Index Modulation Depth Research Articles

Ultra-broadband multi-channel orbital angular momentum mode generator using a helical long-period grating pair

We demonstrate an ultra-broadband multi-channel orbital angular momentum (OAM) mode generator using a helical long-period grating (HLPG) pair in a few-mode fiber. The numbers of the channel of the OAM mode generator can be flexibly adjusted by designing the cascaded length of the HLPG pair. When the cascaded length is 50 cm, the maximum channel number of OAM mode generator reaches 46, and the mode convert efficiencies of the channels are more than 90 %, which is, to the best of our knowledge, the highest number of channels among OAM mode converters. By reducing grating length and enhancing the refractive index modulation depth, the 3 dB bandwidth of the HLPG is significantly increased, and thus the wavelength range of the HLPG pair can be expanded. The maximum wavelength ranges of the channels with coupling efficiency greater than 90 % are measured to be 379 nm experimentally. By adjusting the spiral direction of the helical refractive index modulation, we can achieve multi-channel ± 1 order OAM mode conversion for each channel. The multi-channel OAM mode generator holds substantial potential for applications in mode division multiplexing systems, wavelength filters, and fiber sensing.

Optical Design of a Slitless Astronomical Spectrograph with a Composite Holographic Grism

In the present work, we consider an optical design of a slitless spectrograph for an existing 0.5 m-class telescope. This design concept has a number of advantages such as compact size, simplicity, and simultaneous coverage of a large field of view. A challenge with this design is correcting aberrations caused by placing a dispersing element in a converging beam. To overcome this issue, we propose to use a composite grism, which represents a combination of a prism and a volume-phase holographic grating, the latter which is split into zones with independently optimized parameters. We demonstrate two designs of such a grism. In both designs, the spectrograph operates in the range of 450–950 nm in an F/6.8 beam and covers a field of view of 35.6′ × 7.2′. Through advanced modeling, it is shown that a composite grism having four rectangular zones with different thickness and index modulation depth of the hologram and recorded with an auxiliary deformable mirror decreases the astigmatic elongation by a factor of 85, increases the spectral resolving power by 4.4 times, and reaches R1389 while increasing the average diffraction efficiency by a factor of 1.31. If we reduce the number of zones to only two, replace the deformable mirror with two static corrector plates, and fix the hologram thickness, the corresponding performance gains still remain high: the astigmatism is reduced by a factor of 61, the spectral resolving power is up to 1.7 times higher, reaching R1067, and the efficiency is increased by a factor of 1.27. This shows that the proposed design allows the construction of a simple and compact instrument, providing high performance over the entire field of view and spectral range.

Grating Spectrum Design and Optimization of GMM-FBG Current Sensor

In this study, the performance of a current sensor based on giant magnetostrictive materials (GMM) and fiber Bragg grating (FBG) has been improved by optimizing the spectral characteristics of gratings. By analyzing the influence of FBG on the current sensor characteristics, three key parameters (gate region length, refractive index modulation depth, and toe cutting system) are selected for optimization. The optimal grating parameters are determined to improve the linearity and sensitivity of sensor output. Experimental tests reveal that after grating optimization, the current sensor shows excellent performance parameters, including a linearity of 0.9942, sensitivity of 249.75 mV/A, and good stability in the temperature range of 0–60 °C. This research can provide a reference for improving the grating design and performance of existing GMM-FBG current sensors.

Modelling of a composite waveguide holographic display

Optical designs of waveguide-type augmented reality displays are investigated. Displays based on volume phase holograms are notable for their small size, large exit pupil and high transmittance both in the projected image channel and in the direct vision channel. However, with an increase of the aperture, field of view and working spectral range, the spread of the values of the beam angle of incidence and the wavelength increases when solving the diffraction problem at different points on the hologram surface which imposes restrictions on spatial resolution and diffraction efficiency. To overcome this phenomenon, it is proposed to use a composite hologram which represents a volume phase grating divided into zones with independently varying parameters of the fringes tilt, their shape, the holographic layer thickness and the refraction index modulation depth. We propose an algorithm that allows ray tracing through a hologram recorded by two coherent point sources using an auxiliary aspherical mirror. The initial ray tracing in the hologram recording scheme is performed using the error function minimization by the orthogonal descent and golden section methods. Based on the results obtained, the directional vectors of the diffracted beam are calculated using the Welford equation. Using the tracing results, the hologram diffraction efficiency is computed with the Kogelnik’s coupled wave theory. The proposed algorithms are implemented in the Zemax Optics Studio software. The application of the proposed composite hologram element and the tools for operation modeling are shown on an example of display operating in the range of 510–530 nm with the field of view of 7°36ʹ × 5°48ʹ and the exit pupil diameter of 8 mm. It is shown that the proposed solutions make it possible to increase the diffraction efficiency by 3.45 times. At the same time, the spatial resolution increases by 12.7 % varying across the field of view in the range of 0ʹ44ʺ–1ʹ6ʺ. The use of composite holograms allows one to create displays with higher spatial resolution and brightness of the projected image as well as uniformity of the characteristics across the field of view.

Design and analysis of holographic optical elements for their use as couplers with appreciable efficiency at different optical transmission windows

The diffraction efficiency of a recorded Holographic optical element changes with change in wavelength of reconstruction wave even for on-Bragg angle reconstruction. Diffraction efficiency also falls with change in angle of reconstruction with respect to Bragg angle for reconstruction wave of a given wavelength. Therefore, to achieve appreciable diffraction efficiency operation of Holographic Optical Elements at different operating wavelengths, processing parameters namely film-thickness (d), depth of refractive index modulation (Δn), and fringe spacing (ᴧ) must be optimized accordingly. In present work thickness (d) of the film of the recording medium, depth of refractive index modulation (Δn), and fringe spacing (ᴧ) have been optimized for holographic optical elements to be recorded in dichromated gelatin medium to achieve maximum efficiency operation for three different optical transmission windows 800–900 nm, 1250 – 1350 nm and 1500–1600 nm operating at wavelengths 850 nm, 1310 nm, and 1550 nm respectively. A pair of such designed holographic optical elements can advantageously be used for coupling laser light from one fiber end to another fiber end. It is further shown that a single coupler consisting of properly designed holographic optical elements may be used for optical transmission windows 1250–1350 nm and 1500–1600 nm operating at wavelengths 1310 nm, and 1550 nm respectively.

Proposal and theoretical analysis of a fiber grating sensor interrogation based on dispersive Fourier transformation and a pair of chirped fiber gratings

A novel approach to interrogate a fiber grating sensor based on dispersive Fourier transformation method is proposed and simulated. In the system, two chirped fiber Bragg gratings (CFBG), with one used as a reference grating and the other one as sensing grating, are employed to form a Fabry–Perot (FP) interference structure, used as the spectral-shaping filter. The filter can be modeled as a two-tap delay-line filter. An optical pulse from a mode-locked laser source is reflected and spectrally shaped by the FP structure, and then the shaped spectrum is mapped to the temporal domain by a dispersive element. When the sensing CFBG is experiencing a strain, its wavelengths will be changed, leading to different interference spectra. Using Fourier transform, the frequency of the generated microwave waveform can be achieved, from which the wavelength shift of the sensing grating and the applied strain can be demodulated. A mathematical model to describe the microwave waveform generation is developed, by which the interrogation principle is analyzed. Numerical simulations are implemented to verify the proposed approach. The results present that the sensitivity of the system is 0.01 GHz/με. The influences of key parameters in the system on the microwave spectra are investigated and discussed, including grating length, cavity length, chirp rate and index modulation depth.

Effects of fiber Bragg grating design on dual-grating demodulation performance

Dual-grating demodulation has been both effective and simple in most fiber Bragg grating (FBG) sensors because it involves self-demodulation, and in theory, temperature effects are eliminated. Here, by applying the coupled-mode theory, influences of FBG design parameters such as grating length, refractive index modulation depth, and apodization type on the dual-grating demodulation performance are investigated. It is found that particular performance concerns and priorities can be appropriately addressed by proper selection of FBG design parameters. As an example, experiments using FBGs with properly selected parameters based on our analysis are carried out and compared with the previous experiments using available FBGs. The results show that proper FBG parameter selection can be effective for particular performance requirement.

Optical design and characterization of holographic solar concentrators for photovoltaic applications

In present work, different possible aspects of holographic PV concentrators like wide acceptance angle, wavelength selectivity and maximum efficiency operation have been investigated by controlling different processing parameters like depth of refractive index modulation, film thickness and fringe spacing. We have discussed and analyzed individual as well as cumulative effect of processing parameters on angular selectivity, wavelength selectivity and efficiency. In addition, we are also reporting optimized value of the processing parameters for designing high efficiency holographic concentrator.

Determination of the parameters of a holographic layer from its spectral characteristics

Methods for estimating the main parameters of holographic sensors (refractive index modulation depth and hologram thickness) from transmission spectra in the absence of absorption and light scattering are discussed. The consideration is performed for layers oriented parallel to the holographic layer surface under normal light incidence. Direct numerical solution of the problem of light propagation in a periodic nonabsorbing medium is used to study the reflection and transmission spectra of the holographic layer in a wide range of variation in its thickness and the refractive index modulation depth. A classification of the reflection regimes from the holographic layer is proposed (from weak reflection to the photonic crystal regime). A comparison with the results obtained by the coupled-wave analysis is performed, and the limitations of this method at a significant spectral detuning from resonance and under conditions of strong reflection are revealed. It is shown that the main hologram parameters can be estimated from the experimental transmission spectrum of the phase hologram (in the case of strong reflection) based on the spectral dip parameters.

Design and optimization of all-fiber rotational Raman spectroscope for temperature measurement based on sampled fiber Bragg grating

Atmospheric temperature is a key parameter to characterize the state of the atmosphere. Owing to the independence of the aerosol effect for profiling the temperture, the pure rotational Raman lidar has become one of valid tools. To achieve all-time and high-precision active remote sensing, strong background noise needs to be filtered out, and the inhibition rate outside the band of more than 70 dB is needed for Mie-Rayleigh scattering in a rotational Raman temperature measurement lidar. In this paper, a multiple cascaded light path based on sampled fiber Bragg grating (SFBG) and fiber Bragg grating (FBG) in visible spectrum is presented to obtain characteristic spectrum. All-fiber spectroscopic system with high inhibition rate for Raman thermometry is set up based on the above light path. The core device consists of single mode fibers (460-HP) to ensure the compatibility with optical fiber. The main factors affecting the inhibition rate outside the band of sampled fiber Bragg grating, including refractive index modulation depth, total length of grating, sampling period and duty, are optimally designed by using mode coupling theory and tranmission matrix model. Then the optimized parameters of spectroscope are obtained. The results show that the inhibition rate outside the band is proportional to the refractive index modulation depth and duty, when the total length of grating is a constant. However, a larger sidelobe jamming will be caused by overlarge refractive index modulation depth. The less amount and widened full width half maximun of reflectivity peak appear following overlarge duty. In the Raman spectroscopic system of this paper, the inhibition rates outside the bands of SFBG and FBG are 30 dB and 20 dB, respectively. The inhibition rate of more than 70 dB is realized for Mie-Rayleigh scattering, after passing through two FBGs and one SFBG. The simulated optimum parameters of SFBGs are the effective index of the guide mode of 1.465, the saturation index variation of 0.00005, the SFBG length of 20 mm, the sampled period of 0.4 mm, and the Bragg wavelengths of 528.51 nm and 530.76 nm. By using the American standard model and atmospheric scattering signal model, the all-time signal-to-noise ratio (SNR) and inhibition rate of Mie-Rayleigh scattering and solar background light are simulated and analyzed. The results show that the intensities of solar background light and Mie-Rayleigh scattering signal are weaker than Raman scattering signals at 40 dB and 50 dB, respectively. The detection height in daytime and night can reach up to 1.6 km and 2.6 km under the condition of SNR of more than 100, respectively. Owing to these advantages such as miniaturization, anti-interference and high stability, this spectroscope provides a viable solution for filter systems of ground-based and spaceborne lidars.

Wavelength selective holographic concentrator: Application to concentrated photovoltaics

In present investigation dependence of wavelength selectivity of holographic concentrators on depth of refractive index modulation have been reported through simulation and to validate with theoretical predictions, experimental curves have also been plotted with typically recorded three holographic concentrators on silver halide plate of different depth of refractive index modulations (n1=0.014, 0.018 and 0.024) at available wavelength sources (λ=488nm, 514.5nm, 532nm and 632.8nm) and are found to be in good agreement. In addition intensity distribution of different regions of the spectrum is measured and voltage generated due to incidence of different colors of the spectrum onto the Si solar cell is also being reported.

Simulation Analysis of the Multi-Parameter Influence on FBG Peak Reflectivity

Peak reflectivity is a key reflected index of FBG, and it has great effects on the FBG application characteristic in sensing and communication fields. Theoretical and simulation methods are applied to study the cross influence of multiple parameters, such as grating length, grating pitch, and refractive index modulation depth, on FBG peak reflectivity. Research results can provide system recommendations for adopting proper parameter combinations according to practical manufacturing condition and actual demands.

Optimization of few-mode-fiber based mode converter for mode division multiplexing transmission

Few-mode-fiber (FMF) based mode division multiplexing (MDM) is a promising technique to further increase the transmission capacity of single mode fibers. We propose and numerically investigate a fiber-optical mode converter (MC) using long period gratings (LPGs) fabricated on the FMF by point-by-point CO2 laser inscription technique. In order to precisely excite three modes (LP01, LP11, and LP02), both untilted LPG and tilted LPG are comprehensively optimized through the length, index modulation depth, and tilt angle of the LPG in order to achieve a mode contrast ratio (MCR) of more than 20dB with less wavelength dependence. It is found that the proposed MCs have obvious advantages of high MCR, low mode crosstalk, easy fabrication and maintenance, and compact size.

Influence of hydrothermally-synthesized LaPO4:Tb3+ nanorods on the physical and physico-chemical properties of photo-structured acrylate material

This paper presents some encouraging features on Tb3+-doped LaPO4, used for the first time as nanoparticles (NPs) for photo-structured composite material. First, LaPO4:Tb3+ nanorods are hydrothermally synthesized. TEM analysis point out that their size distribution and their morphology are well defined. Then, a small amount of NPs (2 or 3.9 wt%) is dispersed in acrylate monomers mixture and the photo-patterning is performed by using holography, a technique among the others. It is interesting to note that even if the loading of the NPs is weak, these last ones significantly influence the physical properties of the gratings. Indeed, the observed increase in the refractive index modulation depth is ascribed to both phenomena: the sequestration of LaPO4:Tb3+ nanorods within the periodic structure and the change in the kinetics of photopolymerization. The localization of NPs in the non-illuminated zones, evidenced by fluorescence microscopy, is favoured by the decrease in the rate of polymerization, revealed by infrared spectroscopy.

High-efficiency holograms fixed in lithium niobate after recording using a digital fringe stabilization system

We used a digital feedback control loop system to produce reproducible fixed volume transmission holograms of high diffraction efficiency. Different strategies were investigated to obtain holograms of good quality and the highest refractive index modulation depth. Using this control system, we were able to record holograms with stationary fringes. Additionally to using the stationary fringe recording, a double recording-fixing schedule resulted in being the most appropriate one to produce reproducible holograms of better characteristics. This strategy is discussed and compared with other already established ones.

Study of Strain and Temperature Simultaneous Measurement Technology Based on Sampled Grating

Choice appropriate parameters of the sampled fiber Bragg grating base on the influence of the sampled fiber Bragg grating length, sampling rate, refractive index modulation depth and sampling period to the reflective spectrum of sampled fiber Bragg grating. Get the reflective spectrum of sampled fiber Bragg grating by using transmission matrix method, form the sampled fiber Bragg grating suitable for sensing. Get the strains of the sampled fiber Bragg grating and the data from Temperature-sensor through simulation experiment, then determine the sensing-parameters A, B, C, D by using SPSS13.0 statistics software in regression analysis. Strain measurement ranged from 0με to 1800με，temperature measurement ranged from 0°C to 180°C.

Influence of CdSe/ZnS Quantum Dots in the Polymerization Process and in the Grating Recording in Acrylate Materials

The initiation step of the polymerization of acrylate materials is first studied in detail by UV-visible spectroscopy, showing the involvement of each species of the three-component photosensitizer. Then, the implementation of a combined holographic and physicochemical investigation approach is used to determine the influence of photoluminescent CdSe/ZnS quantum dots (QDs) in the photopolymerization and grating recording process in composites containing those QD nanoparticles. The fluorescence microscopy evidences the dynamic distribution profile of QDs due to their diffusion from the irradiated zones to the interface between the bright and the dark zones and, finally, their accumulation in nonirradiated zones. At the same time, the infrared spectroscopy shows that the presence of QDs provides a noticeable decrease of the polymerization rate, which favors the diffusion of the monomer and QDs. These two phenomena contribute to the enhancement of the refractive index modulation depth.

Coherent recovery of the degree of polarization of light propagating in random anisotropy media

We report on the study of light polarization behavior in random anisotropy scattering media. It is shown that, in the case of low scattering events, the degree of polarization (DOP) demonstrates oscillatory behavior due to the coherent character of light scattering. A strong increase in the DOP is demonstrated by using electro-optic fine tuning of the refractive index modulation depth of the scattering media.

Linear discrete diffraction and transverse localization of light in two-dimensional backbone lattices

We study the linear discrete diffraction characteristics of light in two-dimensional backbone lattices. It is found that, as the refractive index modulation depth of the backbone lattice increases, high-order band gaps become open and broad in sequence, and the allowed band curves of the Floquet-Bloch modes become flat gradually. As a result, the diffraction pattern at the exit face converges gradually for both the on-site and off-site excitation cases. Particularly, when the refractive index modulation depth of the backbone lattice is high enough, for example, on the order of 0.01 for a square lattice, the light wave propagating in the backbone lattice will be localized in transverse dimension for both the on-site and off-site excitation cases. This is because only the first several allowed bands with nearly flat band curves are excited in the lattice, and the transverse expansion velocities of the Floquet-Bloch modes in these flat allowed bands approach to zero. Such a linear transverse localization of light may have potential applications in navigating light propagation dynamics and optical signal processing.

In-fiber all-optical fractional differentiator

We demonstrate that an asymmetrical pi phase-shifted fiber Bragg grating operated in reflection can provide the required spectral response for implementing an all-optical fractional differentiator. There are different (but equivalent) ways to design it, e.g., by using different gratings lengths and keeping the same index modulation depth at both sides of the pi phase shift, or vice versa. Analytical expressions were found relating the fractional differentiator order with the grating parameters. The device shows a good accuracy calculating the fractional time derivatives of the complex field of an arbitrary input optical waveform. The introduced concept is supported by numerical simulations.