Quantum Modelling of Electro-Optic Modulators

Many components that are employed in quantum information and communication systems are well known photonic devices encountered in standard optical fiber communication systems, such as optical beamsplitters, waveguide couplers and junctions, electro-optic modulators and optical fiber links. The use of these photonic devices is becoming increasingly important especially in the context of their possible integration either in a specifically designed system or in an already deployed end-to-end fiber link. Whereas the behavior of these devices is well known under the classical regime, in some cases their operation under quantum conditions is less well understood. This paper reviews the salient features of the quantum scattering theory describing both the operation of the electro-optic phase and amplitude modulators in discrete and continuous-mode formalisms. This subject is timely and of importance in light of the increasing utilization of these devices in a variety of systems, including quantum key distribution and single-photon wavepacket measurement and conformation. In addition, the paper includes a tutorial development of the use of these models in selected but yet important applications, such as single and multi-tone modulation of photons, two-photon interference with phase-modulated light or the description of amplitude modulation as a quantum operation.Comment: 29 pages, 10 figures, Laser and Photonics Reviews (in press

Interrogation of a Sensor Array of Identical Weak FBGs using Dispersive Incoherent OFDR

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.[EN] Incoherent Optical Fourier-Domain Reflectometry incorporating a dispersive delay line is used for the interrogation of an array of three identical fiber Bragg gratings with a Bragg wavelength of 1552.81 nm, reflectivity of 19.3 dB and 10-cm separation. The dispersive delay line induces different delays in the wavelengths reflected by each grating, thus being sensitive to Bragg wavelength shifts. Compared with conventional incoherent Optical Fourier-Domain Reflectometry, dispersive effects decrease the spatial resolution, which in our experiments reached a value of 1.2 cm in fiber at a measurement bandwidth of 10 GHz. As a quasi-distributed temperature sensor, the array shows an accuracy of ±0.5ºC for temperatures up to 100ºC, and an estimated total measurement range of 540ºC. Tradeoffs between bandwidth, scan time, dispersion-dependent spatial resolution, and accuracy, are also analyzed.This work was supported in part by the Generalitat Valenciana, Valencia, within the Research Excellency Award through the GVA PROMETEO Program under Grant 2013/012 and in part by the Ministerio de Economia y Competitividad under Project TEC201-60378-C2-1-R. The work of J. Hervas was supported by the Ministerio de Educacion, Cultura y Deporte through the Formacion Profesorado Scholarship (FPU13/04675).Clement, J.; Torregrosa, G.; Hervás-Peralta, J.; Barrera Vilar, D.; Sales Maicas, S.; Fernandez-Pousa, CR. (2016). Interrogation of a Sensor Array of Identical Weak FBGs using Dispersive Incoherent OFDR. IEEE Photonics Technology Letters. 28(10):1154-1156. https://doi.org/10.1109/LPT.2016.2533163S11541156281

KLT Based Interrogation Technique for FBG Multiplexed Sensor Tracking

[EN] The Karhunen-Loeve transform (KLT) is used to retrieve the wavelength information of several fiber Bragg gratings (FBGs) that are acting as a multiplexed sensor. The modulated light of a broadband source is launched to the FBG cascade in order to capture the electrical frequency response of the system. Thanks to a dispersive media, the wavelengths of the FBGs are mapped in radiofrequency (RF) delays. Wavelength changes are determined by the amplitude change of the samples in the impulse response, a change which is followed by the eigenvalue calculated by the KLT routine. The use of the KLT routine reduces by three orders of magnitude the amount of points needed to have a sub-degree resolution in temperature sensing, while keeping the accuracy almost intact.This work was supported in part by the Spanish MINECO through Project TEC2014-60378, and in part by the Government of Valencia through the Research Excellency Award Program GVA PROMETEO 2013/012. The work of J. Hervas was supported by the MECD FPU Scholarship (FPU13/04675).Hervás-Peralta, J.; Tosi, D.; García-Miquel, H.; Barrera Vilar, D.; Fernandez-Pousa, CR.; Sales Maicas, S. (2017). KLT Based Interrogation Technique for FBG Multiplexed Sensor Tracking. Journal of Lightwave Technology. 35(16):3387-3392. https://doi.org/10.1109/JLT.2016.2613131S33873392351

Fast Incoherent OFDR Interrogation of FBG Arrays Using Sparse Radio Frequency Responses

[EN] We present two implementations of fast, discrete incoherent optical frequency-domain reflectometers (I-OFDR) for the interrogation of equally spaced fiber Bragg grating (FBG) arrays, based on the determination of the array's radio frequency (RF) response at a sparse number of frequencies. FBG reflectivities are determined by use of the inverse discrete Fourier transform (IDFT) of the sparse RF response, in a dynamic range limited by crosstalk induced by FBG positioning errors. The first implementation employs the complete, vector RF response at a number of frequencies equal to the number N of FBGs in the array. In the second, the introduction of a reference reflector allows for an interrogation using the power (phaseless) RF response in 4N - 1 frequencies. Demodulation based on IDFT leads to total interrogation times determined by the network analyzer scan time, which can be as low as 10 mu s per FBG. Depending on the interrogation technique, electrical bandwidth requirements are 12 GHz in our array with 10-cm separation. We implemented both techniques in a N = 10 array, inducing decays in reflectivity by 10 dB in one or several FBGs. Unambiguous detection of FBG decays was obtained in both interrogation methods. Additional tests performed on the measured reflectivities also show that measurement linearity is preserved in the 10-dB decay range. As discrete I-OFDR systems, the proposed techniques show the possibility to reach compromises between interrogation time and dynamic range or accuracy in reflectivity measurements, using the number of interrogation frequencies and the sensor topology.This work was supported in part by Infraestructura GVA-FEDER operative program 2007-2013 and in part by the Spanish MINECO through Project TEC2017-88029-R. The work of J. Clement Bellido was supported by the GVA VALi+d scholarship ACIF/2016/214. The work of J. Hervas was supported by the Spanish MEC scholarship FPU13/04675.Clement, J.; Hervás-Peralta, J.; Madrigal-Madrigal, J.; Maestre, H.; Torregrosa, G.; Fernandez-Pousa, CR.; Sales Maicas, S. (2018). Fast Incoherent OFDR Interrogation of FBG Arrays Using Sparse Radio Frequency Responses. Journal of Lightwave Technology. 36(19):4393-4400. https://doi.org/10.1109/JLT.2018.2821199S43934400361

Microwave Photonics for Optical Sensors

[EN] This paper presents a review and discussion of the applications of Microwave Photonic techniques and functionalities to the field of optical fiber sensors. A specific end-to end model for its characterization is presented here for the first time that yields the sensitivity of the different figures of merit in terms of measurand variations. Experimental techniques to characterize these systems are presented and applications of two specific microwave photonic functionalities to high-resolution discrete and quasi-distributed optical sensing are illustrated. Future directions of research are also highlighted.This work was supported in part by the Spanish MINECO through projects TEC2014-60378-C2-1-R MEMES and in part by the Government of Valencia through the Research Excellency Award Program GVA PROMETEO II/2013/012. The work of J. Hervas was supported by the MECD FPU scholarship (FPU13/04675). The work of Ming Li was supported in part by the National Natural Science Foundation of China under Grants 61377002, 61522509, and 61535012and in part by the Thousand Young Talent programHervás-Peralta, J.; Ricchiuti, AL.; Li, W.; Zhu, NH.; Fernandez-Pousa, CR.; Sales Maicas, S.; Li, M.... (2017). Microwave Photonics for Optical Sensors. IEEE Journal of Selected Topics in Quantum Electronics. 23(2):1-13. https://doi.org/10.1109/JSTQE.2017.2651117S11323

Colloidal Quantum Dots-PMMA Waveguides as Integrable Microwave Photonic Phase Shifters

“© © 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.”A novel scheme for the control of microwave signals carried at optical wavelengths by use of PbS colloidal quantum dots embedded in PMMA waveguides is presented. When these structures are pumped at wavelengths where PbS has efficient absorption (980 or 1310 nm), a phase shift in a signal carried at 1550 nm is induced. Optimal conditions have been analyzed by studying the influence of the microwave signal and the waveguide structure. In a proof-of-concept experiment, a continuous phase shift up to 35° at 25 GHz has been demonstrated, with good thermal stability (<2° at 25 GHz) when the samples are heated 20 °C above room temperature. The potential benefits of the use of this active-waveguide technology in microwave photonics are due to the continuous scan of the phase delay, its high tuning speed, and its small size, which leads to the possibility of integration.This work was supported in part by the Infraestructura FEDER under Grants UPVOV08-3E-008 and FEDER UPVOV10-3E-492, in part by the Research Excellency Award Program GVA PROMETEO 2013/012, Next generation Microwave Photonic Technologies, and in part by the Spanish MCINN under Projects TEC2011-29120-C05-01, TEC2011-29120-C05-02, and TEC2011-29120-C05-05.Ricchiuti, AL.; Suárez Álvarez, I.; Barrera Vilar, D.; Rodríguez Cantó, PJ.; Fernandez-Pousa, CR.; Abargues, R.; Sales Maicas, S.... (2014). Colloidal Quantum Dots-PMMA Waveguides as Integrable Microwave Photonic Phase Shifters. IEEE Photonics Technology Letters. 26(4):402-404. https://doi.org/10.1109/LPT.2013.2295253S40240426

Spectral decomposition of single-tone-driven quantum phase modulation

[EN] Electro-optic phase modulators driven by a single radio-frequency tone ¿ can be described at the quantum level as scattering devices where input single-mode radiation undergoes energy changes in multiples of h¿. In this paper, we study the spectral representation of the unitary, multimode scattering operator describing these devices. The eigenvalue equation, phase modulation being a process preserving the photon number, is solved at each subspace with definite number of photons. In the one-photon subspace F 1, the problem is equivalent to the computation of the continuous spectrum of the Susskind-Glogower cosine operator of the harmonic oscillator. Using this analogy, the spectral decomposition in F1 is constructed and shown to be equivalent to the usual Fock-space representation. The result is then generalized to arbitrary N-photon subspaces, where eigenvectors are symmetrized combinations of N one-photon eigenvectors and the continuous spectrum spans the entire unit circle. Approximate normalizable one-photon eigenstates are constructed in terms of London phase states truncated to optical bands. Finally, we show that synchronous ultrashort pulse trains represent classical field configurations with the same structure as these approximate eigenstates, and that they can be considered as approximate eigenvectors of the classical formulation of phase modulation. © 2011 IOP Publishing Ltd.The authors acknowledge support from the Spanish Government through project TEC2008-02606 and project Quantum Optical Information Technology, QOIT, a CONSOLIDER-INGENIO 2010 Project; and also from Generalitat Valenciana through the PROMETEO research excellency award programme GVA PROMETEO 2008/092Capmany Francoy, J.; Fernandez-Pousa, CR. (2011). Spectral decomposition of single-tone-driven quantum phase modulation. Journal of Physics B Atomic Molecular and Optical Physics. 44(3):35506-35506. https://doi.org/10.1088/0953-4075/44/3/035506S3550635506443Chapuran, T. 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Physical Review Letters, 103(16). doi:10.1103/physrevlett.103.163601Mérolla, J.-M., Mazurenko, Y., Goedgebuer, J.-P., Duraffourg, L., Porte, H., & Rhodes, W. T. (1999). Quantum cryptographic device using single-photon phase modulation. Physical Review A, 60(3), 1899-1905. doi:10.1103/physreva.60.1899Grosshans, F., Van Assche, G., Wenger, J., Brouri, R., Cerf, N. J., & Grangier, P. (2003). Quantum key distribution using gaussian-modulated coherent states. Nature, 421(6920), 238-241. doi:10.1038/nature01289Tsang, M., & Psaltis, D. (2006). Propagation of temporal entanglement. Physical Review A, 73(1). doi:10.1103/physreva.73.013822Tsang, M., Shapiro, J. H., & Lloyd, S. (2008). Quantum theory of optical temporal phase and instantaneous frequency. Physical Review A, 78(5). doi:10.1103/physreva.78.053820Tsang, M., Shapiro, J. H., & Lloyd, S. (2009). Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design. Physical Review A, 79(5). doi:10.1103/physreva.79.053843Bloch, M., McLaughlin, S. W., Merolla, J.-M., & Patois, F. (2007). Frequency-coded quantum key distribution. Optics Letters, 32(3), 301. doi:10.1364/ol.32.000301Kumar, P., & Prabhakar, A. (2009). Evolution of Quantum States in an Electro-Optic Phase Modulator. IEEE Journal of Quantum Electronics, 45(2), 149-156. doi:10.1109/jqe.2008.2002673Olislager, L., Cussey, J., Nguyen, A. T., Emplit, P., Massar, S., Merolla, J.-M., & Huy, K. P. (2010). Frequency-bin entangled photons. Physical Review A, 82(1). doi:10.1103/physreva.82.013804Capmany, J., & Fernández-Pousa, C. R. (2010). Quantum model for electro-optical phase modulation. Journal of the Optical Society of America B, 27(6), A119. doi:10.1364/josab.27.00a119Susskind, L., & Glogower, J. (1964). Quantum mechanical phase and time operator. Physics Physique Fizika, 1(1), 49-61. doi:10.1103/physicsphysiquefizika.1.49CARRUTHERS, P., & NIETO, M. M. (1968). Phase and Angle Variables in Quantum Mechanics. Reviews of Modern Physics, 40(2), 411-440. doi:10.1103/revmodphys.40.411Pegg, D. T., & Barnett, S. M. (1988). Unitary Phase Operator in Quantum Mechanics. Europhysics Letters (EPL), 6(6), 483-487. doi:10.1209/0295-5075/6/6/002Lynch, R. (1995). The quantum phase problem: a critical review. Physics Reports, 256(6), 367-436. doi:10.1016/0370-1573(94)00095-kBarnett, S. M., & Vaccaro, J. A. (Eds.). (2007). The Quantum Phase Operator. doi:10.1201/b16006Blow, K. J., Loudon, R., Phoenix, S. J. D., & Shepherd, T. J. (1990). Continuum fields in quantum optics. Physical Review A, 42(7), 4102-4114. doi:10.1103/physreva.42.4102D’Ariano, G. M., & Paris, M. G. A. (1993). Necessity of sine-cosine joint measurement. Physical Review A, 48(6), R4039-R4042. doi:10.1103/physreva.48.r403