Generalized Mach-Zehnder Interferometer Research Articles

Generalized Mach Zehnder Interferometers Integrated on Si3N4 Waveguide Platform

We demonstrate 3 × 3 and 4 × 4 Generalized Mach Zehnder Interferometers (GMZI) integrated on the Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> waveguide platform and present their experimental performance as switching and variable power splitting modules. The GMZI structures have been theoretically modelled by means of a transfer matrix model, evaluating also the GMZI spectral response in the case of fabrication errors that may lead to variations in GMZI arm lengths, MMI phase shifts and MMI splitting ratios. Both 3 × 3 and 4 × 4 GMZI structures were fabricated as integrated Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> -based circuits and were experimentally characterized with the experimental results being in close agreement with the theoretical predictions. They both reveal a resonant spectral behavior with an FSR of 1.9 nm and low average insertion losses per port that were measured to be 1 ± 0.2 and 2.4 ± 0.4 dB. The two GMZI structures were utilized as 1:3 and 1:4 switching elements, respectively, with average crosstalk levels being always greater than 10 dB for all possible input-output port combinations. Finally, their credentials to serve within linear optical circuit implementations were evaluated through their experimental characterization in variable power splitting applications, showing that the power level at a single output port can take any value between 0 and 100% of the input signal.

Fringe visibility and correlation in Mach–Zehnder interferometer with an asymmetric beam splitter

We study the wave–particle duality in a general Mach–Zehnder interferometer with an asymmetric beam splitter from the viewpoint of quantum information theory. The correlations (including the classical correlation and the quantum correlation) between the particle and the which-path detector are derived when they are in pure state or mixed state at the output of Mach–Zehnder interferometer. It is found that the fringe visibility and the correlations are effected by the asymmetric beam splitter and the input state of the particle. The complementary relations between the fringe visibility and the correlations are also presented.

Fidelity Restorable Universal Linear Optics

Universal multiport interferometers that can be programmed to perform any unitary or linear transformation turn into an important building block for both classical and quantum photonics. These interferometers typically utilize the mathematical framework of U(2) unitary matrix decomposition techniques and comprise a mesh of 2 × 2 beam splitters and phase shifters. All of them are, however, inherently fidelity limited as their U(2)‐based deployment approach leads to imbalanced path losses without supporting any fidelity restoration mechanism. Herein, a novel Universal Generalized Mach–Zehnder Interferometer (UGMZI) architecture is presented that migrates from U(2) decomposition techniques and adopts a recursive U(N) decomposition, exploiting cascaded size‐augmenting N N beam splitters and phase shifters. The design can natively support fidelity restoration and safeguard absolute fidelity, while outperforming the state‐of‐the‐art designs also with respect to phase‐error‐induced fidelity performance properties. Finally, it is demonstrated that its fidelity restoration properties turn the design into the optimal architecture for constructing any real/complex‐valued matrix via the singular value decomposition (SVD) scheme.

Performance Analysis of a Multi-Function Mach-Zehnder Interferometer Based Photonic Architecture on SOI Acting as a Frequency Shifter

A photonic frequency shifter based on generalized Mach-Zehnder interferometer (GMZI) architecture is presented and experimentally validated. The circuit consists of four Mach-Zehnder modulators (MZM) in a 4 × 4 network bounded by two 4 × 4 multimode interference couplers and functionally equivalent to two parallel dual-parallel MZM (DP-MZM). The circuit can offer static bias free operation, virtual connectivity control of the components, and spatial separation of up- and down-converted carriers, which can be collected from separate ports without using any optical demultiplexing filters. Thus, the design permits remote heterodyning (advantages which cannot be obtained using a commercial DP-MZM or filter based optical frequency shifter). Experimental investigation shows deviation from ideal performance due to possible fabrication error and poor fiber-chip coupling. A carrier suppression of &gt;20 dB and spurious sideband suppression &gt;12 dB relative to the principal harmonics is achieved without any tuning for bias adjustment. In addition to the frequency conversion, the integration feasible circuit can also perform as a sub-carrier generator, IQ modulator, and frequency multiplier.

Energy efficient photonic millimeter-wave generation using cascaded polarization modulators

A filter-less millimeter-wave generation scheme consisting of four polarization modulators in series, each followed by a polarizer is proposed to achieve optoelectronic frequency octupling. The cascade of polarization modulator and polarizer provides an intensity modulator whose biasing condition can be set by the polarizer angle and polarization state of the input light to each polarization modulator. A theoretical analysis of the architecture is performed using a transfer function method and validated by industry-standard software simulation tools. The circuit shows high potential in achieving desired performance with lower input RF power when compared to the another configuration based on a generalized Mach–Zehnder interferometer structure. Although the operating range in terms of applied RF drive becomes narrow, low RF input operation can be achieved by this circuit. The effect of imbalances in the key circuit parameters is also investigated in terms of electrical side harmonic suppression ratio.

Complementarity via Minimum Error Measurement in a Two-Path Interferometer**Supported by the National Natural Science Foundation of China under Grant Nos 11434011 and 11575058.

We study the fringe visibility and the which-path information (WPI) of a general Mach–Zehnder interferometer with an asymmetric beam splitter (BS). A minimum error measurement in the detector is used to extract the WPI. Both the fringe visibility V and the WPI Ipath are affected by the initial state of the photon and the second asymmetric BS. The condition in which the WPI takes the maximum is obtained. The complementarity relationship is found, and the conditions for equality are also presented.

Fringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter**Project supported by the National Natural Science Foundation of China (Grant Nos. 11434011, 11575058, and 61833010), the “Science and Technology Innovation Platform and Talent Plan” Excellent Talent Award of Hunan Province, China (Grant No. 2017XK2021), the Science Funds from the Ministry of Science and Technology of China (Grant Nos.

We study the fringe visibility and the distinguishability of a general Mach–Zehnder interferometer with an asymmetric beam splitter. Both the fringe visibility V and the distinguishability D are affected by the input state of the particle characterized by the Bloch vector S = (Sx,Sy,Sz) and the second asymmetric beam splitter characterized by the paramter β. For the total system is initially in a pure state, it is found that the fringe visibility reaches the upper bound and the distinguishability reaches the lower bound when cos β = −Sx. The fringe visibility obtain the maximum only if Sx = 0 and β = π/2 when the input particle is initially in a mixed state. The complementary relationship V2 + D2 ≤ 1 is proved in a general Mach–Zehnder interferometer with an asymmetric beam splitter, and the conditions for the equality are also presented.

Compressive optical interferometry under structural constraints.

Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random spatial patterns that are selected from an appropriate random ensemble. We show here that CS can be exploited in 'native' optics hardware without introducing added components. Specifically, we show that random sub-Nyquist sampling of an interferogram suffices to reconstruct the field modal structure despite the structural constraints of the measurement system set by its limited degrees of freedom. The distribution of the reduced (and structurally constrained) sensing matrices corresponding to random measurements is provably incoherent and isotropic, which helps us carry out CS successfully. We implement compressive interferometry using a generalized Mach-Zehnder interferometer in which the traditional temporal delay is replaced with a linear transformation corresponding to a fractional transform. By randomly sampling the order of the fractional transform, we efficiently reconstruct the modal content of the input beam in the Hermite-Gaussian and Laguerre-Gaussian bases.

Complementarity via error-free measurement in a two-path interferometer

We study both wave-like behavior and particle-like behavior in a general Mach–Zehnder interferometer with an asymmetric beam splitter. An error-free measurement in the detector is used to extract the which-path information. The fringe visibility V and the which-path information Ipath are derived, their complementary relation is found, and the condition for the equality is also presented.

Design and matrix analysis of optical switch with multicast function using general MZI

Based on the analysis of the LiNbO3 Mach-Zehnder interferometer (MZI), a MZI with three optical switch functions (direct connection, cross connection and multicast connection) is demonstrated in this paper. With this MZI, a 4×4 optical switch is then proposed. The optical switch not only switches optical signal from one channel to another (1:1), but also from one channel to several channels (1: k) with non-blocking and duplex communication. Later, a matrix analysis on the optical switch proposed is given. In the end of this paper, an example of the transmission path and the controlling state of the optical switch is demonstrated.

4 × 4 nonblocking optical switch fabric based on cascaded multimode interferometers

We experimentally demonstrate a 4×4 nonblocking silicon thermo-optic (TO) switch fabric consisting of three stages of tunable generalized Mach–Zehnder interferometers. All 24 routing states for nonblocking switching are characterized. The device’s footprint is 4.6 mm×1.0 mm. Measurements show that the worst cross talk of all switching states is −7.2 dB. The on-chip insertion loss is in the range of 3.7–13.1 dB. The average TO switching power consumption is 104.8 mW.

Generalized Mach–Zehnder interferometer architectures for radio frequency translation and multiplication: Suppression of unwanted harmonics by design

A generalized array of N parallel phase modulators electrically driven with a progressive 2π/N phase shift is analyzed. For N-even, the equivalence of this configuration to parallel Mach–Zehnder architectures, and specifically the equivalence for N=4 to a dual parallel Mach–Zehnder modulator is shown. A simple approach to the design of this architecture that determines the static optical phase shifts required in each of the N parallel arms to suppress unwanted harmonics while maximizing the harmonics of interest is developed. The proposed design approach is validated by numerical simulations of N=4 and N=6 architectures with properly determined optical phase shifts. Optical single-side-band modulation (lower and upper) and frequency multiplication of an electrical drive signal with high suppression of unwanted harmonics is shown to be achievable.

4 × 4 Nonblocking Silicon Thermo-Optic Switches Based on Multimode Interferometers

We experimentally demonstrate a silicon 4 × 4 nonblocking thermo-optic (TO) switch using a generalized Mach-Zehnder interferometer constructed on multimode interferometers. All the 24 switching states for nonblocking switching are characterized. The device fabricated using CMOS technologies has a footprint of 2.8 × 0.65 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The measured average on-chip insertion loss is 9 ± 2 dB and the crosstalk for all switching states is better than -12 dB. The average TO switching power consumption is 109 mW. The switching functionality is verified by transmission of a 40-Gb/s quadrature phase-shift keying optical signal.

Generation of two Fano resonances using 4×4 multimode interference structures on silicon waveguides

We propose a novel microring resonator coupled 4×4 generalized Mach Zehnder interferometer (GMZI) structure to produce Fano resonance line shapes. The structure can produce two independent Fano resonance line shapes. Two phase shifters are introduced in two arms of the 4×4 GMZI to control the variation of the Fano line shapes. The other aim of this study is to use silicon waveguides, that are compatible with the existing CMOS (Complementary Metal-Oxide-Semiconductor) fabrication technology, for designing the proposed devices. The transfer matrix method (TMM) and beam propagation method (BPM) are used for analytical analysis and first order design of the device. Finally, we discuss potential applications of the new device for sensing, all-optical switching applications and generation of electromagnetically induced transparency (EIT) effect.

Microring Resonators Based on 6x6 Generalized Multimode Interference Structures using Silicon Waveguides for Photonic Applications

In this paper, we would like to propose a new microring resonator structure based on 6x6 Generalized Mach Zehnder interferometer (GMZI) using silicon waveguides. It is showed that this new kind of the devices works as three separated microring resonators. This characteristic of the device leads to a variety of tasks important to optical communications, including switching, filtering, add-drop multiplexing, sensing and modulation. In our study, silicon waveguides are used for designing the proposed devices. The transfer matrix method (TMM) and the three dimensional beam propagation methods (3D-BPM) are used to optimally design the device.

Duality relations in a two-path interferometer with an asymmetric beam splitter

We investigate quantitatively the wave-particle duality in a general Mach-Zehnder interferometer setup with an asymmetric beam splitter. The asymmetric beam splitter introduces additional a priori which-path knowledge, which is different for a particle detected at one output port of the interferometer and a particle detected at the other. Accordingly, the fringe visibilities of the interference patterns emerging at the two output ports are also different. Hence, in sharp contrast with the symmetric case, here we should concentrate on one output port and distinguish two possible paths taken by the particles detected at that port among four paths. It turns out that two nonorthogonal unsharp observables are measured jointly in this setup. We apply the condition for joint measurability of these unsharp observables to obtain a trade-off relation between the fringe visibility of the interference pattern and the which-path distinguishability.

High-Speed Optical 1 $\times$ 4 Switch Based on Generalized Mach–Zehnder Interferometer With Hybrid Configuration of Silica-Based PLC and Lithium Niobate Phase-Shifter Array

We demonstrate a high-speed optical switch based on a generalized Mach-Zehnder interferometer with a hybrid configuration consisting of a silica-based planar lightwave circuit and lithium niobate phase shifters. The novel switch demonstrated here has one input and four output ports and a switching time of less than 0.1 mus, thanks to the fast response of the electrooptic phase shifters on the LN chip. The insertion loss and extinction ratio of the switch are 4.2 dB and more than 17 dB, respectively

Adaptive quantum estimation of phase shifts

We discuss an adaptive interferometric approach to quantum estimation of phase shifts. In a first step we find optimized two-mode input states for a generalized Mach-Zehnder interferometer. These two states show a small phase variance at the so-called Heisenberg limit. It turns out that they can be generated by entangling a coherent state and a squeezed vacuum at a beam splitter. Moreover, the interferometric setup allows us to describe an adaptive estimation scheme for arbitrary phase shifts if we assume a fixed mean photon number as a quantum resource.

Design of Optical Full Encoders/Decoders for Code-Based Photonic Routers

This paper demonstrates that standard multiplexers as generalized Mach-Zehnder interferometers or waveguide grating routers can be designed to generate/process a set of orthogonal optical codes (OCs) with very high-correlation performances. The same device can be used at the ingress node of a generalized multiprotocol label switching network to generate the photonic labels and at each routing node to perform all the correlations simultaneously. To enhance the code cardinality, without increasing the code length, this paper shows that it is possible to use the proposed encoder/decoder architectures to generate/process multidimensional OCs.

Generalized Mach–Zehnder interferometers for sensing applications

A sensing application of integrated optical (IO) generalized Mach–Zehnder interferometers (GMZIs) is proposed. GMZIs are multiple-arms Mach–Zehnder interferometers (MZIs) and are widely used in optical telecommunications for wavelength-division multiplexing (WDM) and optical switching. In this paper, we show that GMZIs can be used in order to realize highly sensitive IO refractometers that can be usefully employed in chemical and biochemical sensing applications. These devices, with a suitable design, permit sensitive operation over a wide range of indices without the ambiguities of conventional MZIs. Furthermore, in some applications a direct digital readout is possible.