Chirp In Period Research Articles

Reconfigurable optical-force-drive chirp and delay line in micro- or nanofiber Bragg grating

The emergence of optical micro/nano-fiber (MNF) with a subwavelength diameter, which has ultra-light mass and an intense light field, brings an opportunity for develop fiber based optomechanical systems. In this study, we theoretically show an optomechanical effect in silica MNF Bragg gratings (MNFBGs). The light-induced mechanical effect results in continuously distributed strain along the grating. It is shown that the power-related strain introduces an optically reconfigurable chirp in the grating period. We develop new optomechanical coupled-mode equations and theoretically analyze the influence of the optical-force-induced nonlinearity and chirp on the grating performance. Compared with weak Kerr effect, the optomechanics effect dominated in the properties evolution of MNFBGs and significant group velocity reduction and switching effect have been theoretically demonstrated at medium power level. This kind of optomechanical MNFBG with optically reconfigurable chirp may offer a path toward all-optical tunable bandwidth of Bragg resonance and may lead to useful applications such as all-optical switching and optically controlled dispersion and slow/fast light.

Wavenumber scanning-based Fourier transform white-light interferometry

Fourier transform white-light interferometry recovers the optical path difference of an interferometer by measuring the phase change caused by scanning wavelength. However, the optical spectrum, obtained by wavelength scanning method (λ-method), contains a chirp in period. The chirp would induce deviation and decrease the measurement accuracy. An improved method, the wavenumber scanning method (k-method), is proposed and experimentally demonstrated, in which there is no chirp in the optical spectrum. The measurement results using the k-method and the λ-method are compared experimentally. The experimental results show that the standard deviation of the measurement results decreases from 0.015 to 0.004 μm, when an extrinsic Fabry-Perot interferometer with a cavity length of 387 μm is interrogated.

Phase-shifting mask design for interference exposure of chirp blazed grating

An interference exposure system using a phase-shifting mask was proposed for generating periodic sawtooth optical intensity profile with chirp in period. Multiple space-harmonic waves are launched from the mask by diffraction, and the sawtooth optical intensity is formed by interference based on Fourier synthesis after propagation through an air gap. The design concept merely utilizing positive diffraction-order harmonics with tilt illumination of an exposure light and a design algorithm based on time-reversed configuration for calculating required phase shift amount were proposed and discussed. A phase-shifting mask for a blazed grating of very high chirp rate was designed to demonstrate its potential and feasibility. The grating period changes from 2.2 to 3.1 μm gradually within 0.3 mm length. Sawtooth-like optical intensity profile was confirmed by theoretical simulation as well as preliminary experimental results.

Two dimensional silicon waveguide chirped grating couplers for vertical optical fibers

Shallow etched two dimensional gratings for coupling light between silicon-on-insulator nanophotonic waveguides and vertical optical fibers were designed and experimentally characterized. We show that the large second order back reflection could be suppressed effectively by applying a linear chirp in the grating period for two dimensional grating couplers. The total coupling efficiency from an optical fiber to two orthogonal silicon waveguides is independent of the input polarization. An almost linear relationship between the average effective index of the grating region and the fill factor for 1D grating is obtained and verified. We also show that the average effective index for the two dimensional grating is similar to the one dimensional grating with the same fill factor in the light propagation direction, when the fill factor of the etched holes was larger than 0.5.

Analysis of reflection-peak wavelengths of sampled fiber Bragg gratings with large chirp

The reflection-peak wavelengths (RPWs) in the spectra of sampled fiber Bragg gratings with large chirp (SFBGs-LC) are theoretically investigated. Such RPWs are divided into two parts, the RPWs of equivalent uniform SFBGs (U-SFBGs) and the wavelength shift caused by the large chirp in the grating period (CGP). We propose a quasi-equivalent transform to deal with the CGP. That is, the CGP is transferred into quasi-equivalent phase shifts to directly derive the Fourier transform of the refractive index modulation. Then, in the case of both the direct and the inverse Talbot effect, the wavelength shift is obtained from the Fourier transform. Finally, the RPWs of SFBGs-LC can be achieved by combining the wavelength shift and the RPWs of equivalent U-SFBGs. Several simulations are shown to numerically confirm these predicted RPWs of SFBGs-LC.

Sampled Bragg grating with desired response in one channel by use of a reconstruction algorithm and equivalent chirp.

The reconstruction algorithm is first applied to a sampled Bragg grating (SBG) with chirp in the sampling period. This method is demonstrated to achieve various profiles of both reflection and group delay within one channel of the SBG. This method has the advantage that the phase mask does not need any chirp, and only submicrometer precision is needed in the fabrication process. Based on this method, a tunable dispersion compensator is fabricated with a tuning range of 300 ps/nm in a flat band of 1 nm.

Bandwidth equalization of purely phase-sampled fiber Bragg gratings for broadband dispersion and dispersion slope compensation

We propose a purely phase-sampled Bragg grating for dispersion and dispersion slope compensation by introducing a chirp in the grating period and coupling coefficient. The bandwidth of all reflected channels can be equalized by chirping the sampling period at the same time. We show that a trade-off exists between the linearity of dispersion slope and the equalization of reflection channel bandwidths and discuss how the values of the coupling coefficients can be optimized in practice to improve the device performance.

Analysis of chirped-sampled and sampled-chirped fiber Bragg gratings.

We analyze sampled fiber Bragg gratings that have chirp in the grating period, in the sampling function, or in both. In the last-named case the sampling period can be chirped, the sample length can be chirped, or both. We explain the features in the spectral and group-delay (dispersion) responses for gratings that have a single chirp parameter. We then show how the response of sampled gratings that have multiple chirp parameters can be explained in terms of the single-chirp parameter cases.

A novel simple measurement technique of equivalent chirp in the grating period of sampled Bragg grating

In this letter, based on the proposed concept of Moiré sampled Bragg grating (SBG), the equivalent chirp rates of various Fourier orders in a sampled Bragg grating with chirp in the sampling period (CSP) is demonstrated for the first time via a simple novel experimental method using phase mask rotation and dual exposure technique. Difference between experimental data and calculated results is less than 9%.

Correction to "Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application on dispersion management design in a WDM system"

The presented equation leads to a refractive index modulation which is used in the subsequent derivations and calculations. We give a correction to this analytical expression.

Experimental investigation of a sampled grating with a chirp in the sampling period

AbstractIn this letter, a sampled Bragg grating (SBG) with a chirp in the sampling period (CSP) is fabricated and experimentally investigated for the first time. Its spectrum response shows that the effective chirp in the grating period (CGP) varies among stopbands, which is consistent with the previous theoretical predictions. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 128–130, 2001.

Experimental Investigations of a Stress-Gradient Sampled Bragg Grating with a Chirp in the Sampling Period

The spectrum response of a sampled Bragg grating (SBG) with a chirp in the sampling period (CSP) under stress-gradient is experimentally investigated for the first time. It is shown that unlike in a conventional SBG without CSP, the bandwidths of the multiple stopbands vary with the stress asymmetrically around the center Bragg wavelength. These results coincide with the theoretical predictions presented by us. The present experimental demonstration is useful for the application of the SBG with CSP in dispersion slope compensation of fiber in dense wavelength division multiplexing (DWDM) systems.

Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system

Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system

Analysis of waveguide gratings: application of Rouard’s method

This paper describes the adaptation of Rouard’s method, a familiar computational technique used in thin-film coating design, to the analysis of waveguide diffraction gratings. The approach can be used to generate the spectral and the angular characteristics of arbitrary straight-line gratings (periodic or nonperiodic), is easy to implement on a computer, and provides an intuitively appealing picture of the operation of such gratings. The application of the thin-film method is extended to periodic gratings as well as to gratings having either a linear or a quadratic chirp in period. Specific examples are used to compare the results of the thin-film computational method with those predicted by previous authors.