Transient Two-wave Mixing Research Articles

Theory and experiment of transient two-wave mixing in Yb-doped single-frequency fiber amplifiers induced by frequency modulation

This paper presents a theoretical and experimental characterization of an instability phenomenon observed in single-frequency fiber amplifiers when the frequency of the seed laser is modulated. The instability manifests itself as fluctuating elastic back-reflections that occur only when the frequency is decreasing with time. The theory is a generalization of a coupled-mode model developed for a single-frequency fiber amplifier back-seeded with a constant frequency shift relative to the main signal. It can explain most observed features of the experiments in a qualitative and semi-quantitative way. Open questions and directions for further developments are also discussed.

Two-wave mixing in erbium-doped-fibers with spectral-hole burning at 77K

Experimental results on effective two-wave mixing (TWM) via dynamic population gratings in saturable erbium doped fibers (EDFs) at liquid nitrogen temperature (77 K) are reported. It is shown that formation of the spectral holes (SHs) by the recording coherent waves in the wavelength region 1500–1540 nm results in a complex dynamics of the transient TWM response. In addition to conventional slow, even-type response due to amplitude grating formation via spectrally uniform EDF absorption saturation we also observed a dominating contribution due to SH formation. In particular, at the recording wavelength 1527 nm the relaxation time of the SH contribution to the TWM process was significantly shorter (< 4.7 ms) and with the effective recording power ∼4 times lower than that for conventional EDF population grating.

Accelerated two-wave mixing response in erbium-doped fibers with saturable optical absorption

The contribution of the spatially uniform variation of average optical absorption to the dynamics of the transient two-wave mixing (TWM) response is considered. It is shown theoretically and confirmed experimentally that this transient effect, via dynamic population gratings in erbium-doped fibers (EDFs) can ensure a response nearly two times faster in such gratings as compared to the growth rate of fluorescence uniformly excited under similar conditions, and can also result in an additional overshot in the tail of the TWM response. This additional ‘accelerating’ contribution is of even type, and does not influence the odd transient TWM response for the refractive index component of such gratings in the EDFs reported earlier. It is also shown that this effect can be utilized to monitor the formation of the dynamic grating with an auxiliary probe wave of the essentially different non-Bragg wavelength.

Polarization insensitive homodyne detection of optical phase modulation by two-wave mixing in saturable Er-doped fiber

We report linear polarization-insensitive detection of optical phase modulation in an adaptive interferometer based on transient two-wave mixing via dynamic population gratings in saturable Er-doped fiber (EDF). The proposed simple and robust configuration has an all-fiber design based on commercially available elements which makes it promising for applications in optical fiber interferometric sensors and coherent optical communication systems. The experimentally investigated single-mode polarization-maintaining EDF arrangement operated at 1492 nm and demonstrated efficient compensation of the polarization drifts below 100 Hz.

Transient two-wave mixing in a linear configuration of an adaptive interferometer based on Er-doped fiber with saturable absorption

We report results of transient two-wave mixing (TWM) in Er-doped fibers with saturable absorption in a linear configuration of an adaptive interferometric vibrometer with essentially different powers of recording waves. The TWM signal modulation depth detected in the weak (reflected) wave was shown to be twice as strong as in the symmetric configuration with equal recording powers. In accordance with theoretical predictions, the experimentally observed TWM signal amplitude grew continuously with the fiber optical density in the whole investigated range of alpha(0)L approximately 0.2-4. At the recording wavelength 1492 nm it proved to be quite close to the theoretical limit of approximately alpha(0)L/2 for weakly absorbing fibers, and in 1-m-long fiber of high optical density reached maximal value of approximately 0.8. The TWM response time went down with the recording light power and for P(0) approximately 10 mW was in the submillisecond region.

Effective recording of dynamic phase gratings in Yb-doped fibers with saturable absorption at 1064nm

Results of investigation of transient two-wave mixing via dynamic population gratings in Yb-doped fibers with saturable absorption are reported. The recorded gratings are characterized by submillisecond formation times and at wavelength lambda = 1064 nm need cw recording light power of 1 - 10 mW scale. What is important for different applications, the dynamic gratings were found to be predominantly of a phase type with an admixture of a significantly weaker amplitude component only. As in Er-doped fibers, the amplitude grating component proved to be essentially inferior to the theoretical estimation based on the fiber optical density and saturation power.

Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption

Experimental observation of phase (i.e. refractive index) component in the dynamic gratings recorded in erbium-doped optical fiber with saturation of optical absorption is reported. We utilized configuration of transient two-wave mixing with rectangular phase modulation of one of counterpropagating recording waves, where unshifted phase grating resulted in a transient energy exchange. The reported experiments were performed with heavily doped (≈5400ppm erbium) fibers in a wide spectral range of Er3+ fundamental absorption at selected laser wavelengths 1492, 1526, 1549, and 1568nm. Relative contribution of phase grating was especially large (up to ≈100% of the maximal amplitude component) at the opposite sides of the investigated spectral range and was significantly lower in its central part. The amplitude grating was found especially strong at short wavelength side of the spectrum (i.e. at 1492nm), where the grating amplitude proved to be only two times lower than the theoretically predicted from consideration of two-level model.

Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber

Theoretical analysis of the transient two-wave mixing (TWM) of two continuous waves with rectangular phase modulation counter-propagating through the Er-doped optical fiber is presented. Approximate analytic solutions obtained for undepleted interacting waves of low power (neglecting large-scale saturation of the fiber optical absorption) and of high power (with significant spatially uniform large-scale absorption saturation) are complemented by numerical simulation for a broad region of the recording light power. The experimental dependence of the TWM efficiency on the recording power obtained for a single-mode fiber with ≃640 ppm erbium concentration and with initial optical density ≈8.4 at λ = 1526 nm demonstrated the initial, growing and decaying parts predicted theoretically. The maximum experimentally observed relative TWM signal amplitude proved to be approximately 3 times lower than expected.

Two-wave mixing via reflection population gratings

Theoretical analysis of two-wave mixing (TWM) via reflection population grating, aiming to support current experimental investigations of dynamic gratings in Erbium (Er)-doped fibers, is presented. It is shown that for low recording intensities the stationary TWM via reflection saturated absorption gratings is well described in approximation of a spatially uniform grating amplitude. The analysis of the transient TWM is performed both for rectangular and for sinusoidal phase modulation of one of the recording waves and it is shown how the recorded grating amplitude and characteristic recording time can be obtained from the detected signals. It is pointed out that the majority of the existing experimental results on TWM in Er-doped fibers are qualitatively explained within the framework of the developed model.

Observation of spatial migration of excitation in Er-doped optical fibers by means of a population grating technique

The influence of spatial migration of excitation among neighboring Er3+ ions on the dynamics of population grating formation in Er-doped optical fibers is reported. The effect manifests itself in an additional increment in the grating formation rate compared with the fluorescence growth rate observed for the same spatially uniform average light power. The experiments, performed at lambda=1549 nm in the configuration of transient two-wave mixing with two similar single-mode Er-doped fibers with significantly different erbium concentrations (approximately 640 and approximately 5600 parts in 10(6)), demonstrated the essential contribution of this effect to the grating formation rate in the latter fiber. The evaluated diffusion coefficient proved to be approximately 2.3 x 10(-9) cm2/s, which ensures effective migration of the excitation by approximately 48 nm, i.e., by approximately 18 average inter-ion distances in this fiber.

Two-wave mixing of orthogonally polarized waves via anisotropic dynamic gratings in erbium-doped optical fiber

We report on observations of transient two-wave mixing (TWM) of orthogonally polarized waves counterpropagating through an Er-doped single-mode optical fiber. Experiments were performed in a 2-m-long moderately birefringent (with beat length approximately 2 cm) Er-doped fiber without optical pumping at the laser wavelength 1549 nm. The transient TWM signal observed for crossed linear polarizations of the recording waves oriented along two orthogonal birefringence axes of the fiber (i.e., for the interference pattern with spatially modulated state of light polarization only) proved to be approximately half of that observed for parallel polarizations. Direct measurements of the transient polarization hole-burning effect (i.e., that observed for fast switching of the input light linear polarization between two orthogonal orientations of the doped fiber birefringence axes) allow us to attribute formation of the corresponding anisotropic dynamic grating to this effect.

Two-wave mixing of time-varying non-plane-wave optical fields in photorefractive materials

A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.

Picosecond degenerate two-wave mixing

Transient degenerate two-wave mixing is investigated in isotropic media by using picosecond pulses. Efficient two-wave mixing requires that the response time of the optical nonlinearity and the duration of the laser pulses be comparable. The magnitude and the direction of the energy transfer that are due to the coherent coupling of pump and probe are found to depend on the relative delay of the two pulses, the input intensity ratio, and the polarization of the pulses. The energy transfer can occur between equal-intensity input pulses, provided that one of the pulses is delayed with respect to the other.

Transient two-wave mixing in Kerr media

Transient two-wave mixing in Kerr media

Polarization-resolved coherent transient beam combination in optical Kerr media

We have observed transient, coherent beam combination by degenerate two-wave mixing of frequency-doubled Nd:YAG picosecond laser pulses in carbon disulfide, using a circularly polarized pump wave and a linearly polarized probe beam. The important role of beam polarization is observed, and its part in energy transfer is discussed. A theory that treats polarization effects in transient two-wave mixing is presented, applied to the carbon disulfide experiments, and found to be in excellent agreement with the data.

Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers

The ratio of the imaginary part to the real part of the complex nonlinear refractive index has been measured by transient two-wave mixing in acridine-orange-doped fluorophosphate glass, fluorescein-doped boric-acid glass, and ruby at argon-ion wavelengths. The method enables the individual signs of the components of the nonlinear index to be obtained. A simple theory based on a single homogeneously broadened absorption from the ground state agrees with measurements of the phase of the nonlinear index in acridine but not in fluorescein, where our data suggest that excited-state absorption plays an important role.

A simple analytic solution for transient two-wave mixing in photorefractive materials

We present a very simple solution to the coupled partial differential equations which describe the time dependence of hologram formation in photorefractive materials. The equations are solved in the strong pump beam regime and the simple expression is compared with numerical solutions over a range of typical experimental conditions.