Unbalanced Mach-Zehnder Interferometer Research Articles

Development of hybrid photonic integrated wavelength-tunable laser at 2 µm and its application to FMCW LiDAR

This paper reports on the experimental demonstration of a fully integrated frequency-modulated continuous-wave (FMCW) LiDAR sensing system, operating at 2.0 µm. It makes use of a widely tunable hybrid external cavity laser based on the combination of GaSb gain chip and silicon waveguide circuits. The single-frequency laser operation over the full spectral bandwidth of the gain chip is secured using a frequency-selective filter, consisting of two sequential microring resonators in a Vernier configuration. To increase the mode-hop free wavelength tuning range while preserving the linewidth of the laser, the heater of the phase section placed along the bus waveguide is synchronously controlled with two independent heaters placed on each microring resonator. This laser is then implemented for the development of an FMCW LiDAR, consisting of all-optical fiber-based two independent unbalanced Mach-Zehnder interferometers: k-space interferometer for the linearization of continuously swept laser frequency and main interferometer for the measurement of the distributed back-reflection over the distance. The optical frequency of the laser is continuously swept over a ∼100 GHz range (or Δλ=1.47 nm at the operating wavelength) at a modulation speed of 100 Hz. Using this wavelength tunable laser, a light detection and ranging system (LiDAR) is experimentally demonstrated, showing a very high axial resolution of 1.36 mm in air with an extremely high precision of ∼9 µm at a 100 Hz measurement rate.

Experimental Generation of Spin-Photon Entanglement in Silicon Carbide.

A solid-state approach for quantum networks is advantageous, as it allows the integration of nanophotonics to enhance the photon emission and the utilization of weakly coupled nuclear spins for long-lived storage. Silicon carbide, specifically point defects within it, shows great promise in this regard due to the easy of availability and well-established nanofabrication techniques. Despite of remarkable progresses made, achieving spin-photon entanglement remains a crucial aspect to be realized. In this Letter, we experimentally generate entanglement between a silicon vacancy defect in silicon carbide and a scattered single photon in the zero-phonon line. The spin state is measured by detecting photons scattered in the phonon sideband. The photonic qubit is encoded in the time-bin degree of freedom and measured using an unbalanced Mach-Zehnder interferometer. Photonic correlations not only reveal the quality of the entanglement but also verify the deterministic nature of the entanglement creation process. By harnessing two pairs of such spin-photon entanglement, it becomes straightforward to entangle remote quantum nodes at long distance.

High resolution and large measurement range voltage sensing based on an optoelectronic oscillator utilizing an unbalanced Mach-Zehnder interferometer.

A voltage sensor with high resolution and large measurement range based on an optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. The key component in the cavity to select the oscillating signal is a finite impulse response (FIR)-microwave photonic filter (MPF) which consists of a sinusoidal broadband optical signal, an unbalanced Mach-Zehnder interferometer (MZI), a section of dispersion compensating fiber, and a photodetector. The center frequency of the FIR-MPF is mainly determined by the free spectral range (FSR) of the FIR-MPF. In the lower arm of the MZI, a cylindrical piezoelectric ceramic (PZT) wrapped with a section of optical fiber acts as voltage sensing head. Due to the inverse piezoelectric effect of PZT, the variation of the voltage will cause radial deformation of the cylindrical PZT and then lead to the change of the FSR of the MZI, determining the shift of center frequency of FIR-MPF as well as the frequency of the oscillating signal of the OEO. Thus, by monitoring the shift of the oscillation frequency of the OEO using an electric spectrum analyzer or a digital signal processor, a high-speed interrogation and high-resolution voltage measurement can be realized. Additionally, in the proposed scheme, an infinite impulse response (IIR)-MPF consisting of a fiber ring resonator is cascaded with the FIR-MPF to ensure the single-mode oscillation of the OEO. The experimental results show that a total range of 1700 V voltage sensing from - 200 V to 1500 V is accomplished with the voltage sensitivity of 0.25 GHz/100 V and the resolution of 0.3 V. By adjusting the proportion of the length of single mode fiber between two branches of MZI, the impact of temperature can be greatly reduced. The proposed sensor offers advantages such as a large measurement range, high resolution, high-speed interrogation, and stability to temperature disturbances, making it highly suitable for sensing applications in smart grids.

Demonstration of Interferometric Properties of Unbalanced Mach-Zehnder Interferometer

This article presents a demonstration of the interferometric characteristics inherent in an unbalanced Mach-Zehnder Interferometer (MZI), implemented on a silicon-on-insulator platform through precision fabrication techniques. The investigation delves into the intricate relationship between the free spectral range (FSR) and various lengths of unbalanced MZIs. Notably, a comparison between simulation and experimental outcomes reveals a remarkable agreement.

Optical and geometric parameter extraction across 300-mm photonic integrated circuit wafers

The precise quantification of a dielectric waveguide core thickness, core width, core refractive index, and cladding refractive index across a wafer is critical for greater consistency and accuracy in photonic circuit fabrication. However, accurate wafer-scale measurements of these parameters have not yet been demonstrated. We have previously described a method for extracting these four parameters simultaneously from silicon nitride waveguides using unbalanced Mach–Zehnder interferometers on a single die. In this work, we show that this technique can be scaled to characterize these photonic parameters across an entire 300 mm wafer. The refractive indices of the core and cladding materials are found with relative standard deviations of the mean of 0.07% and 0.03%, respectively. The core width offset (bias) and thickness are found with relative standard deviations of 0.3% (2.6 nm) and 0.5% (1.1 nm), respectively. The extracted parameter maps suggest a radial variation of material indices and a planar variation of geometric parameters. We verify the extracted parameters by accurately predicting the performance of an unbalanced Mach–Zehnder interferometer and the degeneracy between different modes in straight waveguides.

ИЗМЕРЕНИЕ ФАЗОВЫХ И АМПЛИТУДНЫХ ШУМОВ ПОЛУПРОВОДНИКОВЫХ ЛАЗЕРОВ. МЕТОДИКА ИЗМЕРЕНИЙ. КАЛИБРОВКА. РЕЗУЛЬТАТЫ

The application of the frequency detector method for measuring the phase noise spectrum of semiconductor lasers has been experimentally demonstrated. The frequency detector is based on an unbalanced Mach-Zehnder interferometer and a photodetector. Analytical relations are obtained that allow one to choose the parameters of the Mach-Zehnder interferometer and perform experimental calibration of the measuring system. A technique is proposed for measuring the spectral components of the phase noise of lasers in the presence of a slow drift of the delay in fiber-optic lines and the frequency of the laser under study. The results of measuring the phase noise of a low-noise DX-1 laser module and high-noise laser diodes LSDLD155 (DFB) and LSFLD155 (FP) are presented. A strong correlation between the amplitude and phase noise levels of these lasers is found. The decisive influence of the noise of LSDLD155 and LSFLD155 lasers on the level of phase noise of optoelectronic (OE) microwave generators built using them is shown. It has been suggested that the low-noise laser module DX-1, which has a phase noise level 20–60 dB lower (in different parts of the spectrum), is not decisive in the level of phase and amplitude noise of an optoelectronic microwave generator. The investigated OE generator was built during the research in this work. The generator has low phase noise: −120 dBc/Hz at a frequency detuning of 10 kHz. Oscillation frequency 6.8 GHz; fiber optic delay line length 200 m.

Athermal, fabrication-tolerant Si-SiN FIR filters for a silicon photonics foundry platform.

A means of athermalizing unbalanced Mach-Zehnder interferometers on a 300 mm silicon photonics foundry platform utilizing Si and SiN layers to produce the path imbalance is demonstrated. This technique can be applied to all other forms of finite impulse response filters, such as arrayed waveguide gratings. Wafer scale performance of fabricated devices is analyzed for their expected performance in the target application: odd-even channel (de)-interleavers for dense wavelength division multiplexing links. Finally, a method is proposed to improve device performance to be more robust to fabrication variations while simultaneously maintaining athermality.

Dual-ring parity-time symmetric brillouin fiber laser with an unbalanced polarization Mach-Zehnder interferometer.

A dual-ring parity-time (PT) symmetric Brillouin fiber laser (BFL) with an unbalanced polarization Mach-Zehnder interferometer (UP-MZI) is proposed and experimentally investigated. An UP-MZI consisting of optical coupler, polarization beam combiner (PBC) and two asymmetric length arms with 10 km and 100 m single-mode fiber, is used to achieve Vernier effect and PT symmetry. Due to the orthogonally polarized lights created in the PBC, the dual-ring PT symmetry BFL with an UP-MZI implements two unbalanced length feedback rings that are connected to one another, one long length ring with a Brillouin gain and the other short length ring with a loss of the same magnitude, to break a PT symmetric and maintain the Vernier effect. By contrast with existing PT symmetry BFL studies, this design does not require same lengths of the gain and loss loops, but can manipulate freely PT symmetry status in accordance with a rational scaling factor between them. Experimental results reveal that the 3-dB linewidth of dual-ring PT symmetry BFL with an UP-MZI is about 4.85 Hz with the threshold input power of 9.5 mW, in accordance with the 97 Hz measured linewidth at the -20 dB power point. Within 60 mins of the stability experiment, the power and frequency stability fluctuation are ±0.02 dB and ±0.137 kHz, respectively. Thanks to the two asymmetric ring lengths, the sidemode suppression ratio (SMSR) is optimized by 54 dB compared to that with the only long ring structure, 26 dB when using only the Vernier effect or 12 dB for existing PT symmetry BFL. This BFL design with single longitudinal mode and high SMSR output can be applied to high coherent communication and Brillouin-based microwave photonics systems with low phase noise.

Optical frequency domain polarimetry based on a self-referenced unbalanced Mach-Zehnder interferometer.

Optical frequency domain polarimetry (OFDP) is an emerging distributed polarization crosstalk rapid measurement method with an ultrawide dynamic range. However, interferometric phase noise induced by the laser source and ambient noise results in a trade-off between measurement length and dynamic range. In this Letter, we solve this problem with a self-referenced unbalanced Mach-Zehnder interferometer. The features of long distance (9.8 km), ultrawide dynamic range (107.8 dB), short measurement time (2 sec), and signal-to-noise ratio improvement against ambient noise are experimentally demonstrated. The method makes it possible to evaluate a long polarization-maintaining fiber in an environment whose state changes rapidly.

Optimal Phase Sensitivity in an Unbalanced Mach-Zehnder Interferometer

In this work we address the problem of phase sensitivity optimization for an unbalanced Mach-Zehnder interferometer. While the quantum Fisher information can be employed in order to obtain the optimum transmission coefficient for the first beam splitter, this is no longer true for the second one, whose optimization is detection-scheme dependent. We thus consider three commonly used detection schemes and provide the optimal solution for each case. We also provide applications of the optimization method showing that for some input states a non-balanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.

Electro-optically tunable optical delay line with a continuous tuning range of ∼220 fs in thin-film lithium niobate.

We demonstrate fabrication of a 30-cm-long thin-film lithium niobate (TFLN) optical delay line (ODL) incorporated with segmented microelectrodes of 24-cm total length using the femtosecond laser lithography technique. The transmission spectra of the unbalanced Mach-Zehnder interferometers (MZIs) reveal an ultra-low propagation loss of 0.025 dB/cm. The device exhibits a low half-wave voltage of 0.45 V, corresponding to a voltage-length product of 10.8 V·cm, which is equivalent to 5.4 V·cm in the push-pull configuration. We also demonstrate a high electro-optic (EO) tuning efficiency of 3.146 fs/V and a continuous tuning range of 220 fs in the fabricated ODL.

Sensitive Evanescence-Field Waveguide Interferometer for Aqueous Nitro-Explosive Sensing

The development of novel chemical nitro-explosive sensors with high sensitivity, low cost and a compact size is essential for homeland security, environmental protection and addressing military challenges. Polymeric optical waveguides based on refractive index sensing are widely used in biochemical detection due to their advantages of large-scale integration, low cost, high sensitivity and anti-electromagnetic interference. In this study, we designed and fabricated a polymer waveguide Mach–Zehnder interferometer (MZI) sensor to detect 2,4-dinitrotoluene (DNT) in water. One phase shifter of the MZI waveguide was functionalized by coating a thin cladding layer of polycarbonate with dipolar chromophores and used as the sensing arm; the other arm was coated with passive epoxy resin cladding and used as the reference arm. The phase difference between the two arms of the MZI was modulated using the refractive index (RI) change in the polycarbonate cladding when dipolar chromophores interacted with electro-deficient DNT. The theoretical sensitivity of the designed MZI can reach up to 24,696 nm/RIU. When used for explosive detection, our fabricated sensor had a maximum wavelength shift of 4.465 nm and good linear relation, with an R2 of 0.96 between the wavelength shift and a concentration ranging from 3.5 × 10−5 to 6.3 × 10−4 mol/L. The sensitivity of our device was 6821.6 nm/(mol/L). The design of an unbalanced MZI sensor, together with the sensing material, provides a new approach to using low-cost, compact and highly sensitive devices for in-field explosive detection.

Unbalanced beam splitters enabling enhanced phase sensitivity of a Mach-Zehnder interferometer using coherent and squeezed vacuum states

An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are $\frac{1}{2}$. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cram\'er-Rao bound. Our results may contribute to the development of practical quantum sensing.

Photonic-chip-based dense entanglement distribution

The dense quantum entanglement distribution is the basis for practical quantum communication, quantum networks and distributed quantum computation. To make entanglement distribution processes stable enough for practical and large-scale applications, it is necessary to perform them with the integrated pattern. Here, we first integrate a dense wavelength-division demultiplexing system and unbalanced Mach-Zehnder interferometers on one large-scale photonic chip and demonstrate the multi-channel wavelength multiplexing entanglement distribution among distributed photonic chips. Specifically, we use one chip as a sender to produce high-performance and wideband quantum photon pairs, which are then sent to two receiver chips through 1-km standard optical fibers. The receiver chip includes a dense wavelength-division demultiplexing system and unbalanced Mach-Zehnder interferometers and realizes multi-wavelength-channel energy-time entanglement generation and analysis. High quantum interference visibilities prove the effectiveness of the multi-chip system. Our work paves the way for practical entanglement-based quantum key distribution and quantum networks.

Optimal phase sensitivity of an unbalanced Mach-Zehnder interferometer

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 [Ataman, 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 detailed examples including both Gaussian and non-Gaussian input states, showing when an unbalanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.

Dual-Polarization Bandwidth-Bridged Bandpass Sampling Fourier Transform Spectrometer from Visible to Near-Infrared on a Silicon Nitride Platform.

On-chip broadband optical spectrometers that cover the entire tissue transparency window (λ = 650–1050 nm) with high resolution are highly demanded for miniaturized biosensing and bioimaging applications. The standard spatial heterodyne Fourier transform spectrometer (SHFTS) requires a large number of Mach–Zehnder interferometer (MZI) arrays to obtain a broad spectral bandwidth while maintaining high resolution. Here, we propose a novel type of SHFTS integrated with a subwavelength grating coupler (SWGC) for the dual-polarization bandpass sampling on the Si3N4 platform to solve the intrinsic trade-off limitation between the bandwidth and resolution of the SHFTS without having an outrageous number of MZI arrays or adding additional active photonic components. By applying the bandpass sampling theorem, the continuous broadband input spectrum is divided into multiple narrow-band channels through tuning the phase-matching condition of the SWGC with different polarization and coupling angles. Thereby, it is able to reconstruct each band separately far beyond the Nyquist criterion without aliasing error or degrading the resolution. We experimentally demonstrated the broadband spectrum retrieval results with the overall bandwidth coverage of 400 nm, bridging the wavelengths from 650 to 1050 nm, with a resolution of 2–5 nm. The bandpass sampling SHFTS is designed to have 32 linearly unbalanced MZIs with the maximum optical path length difference of 93 μm within an overall footprint size of 4.7 mm × 0.65 mm, and the coupling angles of SWGC are varied from 0° to 32° to cover the entire tissue transparency window.

Broadband Fiber-Optic Acoustic Sensors

A broadband fiber-optic acoustic sensing system is proposed and demonstrated, which is configured by a fiber Bragg grating (FBG) and an erbium-doped fiber (EDF) ring laser. As the acoustic waves can shift the FBG reflective spectrum, the wavelength of the laser output shifts accordingly and this shift is subsequently converted into a corresponding phase shift and demodulated by an unbalanced fiber-optic Mach-Zehnder interferometer (MZI). The sensitivity of the presented sensing system is also investigated, which is a function of the optical path difference of the MZI and the linewidth of the FBG. Due to the adaptability and high sensitivity of the system, it can detect signals with frequencies from tens of hertz to hundreds of kilohertz, which shows the potential for acoustic emission detection in real applications.

Ultrahigh-resolution optical vector analyzer for multiple parallel measurements based on frequency-domain analysis.

An ultrahigh-resolution optical vector analyzer (OVA) is reported for multiple parallel measurements based on frequency-domain analysis (FDA). In the proposed system, an optical linearly frequency modulated waveform generated via electro-optic modulation and optical injection locking is launched into an unbalanced Mach-Zehnder interferometer (MZI), in which multiple devices under test (DUTs) are cascaded with different time delays in one arm and a delay reference line in the other arm. The optical signals from the two arms of the MZI are sent to a balanced photo-detector, where a series of electrical signals with different frequencies is generated. With the use of the FDA, the optical spectral response of the DUTs can be separately extracted from the generated electrical signals. An experimental demonstration is performed, in which the frequency responses of a hydrogen cyanide (HCN) gas cell, a phase-shifted fiber Bragg grating, and an optical reflector are characterized simultaneously. The measurement results show that the proposed OVA has a simultaneous characterization capacity of multiple devices at a frequency resolution as high as 200 kHz, a measurement time as short as 490 µs, and a frequency measurement range as wide as 18.5 GHz.

Using the Autler-Townes and ac Stark effects to optically tune the frequency of indistinguishable single photons from an on-demand source

We describe how a coherent optical drive that is near resonant with the upper rungs of a three-level ladder system, in conjunction with a short-pulse excitation, can be used to provide a frequency-tunable source of on-demand single photons. Using an intuitive master equation model, we identify two distinct regimes of device operation: (i) for a resonant drive, the source operates using the Autler-Townes effect, and (ii) for an off-resonant drive, the source exploits the ac Stark effect. The former regime allows for a large frequency-tuning range but coherence suffers from timing jitter effects, while the latter allows for high indistinguishability and efficiency, but with a restricted tuning bandwidth due to high required drive strengths and detunings. We show how both these negative effects can be mitigated by using an optical cavity to increase the collection rate of the desired photons. We apply our general theory to semiconductor quantum dots, which have proven to be excellent single-photon sources, and find that scattering of acoustic phonons leads to excitation-induced dephasing and increased population of the higher-energy level which limits the bandwidth of frequency tuning achievable while retaining high indistinguishability. Despite this, for realistic cavity and quantum dot parameters, indistinguishabilities of over $90%$ are achievable for energy shifts of up to hundreds of $\ensuremath{\mu}\mathrm{eV}$, and near-unity indistinguishabilities for energy shifts up to tens of $\ensuremath{\mu}\mathrm{eV}$. Additionally, we clarify the often-overlooked differences between an idealized Hong-Ou-Mandel two-photon interference experiment and its usual implementation with an unbalanced Mach-Zehnder interferometer, pointing out the subtle differences in the single-photon visibility associated with these different setups.

Optical and geometric parameter extraction for photonic integrated circuits.

We describe an in-situ technique to characterize the material refractive indices and waveguide geometry for photonic integrated circuits over hundreds of nanometers of optical bandwidth. By combining white light spectroscopy with unbalanced Mach-Zehnder interferometers, we can simultaneously and accurately extract the core thickness, core width, core refractive index, and cladding refractive index. This information is important for the technological maturation of photonic integrated circuit foundry fabrication. Capturing the inter-wafer and intra-wafer variation of these parameters is necessary to predict the yield of photonic components and for overall process quality control. Refractive indices are found with a 1-σ error of between 0.1% and 0.5%, and geometric parameters are found with an error of between 3 nm and 7 nm. Our analysis and validation are implemented and verified using the same waveguide layers as are used in the standard photonic wafer build, without any external techniques such as ellipsometry or microscopy.