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Self-pumped phase-conjugate fiber-optic gyro
Abstract
We describe a new type of phase-conjugate fiber-optic gyro that uses self-pumped phase conjugation. The selfpumped configuration is simpler than externally pumped configurations and permits the use of sensing fibers longer than the coherence length of the laser. A proof-of-principle demonstration of rotation sensing with the device is presented.
... Second, it gives us important implications as analyzed below. (Although in the experiment [16], the flexible fiber path was rotating and the other optical parts were not, in a similar experiment [17] all optical parts were rotating together.) The result, φ = 4πRΩL/cλ, can be re-written as φ = 4πvL/cλ where v is the speed of the moving arc segment AB. ...
With a Michelson interferometer using a phase-conjugate mirror (PCM) that reverses the uniform phase shift in a light path, we can conduct a first-order experiment of Special Relativity. Utilization of the PCM changes the basic concepts of an interference experiment. Placing a conventional partially reflecting mirror just in front of the PCM at the end of a light path, we can test the isotropy of the one-way speed of light in a system moving uniformly in a straight line and conduct the one-way Sagnac experiment. According to the reported phase-conjugate Sagnac experiment using a segment light path, we can expect that the phase shift is phi = 4pivL/clambda in the one-way Sagnac experiment with path length L and speed v, even with an increasingly larger radius of the rotation. Based on these and the experimental fact of the generalized Sagnac effect, it is very important to examine whether there is the same phase shift for the test of the one-way speed of light and the first-order experiment using the PCM in a system in straight-line uniform motion. The sensitivities of these experiments are very high.
Phase-conjugate fiber-optic gyros (PCFOG’s) use phase conjugation to compensate for reciprocal phase changes due to thermal and mechanical effects on the fiber, while at the same time. allowing for the measurement of the nonreciprocal phase shift produced by rotation. 1,2 Where the best standard fiber-optic gyros require polarization-preserving fibers and couplers to avoid polarization scrambling that is a source of noise and signal fading, the PCFOG can avoid this problem by using polarization-preserving phase conjugation. ³ This has the advantage of allowing for the use of inexpensive nonpolarization preserving, and even multimode fibers and components. ³⁻⁵ Our first objective was to demonstrate that the PCFOG is sensitive to the nonreciprocal phase shift produced by the Sagnac effect and can be used to sense rotation. A proof of concept experiment was set up for this objective using an externally-pumped crystal of barium titanate as the phase conjugator. This experiment, reported in Ref. 6, provided the first demonstration of rotation sensing with a PCFOG. In this proof of concept demonstration the length of the fiber-optic coil, and therefore the sensitivity of the gyro, was limited by the coherence length of the laser. To solve this problem we set up a PCFOG consisting of a Michelson interferometer in which the light beams from two arms travel as clockwise and counterclokwise beams respectively, in the same fiber optic coil and reflect from the same self-pumped phase-conjugator. We reported the demonstration of rotation sensing with this PCFOG in Ref. 7. Again, since phase conjugation can correct for modal scrambling, a PCFOG can use multimode fibers. However, complete correction of modal scrambling requires a polarization-preserving conjugator, ⁵ and the corresponding experimental setup of a PCFOG is complicated. To solve this problem we set up a PCFOG using a multimode fiber coil, a nonpolarization-preserving conjugator, ⁴ and a spatial filter to discriminate against the portion of the light reflected by the conjugator that does not correct for modal scrambling. This experiment, reported in Ref. 8, provided the first demonstration of rotation sensing with a PCFOG using multimode fiber.
Modal scrambling is a source of noise and signal fading in fiber-optic gyros ¹ and therefore the best fiber-optic gyros use single-mode polarization preserving fiber and couplers ² . Phase-conjugation can be used to correct for modal scrambling ³⁻⁵ and to make fiber-optic gyros ⁶⁻⁹ . In this paper we describe and demonstrate the combination of these two possiblities; a phase-conjugate fiber-optic gyro using multimode fiber.
In this paper, the grating dynamical theory of photorefractive in ring laser resonator is introduced. The condition and the reason of light beam frequency mismatching in the rotating ring resonator are researched. This rotating ring resonator can be used for optic-gyro. In the rotating process, the phase can be changed into the frequency mismatching. By measuring the frequency mismatching, the rotational angle of the ring resonator can be calculated.
All the chapters of the book, except this one, deal with permanent diffractive optical elements, i.e. elements with relative permittivity (both the refractive index and absorption coefficient) that does not depend on the light intensity. In contrast, this chapter is devoted to dynamic optical elements, which are sensitive to light. When a light beam propagates in these elements, the spatial distribution of the refractive index is changed, affecting the propagation of the beam itself at subsequent times. Materials possessing such a property are known as nonlinear optical materials. Among the variety of nonlinear optical effects discovered so far, it is only the photorefractive effect that can be observed at low optical power densities (of the order of mW/cm2). The large effective optical nonlinearity in photorefractive materials has attracted much attention in the past few years. The main purpose of this chapter is to highlight some device potentials and possibilities of practical applications of photor
We review the current status of photorefractive self-pumped optical phase conjugation in the tungsten bronze family of ferroelectric crystals. The tungsten bronze ferroelectrics have emerged as an important class of materials for performing optical phase conjugation in addition to the well known pyroelectric, piezoelectric, and electro-optic applications. The large electro-optic coefficients, open lattice structure, compositional flexibility, and good optical quality of these materials has made possible a new set of self-pumped phase conjugate mirrors. Our initial interest in this class of crystals arose from a number of enlightening discussions with Professor L. Eric Cross who pointed out the multitude of applications possible with the tungsten bronzes. We would like to acknowledge his assistance and encouragement by dedicating this paper to Professor Cross on the occasion of his 65th birthday.
Coherent beam combination through multiple-beam self-pumped phase conjugation in BaTiO3 has been demonstrated to conjugate piston error to at least λ/10. The coupling is shown to occur by a copumping mechanism.
We present experiments demonstrating reciprocity for conjugation of highly scattered light; if a fraction eta of the total scattered light is incident on a phase-conjugate mirror having reflectivity rho, then a fraction rho eta(2) returns back through the scatterer as a phase-conjugate wave, with the remaining fraction rho (eta - eta(2)) being lost due to scattering. Low efficiency results from inability to gather a large fraction of scattering, but the efficiency is higher than is possible without conjugation.
A general theory of polarization and spatial information recovery by modal dispersal and phase conjugation is presented by means of a coherency matrix formalism. The theory is applied to a system that consists of a multimode modal-scrambling fiber terminated by a conventional phase-conjugate mirror that reflects only one polarization component. The degree of polarization and the signal-to-noise ratio of the reconstructed field are discussed as a function of input-beam launching conditions. Some experimental results are also shown for comparison with the theory.
We have studied the four-wave-mixing oscillation obtained when a cell containing sodium and a buffer gas is enclosed in a ring cavity. The beat frequency Deltanu between the two counterrotating beams is shown to depend on the intensity difference (I(1) - I(2)) between the two pump beams. The curve giving Deltanu as a function of (I(1) - I(2)) is a gyrotype curve, which suggests some possible application for optical gyros.
Phase conjugation is used to correct the detrimental effects of modal scrambling in a passive optical gyro that uses multimode fiber. A proof-of-principle demonstration of rotation sensing is presented.
The author presents a tutorial review of various kinds of optical
phase conjugators using photorefractive materials. These include
externally pumped phase conjugators (EPPCs), self-pumped phase
conjugators (SPPCs), and mutually pumped phase conjugators (MPPCs). He
briefly describes optical phase conjugation and the photorefractive
effect. He also describes wave mixing in photorefractive media. The
energy transfer in two-wave mixing and the holographic nature of
four-wave mixing are discussed
Recent theoretical and experimental studies of polarization and
spatial information recovery by modal dispersal and phase-conjugation
are discussed. The fidelity of this phase-conjugation process as a
function of input-beam launching conditions is discussed. Several new
applications of the scheme which involve correction of nonreciprocal
polarization distortions, correction of lossy amplitude distortions,
phase-conjugate multimode fiber-optic interferometers and gyros,
temporal data channeling between beams, and all-optical beam
thresholding are described
Recent developments, both theoretical and experimental, involving
the nonlinear interactions of light in photorefractive crystals are
reviewed. When pumped by light beams in various configurations, certain
crystals, such as barium titanate (BaTiO<sub>3</sub>), respond with the
self-build up of gratings in the crystal and formation of new light
beams. The emphasis here is on these devices, known as photorefractive
oscillators, the mutual light-crystal interactions which govern their
operation, and all-optical applications which are based on these
oscillators
Expressions for the phase of reflection from a photorefractive phase-conjugate mirror are obtained as a function of the intensity and phase of the pump and the probe beams. The phase is independent of these parameters in common photorefractive conditions in which the index grating is spatially shifted 90 degrees with respect to the light-interference pattern. Multiple solutions exist for the phase and intensity of the reflection at large coupling strength. Oscillation conditions involving frequency detuning are obtained for the double phase-conjugate resonator (resonator formed with two phase-conjugate mirrors).
Amplification owing to holographic two-wave mixing in photorefractive crystals can be utilized to achieve unidirectional ring oscillation. Unlike for the conventional gain medium (e.g., He—Ne), the gain bandwidth of photorefractive two-wave coupling is very narrow (a few hertz for BaTiO3). Despite this fact, the ring resonator can still oscillate over a large range of cavity detuning. A theory is presented that describes how the oscillating mode attains the round-trip phase condition.
A new optical rotation sensor is described. It is a ring passive phase conjugator in which the ring may consist of a multimode fiber. A nonreciprocal phase shift in the ‘‘passive’’ like fiber ring activates a grating movement and subsequent frequency detuning of the beams in a photorefractive four‐wave mixer. This device has the advantages of natural reciprocal behavior of phase conjugate beams (essential for rotation sensing) and has several adjustable controlling parameters. It reveals a new class of interferometry in which changes in the ring’s optical phases, the beam’s intensities and losses, and the mixing crystal’s efficiency and electric field modulate a frequency detuning of the oscillating beams.
The first demonstration of rotation sensing with a fiber-optic gyro that
uses the phase-reversal property of polarization-preserving phase
conjugation is reported. In this system, the severely scrambled waves
are restored to their original state of polarization, and the signal
fading and noise due to polarization scrambling is eliminated without
the need for polarization-preserving fiber. In the experimental setup,
an argon laser provides the pumping waves for degenerate four-wave
mixing, and a phase-conjugate reflectivity of 50 percent and a response
time of 0.1 s are obtained. The expected rotation-induced Sagnac phase
shift is achieved within the experimental uncertainties.
Using a single self-pumped crystal of barium titanate, we demonstrate a method for producing the phase conjugate of an incident wave having arbitrary polarization. Our experimental results show that the phase-conjugate wave produced by this method reproduces both the ellipticity and the helicity of the polarization of the incident wave.
Photorefractive resonators exhibit an extremely small frequency difference (Deltaomega/omega~10(-15)) between the oscillating and pumping beams. The observed frequency difference is proportional to cavity-length detuning. This dependence is explained by a photorefractive phase shift that is due to slightly nondegenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for steady-state oscillation. The measured onset or threshold of oscillation as a function of photorefractive gain and intensity agrees with theory.
A new type of interferometer has been constructed that uses a beam splitter and two self-pumped BaTiO(3) crystals as phase-conjugate reflectors in place of the usual interferometer mirrors. Counterpropagating beams of light are spontaneously generated between the two crystals, coupling the pair of phase conjugators. This optical oscillation locks the relative phase of the two phase-conjugate reflections such that they recombine at the beam splitter to form only a single beam as though they were truly time-reversed waves.
A fiber gyroscope is reported that uses polarization-holding fiber in the coil, the phase modulator, and the coupler. The random-drift coefficient, calculated from rms noise levels, was 8.10(-4) deg/ radicalh, within a factor of 2 of an experimentally determined quantum and thermal limit. White-noise behavior was observed for integration time constants from 1 to 40 sec. Device characteristics and performance are presented.
Continuous-wave phase conjugation of an image-bearing beam is demonstrated using a single-domain crystal of BaTiO(3) and nothing else. The device operates by four-wave mixing using the photorefractive effect but without any external pumping beams or external mirrors. The customary pumping beams are derived from the incident beam and are internally reflected inside the crystal adjacent to an edge. The device is self-starting and has a phase-conjugate reflectivity of 30%. Imaging applications are discussed.
We present a theoretical analysis of a ring laser incorporating a wave-front-conjugating coupling element between the counterpropagating waves. Our results demonstrate the possibility both of using a homogeneously broadened laser, such as a solid-state or dye laser, and of a substantial reduction in lock-in frequency.
Fiber-optic rotation sensing with an extrapolated drift of 1 deg/h½ is accomplished by operating the Sagnac interferometer from a truly single-mode common input-output port in connection with a phase-modulation scheme and active polarization stabilization.
The principles of operation of fiber-optic gyroscopes are reviewed. Performance-limiting phenomena are discussed along with methods to reduce their effect on the rotation-rate signal. Current technology and performance of state-of-the-art systems are presented. Finally, a direction of future research and possible applications are indicated.