Three-beam Interference Research Articles

Phase-modulation-induced reconfigurable rotating photonic lattices in atomic vapors.

We propose a method to prepare optically induced rotating hexagonal and honey-comb photonic lattices by employing the phase modulated three-beam interference in atomic vapors with electromagnetically induced transparency. The phase differences among the three beams are dynamically elaborated to synthesize the circular motion (in transverse dimensions) of waveguides in the photonic lattices. Further, we verify this model experimentally in the case of low-speed modulation. A weak Gaussian probe field is sent into the constructed helical photonic lattices to image their structures under electromagnetically induced transparency (EIT). The motion trajectories of the sites on the discretized output patterns exhibit repeated circles, advocating the formation of rotating lattices. By introducing phase modulations to involved beams, we provide a continent way for producing transverse motions in waveguide arrays with reconfigurability in rotational direction, radius, and speed. This work looks forward to promising applications in topological photonics with great popularity.

All-fiber light intensity sensor employing a three-core fiber taper integrated by magnetic fluids

An all-fiber optic light intensity sensor employing a three-core fiber (TCF) taper integrated by magnetic fluids (MFs) is proposed and fabricated. The three-beam interference and evanescent field characteristic of the TCF taper are combined with the laser-generated photothermal effect of the MFs for the first time. The effect of irradiation laser intensity on the interference spectrum of the proposed sensor is investigated experimentally. According to the experimental results, the interferential transmission spectrum is susceptible to the irradiation laser intensity. Under 473 nm laser irradiation, the maximum laser intensity sensitivity reaches −1.64425 nm/(mW/mm2). Moreover, the modal coupling processes of the TCF before and after tapering are investigated experimentally and by simulation. The proposed sensor is attractive because of its sensitive light response, simple structure, easy fabrication, and compact size. This work gives a significant reference for the manufacture and application of optically controlled microfluidic devices integrated by MFs.

Formation of multibeam dynamic gradient interference light fields with refractive optical elements

This paper presents methods for the formation and properties of light fields that controllably vary in time and space, obtained as a result of the interference of three or four coherent light beams using refractive optical elements. The formation of three-beam and four-beam interference fields is carried out using trihedral and tetrahedral glass pyramids respectively. The possibility of the interference field displacement in the transverse plane is ensured by devices for controlled phase changes of at least two of the interfering beams. The directions of propagation of these beams do not lie in the same plane with the optical axis of the original beam incident on the pyramid. In threeand four-beam dynamic interference fields the peak intensity values are higher than in the original laser beams and two-beam interference fields, so it is advisable to use them for processing flat objects with laser radiation, moving the interference maxima along the surface of the object. With a pairwise azimuthal displacement of the propagation directions of four interfering beams around the longitudinal axis, a dynamic interference field is formed, the periodically structured maxima of which cyclically smoothly change their shape from cells to band and back. At different speeds of pairs of directions the interference structure of the maxima rotates around the longitudinal axis. Therefore, this field can be used for therapeutic effects on biological tissues and for mixing microparticles in suspensions and emulsions. Since the local maxima of the intensity of all these interference fields have dimensions of the order of several micrometers while exceeding in value the maximum intensity of the initial light beam, these fields in the cross section are gradient and therefore can be used not only for laser exposure, but also for moving ensembles of microparticles including for sorting and changing concentration.

Axial Resolution Enhancement of Optical Sectioning Structured Illumination Microscopy Based on Three-Beam Interference

As a branch of 3D microscopy, optical sectioning structured illumination microscopy (OS-SIM) has the advantages of fast imaging speed, weak photobleaching and phototoxicity, and flexible and compatible configuration. Although the method of using the one-dimensional periodic fringe pattern projected on the sample can remove the out-of-focus background from the in-focus signal, the axial resolution of the final reconstructed 3D image is not improved. Here, we propose a three-beam interference OS-SIM, namely TBOS, instead of the common-used dual-beam interference OS-SIM (DBOS). The three-beam interference scheme has been adopted in 3D super-resolution SIM (3D-SR-SIM), where the fringe phase shifting needs to be along each of the three orientations. In contrast, TBOS applies phase shifting only in one arbitrary direction. We built a TBOS SIM microscope and performed the 3D imaging experiments with 46 nm diameter fluorescent microspheres and a mouse kidney section. The axial resolution of the 3D image obtained with TBOS was enhanced by a factor of 1.36 compared to the DBOS method, consistent with the theoretical analysis and simulation. The OS-SIM with enhanced axial resolution for 3D imaging may find a wide range of applications in the biomedical field.

Vernier Effect-Based Displacement Sensor Using In-Fiber Hollow Microsphere With a Hole

We demonstrate a compact subnanometer resolution displacement senor based on Vernier effect, which consists of a section of capillary fusion spliced with a single-mode fiber (SMF) and an in-fiber hollow microsphere with a hole (HMH). Two concave erbium-doped fibers (EDFs) obtained by chemical etching are fusion spliced for the hollow microsphere, which further has a hole by vertical polishing and chemical etching. The Newton’s rings phenomenon observed on the endface of EDF is the judgment condition of the hollow microsphere’s ultrathin wall via polishing, and then of the beginning of etching. Consequently, there is no concave area around the hole on the EDF endface, which significantly enhances the endface reflectivity. Combined with the lead-in SMF endface and the inner surface of the HMH, three-beam interference is generated from beams reflected from the three mirrors, which can produce two kinds of Vernier effect. They are analyzed theoretically and thus distinguishable in spectral patterns. Due to the low loss of light transmission in the hollow microsphere, the wider reflection spectra of identifiable interference pattern with Vernier effect are obtained, and the maximum displacement sensitivity can be further improved to 451.5 pm/nm with a subnanometer resolution of 0.044 nm. Plus the high robustness resulting from the in-fiber structure of the hollow microsphere, the displacement sensor shows prospects in health monitoring, surface topography, precision machining and other fields.

Geometric pattern evolution of photonic graphene in coherent atomic medium.

The photonic graphene in atoms not only has the typical photonic band structures but also exhibits controllable optical properties that are difficult to achieve in the natural graphene. Here, the evolution process of discrete diffraction patterns of a photonic graphene, which is constructed through a three-beam interference, is demonstrated experimentally in a 5S1/2 - 5P3/2 - 5D5/2 85Rb atomic vapor. The input probe beam experiences a periodic refractive index modulation when traveling through the atomic vapor, and the evolution of output patterns with honeycomb, hybrid-hexagonal, and hexagonal geometric profiles is obtained by controlling the experimental parameters of two-photon detuning and the power of the coupling field. Moreover, the Talbot images of such three kinds of periodic structure patterns at different propagating planes are observed experimentally. This work provides an ideal platform to investigate manipulation the propagation of light in artificial photonic lattices with tunable periodically varying refractive index.

Effect of three-beam interference on phase-generated carrier demodulation of a fiber-optic interferometric sensor.

Homodyne demodulation using a phase-generated carrier (PGC) has been applied in fiber-optic interferometric sensors to overcome the signal fading and distortion due to the drift of the operating point. An assumption needed for the PGC method to be valid is that the sensor output is a sinusoidal function of the phase delay between the arms of the interferometer, which is readily achieved by a two-beam interferometer. In this work, we theoretically and experimentally study the effect of three-beam interference, whose output deviates from a sinusoidal function of the phase delay, on the performance of the PGC scheme. The results show that the deviation could lead to additional undesirable terms in the in-phase and quadrature components in PGC implementation, which may result in significant signal fading with the drift of the operating point. The theoretical analysis leads to two strategies for eliminating these undesirable terms so that the PGC scheme is valid for three-beam interference. The analysis and the strategies were validated experimentally using a fiber-coil Fabry-Perot sensor with two fiber Bragg grating mirrors, each having a reflectivity of 26%.

Hexagonal optical lattices formed by coherent interference among three fundamental Gaussian beams with oblique incidence

Hexagonal optical lattices (HOLs) are formed when three beams with oblique incidence coherently interfere with each other. Theoretical model considering the orientation of three fundamental Gaussian beams is established to describe all kinds of patterns of HOLs. The formula describing the size and shape of the HOLs are also given. The nested Mach-Zehnder interferometer is employed to generate HOLs in experiment. The relations between the geometry parameters (size and shape) of HOLs and orientations of three beams are experimentally and numerically investigated. The experimental generated HOLs can be well simulated using our theory. Our study about HOLs generated by three-beam interference can be used to fabricate periodic structure modulation for the refractive index of a nonlinear media or create two-dimensional photonic crystals.

Laser interference induced dielectrophoresis for cell manipulation

In this paper, laser interference induced dielectrophoresis (LIIDEP) was presented for cell manipulation and three-dimensional array assembly. Two-beam and three-beam interference systems were built to manipulate yeast cells in deionized water. When the laser power was 60 μW and the sinusoidal AC signal was 6 V at 10 kHz, the two-beam interference pattern manipulated the cells into a single-row array distribution. For three-beam interference, when the laser power was 70 μW and the frequency was 4.5 kHz, the voltage of 2.5 V enabled each spot to control one cell, and 7.5 V enabled many spots to control multiple cells. When the cell concentration was 2 × 107 cells/mL and the electrical signal was 8 V and 4.5 kHz, the cells were assembled into a three-dimensional columnar array. The feature size of laser interference pattern was adjusted to microscale and maintained sharp boundaries, which effectively improved the manipulation accuracy. Compared to the projector or laser as the ODEP light source, LIIDEP has the advantages of high manipulation resolution, good contrast and large dielectrophoretic force. This work provides an effective way for high resolution three-dimensional array manipulation and assembly of a large number of living cells on the microscale in liquid environments.

Tailoring polarization singularity lattices by phase engineering of three-beam interference

Structured optical lattices obtained from interference of three linearly polarized plane waves arranged in a cone geometry produce interlaced polarization singularity structures. These lattices are known to be populated with both C-point and V-point singularities. All the lattice fields abide by the principle of index conservation. In this article, we focused on tailoring these polarization singularity lattices by perturbing the interfering beams with a relative encoded phase. We have shown that a spatial lateral-shifting of the ellipse- and vector field singularities by an order of lattice parameter can be achieved through an appropriate phase engineered design. Similar phase engineering in six and eight beam interference method of lattice generation produces different results. In six and eight beam interference, phase engineering enables realization of C-point only lattices and provides handedness control for the ellipse field singularities, whereas in three beam interference case, there is only a translation shift in the lattice structure.

Comparison of Two- and Three-Beam Interference Pattern Generation in Structured Illumination Microscopy

Structured illumination microscopy (SIM) provides wide-field optical sectioning in the focal plane by modulating the imaging information using fringe pattern illumination. For generating the fringe pattern illumination, a digital micro-mirror device (DMD) is commonly used due to its flexibility and fast refresh rate. However, the benefit of different pattern generation, for example, the two-beam interference mode and the three-beam interference mode, has not been clearly investigated. In this study, we systematically analyze the optical sectioning provided by the two-beam inference mode and the three-beam interference mode of DMD. The theoretical analysis and imaging results show that the two-beam interference mode is suitable for fast imaging of the superficial dynamic target due to reduced number of phase shifts needed to form the image, and the three-beam interference mode is ideal for imaging three-dimensional volume due to its superior optical sectioning by the improved modulation of the illumination patterns. These results, we believe, will provide better guidance for the use of DMD for SIM imaging and also for the choice of beam patterns in SIM application in the future.

Three-beam conjugate enhanced micro-vibration detection

We investigate the three-beam conjugate enhanced micro-vibration detection system. We introduce a conjugate light to the classical dual-beam heterodyne laser vibrometer to generate the three-beam interference. Detection of the micro-vibration signal is then enhanced by matching the power and phase of conjugate light and measured light. We also present the basic principle of three-beam conjugate enhanced micro-vibration detection and the conjugate enhancement conditions. Moreover, the expressions of micro-vibration signal amplitude amplification and resolution enhancement are derived and compared with the demodulation amplitude and limited resolution of classical dual-beam laser vibrometer. Experiments and numerical results further verify the amplitude amplification and resolution enhancement of the three-beam conjugate enhanced micro-vibration system. The archived results indicate that this system is especially suitable for the high-resolution detection of weak vibration targets, e.g., micro-nano structures.

Contrast Analysis of Polarization in Three-Beam Interference Lithography

This paper analyzes the effect of polarization and the incident angle on the contrasts of interference patterns in three-beam interference lithography. A non-coplanar laser interference system was set up to simulate the relationship between contrast, beam polarization, and the incident angle. Different pattern periods require different incident angles, which means different contrast losses in interference lithography. Two different polarization modes were presented to study the effects of polarization with different incident angles based on theoretical analysis simulations. In the case of the co-directional component TE polarization mode, it was demonstrated that the pattern contrast decreases with the increase in the incident angle and the contrast loss caused by the polarization angle error also grew rapidly. By changing the mode to azimuthal (TE-TE-TE) polarization, the contrast of the interference pattern can be ensured to remain above 0.97 even though the incident angle is large. In addition, TE-TE-TE mode can accept larger polarization angle errors. This conclusion provides a theoretical basis for the generation of high-contrast light fields at different incident angles, and the conclusion is also applicable to multi-beam interference lithography.

Method for measuring the relative phases among the three beams in the case of homodyne three-beam interference

A method for measuring the relative phases (RPs) among the three beams in the case of homodyne three-beam interference (TBI) is proposed and verified by the ZEMAX simulation in this paper. The method requires that the interference beams are not on the same plane, that is, any two of the three beams interfere at an angle in different planes. Based on the phase delay of the beam in space, the inclined beams have different phases at different positions within the beams' range. By arranging the photodetector array within the interference area, the RPs can be calculated using the intensity of the interference light received by specific photodetector units. The application of the algorithm for the displacement measurement of the homodyne three-beam interferometer (TBIR) has been verified by simulation. The beam number of three-beam interference is one less than that of two two-beam interference when measuring two relative phases. Compared with the two-beam interferometer, the TBIR applied to two-degree-of-freedom displacement measurement is more compact in structure due to the more compact phase measurement components.

Temperature-independent ultra-sensitive refractive index sensor based on hollow-core silica tubes and tapers.

We demonstrate a simple and ultra-sensitive refractive index (RI) sensor using a hollow-core silica tube (HCST) sandwiched between an up-taper and a down-taper in single mode fibers (SMF). According to our theoretical analysis, the interference spectrum comes from a combination of a three-beam multi-mode interference and anti-resonance effects. RI sensing will affect the mode interference. By demodulating the fringe contrast of the interference spectra, an ultrahigh sensitivity of -120.18 dB/RIU is achieved, implying a RI resolution of ∼ 8×10-6 in the RI range from 1.35 to 1.43. What's more, the sensor has great temperature insensitivity of -0.0085 dB/°C, indicating an extremely low cross sensitivity of 7×10-5 RIU/°C, which further benefits its practical application. The proposed configuration does not require special fiber or fabrication technique. In addition, the sensor's other merits such as simple and compact structure and ease offabrication offer the potential in biochemical sensing applications.

The influence of phase difference on the effect of multi-beam interference processing

The influence of phase difference in laser interference lithography system is often ignored by researchers. In this paper, we simulated the interference process of dual-beam, three-beam and four-beam, and the influence of phase difference on the interference effect was discussed in detail. The simulation results show that in the process of dual-beam and three-beam interference, the change of phase difference causes the shift of the interference pattern but does not change the laser intensity distribution of the interference field, and has no effect on the actual interference processing; while in the process of four-beam interference, the change of phase difference can change the laser intensity of the interference field. Based on this, we built a four-beam interference processing system with dual-channel mutual injection solid-state laser as the laser source to process aluminum materials. The phase of the beam is changed by adjusting the optical path of the output laser, and the interference processing effect is observed when there are different phase differences between the beams. The experimental results show that in the process of four-beam interference processing, when the phase difference between beams is not zero, the interference processing will be greatly affected, and the processing results will appear some phenomena, such as small depth of concave holes, irregular shape, unclear boundary between concave holes and so on.

Structured illumination microscopy based on asymmetric three-beam interference

Structured illumination microscopy (SIM) is a rapidly developing super-resolution technology. It has been widely used in various application fields of biomedicine due to its excellent two- and three-dimensional imaging capabilities. Furthermore, faster three-dimensional imaging methods are required to help enable more research-oriented living cell imaging. In this paper, a fast and sensitive three-dimensional structured illumination microscopy based on asymmetric three-beam interference is proposed. An innovative time-series acquisition method is employed to halve the time required to obtain each raw image. A segmented half-wave plate as a substantial linear polarization modulation method is applied to the three-dimensional SIM system for the first time. Although it needs to acquire 21 raw images instead of 15 to reconstruct one super-resolution image, the SIM setup proposed in this paper is 30% faster than the traditional spatial light modulator-SIM (SLM-SIM) in imaging each super-resolution image. The related theoretical derivation, hardware system, and verification experiment are elaborated in this paper. The stable and fast 3D super-resolution imaging method proposed in this paper is of great significance to the research of organelle interaction, intercellular communication, and other biomedical fields.

High sensitivity, low temperature-crosstalk strain sensor based on a microsphere embedded Fabry–Perot interferometer

In this article, a high sensitivity, low temperature-crosstalk strain sensor based on a microsphere embedded Fabry–Perot interferometer (FPI) is reported and experimentally demonstrated. The sensor is fabricated by embedding a microsphere inside a tapered hollow-core fiber (HCF) whose ends are enclosed by two standard single-mode fibers (SMFs). The reflections occurring at the SMF/HCF interface and the surfaces of the microsphere, result in a three-beam interference. The cavity length of the formed FPI can be flexibly changed by controlling the diameter of the tapered HCF and the size of the embedded microsphere, and the maximum extinction ratio (ER) of the reflection spectrum is greater than 11 dB. This novel microsphere embedded FPI structure significantly enhances the sensing performance of traditional FPIs for strain measurement, providing a high strain sensitivity of 16.2 pm/με with a resolution of 1.3 με. Moreover, it is demonstrated that this strain sensor has a very low temperature-strain cross-sensitivity of 0.086 με/oC, which greatly enhances the potential for applications in the field of precision strain measurement.

Optical and Structural Phenomena at Multipulse Interference Femtosecond Laser Fabrication of Metasurfaces on a Thin Film of Amorphous Silicon

The formation of hexagonal microarrays of nanoholes (metasurfaces) in a 50-nm hydrogenated amorphous silicon film by means of three-beam interference of femtosecond laser pulses of the visible range (wavelength 515 nm) is studied experimentally with various exposures of the film. Characterization of arrays by scanning electron and optical microscopy, as well as optical transmission and reflection microspectroscopy, shows that an increase in the number of fixed energy laser pulses leads to a gradual evaporative formation of nanoholes in the film and, overall, the metasurface. Raman microspectroscopy reveals a simultaneous growth of the volume content of the crystal phase.

Fabrication of hierarchical moth-eye structures with durable superhydrophobic property for ultra-broadband visual and mid-infrared applications.

Multifunctional antireflective coatings have practical applications as important optical components in many fields, particularly for optical devices and imaging systems. However, a good antireflection application in the visible region is often unsatisfactory for mid-infrared devices, and the difficulty in obtaining multiple capabilities simultaneously is one of the main factors limiting their applications. In this work, hierarchical moth-eye structures with superhydrophobicity were fabricated via inductively coupled plasma reactive ion etching (ICP-RIE) using nanodisk-array masks, which were formed by three-beam laser interference lithography (LIL), for improving the ultra-broadband optical properties. The uniform antireflection efficiency, which was close to 1% reflectivity covering over the visible and mid-infrared wavelength range, was exhibited by the moth-eye structures with high-quality pillar arrays. Additionally, irregular nanostructures were tailored onto the top of the pillars to generate hierarchical moth-eye structures for simultaneously obtaining both the superhydrophobic and anticorrosive properties. The fabricated antireflective structures, with the features of self-cleaning and durability, have the advantage of being for long-term use in harsh environments.