi Zeni, and Nunzio Cennamo

    Institute of Electrical and Electronics Engineers (IEEE)
    A versatile and low-cost plasmonic biosensor was designed, realized, and tested by combining a bioreceptor layer with a probe based on two plastic optical fibers (POFs) built-in with a sensing chip carried out via a multilayer on UV-curable optical adhesives. The proposed sensitive multilayer has been developed to excite the surface plasmon resonance (SPR) phenomenon on a gold surface in contact with the monitored bioreceptor layer. More specifically, a binding interaction between a bioreceptor layer and its analyte has been studied for the first time by exploiting SPR platforms based on UV-curable optical adhesives. First, a resin block with a V-shaped channel on its surface was designed and printed using a 3-D printer to locate the source and receiver on the same side. Then, the channel was covered by a silver layer to obtain the mirror effect. After this, it was filled with an UV-curable optical adhesive, with two POFs fixed at the end of the trench, in order to obtain the core of the sensor’s waveguide. Finally, an optical buffer layer and a gold nanofilm were deposited on the core to excite the SPR phenomenon efficiently. The obtained SPR probe was first tested as a refractometer to obtain the bulk sensitivity, and then, following a functionalization process, binding tests were carried out to detect immunoglobulin (IgG) in the buffer. The experimental results show an ultralow detection limit of 1.17 fM, a detection range from 1 to 250 fM, and a sensitivity at low concentrations of 3.42 nm/fM.

  • Immuno-SPR biosensor for the detection of Brucella abortus
    Laura Pasquardini, Nunzio Cennamo, Francesco Arcadio, Chiara Perri, Alessandro Chiodi, Girolamo D’agostino, and Luigi Zeni

    Springer Science and Business Media LLC
    AbstractA proof of principle biosensor for the Brucella abortus recognition onsite is presented. The system is based on a plasmonic optical fiber probe functionalized with an oriented antibody layer immobilized on a short polyethyleneglycol (PEG) interface through carbodiimide chemistry and protein G as an intermediate layer. The biosensor is inserted in a holder built in 3D printing technology, obtaining a custom holder useful for housing the sample to be measured and the equipment. The removable sensor chip is a low-cost Surface Plasmon Resonance (SPR) platform based on D-shaped plastic optical fibers (POFs), built-in in 3D printed connectors, used here for the first time to detect bacteria via a bio-receptor layer specific for its membrane protein. The performances of the biosensor in Brucella abortus recognition are tested by using two different SPR-POF probes combined with the same bio-receptor layer. The best sensor configuration has presented a sensitivity at low concentrations of one order of magnitude greater than the other. A limit of detection (LoD) of 2.8 bacteria/mL is achieved well competitive with other systems but without the need for amplification or special sample treatments. Specificity has been tested using Salmonella bacteria, and reproducibility, regenerability and stability are moreover evaluated. These experimental results pave the way for building an efficient and specific biosensor system for Brucella abortus detection onsite and in a few minutes. Moreover, the proposed POF-based SPR biosensor device, with respect to the already available technologies, could be a Point-of-care-test (POCT), simple to use, small-size and portable, low-cost, don’t necessary of a microfluidic system, and can be connected to the Internet (IoT).

  • Soft molecularly imprinted nanoparticles with simultaneous lossy mode and surface plasmon multi-resonances for femtomolar sensing of serum transferrin protein
    Francesco Arcadio, Laurent Noël, Domenico Del Prete, Devid Maniglio, Mimimorena Seggio, Olivier Soppera, Nunzio Cennamo, Alessandra Maria Bossi, and Luigi Zeni

    Springer Science and Business Media LLC
    AbstractThe simultaneous interrogation of both lossy mode (LMR) and surface plasmon (SPR) resonances was herein exploited for the first time to devise a sensor in combination with soft molecularly imprinting of nanoparticles (nanoMIPs), specifically entailed of the selectivity towards the protein biomarker human serum transferrin (HTR). Two distinct metal-oxide bilayers, i.e. TiO2–ZrO2 and ZrO2–TiO2, were used in the SPR–LMR sensing platforms. The responses to binding of the target protein HTR of both sensing configurations (TiO2–ZrO2–Au-nanoMIPs, ZrO2–TiO2–Au-nanoMIPs) showed femtomolar HTR detection, LODs of tens of fM and KDapp ~ 30 fM. Selectivity for HTR was demonstrated. The SPR interrogation was more efficient for the ZrO2–TiO2–Au-nanoMIPs configuration (sensitivity at low concentrations, S = 0.108 nm/fM) than for the TiO2–ZrO2–Au-nanoMIPs one (S = 0.061 nm/fM); while LMR was more efficient for TiO2–ZrO2–Au-nanoMIPs (S = 0.396 nm/fM) than for ZrO2–TiO2–Au-nanoMIPs (S = 0.177 nm/fM). The simultaneous resonance monitoring is advantageous for point of care determinations, both in terms of measurement’s redundancy, that enables the cross-control of the measure and the optimization of the detection, by exploiting the individual characteristics of each resonance.

  • Tuning of the Brillouin scattering properties in microstructured optical fibers by liquid infiltration
    Ester Catalano, Raffaele Vallifuoco, Luigi Zeni, Alexis Dufour, Emmanuel Marin, Sylvain Girard, and Aldo Minardo

    Springer Science and Business Media LLC
    AbstractWe demonstrate the possibility to modify the Brillouin scattering properties of a microstructured pure-silica core optical fiber, by infiltrating a liquid inside its holes. In particular, we show that the dependence of the Brillouin frequency shift (BFS) on the temperature can be reduced by infiltration, owing to the large negative thermo-optic coefficient of the liquid. Infiltrating a chloroform-acetonitrile mixture with a refractive index of 1.365 inside the holes of a suspended-core fiber with a core diameter of 3 µm, the BFS temperature sensing coefficient is reduced by ≈ 21%, while the strain sensitivity remains almost unaltered. Besides tuning the temperature sensing coefficient, the proposed platform could find other applications in Brillouin sensing, such as distributed electrical and magnetic measurements, or enhanced Brillouin gain in fibers infiltrated with high nonlinear optical media.

  • Optimization of the immunorecognition layer towards Brucella sp. on gold surface for SPR platform
    Laura Pasquardini, Lia Vanzetti, Roberto Canteri, Nunzio Cennamo, Francesco Arcadio, Chiara Perri, Girolamo D’Agostino, Rosalba Pitruzzella, Riccardo Rovida, Alessandro Chiodi,et al.

    Elsevier BV

  • Analysis of low-cost inkjet-printed Optical platforms covered by Molecularly Imprinted Polymers to detect furfural in water
    Nunzio Cennamo, Francesco Arcadio, Aldo Minardo, Domenico Del Prete, Luigi Zeni, Maria Pesavento, Giancarla Alberti, Vincenzo Marletta, and Bruno Andò

    Institute of Electrical and Electronics Engineers (IEEE)

  • Intrinsic and extrinsic polymer optical fiber schemes for highly sensitive plasmonic biosensors


  • Sensing Approaches Exploiting Molecularly Imprinted Nanoparticles and Lossy Mode Resonance in Polymer Optical Fibers
    Francesco Arcadio, Laurent Noël, Domenico Del Prete, Mimimorena Seggio, Luigi Zeni, Alessandra Maria Bossi, Olivier Soppera, and Nunzio Cennamo

    MDPI AG
    In this work, two different lossy mode resonance (LMR) platforms based on plastic optical fibers (POFs) are developed and tested in a biochemical sensing scenario. The LMR platforms are based on the combination of two metal oxides (MOs), i.e., zirconium oxide (ZrO2) and titanium oxide (TiO2), and deposited on the exposed core of D-shaped POF chips. More specifically, two experimental sensor configurations were obtained by swapping the mutual position of the Mos films over to the core of the D-shaped POF probe. The POF–LMR sensors were first characterized as refractometers, proving the bulk sensitivities. Then, both the POF–LMR platforms were functionalized using molecularly imprinted nanoparticles (nanoMIPs) specific for human transferrin (HTR) in order to carry out binding tests. The achieved results report a bulk sensitivity equal to about 148 nm/RIU in the best sensor configuration, namely the POF-TiO2-ZrO2. In contrast, both optical configurations combined with nanoMIPs showed an ultra-low detection limit (fM), demonstrating excellent efficiency of the used receptor (nanoMIPs) and paving the way to disposable POF–LMR biochemical sensors that are easy-to-use, low-cost, and highly sensitive.

  • MIP-Assisted 3-Hole POF Chip Faced with SPR-POF Sensor for Glyphosate Detection
    Giancarla Alberti, Stefano Spina, Francesco Arcadio, Maria Pesavento, Letizia De Maria, Nunzio Cennamo, Luigi Zeni, and Daniele Merli

    MDPI AG
    The present study proposes the application of a recently developed optical–chemical sensor system to glyphosate detection. The device probes the refractive index variation in a chip based on a plastic optical fiber (POF) in which three orthogonal micro-holes were created and filled with an acrylic-based molecularly imprinted polymer (MIP). This sensitive chip, connected in series to a gold-coated SPR-POF platform, can modify the surface plasmon resonance (SPR) phenomena by exploiting the multimode characteristic of the POFs. Therefore, the gold film of the SPR-POF platform is not covered by the MIP layer, improving the sensor’s performance because the interaction between the analyte (glyphosate) and the polymer recognition cavities occurs in the core and not in the cladding of the waveguide. Indeed, the sample solution is dropped on the MIP-based chip while a water drop is constantly maintained above the gold surface of the reference SPR-POF platform to excite the surface plasmons, modulated by the MIP interaction with the target analyte. The device is here for the first time applied for glyphosate sensing in water samples. The high sensitivity and selectivity are proven, and tests on real samples highlight the good performances of the developed sensors.

  • Analysis of Plasmonic Sensors Performance Realized by Exploiting Different UV-Cured Optical Adhesives Combined with Plastic Optical Fibers
    Francesco Arcadio, Chiara Marzano, Domenico Del Prete, Luigi Zeni, and Nunzio Cennamo

    MDPI AG
    Polymer-based surface plasmon resonance (SPR) sensors can be used to realize simple, small-size, disposable, and low-cost biosensors for application in several fields, e.g., healthcare. The performance of SPR sensors based on optical waveguides can be changed by tuning several parameters, such as the dimensions and the shape of the waveguides, the refractive index of the core, and the metal nanofilms used to excite the SPR phenomenon. In this work, in order to develop, experimentally test, and compare several polymer-based plasmonic sensors, realized by using waveguides with different core refractive indices, optical adhesives and 3D printed blocks with a trench inside have been used. In particular, the sensors are realized by filling the blocks’ trenches (with two plastic optical fibers located at the end of these) with different UV-cured optical adhesives and then covering them with the same bilayer to excite the SPR phenomenon. The developed SPR sensors have been characterized by numerical and experimental results. Finally, in order to propose photonic solutions for healthcare, a comparative analysis has been reported to choose the best sensor configuration useful for developing low-cost biosensors.

  • An optical fiber-based point-of-care test for periodontal MMP-8 detection: A proof of concept
    Luigi Guida, Debora Bencivenga, Marco Annunziata, Francesco Arcadio, Adriana Borriello, Fulvio Della Ragione, Alessandro Formisano, Angelantonio Piccirillo, Luigi Zeni, and Nunzio Cennamo

    Elsevier BV

  • A Novel Approach to Realize Plasmonic Sensors via Multimode Optical Waveguides: A Review
    Francesco Arcadio, Domenico Del Prete, Luigi Zeni, and Nunzio Cennamo

    MDPI AG
    In recent decades, the Surface Plasmon Resonance (SPR) phenomenon has been utilized as an underlying technique in a broad range of application fields. Herein, a new measuring strategy which harnesses the SPR technique in a way that is different from the classical methodology was explored by taking advantage of the characteristics of multimode waveguides, such as plastic optical fibers (POFs) or hetero-core fibers. The sensor systems based on this innovative sensing approach were designed, fabricated, and investigated to assess their ability to measure various physical features, such as magnetic field, temperature, force, and volume, and to realize chemical sensors. In more detail, a sensitive patch of fiber was used in series with a multimodal waveguide where the SPR took place, to alter the mode profile of the light at the input of the waveguide itself. In fact, when the changes of the physical feature of interest acted on the sensitive patch, a variation of the incident angles of the light launched in the multimodal waveguide occurred, and, as a consequence, a shift in resonance wavelength took place. The proposed approach permitted the separation of the measurand interaction zone and the SPR zone. This meant that the SPR zone could be realized only with a buffer layer and a metallic film, thus optimizing the total thickness of the layers for the best sensitivity, regardless of the measurand type. The proposed review aims to summarize the capabilities of this innovative sensing approach to realize several types of sensors for different application fields, showing the high performances obtained by exploiting a simple production process and an easy experimental setup.

  • Polymer Doping as a Novel Approach to Improve the Performance of Plasmonic Plastic Optical Fibers Sensors
    Rosalba Pitruzzella, Riccardo Rovida, Chiara Perri, Alessandro Chiodi, Francesco Arcadio, Nunzio Cennamo, Laura Pasquardini, Lia Vanzetti, Michele Fedrizzi, Luigi Zeni,et al.

    MDPI AG
    In this work, Fe2O3 was investigated as a doping agent for poly(methyl methacrylate) (PMMA) in order to enhance the plasmonic effect in sensors based on D-shaped plastic optical fibers (POFs). The doping procedure consists of immerging a premanufactured POF sensor chip in an iron (III) solution, avoiding repolymerization and its related disadvantages. After treatment, a sputtering process was used to deposit a gold nanofilm on the doped PMMA in order to obtain the surface plasmon resonance (SPR). More specifically, the doping procedure increases the refractive index of the POF’s PMMA in contact with the gold nanofilm, improving the SPR phenomena. The doping of the PMMA was characterized by different analyses in order to determine the effectiveness of the doping procedure. Moreover, experimental results obtained by exploiting different water–glycerin solutions have been used to test the different SPR responses. The achieved bulk sensitivities confirmed the improvement of the plasmonic phenomenon with respect to a similar sensor configuration based on a not-doped PMMA SPR-POF chip. Finally, doped and non-doped SPR-POF platforms were functionalized with a molecularly imprinted polymer (MIP), specific for the bovine serum albumin (BSA) detection, to obtain dose-response curves. These experimental results confirmed an increase in binding sensitivity for the doped PMMA sensor. Therefore, a lower limit of detection (LOD), equal to 0.04 μM, has been obtained in the case of the doped PMMA sensor when compared to the one calculated for the not-doped sensor configuration equal to about 0.09 μM.

  • A Novel Microchannel-in-a-Fiber Plasmonic Sensor
    Francesco Arcadio, Ricardo Oliveira, Domenico Del Prete, Aldo Minardo, Luigi Zeni, Lúcia Bilro, Nunzio Cennamo, and Rogério Nunes Nogueira

    Institute of Electrical and Electronics Engineers (IEEE)
    In this work, a novel surface plasmon resonance (SPR) sensor has been designed, realized, and investigated. The SPR platform was created by using a D-shaped plastic optical fiber shell (POFS), obtained by removing the graded index core region from the fiber’s protective jacket, to create a microchannel. The latter was then coated with a gold nanofilm to obtain the plasmonic-sensitive region. The sensor’s structure includes an integrated measuring cell, being the solution under test injected into the microchannel using a peristaltic pump. The microchannel dimension (<inline-formula> <tex-math notation="LaTeX">$160 \\mu \\text{m}$ </tex-math></inline-formula>) allows for avoiding microfluidic systems, typically adopted in this kind of SPR configuration. As a proof of concept, the plasmonic sensor has been tested as a refractometer using different water–ethanol solutions, with a refractive index (RI) ranging from 1.332 to 1.352. The experimental results have highlighted a sensitivity and a resolution equal to about 1026 nm/RIU and <inline-formula> <tex-math notation="LaTeX">$1.95\\times 10^{-{4}}$ </tex-math></inline-formula> RIU, respectively. These values testify to the proposed sensor’s goodness and its suitability for biochemical sensing applications.

  • Towards a point-of-care test to cover atto-femto and pico-nano molar concentration ranges in interleukin 6 detection exploiting PMMA-based plasmonic biosensor chips
    Nunzio Cennamo, Angelantonio Piccirillo, Debora Bencivenga, Francesco Arcadio, Marco Annunziata, Fulvio Della Ragione, Luigi Guida, Luigi Zeni, and Adriana Borriello

    Elsevier BV

  • Estradiol Detection for Aquaculture Exploiting Plasmonic Spoon-Shaped Biosensors
    Francesco Arcadio, Mimimorena Seggio, Luigi Zeni, Alessandra Maria Bossi, and Nunzio Cennamo

    MDPI AG
    In this work, a surface plasmon resonance (SPR) biosensor based on a spoon-shaped waveguide combined with an estrogen receptor (ERα) was developed and characterized for the detection and the quantification of estradiol in real water samples. The fabrication process for realizing the SPR platform required a single step consisting of metal deposition on the surface of a polystyrene spoon-shaped waveguide featuring a built-in measuring cell. The biosensor was achieved by functionalizing the bowl sensitive surface with a specific estrogen receptor (ERα) that was able to bind the estradiol. In a first phase, the biosensor tests were performed in a phosphate buffer solution obtaining a limit of detection (LOD) equal to 0.1 pM. Then, in order to evaluate the biosensor’s response in different real matrices related to aquaculture, its performances were examined in seawater and freshwater. The experimental results support the possibility of using the ERα-based biosensor for the screening of estradiol in both matrices.