Two-mode Operator Research Articles

Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers

We investigate theoretically the static and dynamic characteristics of an optically injected vertical-cavity surface-emitting laser (VCSEL), under both single- and two-mode operation. Our model includes the spatial dependence of both the carrier density and the optical field. We find that within the locking range, a two-mode VCSEL can be forced to operate in a single transverse mode under appropriate conditions. Outside the locking range, the VCSEL shows a rich variety of nonlinear dynamics. Results show that the static and dynamic behaviours depend strongly on the frequency detuning, the injection power and the strength of the intermodal coupling induced by spatial hole burning. In particular, strong intermodal coupling can reduce the sensitivity of the VCSEL toward external injection, in terms of both static (locking) and dynamic (nonlocking) behaviours.

Probe measurements of local carrying gas fraction in trickle-bed reactor

The possibility of measuring local carrying gas fraction in a pilot-size trickle-bed reactor was explored. The reactor bed was randomly packed with equal-size spherical particles. The two-phase mixture was composed of air and water. The carrying gas phase was detected by resistivity probes mounted in pores. To reduce the eventual bias caused by a localized flow the regime in a single pore, the local carrying gas fraction was defined by the allowability criterion, which relies on the correlation of the flow regime in a single pore with those of the surrounding pores. For this purpose the probes were fixed in an arrangement with the scale length greater than the particle diameter. Phase discrimination in different two-phase flow regimes was carried out by using the principles of artificial intelligence. A statistical analysis of probe signals revealed possible two-mode reactor operation. The results showed that local carrying gas fraction measurements in a pilot-size trickle-bed reactor over different modes of operation are possible. A comparison of the integrated carrying gas fraction profile with the global gas saturation showed rather good agreement.

Two-Mode Wigner Operator in <η| Representation

We derive the <η| representation of two-mode Wigner operator, where the <η| state is the common eigenstate of two particles' relative position and total momentum. By virtue of this representation we can conveniently obtain Wigner functions of some two-mode states and the Weyl correspondence functions of two-mode unitary phase operators.

Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers

We present a numerical study of the effects of optical feedback on the static and dynamic characteristics of vertical-cavity surface-emitting lasers (VCSELs) under both single-mode and two-mode operations. Our model includes transverse effects such as carrier diffusion and spatial hole burning (SHB) and is therefore capable of including gain-saturation-induced coupling among transverse modes. For short external cavities (/spl sim/30 /spl mu/m), optical feedback can completely suppress higher-order transverse modes. For relatively long external cavities (/spl sim/1 cm), VCSELs follow a period-doubling route to chaos. Numerical results show that multimode VCSELs exhibit self-pulsations at higher feedback levels compared with the single-mode case.

Highly Sensitive and Widely Dynamic Fiber-Coiled Deformation Sensor Immune from External Disturbances

This paper describes a double fiber-coiled interferometric deformation sensor fabricated using paired polarization maintaining single-mode fibers. A change in bending-induced birefringence plays a fundamental role in the sensor performance as the fiber-coil is being deformed across its cross-section. Differential optical heterodyne detection processes allow us to implement two-mode operations; one is widely dynamic operation and the other highly sensitive operation around a target region. The deformation sensitivity for one-turn fiber-coil is 2.5 deg/mm for the widely dynamic operation, whereas 9.5X10 deg/mm for the highly sensitive operation. The double fiber-coiled deformation sensor can eliminate external, undesirable temperature disturbances.

Polarimetric Er^3+-doped fiber distributed-feedback laser sensor for differential pressure and force measurements

We propose and demonstrate a polarimetric Er(3+) -doped fiber distributed-feedback laser sensor in which a force applied transversely along the fiber laser induces a birefringence that gives rise to a change in the beat frequency between the two orthogonally polarized laser modes. We measure a sensitivity of ~9.6 GHzysNymmd, a wide dynamic range with stable two-mode operation for frequency separations up to 50 GHz, and high sensor resolution owing to the narrow beat frequency bandwidth of <10 kHz. The temperature sensitivity is dominated by the temperature dependence of the inherent birefringence, which was measured to be -130 kHz/ degrees C. The sensor permits independent pressure-force and temperature measurements.

A convenient representation for the two-mode phase operator [formula omitted

We find a representation in which the two-mode phase operator ( a + b †) ( a † + b) manifestly exhibits its phase behavior. With this representation, the phase operator is more applicable to further illustrating the Shapiro-Wagner phase measurement approach. The technique of integration within an ordered product of operators is essential in our discussion.

Increased threshold for the first-order lateral mode lasing in low-ridge waveguide high power QW lasers

A self-consistent two-dimensional model is extended to include two-mode operation and is applied to study the characteristics of ridge-waveguided high power InGaAs-GaAs quantum-well lasers. This work provides physical insight into the most recent experimental result that use low-ridges and thin p-claddings to give high single lateral mode output and a low threshold.

Fock representation for two-mode quantum phase operators' eigenstates

The quantum phase description of Noh, Foug?res and Mandel (NFM) leads to a two-mode theory of phase in the strong local oscillator limit. We show that the explicit form of the eigenstates of the sine and the cosine phase operators in two-mode Fock space can be constructed. This brings great convenience to the NFM quantum phase approach.

Linear Cold-Fluid Theory of a Free-Electron Laser11The project supported by National Natural Science Foundation of China and Natural Science Foundation of Gansu Province

The linear cold-fluid theory of a free-electron laser is given where the laser field must be in the two-mode operation. The ration between the two modes of laser field is obtained. The dispersion relation is discussed in the Raman- and Compton-regimes and the space-charge wave theory is worked out.

双光子双模激光的朗之万理论

Mode coupling of a two-photon two-mode laser operating near above threshold is discussed with Langevin quantum theory. Characteristics of the coupling shows not only the mutual enhancement of the two modes, as well as the enhancement of mode 2 with suppre

Nonclassical properties of nondegenerate parametric oscillators and amplifiers using two-mode operators

Two-mode quadrature-phase amplitudes are used to describe two-mode squeezing in nondegenerate parametric amplification and oscillation with linear absorption losses. A comparison with the usual description by means of one-mode operators is performed and the relation between two-mode operators and heterodyne detection is discussed. The generalized Fokker-Planck equation for the Wigner quasiprobability distribution has been obtained in terms of the two-mode variables and second-order correlations are discussed. Intra-and inter-beam second-order coherences are given and the intensity fluctuations in the difference of the signal and idler photocurrents calculated. Limits on the simultaneity in the coincidence detection are discussed and finally, it is shown that the quadrature-phase amplitudes are the complex amplitudes for the quantities measured by heterodyne detection.

From photon counts to quantum phase

We derive an exact expression for the joint count probability in an eight-port homodyne detector, when the signal field is in an arbitrary state, the local oscillator is in a coherent state and the other two input states are the vacuum. In the limit of a strong local oscillator this photon count statistics is the scaled Q-function of the signal state. The phase distribution corresponding to this measurement scheme is then the Q-function of the signal field integrated over radius. The physical reason for the Q-function lies in the simultaneous measurement of two two-mode operators. We discuss the dependence of the photon count statistics on the local oscillator intensity using the example of a one-photon Fock state.

Squeezing in the triatomic linear molecule model revealed by virtue of the IWOP technique

For a typical triatomic linear molecule with different atomic masses one finds a unitary operator which is closely related to squeezing transformations caused by frequency jumps. The coordinate representation of the unitary operator is identified, which provides an alternative approach for calculating the wavefunction of internal motion of the molecule. The author also shows that the unitary operator is equivalent to a two-mode squeezing-rotating combination operator multiplied from the right by two single-mode squeezing operators. The discussion is mainly based on the technique of integration within an ordered product (IWOP) of operators.

Dynamics of a two-mode two-photon Jaynes–Cummings model interacting with correlated SU(1, 1) coherent states

We study the quantum dynamics of a two-mode two-photon Jaynes–Cummings model of a two-level atom interacting with the correlated two-mode SU(1, 1) coherent states. The collapse and revival patterns in this case are noted to be quite different from those in the case of uncorrelated coherent states and correlated pair-coherent states. As an example of the time evolution of the field statistics we show that violation of the Cauchy–Schwartz inequality by the initial field states may be nullified. We also discuss the evolution of the variance of the two-mode field quadrature operator.

Intermodal tuning behavior of an etalon-tuned three-mirror TEA CO/sub 2/ laser

The detailed tuning behavior within a single ro-vibrational line of a TEA CO/sub 2/ laser was studied by using a wedged etalon and a pyroelectric array. The fine tuning of the laser was performed by using a temperature controlled etalon inside a three-mirror resonator. As the laser wavelength was scanned at a constant rate, single-longitudinal-mode pulses were observed approximately 82% of the time. Two-mode operation occurred over a narrow tuning range near the midpoint between successive cavity modes. The detailed structure of the staircase-like mode-to-mode tuning curve and the corresponding output intensity variations are explained using a simple theoretical model. >

Steady-state and superradiant many-mode dynamics in a high-gain amplifier with a waveguide

We investigate many-mode dynamics in the steady-state and superradiant regimes of an FEL with a rectangular waveguide for high-gain amplification of microwave radiation. At steady state a recent many-mode Hamiltonian formulation allows us to derive analytical results for two-mode (TE 01 + TE 21) operation, such as the instability threshold for exponential gain, and to explain the main many-mode effects, i.e., higher peak powers, reduced saturation lengths and broader accessible energy ranges, compared with the amplification of the fundamental (TE 01) mode alone. Numerical investigation shows that multimode excitation leads to enhanced peak powers and shortened dynamics also both in strong and in weak superradiance. In these regimes, differently from steady-state, the fundamental TE 01-mode exhibits higher peak powers and efficiencies when higher-order modes are present.

Self-consistent cold-fluid theory of a free-electron laser

The self-consistent cold-fluid theory of a free-electron laser is given and the dispersion relation is obtained and discussed in this paper, where the laser field must be in the two-mode operation.

Two-mode adaptive beamformer using a systolic array

An adaptive beamformer using the least squares algorithm usually employs exponential windowing of the input data. In the paper, the authors show that complete suppression of interferences is impossible when an exponential window is applied. To avoid this, a two-mode operation using a systolic array is proposed. Switching is made from an adaptive mode to a frozen mode when the system converges and vice versa when the radio environment changes, by monitoring the change in the magnitude of one of the weights. The proposed method gives exact extraction of the desired signal and is capable of fast suppression of new interferences.

A hamiltonian model of FEL many-mode dynamics in a high-gain amplifier with a waveguide

Free Electron Laser dynamics is investigated in the presence of a rectangular waveguide for high-gain amplification of microwave radiation. Scale hamiltonian equations for the electrons and many radiation modes are derived in the steady-state Compton regime. In the relevant case of two-mode (TE 01 + TE 21) operation, the linear theory predicts the instability threshold of the system and explains basic effects of mode competition, such as higher peak powers, broader accessible energy ranges and reduced saturation lengths, compared with the amplification of the fundamental (TE 01) mode alone.