We report on a robust scheme for wideband variable-phase interferometer stabilization based on active modulation. In contrast to previous schemes, the correction signal is generated without using second harmonics, whose low amplitude often requires employing narrowband lock-in amplifiers. Resonances in the element modulating the phase are attenuated to enable high gain without high-frequency oscillations. Operation over a 3-kHz bandwidth is demonstrated.[Read More….]
(a) Schematic description of the experimental setup. ASE: amplified spontaneous emission. EDFA: erbium-doped fiber amplifier. ODL: optical delay line. FB: feedback. PZT: piezoelectric transducer. (b) Amplitude of frequency response of the PZT h^(f) . The first resonance is obtained at f=18kHz . (c) Spectrum of the signal detected by the photodiode with sine modulation at 70 kHz obtained for two values of ϕ . The first and second harmonics are marked by arrows.
A highly sensitive compact hydrophone, based on a pi-phase-shifted fiber Bragg grating, has been developed for the measurement of wideband ultrasonic fields. The grating exhibits a sharp resonance, whose centroid wavelength is pressure sensitive. The resonance is monitored by a continuous-wave (CW) laser to measure ultrasound-induced pressure variations within the grating. In contrast to standard fiber sensors, the high finesse of the resonance—which is the reason for the sensor’s high sensitivity—is not associated with a long propagation length. Light localization around the phase shift reduces the effective size of the sensor below that of the grating and is scaled inversely with the resonance spectral width. In our system, an effective sensor length of 270 μm, pressure sensitivity of 440 Pa, and effective bandwidth of 10 MHz were achieved. This performance makes our design attractive for medical imaging applications, such as optoacoustic tomography, in which compact, sensitive, and wideband acoustic detectors are required. [Read More…]
Fig. 1 Schematic description of the detection scheme. A CW laser is used to monitor the reflection of an FBG.
We demonstrate a new technique that enables us to measure the structure of highly reflecting fiber Bragg gratings. The impulse response function is measured from both sides of the grating using a low-coherence spectral interferometry technique. An inverse scattering algorithm is used to extract the refractive-index profiles from the measured impulse responses. The reconstruction of the grating is performed by combining the refractive-index profiles, measured from both sides of the grating. The transfer function of the optical spectrum analyzer is measured and used to correct the measured results. The interrogation of an apodized grating with a reflectivity of 99.91% is demonstrated. [Read more…]
Fig. 1. Schematic description of the experimental setup used to measure the structure of highly reflecting fiber Bragg gratings. The interference spectrum of a wave reflected from the grating and a wave reflected from a reference mirror is measured from both sides of the grating by changing the state of the optical switches. PC is a polarization controller.
We demonstrate a new method for measuring changes in temperature distribution caused by coupling a high-power laser beam into an optical fiber and by splicing two fibers. The measurement technique is based on interrogating a fiber Bragg grating by using low-coherence spectral interferometry. A large temperature change is found owing to coupling of a high-power laser into a multimode fiber and to splicing of two multimode fibers. Measurement of the temperature profile rather than the average temperature along the grating allows study of the cause of fiber heating. The new measurement technique enables us to monitor in real time the temperature profile in a fiber without the affecting system operation, and it might be important for developing and improving the reliability of high-power fiber components. [Read more…]
Fig. 1 Schematic description of the experimental setup used to measure the temperature profile caused (a) by coupling a high-power argon-ion laser beam into a fiber and (b) by splicing two optical fibers.
We demonstrate a new inverse scattering algorithm for reconstructing the structure of highly reflecting fiber Bragg gratings. The method, called integral layer-peeling (ILP), is based on solving the Gel’fand-Levitan-Marchenko (GLM) integral equation in a layer-peeling procedure. Unlike in previously published layer-peeling algorithms, the structure of each layer in the ILP algorithm can have a nonuniform profile. Moreover, errors due to the limited bandwidth used to sample the reflection coefficient do not rapidly accumulate along the grating. Therefore, the error in the new algorithm is smaller than in previous layer peeling algorithms. The ILP algorithm is compared to two discrete layer-peeling algorithms and to an iterative solution to the GLM equation. The comparison shows that the ILP algorithm enables one to solve numerically difficult inverse scattering problems, where previous algorithms failed to give an accurate result. The complexity of the ILP algorithm is of the same order as in previous layer peeling algorithms. When a small error is acceptable, the complexity of the ILP algorithm can be significantly reduced below the complexity of previously published layer-peeling algorithms.. [Read more…]
Fig. 1. Reconstructed modulation index n1(z) of a uniform grating with a refractive index modulation amplitude n1=6.5×10−4, a length of 4 mm, and a maximum reflectivity of 99.99%, calculated using the ILP algorithm (solid line), the FDLP algorithm (dashed line), and iterative solution to the GLM equation with 70 iterations (dotted line). The reflection spectrum was sampled over a bandwidth of 40 nm with a resolution of 0.01 nm. The figure shows that an excellent reconstruction of the grating was obtained using the ILP algorithm, while the FDLP algorithm and the iterative solution to the GLM equation gave a large error. The inset of the figure shows a zoom on the profile close to the input end of the grating.
We demonstrate an inverse scattering algorithm for reconstructing the structure of lossy fiber Bragg gratings. The algorithm enables us to extract the profiles of the refractive index and the loss coefficient along the grating from the grating transmission spectrum and from the reflection spectra, measured from both sides of the grating. Such an algorithm can be used to develop novel distributed evanescent-wave fiber Bragg sensors that measure the change in both the refractive index and the attenuation coefficient of the medium surrounding the grating. The algorithm can also be used to analyze and to design fiber Bragg gratings written in fiber amplifiers. A novel method to overcome instability problems in extracting the parameters of the lossy grating is introduced. The new method also makes it possible to reduce the spectral resolution needed to accurately extract the grating parameters. [Read more…]
Fig. 1 Reconstruction of a grating with a chirped Gaussian coupling coefficient, 𝑞(𝑧)=600 exp[−105(𝑧−𝐿/2)2(2.5+20𝑖)] m−1 and with a sinusoidal loss profile 𝛼=70[1−cos(10𝜋𝑧/𝐿)] m−1 written in the region [0, L=1 cm]. The reconstructed parameters (solid curves) are compared with the original parameters (dashed curves). The reflection spectra, obtained from both sides of the grating, and the transmission spectrum were sampled over a bandwidth of 10 nm with a spectral resolution of 0.02 nm.
We demonstrate theoretically a new method to accurately interpolate the complex reflection spectrum of fiber Bragg gratings with a finite length at any desired frequency resolution. The required sampling resolution is significantly smaller than can be expected by directly using the sampling theorem for obtaining a low-error characterization of the reflection spectrum. A further decrease in the required sampling resolution by a factor of two is obtained by sampling both the complex reflection and the complex transmission functions. The new reconstruction technique may enable to significantly reduce the time needed to characterize fiber Bragg gratings and to interrogate fiber Bragg sensors. [Read more…]
Fig. 1 (a) The reflectivity and (b) the impulse response function of a uniform fiber Bragg grating with a maximum reflectivity of 99% and a length of L=4 mm . The sampled points used to characterize the reflection function with a sampling period of Δλ=0.1 nm are marked in the figure.
We develop a novel method that enables one to reconstruct the structure of highly reflecting fiber Bragg gratings from noisy reflection spectra. When the reflection spectrum is noisy and the grating reflectivity is high, noise in the Bragg zone of the reflection spectrum is amplified by the inverse scattering algorithms and prevents the reconstruction of the grating. Our method is based on regularizing the reflection spectrum in frequencies inside the Bragg zone by using the data on the grating spectrum outside the Bragg zone. The regularized reflection spectrum is used to reconstruct the grating structure by means of inverse scattering. Our method enables one to analyze gratings with a high reflectivity from a spectrum that contains a high level of noise. Such gratings could not be analyzed by using methods described in previous work [IEEE J. Quantum Electron. 39, 1238 (2003)]. [Read more…]
Fig. 1 Reconstruction of a uniform grating with coupling coefficient q = 500 m-1 and length L = 1 cm from a noisy reflection spectrum. The figure compares the reconstruction obtained with the method developed in Ref. 9 (solid curve) with a direct reconstruction by the ILP algorithm (dashed curve) and with a reconstruction by the method presented in this paper (dotted curve). The reflection spectrum of the grating was sampled with a bandwidth of 10 nm and resolution of 0.002 nm. The standard deviation of the noise variables, added to the complex reflection spectrum, was equal to 5 × 10-5. The ILP algorithm as well as the algorithm presented in this paper have accurately reconstructed the grating profile.
We demonstrate, for the first time to our knowledge, reconstruction of the structure of a long-period grating from its measured core-to-core transmission spectrum intensity. The reconstruction is obtained by writing an auxiliary grating in cascade to the interrogated grating. Our reconstruction technique is based on using the Hilbert transform and a phase-retrieval algorithm. Using our method, we have reconstructed the structure of a uniform long-period grating with a 47% coupling efficiency. [Read more…]
Handmade Software, Inc. Image Alchemy v1.12
Fig. 1 Experimental system used to reconstruct the interrogated grating structure. An auxiliary grating is written to obtain a unique reconstruction.
In order to reconstruct the structure of a long-period grating, both the complex core-to-core transmission function and the complex core-to-cladding transmission function should be known. However, in practice, only the core-to-core transmission function of the grating can be measured. We demonstrate theoretically the reconstruction of long-period gratings from only the core-to-core transmission function. The reconstruction is performed by extracting the complex core-to-cladding transmission function of the grating from its core-to-core transmission function. Generally, the extraction is not unique; however, we show that by writing an additional grating in cascade to the interrogated grating, a unique reconstruction can be obtained. In weak long-period gratings, only the amplitude of the core-to-core transmission function is needed to reconstruct the grating. The results of our work can enable the experimental reconstruction of long-period gratings from their transmission function as well as the development of novel distributed sensors. [Read more…]
Fig. 1 Schematic description of the grating structure analyzed in the paper. Two cascaded LPGs with lengths 𝐿1 and 𝐿2 are separated by a gap with a length 𝐿𝑓 . The fields of the core mode and cladding mode at the input end of the structure are denoted by 𝑢2(𝑘,𝑧=0) and 𝑢1(𝑘,𝑧=0) , respectively. The core-to-core and core-to-cladding transmission functions of the first grating are denoted by 𝑎1(𝑘) and 𝑏1(𝑘) , respectively, and the core-to-core and core-to-cladding transmission functions of the total structure are denoted by 𝑎tor(𝑘) and 𝑏tot(𝑘) , respectively.
