Theoretical and Experimental Investigation of the Effect of Pump Laser Frequency Fluctuations on Signal-to-Noise Ratio of Brillouin Dynamic Grating Measurement with Coherent FMCW Reflectometry.

Signal-dependent speckle-like noise has constituted a serious factor in Brillouin-grating based frequency-modulated continuous-wave (FMCW) reflectometry and it has been indispensable for improving the signal-to-noise ratio (S/N) of the Brillouin dynamic grating measurement to clarify the noise generation mechanism. In this paper we show theoretically and experimentally that the noise is generated by the frequency fluctuations of the pump light from a laser diode (LD). We could increase the S/N from 36 to 190 merely by driving the LD using a current source with reduced technical noise. On the basis of our experimental result, we derived the theoretical formula for S/N as a function of distance, which contained the second and fourth-order moments of the frequency fluctuations, by assuming that the pump light frequency was modulated by the technical noise. We calculated S/N along the 1.35 m long optical fiber numerically using the measured power spectral density of the frequency fluctuations, and the resulting distributions agreed with the measured values in the 10 to 190 range. Since higher performance levels are required if the pump light source is to maintain the S/N as the fiber length increases, we can use the formula to calculate the light source specifications including the spectral width and rms value of the frequency fluctuations to achieve a high S/N while testing a fiber of a given length.

Signal-to-Noise Ratio of Brillouin Grating Measurement with Micrometer-Resolution Optical Low Coherence Reflectometry.

Signal-dependent speckle-like noise was the dominant noise in a Brillouin grating measurement with micrometer-resolution optical low coherence reflectometry (OLCR). The noise was produced by the interaction of a Stokes signal with beat noise caused by a leaked pump light via square-law detection. The resultant signal-to-noise ratio (SNR) was calculated and found to be proportional to the square root of the dynamic range (DR) defined by the ratio of the Stokes signal magnitude to the variance of the beat noise. The calculation showed that even when we achieved a DR of 20 dB on a logarithmic scale, the SNR value was only 7 on a linear scale and the detected signal tended to fluctuate over ±14% with respect to the mean level. We achieved an SNR of 24 by attenuating the pump light power entering the balanced mixer by 55 dB, and this success enabled us to measure the Brillouin spectrum distributions of mated fiber connectors and a 3-dB fused fiber coupler with a micrometer resolution as examples of OLCR diagnosis.

Beat noise reduction utilizing the transient acoustic-wave response of an optical fiber in Brillouin grating-based optical low coherence reflectometry.

We periodically generated a transient Brillouin grating by using continuous-wave pump light and 50 MHz pulse-wave pump light with optical low coherence reflectometry (OLCR). We extracted the Stokes light generated by the decaying part of the grating with an optical switch, and this enabled us to block the pulse-wave pump light from entering the balanced mixer, resulting in a reduction in the noise caused by the beat between the local oscillator light and the pump light. For the first time, to the best of our knowledge, we succeeded in detecting a Stokes light with an OLCR, despite the fact that the states of polarization of the probe and pump light waves were parallel, and this encouraged us to construct a polarization-independent OLCR for diagnosing optical modules and three-dimensional objects.

Measurement of a true Brillouin grating distribution generated at mated fiber connectors with optical low coherence reflectometry coupled with dispersive Fourier spectroscopy.

We previously reported a reflectogram from mated fiber connectors that was measured at a spatial resolution of 100 µm with Brillouin-gating-based optical low coherence reflectometry, and that agreed with a theoretical curve calculated by assuming that there was a step-like Brillouin grating distribution [Electron. Lett.53, 423 (2017)]. The agreement meant that the reflectogram was determined by the coherence function of the low coherence light and did not mean that we could observe the Brillouin grating distribution generated around the fiber connector joint. In this paper, we focused on increasing the spatial resolution to reveal the actual distribution by broadening the low coherence light, removing the erbium-doped fiber amplifier from the probe port of the interferometer to reduce the dispersion and phase fluctuations, and introducing dispersive Fourier spectroscopy to numerically and completely eliminate the residual dispersion. Although the signal-to-noise ratio (S/N) of a reflectogram obtained by a single translation of the stage was only 4, we succeeded in increasing the S/N 15-fold by averaging 200 samples acquired with repetitive measurements while maintaining a spatial resolution of 30 µm. We were able to clearly observe 320 and 430 µm wide transitions in a Brillouin grating distribution generated around the joint.

Fabrication of a silica-based complex Fourier-transform integrated-optic spatial heterodyne spectrometer incorporating 120° optical hybrid couplers.

We demonstrate a silica-based planar waveguide spatial heterodyne spectrometer incorporating 120° optical hybrid 3×3 MMI couplers as the output couplers in 32 MZIs, which enabled us to derive the spectrum without use of the previously reported dynamic phase shifting. The free spectral range was 640 GHz, and the spectral resolution was 14 GHz. We used a CO2 laser irradiation method to calibrate the light powers from all the output ports of the couplers and to measure the optical phases and amplitudes at the individual MZIs. We solved the resultant system of three linear equations at each MZI and performed a complex Fourier transformation to derive a narrowband light spectrum. The background noise level of the retrieved spectrum was 0.05 with respect to the peak even when no window function was applied.

Coherent frequency-modulated continuous wave reflectometry for measuring stationary Brillouin grating induced under uniform pumping by counterpropagating nonmodulated light waves.

We describe theoretically and experimentally how valuable information on the distributed Brillouin spectra of an optical waveguide is derived from the stationary Brillouin grating measurement under uniform pumping over the waveguide by using the coherent frequency-modulated continuous wave reflectometry. We upconvert the frequencies of the probe and pumping light waves by the Brillouin frequency with one modulator and detect the Stokes light in the same way that we detect the Fresnel and Rayleigh backreflections in the fiber. The intrinsic coherent spike is reduced by using the lock-in detection and the least squares method to reveal the distributed Brillouin spectra of a short optical fiber consisting of two different fibers spliced together.

RF frequency sextupling via an optical two-tone signal generated from two modulation lightwaves from one Mach-Zehnder optical modulator.

An optical two-tone (OTT) signal is generated with a wide frequency separation, based on the suppression of ± 1st-order optical sidebands without using optical band-rejection filtering. By combining two orthogonally polarized lightwaves modulated with different modulation indices, each optical sideband constituting the combined lightwave has a different polarization. Some of these optical sidebands can be suppressed using a polarizer. By using a single Mach-Zehnder optical modulator to achieve two optical modulations, an OTT signal with a 60-GHz frequency-separation was successfully generated with 32-dB suppression of undesired ± 1st-order optical sidebands. An rf signal was also obtained from the OTT signal.

Optical two-tone signal generation without use of optical filter for photonics-assisted radio-frequency quadrupling.

Optical two-tone (OTT) signal generation is demonstrated without optical wavelength filtering for wavelength-free operation in radio-frequency (RF) upconversion assisted by photonics. This principle is based on selective polarization manipulation for the optical carrier; the optical carrier's polarization is first tilted, and the carrier is then suppressed using a polarizer. Owing to optimized conditions obtained from theoretical calculation and the high polarization extinction ratio achieving a 25.7-dB carrier suppression, a 40-GHz separated OTT signal is successfully generated by an optical intensity modulator driven by a 10-GHz sinusoidal RF signal. Conversion into a frequency-quadrupled RF signal is also demonstrated experimentally.

Detailed calculation of spectral noise caused by measurement errors of Mach-Zehnder interferometer optical path phases in a spatial heterodyne spectrometer with a phase shift scheme.

We calculate the root mean square (rms) value of the spectral noise caused by optical path phase measurement errors in a spatial heterodyne spectrometer (SHS) featuring a complex Fourier transformation. In our calculation the deviated phases of each Mach-Zehnder interferometer in the in-phase and quadrature states are treated as statistically independent random variables. We show that the rms value is proportional to the rms error of the phase measurement and that the proportionality coefficient is given analytically. The relationship enables us to estimate the potential performance of the SHS such as the sidelobe suppression ratio for a given measurement error.

Correction for phase-shift deviation in a complex Fourier-transform integrated-optic spatial heterodyne spectrometer with an active phase-shift scheme.

We report that a spectrum can be retrieved with a planar waveguide spatial heterodyne spectrometer (SHS) incorporating an active phase-shift scheme, where the phase shifts are distributed around π/2. This was confirmed experimentally with an SHS that had 32 interleaved Mach-Zehnder interferometers and whose free spectral range was 625 GHz. The phase shifts ranged from 0.71 to 2.2 rad against the target of π/2 rad.

Fabrication of Fourier-transform, integrated-optic spatial heterodyne spectrometer on silica-based planar waveguide.

We describe a configuration of the integrated-optic spectrometer based on Fourier-transform spectroscopy. The original source spectrum has been successfully retrieved with 20 GHz resolution by the spectrometer implemented in a silica-based planar waveguide.

Maclaurin-series method for calculating dispersion in arrayed-waveguide grating multiplexers.

We present a Maclaurin-series method for calculating the dispersion from phase error and amplitude distributions in arrayed waveguide grating (AWG) multiplexers. By using this method, we can easily derive the intercept, the gradient, and the curvature of the dispersion in the center frequency region of a passband. A third-order Maclaurin series was calculated by using the measured phase error and amplitude distributions of AWGs having a channel frequency spacing of 12.5 GHz. The calculated results are in good agreement with the dispersions measured with an optical network analyzer. We also discuss the physical effect of the phase error on dispersion by assuming certain limited cases.

Phase-modulation method for AWG phase-error measurement in the frequency domain.

We report a phase-modulation method for measuring arrayed waveguide grating (AWG) phase error in the frequency domain. By combining the method with a digital sampling technique that we have already reported, we can measure the phase error within an accuracy of +/-0.055 rad for the center 90% waveguides in the array even when no carrier frequencies are generated in the beat signal from the interferometer.

Method for measuring the phase error distribution of a wideband arrayed waveguide grating in the frequency domain.

We describe a method for measuring the phase error distribution of an arrayed waveguide grating (AWG) in the frequency domain when the free spectral range (FSR) of the AWG is so wide that it cannot be covered by one tunable laser source. Our method is to sweep the light frequency in the neighborhoods of two successive peaks in the AWG transmission spectrum by using two laser sources with different tuning ranges. The method was confirmed experimentally by applying it to a 160 GHz spaced AWG with a FSR of 11 THz. The variations in the derived phase error data were very small at +/-0.02 rad around the central arrayed waveguides.