> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract—We report a broadband optical delay line programmable for delays up to 1  with nanosecond resolution, while preserving an arbitrary and unknown polarization state of the original light. The delay line comprises bidirectional pass in cascaded segments of standard single-mode fibers, along with terminal reflection from Faraday mirrors (FMs) at both ends. Each segment contains either a short path or a long path, selected by an optical switch. The FMs auto-compensate for random polarization fluctuations introduced by the optical fibers, thereby restoring the initial polarization state. Broadband operation of the delay line was assessed by investigating dispersion of both the fiber and the FMs. Surprisingly, we found that the two-pass propagation in the fiber can mitigate dispersive distortion introduced by the FM. Numerical experiments demonstrated that the output polarization state of the delay line has a mean fidelity better than 99% over a range of 50-nm deviation from the central wavelength. Remarkably, the mean fidelity often surpasses that in the absence of the fiber itself. Index Terms—Optical delay line, quantum memory, dispersion, Faraday mirror, polarization distortion, optical signal processing, optical communication I. INTRODUCTION PTICAL delay lines are designed to temporarily store optical signals with minimal loss and distortion. They play a crucial role in various applications of all-optical switching and signal processing [1-3]. They are essential in optical communications for optical packet synchronization and buffering, and also for simplifying several communication schemes, including rate-adjustable phase-shift keying (PSK) [4] and hybrid differential PSK-multipulse position modulation (MPPM) [5-8]. Programmable optical delay lines can also stimulate new areas of research in delay-sensitive optical systems, such as optical-chaos systems based on delayed feedback [9,10]. This work was supported by the Academy of Scientific Research and Technology (ASRT) through JESOR Program under Grant 5283. (Corresponding authors: Salem Hegazy and Bahaa Saleh.) Salem F. Hegazy is with The National Institute of Laser Enhanced Sciences, Cairo University, Giza 12613, Egypt (e-mail: salem@niles.cu.edu.eg). Salah S. A. Obayya is with The Center for Photonics and Smart Materials, Zewail City of Science and Technology, Giza 12578, Egypt and also with The The delay and storage of photons with arbitrary and unknown polarization states is important in several quantum information and quantum computation applications. It is useful in switching, buffering, and routing of polarization-coded quantum signals [11] and polarization-entangled photons [12,13]. Additionally, it can be integrated into quantum key distribution systems [14- 17] to scramble the critical timing information. Optical delays are generally realized using two approaches. The first offers continuous delay tuning by control of group velocity in optical structures such as Bragg gratings [18], photonic-crystal waveguides [19-21], and resonators [22,23]. Resonators are preferred due to their compact size and simple structure [24,25]; their group delay is varied by detuning the resonance wavelength. However, there is always a trade-off between optical bandwidth, group velocity dispersion, and maximum achievable delay [26]. As a result, this approach is suitable for achieving relatively short delays, limited by the delay-bandwidth product. The second approach for implementing optical delay involves modifying routing paths through serial or parallel line topologies using 2×2 or × optical switches [27, 28]. These switchable delay lines can be realized using both fiber- optic components and integrated photonics [29]. Ideally, the output of a delay line is a lagging replica of its input. However, in practice, because of thermal and mechanical variations, optical fibers induce slow drifts and fluctuations in phase and polarization, altering the polarization state of the output signal. Therefore, while fiber-optic implementations can achieve much longer delays compared to integrated photonics, they often suffer from poor stability [30]. Also, delaying the optical signal while preserving its arbitrary polarization state cannot be accomplished by use of a polarization-maintaining fiber, which preserves only the polarization of its two principal Department of Electronics and Communications Engineering, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt (e-mail: sobayya@zewailcity.edu.eg). Bahaa E. A. Saleh is with CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL 32816 USA (e-mail: besaleh@ creol.ucf.edu). Programmable Broadband Polarization- Preserving Optical Delay Line with Faraday Mirrors Salem F. Hegazy, Member, IEEE, Salah S. A. Obayya, Fellow, IEEE, Fellow, OSA, and Bahaa E. A. Saleh, Life Fellow, IEEE, Fellow, OSA O