Fringe Contrast Research Articles

Multiplexable high-temperature stable and low-loss intrinsic Fabry-Perot in-fiber sensors through nanograting engineering.

This paper presents a method of using femtosecond laser inscribed nanograting as low-loss- and high-temperature-stable in-fiber reflectors. By introducing a pair of nanograting inside the core of a single-mode optical fiber, an intrinsic Fabry-Perot interferometer can be created for high-temperature sensing applications. The morphology of the nanograting inscribed in fiber cores was engineered by tuning the fabrication conditions to achieve a high fringe visibility of 0.49 and low insertion loss of 0.002 dB per sensor. Using a white light interferometry demodulation algorithm, we demonstrate the temperature sensitivity, cross-talk, and spatial multiplexability of sensor arrays. Both the sensor performance and stability were studied from room temperature to 1000°C with cyclic heating and cooling. Our results demonstrate a femtosecond direct laser writing technique capable of producing highly multiplexable in-fiber intrinsic Fabry-Perot interferometer sensor devices with high fringe contrast, high sensitivity, and low-loss for application in harsh environmental conditions.

Biselective pulses for large-area atom interferometry

We present designs for the augmentation 'mirror' pulses of large-momentum-transfer atom interferometers that maintain their fidelity as the wavepacket momentum difference is increased. These bi-selective pulses, tailored using optimal control methods to the evolving bi-modal momentum distribution, should allow greater interferometer areas and hence increased inertial measurement sensitivity, without requiring elevated Rabi frequencies or extended frequency chirps. Using an experimentally validated model, we have simulated the application of our pulse designs to large-momentum-transfer atom interferometry using stimulated Raman transitions in a laser-cooled atomic sample of $^{85}$Rb at 1 $\mu$K. After the wavepackets have separated by 42 photon recoil momenta, our pulses maintain a fringe contrast of 90% whereas, for adiabatic rapid passage and conventional $\pi$ pulses, the contrast is less than 10%. Furthermore, we show how these pulses may be adapted to suppress the detrimental off-resonant excitation that limits other broadband pulse schemes.

Polarization Singularities and Intensity Degeneracies

In optical testing, the well known peak valley detection ambiguity exhibited by degenerate interference intensity patterns is due to phase. The interplay between phase and polarization is evident in coherence theory. So the theme of intensity degeneracy arising due to polarization is taken up in this article for discussion. Fringes with high contrast (visibility) occur when the interfering beams are in same state of polarization (SOP). But when multiple beams are involved in interference, high contrast fringes are possible even if the SOP of each of the interfering beams is different. We show the superposition of multiple beams in different SOPs form lattice patterns consisting of polarization singularities and the intensity distribution in the interference patterns exhibit high contrast. By changing the SOPs of the individual beams, same intensity distributions can be produced. These intensity patterns are termed as degenerate intensity patterns, but have different polarization distributions. The SOP changes must follow certain rules to achieve degenerate intensity patterns. We also demonstrate intensity degeneracies in Fraunhoffer diffraction patterns of apertures illuminated by beams having polarization singularities. This study therefore illustrates the limitations on intensity based measurements in identifying polarization singularities as these singularities are expected to play a major role in future in diverse areas of optics.

Selective Mode Excitation in a Few-Mode Photonic Crystal Fiber for Strain Sensing With Restrained Temperature Response

Photonic crystal fibers (PCFs) with various micro to nano-scale features are of intensive interest for fiber sensing. Flexible fiber structures enable the selective control of fiber properties, such as transmission modes, dispersion tailoring, trigger of multiple nonlinear effects, and so on. In this article, three pieces of few-mode PCFs (FM-PCFs) are designed and fabricated. Guided modes in each fiber are theoretically analyzed and experimentally observed through careful excitation. Later one of the PCFs (PCF1) is used as a fiber interferometer, based on the analyses of intermodal couplings/interferences of all PCFs. The intermodal interferences between linearly polarized (LP) core modes LP01/LP11 of PCF1 are experimentally investigated, using selective mode excitation technique. The fringe contrast and intensity of the interferences can be precisely manipulated by varying the relative energies of the LP01 and LP11 modes, as the basis for the intermodal interferometer. Different from most previous studies, the interferences are mainly limited to the two core modes, which intrinsically reduces the cross-influence from temperature variations, when this fiber is used for strain sensing. Experimentally, a strain sensor using this FM-PCF based Mach–Zehnder (MZ) interferometer, is demonstrated with a restrained temperature response. This work provides significant guidance for the construction of FM-PCF based fiber sensors with simple fabrication procedure and precisely controlled interference, and most critically, with reduced cross-sensitivity between temperature and strain.

Three-Dimensional Cooling of an Atom-Beam Source for High-Contrast Atom Interferometry

We present a compact, two-stage atomic beam source that produces a continuous, narrow, collimated and high-flux beam of rubidium atoms with sub-Doppler temperatures in three dimensions, which features very low emission of near-resonance fluorescence along the atomic trajectory. The atom beam source originates in a pushed two-dimensional magneto-optical trap (2D$^+$ MOT) feeding a slightly off-axis three-dimensional moving optical molasses stage that continuously cools and redirects the atom beam. The capture velocity of the moving optical molasses is deliberately chosen to be low, $\sim 3$ m/s, to reduce fluorescence, and the cooling light is detuned by several atomic linewidths from resonance to reduce the absorption cross-section of cooling-induced fluorescence. Near-resonance light from the 2D$^+$ MOT and the push beam does not propagate to the output atomic trajectory due to a 10 degree bend in the atomic trajectory. The atomic beam emitted from the two-stage source has a flux up to $1.6(3)\times 10^9\;\textrm{atoms/s}$, with an optimized temperature of $15.0(2)\;\mu$K. We employ continuous Raman-Ramsey interference measurements at the atom beam output to study the sources of decoherence in the presence of continuous cooling, and demonstrate that the atom beam source effectively preserves high fringe contrast even during cooling. This cold-atom beam source is appropriate for use in atom interferometers and clocks, where continuous operation eliminates dead time, the slow atom beam velocity (6 - 16 m/s) improves sensitivity, the narrow 3D velocity distribution improves fringe contrast, and the low reabsorption of scattered light mitigates decoherence caused by the continuous cooling process.

Effects of wave-front tilt and air density fluctuations in a sensitive atom interferometry gyroscope.

We present a matter wave gyroscope with a Sagnac area of 5.92 cm2, achieving a short-term sensitivity of 167 nrad/s/Hz1/2. The atom interferometry gyroscope is driven by a π/2 - π - π - π/2 Raman pulse sequence based on an atom fountain with a parabolic trajectory. The phase-locked laser beams for Raman transitions partly propagate outside of the vacuum chamber and expose to the air when passing through the two arms of the vacuum chamber. This configuration leads to the tilt of the laser's wave-front and suffers the fluctuation of air density. The impacts on both the fringe contrast and long-term stability are experimentally investigated in detail, and effective schemes are developed to improve the performance of our atom gyroscope. The method presented here could be useful for developing large atom interferometry facilities with separated vacuum chambers.

Unambiguous refractive-index measurement in a wide dynamic-range using a hybrid fiber Fabry-Perot interferometer assisted by a fiber Bragg grating

We demonstrate the unambiguous measurement of the refractive index (RI) in a wide measurement range (from 1.0003 to 1.6068 RIU at 1550 nm), using a fiber Bragg grating (FBG) and a hybrid fiber Fabry-Perot interferometer (HFFPI) arranged in series. The spectrum of the reflectivity (RHFFPI) is composed by the interference pattern and the narrowband grating peak. In optical domain the wavelength of the grating peak is used to monitor the temperature, while the RI changes are monitored by the fringe contrast of the interference pattern. Nevertheless, the fringe contrast exhibited an ambiguous behavior that limits the RI measurement range to substances with a RI smaller than that of the core of the optical fiber used. In Fourier domain the spectrum of the RHFFPI showed the three characteristic interference peaks of an HFFPI but superimposed on a broad pedestal, due to the FBG. The amplitude of the three peaks was maximum when the fiber tip is surrounded by air, but two of them diminished when the RI of the external medium (next) increased. The amplitude of the second and third peaks decreased below the level of the pedestal, that is, peaks turned into dips, when next was larger than the single-mode fiber refractive index (nSMF). Importantly, to the best of our knowledge, a one to one relationship between the amplitude of the Fourier peaks and next was established even for values larger than nSMF, for the first time. Additionally, this device allows the simultaneous measurement of refractive index and temperature with good sensitivity and stability since both devices (HFFPI and FBG) are intrinsically immune to the power fluctuations of the optical signal, which is crucial for strict real-world applications such as biosensing.

Analysis of the Errors Caused by Disturbed Multimode Fibers in the Interferometer with Fiber-Coupled Delivery.

In this paper, the errors of the displacement measurement interferometer with multi-mode fiber-coupled delivery are analyzed when the fibers are disturbed. Simulation results show that the characteristic frequency of the measurement error is consistent with that of disturbance, and the error has higher order frequency components. The experiments are designed for the effect of fringe contrast on the measurement error. The experimental results show that the measurement error is rather sensitive to the interference angle between the measurement arm and the reference arm in the multi-mode fibers, but not to the irradiance ratio of the measurement arm and the reference arm. In an interferometer with multimode fiber, the interference angle between the measurement arm and the reference arm needs to be restricted. This conclusion provides a theoretical basis for designing an interferometer measurement system with interference angle that is adaptive to wider application.

Three-dimensional-printed Fabry-Perot interferometer on an optical fiber tip for a gas pressure sensor.

We demonstrate a three-dimensional (3D)-printed miniature optical fiber-based polymer Fabry-Perot (FP) interferometric pressure sensor based on direct femtosecond laser writing through two-photon polymerization. An unsealed cylinder column with a suspended polymer diaphragm is directly printed on a single-mode fiber tip to form an FP cavity. Here, two FP cavities with different lengths and the same diaphragm thickness (5 µm) are presented. The fabricated FP interferometer has a fringe contrast larger than 15 dB. The experimental results show that the fabricated device with a 140 µm cavity length has a linear response to the change of pressure with a sensitivity of 3.959 nm/MPa in a range of 0-1100 kPa, and the device with a 90 µm cavity length has a linear pressure sensitivity of 4.097 nm/MPa. The temperature sensitivity is measured to be about 160.2 pm/°C and 156.8 pm/°C, respectively, within the range from 20 to 70°C. The results demonstrate that 3D-printing techniques can be used for directly fabricating FP cavities on optical fiber tips for sensing applications.

Fizeau Mask Interferometry of Solar Features Using the Multi-application Solar Telescope at the Udaipur Solar Observatory

Efforts are made to demonstrate high-resolution observations of the solar atmosphere using spatial interferometry. Covering the telescope pupil with a Fizeau mask consisting of two small circular apertures separated by a vector distance known as the baseline is the first step towards interferometric imaging. A mask with two circular holes of diameter 7 cm each and separated by a distance of 19 cm is placed in the pupil plane of the Multi-application solar telescope at Udaipur solar observatory. The fringe pattern observed in the image plane signifies the presence of solar structures with sizes smaller than the fringe period. The study is extended with baselines of 29 cm and 38 cm. It is observed that an increase in the baseline causes a reduction in the fringe period and the fringe contrast. Observations are carried out in two spectral lines/bands, centered at 656.3 nm and 861.0 nm using filters of bandwidth 1 nm and 330 nm, respectively. The effect of bandwidth on the fringe visibility is also discussed based on the bandwidth decorrelation function.

A fiber optic temperature sensor based on interference fringe contrast demodulation

We propose and verify a fiber optic temperature sensor whose demodulation method is measuring the spectra contrast, which is quantified by the amplitude of the fast Fourier transform (FFT) of interference fringes within a certain small wavelength range. A section of polarization-maintaining fiber (PMF) is spliced in the sensing arm of the Mach-Zehnder interferometer (MZI). Due to the birefringence of the PMF, a visible envelope is formed in the interference fringes. Within a certain range of optical frequency (i.e. wavelength), the change of birefringence caused by external temperature will drive the envelope drift, and the amplitude of interference fringe after fast Fourier transform will also change correspondingly. By measuring the change of amplitude, the purpose of demodulating external temperature can be realized. Experimental results show high sensitivity better than 2.1 dB/°Cwith a high accuracy of 0.00048 °C, comparing with the envelope drift measuring results 1.62 nm/°C with resolution of 0.012 °C. The resolution of this scheme is increased by two orders of magnitude compared with measuring the envelope drift. Moreover, merits of our sensor in terms of immune to phase shift of reference arm and the power fluctuation of light source benefit our practical application for such as electric power system monitoring.

Temperature-independent curvature sensor based on in-fiber Mach-Zehnder interferometer using hollow-core fiber

An in-fiber Mach–Zehnder Interferometer (MZI), based on hollow core fiber (HCF), for measuring curvature is fabricated and experimentally demonstrated. The sensing part was fabricated by splicing a section of HCF between two sections of multimode fiber (MMF), and different HCF lengths were investigated in order to achieve the highest curvature sensitivity. These devices were tested in a transmission configuration using lead-in and lead-out single mode fibers (SMF). The sensor was attached to a steel sheet by using the polymer Polydimethylsiloxane (PDMS) for accurate control of the applied curvature. The modal analysis was carried out using a commercial software based on finite element method (FEM) and by incorporating some of the experimental data, it was feasible to determine the two dominant modes that interfere in this sensor. The devices were characterized by measuring the fringe contrast variations due to the curvature changes. The interferometer fabricated with a HCF 2.5 mm in length HCF showed the highest curvature sensitivity, −17.28 ± 2.30 dB/m−1, in a range from 1.84 m−1 to 2.94 m−1. Moreover, the sensor that exhibited a better performance was fabricated with a HCF length of 1 mm, combining the most extensive curvature range (from 0.95 m−1 to 2.68 m−1) and an adequate sensitivity (−11.80 ±1.30 dB/m−1). The analysis of the interferometric signal of this device in Fourier domain, allows us to establish a one to one relationship between the contrast and the curvature in a broader range (from 0 m−1 to 2.94 m−1). Moreover, the fringe contrast showed a very low dependency on temperature (from 30 °C to 90 °C), depicting that this device was not affected by temperate fluctuation.

Microwave Pulse-Coherent Technique-Based Clock With a Novel Magnetron-Type Cavity

We report a high-performance pulsed optically pumped (POP) Rb clock based on a novel magnetron-type microwave cavity. The cavity has a volume of 30 mL, enabling a highly homogenous microwave field distribution. With the laser frequency tuning to the ground-state hyperfine level F = 2 of the D2 line, we observe a Ramsey fringe contrast of 52% in terms of optical absorption detection. The resultant shot noise limit is estimated to be [Formula: see text]. The clock frequency stability is measured as [Formula: see text] (1-100 s), which is limited by the relative intensity noise of the light.

A tunable fiber-optic Fabry–Perot cavity formed between a silica microsphere and a target

In this paper, a tunable fiber-optic Fabry–Perot (FP) cavity is proposed and demonstrated experimentally. The microsphere formed by melting the end of a single mode fiber(SMF) is used as one of the reflective surfaces of the FP cavity. Compared with the interference in FP cavities formed by a pair of parallel interfaces, the FP interference generated between a convex surface and a perpendicular plane can result in a higher fringe contrast when the length of the cavity is much larger. Utilizing this characteristic, a large-scale displacement response up to 3.3 mm can be achieved with the highest sensitivity of 37 pm/μm. This method has the advantages of low cost, a simple fabrication process and high tolerance to the reflectivity of the measured object.

Quantitative phase imaging based on Fresnel diffraction from a phase plate

The structural complexity and instability of many interference phase microscopy methods are the major obstacles toward high-precision phase measurement. In this vein, improving more efficient configurations as well as proposing methods are the subjects of growing interest. Here, we introduce Fresnel diffraction from a phase step to the realm of quantitative phase imaging. By employing Fresnel diffraction of a divergent (or convergent) beam of light from a plane-parallel phase plate, we provide a viable, simple, and compact platform for three-dimensional imaging of micrometer-sized specimens. The recorded diffraction pattern of the outgoing light from an imaging system in the vicinity of the plate edge can be served as a hologram, which would be analyzed via the Fourier transform method to measure the sample phase information. The period of diffraction fringes is adjustable simply by rotating the plate without the reduction of both the field of view and fringe contrast. The high stability of the presented method is affirmatively confirmed through comparison of the result with that of the conventional Mach–Zehnder based digital holographic method. Quantitative phase measurements on silica microspheres, onion skins, and red blood cells ensure the validity of the method and its ability for monitoring nanometer-scale fluctuations of living cells, particularly in real-time.

Application of magnetic field for improvement of energy spread of an electron beam

Electron diffraction is not solely a powerful method to study fundamental physics but has also been applied to quantum sensors. A low-coherence electron source results in a drop of fringe contrast. One approach to enhance a visibility of the diffraction pattern is to improve a longitudinal coherence of an electron beam. When electrons pass through a magnetic field, they experience a force which bends them to circular paths. Electrons with different energies will travel along the different paths. By placing a slit behind the magnetic field, the width of the electron energy distribution will become narrower and hence an improvement of the beam coherence. However, this method reduces the intensity of the electron beam. The simulation was performed to optimize the slit width for electron diffraction experiments with respect to the energy spread of the beam and electron flux.

Decoherence and visibility enhancement in multipath interference

We theoretically analyze the observations reported in a four-path quantum interference experiment via multiple beam Ramsey interference [Phys. Rev. Lett. 86, 559 (2001)]. In this experiment, a selective scattering of photons from just one interfering path causes decoherence. However, contrary to expectations, there is an increase in the contrast of the interference pattern, demonstrating that path selective decoherence can not only lead to a decrease, but under certain conditions, to an increase of the fringe contrast. Here we explain this seemingly counter-intuitive effect based on a model for a multi-path interference, with four to six slits, in the presence of decoherence. The effect of the environment is modeled via a coupling to a bath of harmonic oscillators. When decoherence is introduced in one of the multiple paths, an enhancement in fringe contrast is seen under certain conditions. A similar effect is shown to appear if instead of path-selective decoherence, a selective path detector is introduced. Our analysis points to the fact that while traditional fringe visibility captures the wave nature in the two-path case, it can fail in multi-path situations. We explain the enhancement of fringe visibility and also show that quantum coherence based on the l1 norm of coherence, in contrast to traditional visibility, remains a good quantifier of wave nature, even in such situations. The enhancement of fringe contrast in the presence of environmental decoherence underscores the limitations of traditional visibility as a good measure for wave nature in quantifying complementarity and also makes it an unlikely candidate for quantifying decoherence. Our analysis could lead to better insight in ways to quantify decoherence in multi-path interference, and in studies that seek to exploit quantum superpositions and quantum coherence for quantum information applications.

Decoration of Porous Silicon with Gold Nanoparticles via Layer-by-Layer Nanoassembly for Interferometric and Hybrid Photonic/Plasmonic (Bio)sensing.

Gold nanoparticle layers (AuNPLs) enable the coupling of morphological, optical, and electrical properties of gold nanoparticles (AuNPs) with tailored and specific surface topography, making them exploitable in many bioapplications (e.g., biosensing, drug delivery, and photothermal therapy). Herein, we report the formation of AuNPLs on porous silicon (PSi) interferometers and distributed Bragg reflectors (DBRs) for (bio)sensing applications via layer-by-layer (LbL) nanoassembling of a positively charged polyelectrolyte, namely, poly(allylamine hydrochloride) (PAH), and negatively charged citrate-capped AuNPs. Decoration of PSi interferometers with AuNPLs enhances the Fabry-Pérot fringe contrast due to increased surface reflectivity, resulting in an augmented sensitivity for both bulk and surface refractive index sensing, namely, about 4.5-fold using NaCl aqueous solutions to infiltrate the pores and 2.6-fold for unspecific bovine serum albumin (BSA) adsorption on the pore surface, respectively. Sensitivity enhancing, about 2.5-fold, is also confirmed for affinity and selective biosensing of streptavidin using a biotinylated polymer, namely, negatively charged poly(methacrylic acid) (b-PMAA). Further, decoration of PSi DBR with AuNPLs envisages building up a hybrid photonic/plasmonic optical sensing platform. Both photonic (DBR stop-band) and plasmonic (localized surface plasmon resonance, LSPR) peaks of the hybrid structure are sensitive to changes of bulk (using glucose aqueous solutions) and surface (due to BSA unspecific adsorption) refractive index. To the best of our knowledge, this is the first report about the formation of AuNPLs via LbL nanoassembly on PSi for (i) the enhancing of the interferometric performance in (bio)sensing applications and (ii) the building up of hybrid photonic/plasmonic platforms for sensing and perspective biosensing applications.

Sapphire derived fiber based Fabry-Perot interferometer with an etched micro air cavity for strain measurement at high temperatures.

A sapphire derived fiber (SDF) based Fabry-Perot interferometer (FPI) with an etched micro air cavity for strain measurement at high temperatures is proposed. The FPI is formed by splicing a section of SDF between an etched single mode fiber (ESMF) and a capillary. The SDF's core containing 51.3mol.% aluminum provides the intrinsic Fabry-Perot interferometer cavity with an enhanced fringe contrast through the narrow etched air cavity reflector. Because the different Poisson effects of the cladding and the core have different deformations under axial stress, the transverse strain imposed from the cladding to the core was introduced to the additive model. The strain sensitivity of the FPI was theoretically analyzed and experimentally demonstrated at room temperature. A thermal annealing process was performed to study the stability in high temperatures and to release the residual stress during the sensor's fabrication. The strain calibration was carried out subsequently from 20℃ to 1000℃. Benefiting from the doping in the core and diffusion in the cladding of the high temperature resistant material Al2O3, the proposed sensor was proved to operate well in 950℃ and was also characteristized by a sensitivity of 1.19 pm/µɛ and 1.06 pm/µɛ in the process of loading and unloading strain separately.

Temperature insensitive air-cavity Fabry-Perot gas pressure sensor based on core-offset fusion of hollow-core fibers

A temperature insensitive air-cavity Fabry-Perot Interferometer (FPI) based on core-offset fusion (FPI-CFH) of hollow-core fibers with different inner diameters was developed. This sensing structure consists of input single mode fiber (SMF), two short sections of hollow-core fibers (HCF1 and HCF2), and a gold film. The HCF1 with an inner diameter of 70 μm is used to construct air-cavity FPI, and the HCF2 with an inner diameter of 10 μm is offset spliced with HCF1 to provide a flat reflective surface of air-cavity FPI, which can increase the reflection to enhance the fringe contrast, and meanwhile the microfluidic channel of HCF2 is used for the gas inlet. The left end-face of HCF2 is coated with gold film (the thickness of ∼50 nm) to improve the light reflectivity, so that, increasing the fringe contrast of air-cavity FPI spectrum. The experimental results show that the proposed FPI-CFH sensor has a high gas pressure sensitivity of 4.314 nm/MPa with a good linear response (the value of R-Square is 0.9987) when the gas pressure increases from 400 to 1000 kPa, and what's more, the proposed sensor has a negligible temperature cross-sensitivity (0.0051nm/°C) in the range of 20–80 °C due to the structure of all-fiber and the essential characteristics of air-cavity FPI. The maximal relative error of the proposed sensor in the measurement process of gas pressure decrease is less than 1%, which illustrates the sensor has good precision and repeatability. Moreover, the proposed sensor has good stability in a long-term gas pressure testing. Therefore, the proposed FPI-CFH sensor can achieve high precision gas pressure sensing but is insensitive to the variation of temperature.