Nonlinear Mach-Zehnder Interferometer Research Articles

All-optical 1 × N switching device by use of the phase modulation of spatial solitons

We proposed a new all-optical switching device by using the phase modulation of spatial solitons. The proposed structure is composed of an asymmetric nonlinear Mach-Zehnder interferometer (NMZI) with different lengths for the two arms, the uniform nonlinear medium, and the nonlinear output waveguides. The asymmetric NMZI functions like a phase shifter. The all-optical switching scheme employs angular deflection of spatial solitons controlled by phase modulation created in the asymmetric NMZI. By properly launching the input power and varying the lengths of the delay branch and the uniform nonlinear medium, it is possible for this device to be generalized to a 1 x N all-optical switching device.

Decoherence of the field in quantum nondemolition photon number measurement using the Kerr nonlinearity

The role of decoherence of an electromagnetic field in the process of quantum nondemolition measurement of the number of photons using a nonlinear Mach-Zehnder interferometer is investigated. This decoherence is caused by distributed losses in a Kerr medium. A long interaction time between the field and the medium is required to achieve a high accuracy in the photon number measurement. The losses in the Kerr medium accompanying the resonance four-wave interaction between the measured and the probe fields lead to a measurement error close to unity at γτ ≫1 (γ is the rate of losses in the medium, and τ is the time of interaction between the field and the medium); consequently, nondemolition quantum measurement turns out to be impossible in the scheme considered. Under these conditions, an increase in the intensity of the probe field does not result in achievement of the required measurement accuracy.

Noise figure of phase-sensitive parametric amplifier using a mach-zehnder interferometer with lossy kerr media and noisy pump

The noise figure (NF) of a phase-sensitive parametric amplifier using a nonlinear Mach-Zehnder interferometer (NMZI) with Kerr media is analyzed for amplitude-modulation signals. In the analysis, the distributed loss of the Kerr media and the excess noise of the pump light are taken into account. As for the distributed loss of the Kerr media, the quantum Langevin equation for the NMZI is derived and solved. The results elucidate a simple degradation factor in the NF representation of the amplifier. This factor implies that the NF can be less than the standard quantum limit (SQL) of 3 dB, even if the total loss of the Kerr media exceeds 3 dB. As for the excess noise of the pump light, the semi-classical small signal analysis is utilized. The results clearly indicate that the signal-to-noise ratio of the pump light must be four times higher than that of the input signal in order to realize a low-noise optical amplifier under the SQL of 3 dB.

A Mach-Zehnder-interferometer-based low-loss combiner

Passive optical combiners have an unwanted 3-dB loss. This is avoided with optical switches, but these need control functions to synchronize with the optical signals. A nonlinear Mach-Zehnder interferometer can provide the combiner function without control signals. In the experiment reported here, this combiner was realized with a fiber component. Semiconductor optical amplifiers (SOAs) acted as the nonlinear phase shifting elements. Thus a proof-of-principle for the self-routing combiner is obtained: optical signals on either of the two input ports are guided to one and the same output port without any control mechanism in the interferometer. The nonlinear effect used is self-phase modulation, caused by carrier depletion in the SOAs as they approach saturation. The optical power at which the nonlinear switching occurred was about -2 dBm. The residual combiner loss was only 0.7 dB.

Interferometry of spontaneous parametric light scattering

The interference of biphotonic light produced in the process of spontaneous parametric scattering (SPS) in two spatially separated non-centrally symmetric crystals is considered. A scheme of the nonlinear Mach—Zehnder interferometer is realised. It is shown that in this case, the frequency-angular intensity distribution in the far-field zone (the SPS spectrum) contains information not only on non-centrally symmetric crystals, where biphotonic fields are created, but also on the optical properties of the medium located between the scattering crystals. The algorithms for the determination of the dispersion law in this medium are developed.

Magneto-optical control of bright atomic solitons

In previous work we showed that bright atomic solitons can arise in spinor Bose-Einstein condensates in the form of gap solitons even for repulsive many-body interactions. Here we further explore the properties of atomic gap solitons and show that their internal structure can be used to both excite them and control their centre-of-mass motion using applied laser and magnetic fields. As an illustration we demonstrate a nonlinear atom-optical Mach-Zehnder interferometer based on gap solitons.

Efficient nonlinear phase shifts due to cascaded second-order processes in a counterpropagating quasi-phase-matched configuration

A counterpropagating quasi-phase-matched configuration is examined that is capable of efficiently producing second-order cascaded nonlinear phase shifts with minimal power lost to the second harmonic. For all-optical switching in a nonlinear Mach-Zehnder interferometer, the calculated minimum input power needed for switching (i.e., to yield a +/-pi/2 phase shift) is 40 times smaller than the power needed in the standard typeI copropagating configuration. The throughput of this counterpropagating device is 96% at the optimum switching point.

Effects of group-velocity dispersion in all-optical switching devices using highly nonlinear optical waveguides

The effects of group-velocity dispersion (GVD) in nonlinear Mach–Zehnder interferometers and nonlinear directional couplers composed of highly nonlinear optical waveguides are analyzed. The criteria for avoiding the switching-performance degradation that results from GVD-related effects are clarified in terms of the lowest soliton order N. The major factor that restricts the lowest N value depends on the device configuration as well as on the extent of the walk-off between the gate and the signal pulses. The lowest switching energy can be estimated by use of the lowest N value and a figure of merit of the nonlinear material.

Squeezed light generation by means of cascaded second-order nonlinearity

This paper shows that the experimental configuration for self-diffraction experiments can be applied to squeezed light (SL) generation. Nonlinear processes arising from cascading of the second order χ (2) nonlinearity are responsible for the pump waves squeezing far from the perfect phase matching points for second harmonic and sum frequency generation. The operation of squeezing is performed by interference of co-travelling waves which depending on phase matching conditions for the cascaded processes, are affected either by self-phase modulation (SPM) (as in the nonlinear Mach-Zehnder interferometer) or by cross-phase modulation (CPM) (as in the type-II phase matched second harmonic generation scheme). Since large values of induced third order nonlinearities χ ind (3) are manifested in the presence of cascaded χ (2), this scheme of SL generation may be of great practical interest. Diffracted waves may also be used to create squeezed vacuum.

Quantum-nondemolition measurements and the "collapse of the wave function"

This paper intends to clarify some issues in the theory of quantum measurement by taking advantage of the self-consistent quantum formulation of nonlinear optics. A quantum-nondemolition measurement of the photon number of an optical pulse can be performed with a nonlinear Mach-Zehnder interferometer followed by a balanced detector. The full quantum-mechanical treatment shows that the shortcut in the description of the quantum-mechanical measurement, the so-called ``collapse of the wave function,'' is not needed for a self-consistent interpretation of the measurement process. Coherence in the density matrix of the signal to be measured is progressively reduced with increasing accuracy of the photon-number determination. The quantum-nondemolition measurement is incorporated in the double-slit experiment and the contrast ratio of the fringes is found to decrease systematically with increasing information on the photon number in one of the two paths. The ``gain'' in the measurement can be made arbitrarily large so that postprocessing of the information can proceed classically.

All-optical switching devices based on large nonlinear phase shifts from second harmonic generation

We show that the large nonlinear phase shifts obtained from phase-mismatched second harmonic generation can be used to implement all-optical switching devices such as a nonlinear Mach–Zehnder interferometer and a nonlinear directional coupler.

Quantum limits to all-optical switching in the nonlinear Mach–Zehnder interferometer

A Mach–Zehnder interferometer with a nonlinear medium in each arm is treated as an all-optical switching device. In a classical treatment, the interferometer can, in principle, operate as an ideal switch, but quantization of the electromagnetic fields limits the switching capability. In this treatment we illustrate the fundamental quantum limits that apply to switching in all-optical devices by studying the nonlinear Mach–Zehnder interferometer. In particular the input states are assumed to be coherent states and the reduction in the quality of the switching device is discussed.

Entangled coherent states.

The nonlinear Mach-Zehnder interferometer is presented as a device whereby a pair of coherent states can be transformed into an entangled superposition of coherent states for which the notion of entanglement is generalized to include nonorthogonal, but distinct, component states. Each mode is directed to a homodyne detector. We show that there exist nonclassical intensity correlations at the output ports of the homodyne detectors which facilitate a test of local realism. In contradistinction to previous optical schemes which test local realism, the initial state used here possesses a positive Glauber-Sudarshan representation and is therefore a semiclassical state. The nonlinearity itself is responsible for generating the nonclassical state.

All-optical switching in a 200-m twin-core fiber nonlinear Mach–Zehnder interferometer

All-optical switching is demonstrated in a 200-m-long fiber nonlinear Mach-Zehnder interferometer. The only stabilization mechanism used is passive enclosure of the interferometer. Stable operation is obtained by using a twin-core fiber. The experiment demonstrates the feasibility of use of fiber nonlinear Mach-Zehnder interferometers for ultrafast switching and pipeline logic.

Noise reduction in quantum nondemolition measurement with a nonlinear Mach–Zehnder interferometer using squeezed vacuum

A quantum nondemolition measurement of photon number taken with a nonlinear Mach–Zehnder interferometer is analyzed. When this interferometer is excited by a coherent input, it shows a large amount of noise, caused by the self-phase modulation. We demonstrate how this noise can be suppressed by applying a squeezed vacuum to the unexcited port of the interferometer.

Generation of sub-Poissonian photon number distribution.

An optimization of a nonlinear Mach-Zehnder interferometer to produce sub-Poissonian photon number distribution is proposed. We treat the system quantum mechanically and estimate the mirror parameters, the nonlinearity of the medium in the interferometer, and the input power to obtain minimal output uncertainty in the photon number. The power efficiency of the system is shown to be high.

Squeezing of pulses in a nonlinear interferometer

A symmetric nonlinear Mach–Zehnder interferometer containing a Kerr medium performs the operation of squeezing. The operation is performed by the interference of cotraveling waves, and the pump wave is removed. This mechanism is broadband. We analyze the operation of the interferometer and determine the degree of shot-noise reduction achieved in a balanced detector. A modification of the interferometer into a fiber ring reflector is described that accomplishes the squeezing and the pump separation.

Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer.

The output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty. This interferometer includes an optical Kerr medium in one arm with a coherent-state input. Unusual ``crescent''-shaped squeezing which preserves photon number is revealed in the unitary evolution associated with a self-phase-modulation in the Kerr medium. Photon-number uncertainty 〈\ensuremath{\Delta}n${^}^{2}$〉 can be reduced by interference with a coherent-state reference wave. It can be minimized to 〈n^${〉}^{1/3}$, far below the limit 〈n^${〉}^{2/3}$ achieved by an ordinary squeezed state. The increased phase uncertainty due to self-phase-modulation and the reduced photon-number uncertainty still preserve the minimum-uncertainty product 〈\ensuremath{\Delta}n${^}^{2}$〉〈\ensuremath{\Delta}\ensuremath{\Phi}${^}^{2}$〉\ensuremath{\sim}(1/4). .AE