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Showing papers on "Fiber Bragg grating published in 1992"


Book
01 Jan 1992
TL;DR: In this article, the authors present an overview of the main components of WDM lightwave communication systems, including the following: 1.1 Geometrical-Optics Description, 2.2 Wave Propagation, 3.3 Dispersion in Single-Mode Fibers, 4.4 Dispersion-Induced Limitations.
Abstract: Preface. 1 Introduction. 1.1 Historical Perspective. 1.2 Basic Concepts. 1.3 Optical Communication Systems. 1.4 Lightwave System Components. Problems. References. 2 Optical Fibers. 2.1 Geometrical-Optics Description. 2.2 Wave Propagation. 2.3 Dispersion in Single-Mode Fibers. 2.4 Dispersion-Induced Limitations. 2.5 Fiber Losses. 2.6 Nonlinear Optical Effects. 2.7 Fiber Design and Fabrication. Problems. References. 3 Optical Transmitters. 3.1 Semiconductor Laser Physics. 3.2 Single-Mode Semiconductor Lasers. 3.3 Laser Characteristics. 3.4 Optical Signal Generation. 3.5 Light-Emitting Diodes. 3.6 Transmitter Design. Problems. References. 4 Optical Receivers. 4.1 Basic Concepts. 4.2 Common Photodetectors. 4.3 Receiver Design. 4.4 Receiver Noise. 4.5 Coherent Detection. 4.6 Receiver Sensitivity. 4.7 Sensitivity Degradation. 4.8 Receiver Performance. Problems. References. 5 Lightwave Systems. 5.1 System Architectures. 5.2 Design Guidelines. 5.3 Long-Haul Systems. 5.4 Sources of Power Penalty. 5.5 Forward Error Correction. 5.6 Computer-Aided Design. Problems. References. 6 Multichannel Systems. 6.1 WDM Lightwave Systems. 6.2 WDM Components. 6.3 System Performance Issues. 6.4 Time-Division Multiplexing. 6.5 Subcarrier Multiplexing. 6.6 Code-Division Multiplexing. Problems. References. 7 Loss Management. 7.1 Compensation of Fiber Losses. 7.2 Erbium-Doped Fiber Amplifiers. 7.3 Raman Amplifiers. 7.4 Optical Signal-To-Noise Ratio. 7.5 Electrical Signal-To-Noise Ratio. 7.6 Receiver Sensitivity and Q Factor. 7.7 Role of Dispersive and Nonlinear Effects. 7.8 Periodically Amplified Lightwave Systems. Problems. References. 8 Dispersion Management. 8.1 Dispersion Problem and Its Solution. 8.2 Dispersion-Compensating Fibers. 8.3 Fiber Bragg Gratings. 8.4 Dispersion-Equalizing Filters. 8.5 Optical Phase Conjugation. 8.6 Channels at High Bit Rates. 8.7 Electronic Dispersion Compensation. Problems. References. 9 Control of Nonlinear Effects. 9.1 Impact of Fiber Nonlinearity. 9.2 Solitons in Optical Fibers. 9.3 Dispersion-Managed Solitons. 9.4 Pseudo-linear Lightwave Systems. 9.5 Control of Intrachannel Nonlinear Effects. Problems. References. 10 Advanced Lightwave Systems. 10.1 Advanced Modulation Formats. 10.2 Demodulation Schemes. 10.3 Shot Noise and Bit-Error Rate. 10.4 Sensitivity Degradation Mechanisms. 10.5 Impact of Nonlinear Effects. 10.6 Recent Progress. 10.7 Ultimate Channel Capacity. Problems. References. 11 Optical Signal Processing. 11.1 Nonlinear Techniques and Devices. 11.2 All-Optical Flip-Flops. 11.3 Wavelength Converters. 11.4 Ultrafast Optical Switching. 11.5 Optical Regenerators. Problems. References. A System of Units. B Acronyms. C General Formula for Pulse Broadening. D Software Package.

4,125 citations


Journal ArticleDOI
TL;DR: In this paper, an unbalanced-interferometer wavelength discriminator was used for the detection of dynamic strain induced wavelength shifts in fiber Bragg grating sensors, which is capable of sub-nanostrain resolution (0.6 ne/√(Hz) at 500 Hz).
Abstract: A technique for the detection of dynamic strain induced wavelength shifts in fibre Bragg grating sensors is reported that is based on an unbalanced-interferometer wavelength discriminator, which is capable of subnanostrain resolution (0.6 ne/√(Hz) at 500 Hz) sensing.

510 citations


Journal ArticleDOI
TL;DR: In this article, a passive and self-referencing wavelength detection system that measures the wavelength of the narrowband back-reflected spectrum of guided-wave Bragg gratings is described.
Abstract: A novel, passive, and self-referencing wavelength detection system (WDS) that measures the wavelength of the narrowband back-reflected spectrum of guided-wave Bragg gratings is described. This letter also reports on the use of such a detection system with fiber-optic Bragg gratings used as absolute strain sensors. The wavelength detection system demonstrated a 1% strain resolution of the total strain measurement range. >

333 citations


Journal ArticleDOI
TL;DR: A single-mode linear-cavity fiber laser that utilizes intracore Bragg reflectors for cavity feedback has been continuously tuned, without mode hopping, when both the gratings and enclosed fiber are stretched uniformly.
Abstract: A single-mode linear-cavity fiber laser that utilizes intracore Bragg reflectors for cavity feedback has been continuously tuned, without mode hopping, when both the gratings and enclosed fiber are stretched uniformly. Continuous tuning is achieved in a 1.54-microm erbium fiber laser since the change in the reflected wavelength from a Bragg reflector tracks the change in the cavity resonance wavelength.

223 citations


Patent
29 Oct 1992
TL;DR: An index grating is imprinted in the core of an optical fiber using a specially designed silica glass phase grating mask The phase mask is held in close proximity to the optical fiber.
Abstract: An index grating is imprinted in the core of an optical fiber using a specially designed silica glass phase grating mask The phase mask is held in close proximity to the optical fiber Laser irradiation of the phase mask with ultraviolet light at normal incidence imprints (photoinduces) into the optical fiber core the interference pattern created by the phase mask

199 citations


Journal ArticleDOI
TL;DR: In this paper, a temperature sensor based on fiber-optic Bragg grating elements is described, and a high sensitivity to thermally induced Bragg wavelength shifts is obtained using an interferometric detection approach.
Abstract: A differential temperature sensor based on fiber-optic Bragg-grating elements is described. A high sensitivity to thermally induced Bragg wavelength shifts is obtained using an interferometric detection approach. Results presented show a temperature resolution of >

134 citations


Patent
27 Jul 1992
TL;DR: In this article, a two-section narrow band transmission filter with cascaded gratings is used to remove undesired spontaneous emission from an in-fiber Bragg grating reflector.
Abstract: Optical systems including an optical amplifier and a narrow bandwidth optical filter for removing undesired spontaneous emission. An in-fiber Bragg grating reflector reflects substantially only the input amplified signal back to a circulator port of an optical circulator where the desired amplified signal is coupled from the next circulator port. The undesired emission exits from the grating reflector and is removed from the system. Cascaded grating reflectors are used in a wavelength division multiplexing (WDM) system. A two section narrow band transmission filter with cascaded gratings.

130 citations


Journal ArticleDOI
TL;DR: Narrow-line, permanent Bragg reflection gratings have been created in Ge-doped silica-core optical fibers by interfering beams of a single 20-ns pulse of KrF excimer laser light.
Abstract: Narrow-line, permanent Bragg reflection gratings have been created in Ge-doped silica-core optical fibers by interfering beams of a single 20-ns pulse of KrF excimer laser light. Of the fibers studied, the highest reflectance value of ~2% was observed with a linewidth (FWHM) of 0.1 nm, which corresponds to a 2-mm grating length with an index modulation of ~3 x 10(-5).

126 citations


Journal ArticleDOI
TL;DR: A transient tunable Bragg reflection grating has been established in an erbium-doped fiber amplifier by the effect of a standing wave produced by counterpropagating cw light.
Abstract: A transient tunable Bragg reflection grating has been established in an erbium-doped fiber amplifier by the effect of a standing wave produced by counterpropagating cw light. Less than 1 mW of cw light was required to establish a grating with a 75% reflection coefficient at 1536 nm and an optical bandwidth (FWHM) of 16 MHz. Possible applications include dispersion compensation and dense wavelength-division multiplexing.

125 citations


Journal ArticleDOI
TL;DR: In this paper, the design constraints required to achieve single-longitudinal mode operation from a standing-wave, homogeneously broadened, three-level, fiber laser which utilizes intracore Bragg reflectors for cavity feedback are presented.
Abstract: The design constraints required to achieve single-longitudinal-mode operation from a standing-wave, homogeneously broadened, three-level, fiber laser which utilizes intracore Bragg reflectors for cavity feedback are presented. In particular, a closed-form solution to the laser rate equations is found which bounds the region in which only single longitudinal mode operation is supported. The principal resonator geometry to be considered is a two-reflector cavity which utilizes only Bragg reflectors for feedback. Analytical and experimental results are discussed. >

104 citations


Proceedings ArticleDOI
01 Jan 1992
TL;DR: In this article, reflection gratings and out-coupling taps for sensors can be written holographically within the core of many commercial fibers available today and have been tested to temperatures in excess of 500 degree(s)C. The fiber gratings, and the different types of sensors they can make, conveniently lend themselves to WDM, TDM, and FDM types of multiplexing schemes.
Abstract: Bragg reflection gratings and out-coupling taps for sensors can be written holographically within the core of many commercial fibers available today. The gratings appear to be permanent and have been tested to temperatures in excess of 500 degree(s)C. Quasi-distributed temperature, strain, pressure, chemical, and interferometric type sensors can be made with the wavelength selective, reflection gratings, and taps. The fiber gratings, and the different types of sensors they can make, conveniently lend themselves to WDM, TDM, and FDM types of multiplexing schemes. Instrumentation to detect the multiple sensors and measure their spectral shift for localized and quasi-distributed sensing is currently under development.

Patent
27 Jul 1992
TL;DR: In this article, an in-fiber Bragg grating is used to flatten the gain slope of a fiber optical amplifier or optical fiber laser by diverting excess spontaneous emission therefrom.
Abstract: An in-fiber Bragg grating is used to flatten the gain slope of a fiber optical amplifier or optical fiber laser. The grating can be formed using photorefractive techniques, and is placed within a guided wave portion of a doped optical fiber. The grating is oriented at a nonperpendicular angle with respect to a longitudinal axis of the fiber, and has an interaction wavelength that is selected to flatten the gain slope of the device by diverting excess spontaneous emission therefrom. The interaction wavelength is preferably selected to correspond to a wavelength at or near that at which the spontaneous emission produced by the fiber peaks.

Journal ArticleDOI
TL;DR: In this paper, the authors report on the development of a wavelength demodulation system that is inexpensive and easily implemented with a minimum of equipment, which can process many fiber optic sensors, yet be small enough to be integrated within the structural interface and thereby address the interconnect problem.
Abstract: Smart materials and adaptive structures will require structurally integrated fiber optic sensing systems that can operate in practical situations including harsh environments. The intracore fiber optic Bragg grating has considerable potential to serve as the sensor of choice for this emerging field. However, its role has been impeded by the lack of a simple, passive and fast method of determining the wavelength of its narrow back-reflected optical signal. The authors report on the development of just such a wavelength demodulation system that is inexpensive and easily implemented with a minimum of equipment. Furthermore, they shall show that this approach lends itself to the development of an optoelectronic chip that could process many fiber optic sensors, yet be small enough to be integrated within the structural interface and thereby address the interconnect problem-potentially one of the most critical facing the development of practical smart structures.

Patent
23 Jul 1992
TL;DR: In this article, an optical fiber for amplifying or sourcing a light signal in a single transverse mode is presented. But, it requires only conventional and readily available diode-based pump sources, and the amplifier provides power and small signal gains comparable to the best observed.
Abstract: An optical fiber for amplifying or sourcing a light signal in a single transverse mode The fiber comprises a host glass doped with erbium (Er) and a sensitizer such as ytterbium (Yb) or iron (Fe) Preferably the host glass is doped silicic glass (eg, phosphate or borate doped) Electrical energy is provided to diode lasers that pump the Nd laser rod, which in turn pumps the fiber Such a configuration for pumping the fiber provides a high energy transfer from the diodes to the Nd laser rod, which in turn enables high pumping powers to be coupled into the single-mode co-doped fiber Based on the amplification characteristics of the co-doped fiber and the efficient coupling of power from the laser diodes, the amplifier provides power and small signal gains comparable to the best observed, while requiring only conventional and readily available diode-based pump sources

Patent
23 Jan 1992
TL;DR: In this article, a wavelength selective optical fiber coupler has been proposed for the field of optical communications, which includes a first substrate that has an optical input end for receiving a first optical signal.
Abstract: A wavelength selective optical fiber coupler having various applications in the field of optical communications is disclosed. The coupler includes a first substrate that has an optical input end for receiving a first optical signal. A first grating is formed in the first substrate. A second substrate has an optical input end for receiving a second optical signal. A second grating is formed in the second substrate. The first and second gratings are joined to transfer energy from the second optical signal to the first substrate for combination with the first optical signal. The combined signals are output from an optical output end of the first substrate. The gratings can comprise, for example, in-fiber gratings. Alternatively, at least one of the gratings can be provided in a polished optical block. The coupler can be used to combine a plurality of pump lasers operating at slightly different wavelengths, for input to an optical fiber amplifier having a broad pump band. A specific embodiment of a high power optical fiber amplifier using a neodymium fiber pump laser is also disclosed.

Journal ArticleDOI
TL;DR: In this article, the authors measured the broadening of a 100-fs pulse to more than 5 ps after passing through 400 m of fiber near lambda sub-sub 0/ and showed that the measured asymmetric and oscillatory pulse shape is in agreement with calculations.
Abstract: Subpicosecond optical pulses propagating in single-mode fibers are severely distorted by third-order dispersion even at the fiber's zero-dispersion wavelength ( lambda /sub 0/). Using cross-correlation techniques, the authors measured the broadening of a 100-fs pulse to more than 5 ps after passing through 400 m of fiber near lambda /sub 0/. The measured asymmetric and oscillatory pulse shape is in agreement with calculations. A grating and telescope apparatus was configured to simultaneously equalize both third- and second-order dispersion for wavelengths slightly longer than lambda /sub 0/. Nearly complete compensation has been demonstrated for fiber lengths of 400 m and 3 km of dispersion-shifted fiber at wavelengths of 1560-1580 nm. For the longer fibers, fourth-order dispersion due to the grating becomes important. >

Patent
04 Mar 1992
TL;DR: In this paper, a fiber optic probe is used for supplying and collecting instrumentation light in shock experiments, where the probe comprises two optical fibers and the necessary lens elements to concentrate laser light coming from one of the fibers onto a specimen, and to collect reflected laser light from the specimen into the second fiber.
Abstract: A fiber optic probe for supplying and collecting instrumentation light in shock experiments. The fiber optic probe comprises two optical fibers and the necessary lens elements to concentrate laser light coming from one of the fibers onto a specimen, and to collect reflected laser light from the specimen into the second fiber. The fibers and lens elements are mounted in a special frame which facilitates better alignment of the lens/fiber arrangement by precise control of the flexing of the fiber optic probe's frame. Improved reflected light gathering efficiency and improved depth of field are achieved by the choices of the optical fiber diameters and by using good optical design practice. Inexpensive components and fabrication techniques allow for the economical use of these probes even when one is destroyed with each experiment.

Journal ArticleDOI
TL;DR: An integrated, distributed Bragg reflector laser in a Nd-doped, glass, channel waveguide is reported for the first time in this paper, which lases in a single longitudinal mode with a pump threshold of 50 mW and a slope efficiency of 1%.
Abstract: An integrated, distributed Bragg reflector laser in a Nd‐doped, glass, channel waveguide is reported for the first time. The waveguide is fabricated using Ag+ thermal ion exchange in a soda‐lime‐silicate‐glass containing 2% Nd2O3 by weight. The distributed Bragg reflector grating is produced holographically in photoresist and then etched into the waveguide using argon ion milling. The device lases in a single longitudinal mode with a pump threshold of 50 mW and a slope efficiency of 1%.

Patent
19 May 1992
TL;DR: In this article, the authors describe a technique for improving the sensitivity of a resonant mirror sensor which has particular applications in areas involving sensing at an interface such as immunosensing using immobilized antibodies.
Abstract: This invention describes a technique for improving the sensitivity of a resonant mirror sensor which has particular applications in areas involving sensing at an interface such as immunosensing using immobilized antibodies. By the introduction of a Bragg grating structure in the sensor, there is produced enhanced dispersion and hence enhanced sensitivity in the region close to the band edge. This improves the detection limit of the sensor without changing the composition or involving the sensor size and allows more sensitive operation at reduced incident angles.

Patent
02 Dec 1992
TL;DR: In this paper, a method for demodulating, processing and multiplexing the signals from an array of structurally integrated Bragg grating laser sensors in an optoelectronic element is presented.
Abstract: The present invention discloses a method for demodulating, processing and multiplexing the signals from an array of structurally integrated Bragg grating laser sensors in an optoelectronic element in order that this sensing information can be transmitted from the structure by means of a single channel and a user friendly interconnect or free-space propagation. The invention also discloses a method for determining the wavelength of narrowband optical signals such as arises from Bragg grating laser sensors and includes, for each sensor, processing the optical signal through a spectral filter with a spectral transmission function that can be accurately translated by a control parameter which has been calibrated with respective to wavelength. The filtered signal is compared to the reference signal at different values of the control parameter to determine a value of the control parameter where a predetermined relationship of the spectrally filtered signal and the reference signal is achieved. This allows the wavelength to be determined. Apparatus for carrying out the method is also disclosed. A preferred embodiment involving the use of a multiple quantum well electroabsorption device to perform both spectral filtering and detection is also disclosed. The method and apparatus have particular application with lasers and laser sensing arrangements for smart structures.

Journal ArticleDOI
TL;DR: In this article, a high-power, laser-diode-pumped, Q-switched fiber laser operating at 1.053 mu m with 2-ns duration at up to 1-kHz repetition rates for an adsorbed pump power of only 22 mW at 810 nm.
Abstract: A high-power, laser-diode-pumped, Q-switched fiber laser operating at 1.053 mu m which is suitable for use in time-multiplexed fiber sensor applications is described. The laser emits >1-kW pulses at 1.053 mu m with 2-ns duration at up to 1-kHz repetition rates for an adsorbed pump power of only 22 mW at 810 nm. Tunable Q-switched operation over a 40-nm wavelength range has also been demonstrated. >

Patent
03 Nov 1992
TL;DR: In this paper, a ring-resonator with a length of singlemode optical fiber, a gain medium of rare earth-doped fiber, broad-band fiber Fabry-Perot filter for wavelength tuning of the laser, a narrowband fiber filter for suppression of longitudinal ring modes, and an optical isolator for preventing interetalon interactions between the tandem fiber fabry-perot filters.
Abstract: A single-frequency fiber-optic ring laser exhibits improved frequency stability, reduced laser intensity noise, broad tunability and narrow linewidth. The fiber-optic ring laser includes a ring-resonator with a length of single-mode optical fiber, a gain medium of rare earth-doped fiber, a broad-band fiber Fabry-Perot filter for wavelength tuning of the laser, a narrow-band fiber Fabry-Perot filter for suppression of longitudinal ring modes and an optical isolator for preventing interetalon interactions between the tandem fiber Fabry-Perot filters. Selective positioning of the tandem fiber Fabry-Perot filters, relative to the ring laser's gain medium and output coupler, results in laser intensity noise reduction to the standard quantum limit.

Journal ArticleDOI
TL;DR: A two-mode fiber switch made of a short length of erbium-doped fiber in which switching is accomplished by a nonlinearity that is resonantly enhanced by the dopant is described.
Abstract: We describe a two-mode fiber switch made of a short length of erbium-doped fiber in which switching is accomplished by a nonlinearity that is resonantly enhanced by the dopant. In a 0.95-m fiber pumped with a 1.48-μm laser diode, a 906-nm signal is switched with only 8 mW of absorbed power at a signal absorption loss of 0.25 dB.

Journal ArticleDOI
TL;DR: In this paper, a model based on birefringence dispersion is proposed for a Fabry-Perot Nd-doped fiber laser, where wide wavelength tunability is achieved either by rotating the polarizer or by varying, with an in-line polarization controller.
Abstract: When an intracavity polarizer is introduced into a Fabry-Perot Nd-doped fiber laser, wide wavelength tunability is achieved either by rotating the polarizer or by varying, the fiber birefringence with an in-line polarization controller. The intracavity polariser also produces considerable line-narrowing. A model based on birefringence dispersion is proposed. >

Patent
17 Aug 1992
TL;DR: In this paper, a highly sensitive optical fiber interferometer sensor comprising a laser light source, a [2×2] optical fiber coupler to split the beam in two, a differential transducer which converts a signal of interest into optical phase shift in the laser light transmitted through the two optical fibers in the interferometers and a [3×3] optical fibre complex which recombines the two beams, producing interference which can be electronically detected.
Abstract: A highly sensitive optical fiber interferometer sensor comprising a laser light source, a [2×2] optical fiber coupler to split the beam in two, a differential transducer which converts a signal of interest into optical phase shift in the laser light transmitted through the two optical fibers in the interferometer and a [3×3] optical fiber complex which recombines the two beams, producing interference which can be electronically detected. The use of the [3×3] coupler permits Passive Homodyne demodulation of the phase-modulated signals provided by the interferometer without feedback control or modulation of the laser itself and without requiring the use of electronics within the interferometer.

Journal ArticleDOI
TL;DR: In this article, the photoinduced gratings observed in both Bragg grating and second-harmonic generation fibers were found to be induced and bleached by one and two-photon absorption processes, respectively.
Abstract: Ge E’ centers photoinduced in Ge‐doped silica by 5 eV photons of various intensities and fluences were found by electron spin resonance to be induced and bleached by one‐ and two‐photon absorption processes, respectively. The observation that Ge E’‐type centers are the only paramagnetic centers induced by very low intensity 5 eV photons in Ge‐doped silica supports the proposal that Ge E’‐type centers are responsible for the photoinduced gratings observed in both Bragg grating and second‐harmonic generation fibers.

Journal ArticleDOI
TL;DR: In this article, the authors demonstrate that it is possible to fabricate efficient microlenses directly on the ends of polarization-maintaining fiber, which are able to couple more than 70% of the light from a laser diode into the fiber, are made by micromachining an aspheric surface over the core region of the fiber with a CO/sub 2/ laser.
Abstract: The authors demonstrate that it is possible to fabricate efficient microlenses directly on the ends of polarization-maintaining fiber. The lenses, which are able to couple more than 70% of the light from a laser diode into the fiber, are made by micromachining an aspheric surface over the core region of the fiber with a CO/sub 2/ laser, as the fiber spins and is directed by computer about the beam. >

Journal ArticleDOI
TL;DR: In this paper, the authors present a control loop which ensures single-mode operation of a tunable distributed-Bragg-reflector (DBR) laser, which uses no external optics.
Abstract: The authors present a control loop which ensures single-mode operation of a tunable distributed-Bragg-reflector (DBR) laser. This control loop uses no external optics. The error signal is derived from an integrated detector which measures the light transmitted through the Bragg section. Using this signal to control the current to the Bragg section, the laser is tuned to where the side-mode-suppression ratio is high. This guarantees that the laser remains single-mode, even when modulated. This servo is capable of application in wavelength-division-multiplexed (WDM) systems. >

Patent
28 Oct 1992
TL;DR: A superfluorescent broadband fiber laser source comprises an optical fiber doped with a laser material and having one end pumped with pump light of sufficient intensity to produce amplified spontaneous emission within the fiber and forward and backward waves therefrom as mentioned in this paper.
Abstract: A superfluorescent broadband fiber laser source comprises an optical fiber doped with a laser material and having one end pumped with pump light of sufficient intensity to produce amplified spontaneous emission within the fiber and forward and backward waves therefrom. The polarizations of the backward wave experiences a 45° rotation as it travels into and another 45° rotation as it passes back out of a 45° Faraday rotator mirror device. An amplified polarization=rotated beam from the doped fiber is divided into orthogonally polarized beams in a polarization beam splitter coupler. A return polarized signal from an interferometer is passed through the doped fiber, the Faraday rotator mirror device and the doped fiber for producing a polarized output signal that has been amplified by four passes through the doped fiber.

Journal ArticleDOI
TL;DR: In this paper, an electro-optic modulation of a guided light beam has been observed in an unpoled thin film of Pb(Zr0.53 Ti0.47)O3 prepared by the sol-gel method on a [100] SrTiO3 substrate.
Abstract: Linear electro-optic modulation of a guided light beam has been observed in an unpoled thin film of Pb(Zr0.53 Ti0.47)O3 prepared by the sol-gel method on a [100] SrTiO3 substrate. For the TE1 mode of a two-mode waveguide, an effective Pockels coefficient of ∼ 50 pm/V, at a wavelength of 633 nm, was determined by the method of diffraction by an induced electro-optic Bragg grating.