The Annular Groove Phase Mask (AGPM) is a vectorial vortex phase mask. It acts as a half-wave plate with a radial fast axis orientation operating in the mid infrared domain. When placed at the focus of a telescope element provides a continuous helical phase ramp for an on axis sources, which creates the orbital angular momentum. Thanks to that phase, the intensity of the central source is canceled by a down-stream pupil stop, while the off axis sources are not affected. However due to experimental conditions the nulling is hardly perfect. To improve the null, a Mach-Zehnder interferometer containing Dove prisms differently oriented can be proposed to sort out light based on its orbital angular momentum (OAM). Thanks to the differential rotation of the beam, a π phase shift is achieved for the on axis light affected by a non zero OAM. Therefore the contrast between the star and its faint companion is enhanced. Nevertheless, due the Dove prisms birefringence, the performance of the interferometer is relatively poor. To solve this problem, we propose to add a birefringent wave-plate in each arm to compensate this birefringence. In this paper, we will develop the mathematical model of the wave front using the Jones formalism. The performance of the interferometer is at first computed for the simple version without the birefringent plate. Then the effect of the birefringent plate is be mathematically described and the performance is re-computed.
This paper describes the development of a photonic local oscillator (LO) source based on a 3-stage Mach-Zehnder modulator (MZM) device. The MZM laser synthesizer demonstrates the feasibility of providing the photonic reference LO for the Atacama Large Millimeter Array telescope located in Chile. This MZM approach to generating an LO by radio RF modulation of a monochromatic optical source provides the merits of wide frequency coverage of 4-130 GHz, tuning speed of about 0.2 seconds, and residual integrated phase noise performance of 0.3 degrees RMS at 100 GHz.
For the first time an all optical flip-flop is demonstrated based on two coupled Mach-Zehnder interferometers which contain semiconductor optical amplifiers in their arms. The flip-flop operation is discussed and it is demonstrated using commercially available fiber pigtailed devices. Being based on Mach-Zehnder interferometers, the flip-flop has potential for very high speed operation.
We present an analysis of quantum-limited DPSK receivers with optical Mach-Zehnder interferometer (MZI) demodulation. It is shown for the first time that the quantum limits for DPSK/MZI receivers with single-port and balanced detections exactly differ from 3-dB in receiver sensitivity, obtained by both Poisson and Gaussian noise statistics.
The performance of a dual parallel differential Mach-Zehnder modulator broadband linearization architecture is analysed. This study provides experimental and analytical results showing an enhancement up to 20 dB in the 3rd-order intermodulation distortion factor at 5 GHz using RF and optical asymmetrical feeding factors.
A Mach-Zehnder interferometer with absorbing Fabry-Pérot cavities is used to measure the optical phase differences upon rotation around a vertical axis. The details of the expected experimental results are described based on the idea that a conducting medium can introduce phase differences due to changes in material conductivity that are expected to occur when a medium moves with respect to a reference frame. Experimental details and results are discussed.
We demonstrate that the interaction of loop and nonlinear Fano resonances results in a formation of hybrid resonant states in Mach-Zehnder type interferometers, providing with opportunities for an advanced phase manipulation. The nonlinear response of such structures can be greatly enhanced, leading to a low threshold 100% switching operation. We further propose one of the possible realizations based on nonlinear photonic crystal circuits, suitable for optimal all-optical switching.
We introduce a concept of the Mach-Zehnder-Fano interferometer by inserting a cavity exhibiting Fano resonance into a conventional interferometer. By employing the scattering-matrix approach, we demonstrate that the transmission is sensitive to a position of the cavity such that an asymmetric structure exhibits a series of narrow resonances with almost perfect reflection. We discuss how to implement this novel geometry in two-dimensional photonic crystals and use direct numerical simulations to demonstrate novel regimes of the resonant transmission and reflection.
We propose an analytical approach to design flattened wavelength splitters with cascaded Mach-Zehnder interferometers when wavelength dependence of the directional couplers cannot be neglected. We start from a geometrical representation of the action of a doubly point symmetrical filter, assuming no wavelength dependence of the couplers. Next we derive the analytical formulas behind its working principle and we extend them to the wavelength dependent case. We also show how the geometrical representation allows to broaden the class of working structures.
Here, we demonstrate a spectrally broadband, GHz-fast Mach-Zehnder interferometeric modulator, exhibiting a miniscule VpL of 95 V-um, deploying a sub-wavelength short electrostatically tunable plasmonic phase-shifter, based on heterogeneously integrated ITO thin films into silicon photonics.
We demonstrate the first active optical isolator and circulator implemented in a linear and reciprocal material platform using commercial Mach-Zehnder modulators. In a proof-of-principle experiment based on single-mode polarization-maintaining fibers, we achieve more than 12.5 dB isolation over an unprecedented 8.7 THz bandwidth at telecommunication wavelengths, with only 9.1 dB total insertion loss. Our architecture provides a practical answer to the challenge of non-reciprocal light routing in photonic integrated circuits.
We present a quantitative experimental analysis of a surface plasmon polariton (SPP) interferometer relying on elliptical Bragg mirrors. By using a leakage radiation microscope we observe oscillation fringes with unit visibility at the two interferometer exits. We study the properties of the SPP beam splitter and determine experimentally both the norm and phase of the SPP reflection and transmission coefficients.
In this paper we address the problem of optimizing an unbalanced Mach-Zehnder interferometer, for a given pure input state and considering a specific detection scheme. While the optimum transmission coefficient of the first beam splitter can be uniquely determined via the quantum Fisher information only [Phys. Rev. A 105, 012604 (2022)], the second beam splitter transmission coefficient is detection-scheme dependent, too. We systematically give analytic solutions for the optimum transmission coefficient of the second beam splitter for three types of widely used detection schemes. We provide de…
Entanglement distillation is the process of concentrating entanglement from a given quantum state. We present a technique for distillation of bi-partite polarization entanglement using interferometry. This technique can be optimized to extract maximal entanglement from any pure or mixed entangled state. A model for this method is presented and in particular we present experimental results for pure states when using polarizing Mach-Zehnder interferometers. These experimentally distilled states always demonstrate an increased violation of Bell's inequality.
We have demonstrated stabilization of a fiber-optic Mach-Zehnder interferometer, with a centimeter-scale path difference, to the transmission minimum for the carrier wave of a frequency-modulated laser beam. A time-averaged extinction of 32 dB, limited by the bandwidth of the feedback, was maintained over several hours. The interferometer was used to remove the carrier wave from a 780 nm laser beam that had been phase modulated at 2.7 GHz.
We experimentally stabilise the polarisation drift between the arms of an 8 km-long fibre-optical Mach-Zehnder interferometer, while simultaneously compensating the phase fluctuations. The single photons are wavelength-multiplexed with three classical channels, which are used as feedback for the control systems. Two of these channels are used for the active polarisation control systems, while the other is used to phase-lock the interferometer. We demonstrate long-term stabilisation of the single-photon visibility when polarisation control is used.
This paper presents an analysis of how to calculate bit error ratio (BER) with physical explanation for optically pre-amplified DPSK receivers using optical Mach-Zehnder interferometer (MZI) demodulation and balanced detection. It is shown that BER calculation method for this kind of receivers is different from the conventional calculation method used widely for IM/DD receivers. An analytical relationship in receiver sensitivity between DPSK receivers using MZI demodulation with balanced detection and IM/DD receivers (or DPSK receivers using MZI demodulation and single-port detection) is given…
An integrated hybrid thin-film lithium niobate (TFLN) electro-optic Mach-Zehnder modulator (MZM) is shown at near-infrared wavelengths. The design uses TFLN bonded to planarized silicon nitride waveguide circuits, and does not require etching or patterning of TFLN. The push-pull MZM achieves a half-wave voltage length product ($V_πL$) of 0.8 V$.$cm at 784 nm. MZM devices with 0.4 cm and 0.8 cm modulation length show a broadband electro-optic response with a 3 dB bandwidth beyond 100 GHz, with the latter showing a bandwidth to half-wave voltage ratio of 100 GHz/V.
We derive equations that quantify silicon Mach-Zehnder Interferometer (MZI) modulator impact upon optical link budget for NRZ transmissions based solely upon modulator extinction ratio (ER), the efficiency-loss figure of merit (FOM), and peak-to-peak drive voltage (Vpp). Our modulator link penalty equations transform the modulator efficiency-loss FOM from a simple device quality metric into a means of predicting how design and technology choices impact system margin. Our results indicate that, with a 17.8 V-cm FOM and 1 Vpp drive, designing an MZI to have an ER anywhere within the large range …
In this paper we describe within the formalism of Quantum Optics (QO) a double Mach-Zehnder interferometer (MZI). For single photon Fock states this experimental setup is shown to exhibit a counter-intuitive behavior: for certain values of the path length difference of the first MZI, the singles photon-count statistics at the output detectors does not change, whatever the difference in path length for the second MZI. For simultaneously impinging light quanta, we show that this setup is able to show the same HOM antibunching effect previously obtained with a beam splitter. However, by adding su…
We utilize various techniques to characterize the residual phase modulation of a fiber-based Mach-Zehnder electro-optical intensity modulator. A heterodyne technique is used to directly measure the phase change due to a given change in intensity, thereby determining the chirp parameter of the device. This chirp parameter is also measured by examining the ratio of sidebands for sinusoidal amplitude modulation. Finally, the frequency chirp caused by an intensity pulse on the nanosecond time scale is measured via the heterodyne signal. We show that this chirp can be largely compensated with a sep…
We describe a resonantly enhanced Mach-Zehnder modulator (MZM) that can be operated over a wide temperature range of 55C without being actively biased, while providing a significant resonant enhancement of 6.8 at the nominal wavelength / temperature compared to a linear MZM driven with a distributed driver. More importantly, it enables a ~20X improvement in power consumption compared to a 50 Ω matched linear traveling wave modulator with comparable phase shifter technology, drive voltage and output optical modulation amplitude. Passive biasing of the Mach-Zehnder interferometer is further impl…
We experimentally demonstrate stable and user-adjustable single-photon interference in a 1 km long fiber- optical Mach-Zehnder interferometer, using an active phase control system with the feedback provided by a classical laser. We are able to continuously tune the single-photon phase difference between the interferometer arms using a phase modulator, which is synchronized with the gate window of the single-photon detectors. The phase control system employs a piezoelectric fiber stretcher to stabilize the phase drift in the interferometer. A single-photon net visibility of 0.97 is obtained, yi…
Photonic integrated circuits (PICs) are the foundation of on-chip optical technologies. Mach-Zehnder modulators are appealing building blocks of PICs which mostly rely on weak and volatile optical effects in materials. In contrast, phase change materials such as GSST are promising candidates to realize efficient and nonvolatile reconfigurable optical devices. However, the phase transitions of PCMs are accompanied by large changes in the imaginary parts of their refractive indices which make the design of MZMs challenging. In this paper, two interesting design methods named as loss-balancing an…
Interferometry is a widely-used technique for precision measurements in both classical and quantum contexts. One way to increase the precision of phase measurements, for example in a Mach-Zehnder interferometer (MZI), is to use high-intensity lasers. In this paper we study the phase sensitivity of a MZI in two detection setups (difference intensity detection and single-mode intensity detection) and for three input scenarios (coherent, double coherent and coherent plus squeezed vacuum). For the coherent and double coherent input, both detection setups can reach the quantum Cramer-Rao bound, alt…
Broadband integrated thin-film lithium niobate (TFLN) electro-optic modulators (EOM) are desirable for optical communications and signal processing in both the O-band (1310 nm) and C-band (1550 nm). To address these needs, we design and demonstrate Mach-Zehnder (MZ) EOM devices in a hybrid platform based on TFLN bonded to foundry-fabricated silicon photonic waveguides. Using a single silicon lithography step and a single bonding step, we realize MZ EOM devices which cover both wavelength ranges on the same chip. The EOM devices achieve 100 GHz EO bandwidth (referenced to 1 GHz) and about 2-3 V…
By the means of the standard quantum mechanics formalism I present an explicit derivation of the structure of power spectra in Danan {\em et al.} and Zhou {\em et al.} experiments with nested dynamically changing Mach-Zehnder interferometers. The analysis confirms that we observe prominent, first-order peaks on frequencies related to some of the elements of the interferometer, but not on others. However, as I shall demonstrate, there are also other, weaker effects related to all relevant elements of the setup. In case of the Danan {\em et al.} setup, there are even peaks at all frequencies of …
We report on a new mechanism of giant phase modulation. The phenomenon arises when a dispersed photonic mode (slow light) strongly couples to an excitonic resonance. In such a case, even a small amount of optically injected carriers creates a potential barrier for the propagating exciton-polariton which provokes a considerable phase shift. We evidence this effect by fabricating an exciton-polariton Mach-Zehnder interferometer, modulating the output intensity by constructive or destructive interferences controlled by optical pumping of a micrometric size area. The figure of merit for a π phase …
In this paper, we present a coherent state-vector method which can explain the results of a nested linear Mach-Zehnder Interferometric experiment. Such interferometers are used widely in Quantum Information and Quantum Optics experiments and also in designing quantum circuits. We have specifically considered the case of an experiment by Danan \emph{et al.} (Phys. Rev. Lett. \textbf{111}, 240402 (2013)) where the outcome of the experiment was spooky by our intuitive guesses. However we have been able to show by our method that the results of this experiment is indeed expected within the standar…
Imperfections in integrated photonics manufacturing have a detrimental effect on the maximal achievable visibility in interferometric architectures. These limits have profound implications for further photonics technological developments and in particular for quantum photonics technologies. Active optimisation approaches, together with reconfigurable photonics, have been proposed as a solution to overcome this. In this paper, we demonstrate an ultra-high (>60 dB) extinction ratio in a silicon photonic device consisting of cascaded Mach-Zehnder interferometers, in which additional interferomete…
We describe and analyse the operation and stabilization of a Mach--Zehnder interferometer, which separates the carrier and the first-order sidebands of a phase-modulated laser field, and which is locked using the Hänsch--Couillaud method. In addition to the necessary attenuation, our interferometer introduces, via total internal reflection, a significant polarization-dependent phase delay. We employ a general treatment to describe an interferometer with an object which affects the field along one path, and we examine how this phase delay affects the error signal. We discuss the requirements ne…
We demonstrate a 2-grating free electron Mach-Zehnder interferometer constructed in a transmission electron microscope. A symmetric binary phase grating and condenser lens system forms two spatially separated, focused probes at the sample which can be scanned while maintaining alignment. The two paths interfere at a second grating, creating in constructive or destructive interference in output beams. This interferometer has many notable features: positionable probe beams, large path separations relative to beam width, continuously tunable relative phase between paths, and real-time phase infor…
The double-slit interferometer and the Mach-Zehnder interferometer (MZI) with balanced beam splitters are prototypical setups for investigating the quantum wave-particle duality. These setups induced a quantitative association of interferometric visibility (IVI) with the wave aspect of a single quantum system (WAQ). Recently, it was realized that quantum coherence (QC) can be better suited than IVI for quantifying the WAQ in complementarity relations. In this article, we investigate a MZI with biased beam splitters both in the input and the output, and we show that in some cases the IVI is not…
Often cited dictums in Quantum Mechanics include "observation disturbance causes loss of interference" and "ignorance is interference". In this paper we propose and describe a series of experiments with modified Mach-Zehnder interferometers showing that one has to be careful when applying such dictums. We are able to show that without interacting in any way with the light quantum (or quanta) expected to behave "wave-like", interference fringes can be lost by simply gaining (or having the potential to gain) the which-path knowledge. Erasing this information may revive the interference fringes. …
In this work, we discuss two phase-measurement methods for the Mach-Zehnder interferometer (MZI) in the presence of internal losses and give the corresponding optimum conditions. We find theoretically that when the core parameters (reflectivities, phase difference) are optimized, the phase sensitivity of the two methods can reach a generalized bound on precision: standard interferometric limit (SIL). In the experiment, we design an MZI with adjustable beam splitting ratios and losses to verify phase sensitivity optimization. The sensitivity improvements at loss rates from 0.4 to 0.998 are demo…
Quantum Scattering Model of Dual Parallel Mach Zehnder Electro Optic Modulators: General Formalism, Impairments, and Applications to Frequency-Bin Photonic Quantum States
Universitat Politècnica de València（瓦伦西亚理工大学）；Universidad Miguel Hernández de Elche（埃尔切米格尔·埃尔南德斯大学）；Universidad de Vigo（维戈大学）
Two optical fiber Mach-Zehnder interferometers were constructed in an environment with a temperature stabilization of better than 1 mK per day. One interferometer with a length of 2 m optical fiber in each arm with the main direction of the arms parallel to each other. A path (length 175 mm) filled with atmospheric air is inserted in one arm. Another interferometer with a length of 2 m optical fiber in each parallel arm acts as a control. In each arm 1 m of fiber was wound around a ring made of piezo material enabling the control of the length of the arms by means of a voltage. The influence o…
Here, we experimentally demonstrate an Indium Tin Oxide (ITO) Mach-Zehnder interferometer heterogeneously integrated in silicon photonics. The phase shifter section is realized in a novel lateral MOS configuration, which, due to favorable electrostatic overlap, leads to efficient modulation (VπL = 63 Vum). This is achieved by (i) selecting a strong index changing material (ITO) and (ii) improving the field overlap as verified by the electrostatic field lines. Furthermore, we show that this platform serves as a building block in an endfire silicon photonics optical phased array (OPA) with a hal…
High bandwidth, low voltage electro-optic modulators with high optical power handling capability are important for improving the performance of analog optical communications and RF photonic links. Here we designed and fabricated a thin-film lithium niobate (LN) Mach-Zehnder modulator (MZM) which can handle high optical power of 110 mW, while having 3-dB bandwidth greater than 110 GHz at 1550 nm. The design does not require etching of thin-film LN, and uses hybrid optical modes formed by bonding LN to planarized silicon photonic waveguide circuits. A high optical power handling capability in th…
We address in this work the phase sensitivity of a Mach-Zehnder interferometer with Gaussian input states. A squeezed-coherent plus squeezed vacuum input state allows us to unambiguously determine the optimal phase-matching conditions in order to maximize the quantum Fisher information. Realistic detection schemes are described and their performance compared in respect with the quantum Cramér-Rao bound. The core of this paper discusses in detail the most general Gaussian input state, without any apriori parameter restrictions. Prioritizing the maximization of various terms in the quantum Fishe…
On-chip high extinction ratio Mach-Zehnder interferometers (MZI) have always attracted interest from researchers as it can be used in many applications in astrophotonics, optical switching, programmable photonic circuits, and quantum information. However, in previous research studies, ultra-high extinction ratio on-chip MZIs have only been achieved by using a multi-stage MZI approach. In this paper, we investigate a high extinction ratio single-stage MZI based on two cascaded multimode interferometers (MMI). We determine that TM noise is an important factor that can prevent us from achieving a…
We propose an alternative scheme for phase estimation in a Mach-Zehnder interferometer (MZI) with photon recycling. It is demonstrated that with the same coherent-state input and homodyne detection, our proposal possesses a phase sensitivity beyond the traditional MZI. For instance, it can achieve an enhancement factor of 9.32 in the phase sensitivity compared with the conventional scheme even with a photon loss of 10% on the photon-recycled arm. From another point of view, the quantum Cramer-Rao bound (QCRB) is also investigated. It is found that our scheme is able to achieve a lower QCRB tha…
Technical University of Denmark（丹麦技术大学）；Huazhong University of Science and Technology（华中科技大学）
Photonic integrated circuits are facilitating the development of optical neural networks, which have the potential to be both faster and more energy efficient than their electronic counterparts since optical signals are especially well-suited for implementing matrix multiplications. However, accurate programming of photonic chips for optical matrix multiplication remains a difficult challenge. Here, we describe both simple analytical models and data-driven models for offline training of optical matrix multipliers. We train and evaluate the models using experimental data obtained from a fabrica…
