Theoretical study of ultrafast index dynamics in semiconductor optical amplifiers

Analysis of non-linear refractive index influences on four-wave mixing conversion efficiency in semiconductor optical amplifiers

Development of modern optical fiber networks puts an increasing demand on the optical hardware. All-optical signal processing components enable the highest switching rates and allow all-optical regeneration of pulse streams without converting the optical signal into electrical current. The subject of our research is self-switching in a Mach-Zehnder interferometer (MZI) and its applications in optical telecommunication networks. In this device, light injected in one of the input ports is unequally distributed over the two interferometer arms. Due to the intensity dependent refractive index in the interferometer arms, there can be a nonlinear phase shift induced between the optical signals of unequal intensities. The two signals therefore interfere destructively or constructively depending on the input power: in this way we obtain nonlinear self-switching. Two mechanisms of nonlinear phase shifting were considered: active, based on semiconductor optical amplifiers (SOAs), and passive, based on quantum dots (QDs). Interferometers of two types were developed: 2-to-2 (two input ports and two output ports) and 2-to-1 (two input ports and one output port). The 2-to-2 SOA-MZIs based on self-switching have been investigated for two applications. One of them is the pattern effect compensator. If SOAs are employed for all-optical signal amplification, e.g. in optical access networks, an unwanted pulse distortion (known also as the pattern effect) takes place, as a result of the SOA gain saturation. Our component allows pattern-free amplification of the optical signals at bitrates up to 20 Gb/s. At 10 Gb/s it shows an extended input power range (up to 7 dB improvement) and comparable gain, which makes it suitable to be used as an optical amplifier. Another application of the 2-to-2 SOA-MZI is a 2R-regenerator. Optical amplifiers used in long distance optical links add noise to the optical signal, causing signal degradation. The signal can be regenerated by passing it through an optical gate with a nonlinear transfer function. The 2-to-2 SOA-MZI has such a nonlinear transfer function. The regeneration capabilities were demonstrated at 2.5 Gb/s by an improvement of the receiver sensitivity of about 2.5 dB. The dynamic characterization of the chips was carried out in a close cooperation with the research group COM at the Technical University of Denmark within the ePIXnet "network of excellence". The 2-to-1 MZI based on self-switching can be used as a low-loss optical combiner. An essential function in optical fiber networks is the combining of optical signals. A serious disadvantage of the conventional type of combiners used in the networks is that they let only half of the power (3 dB) through. In order to compensate for this loss, passive optical combiners are often used in combination with an in-line SOA. The first realization of the low-loss optical combiner uses SOAs as active phase shifters. Such an active low-loss combiner shows an improvement of transmission of over 2 dB compared to a conventional combiner with an in-line SOA. It is therefore expected that the output optical signal-to-noise ratio of the self-switching SOA-MZI is more than 2 dB better than that of a conventional combiner with an in-line SOA. While for the pattern effect compensator and the 2R-regenerator SOAs are used not only for inducing the nonlinear phase shift, but also for sufficient amplification, for the low-loss optical combiner the preferred nonlinear effects should be passive: combination of the signal is a passive function. Therefore, the second realization is based on a novel material, quantum dots. QDs provide improved all-optical nonlinearities resulting in a very small switching energy and large refractive index changes. Such a passive 2-to-1 QD-MZI based on self-switching showed an improvement up to 1.7 dB with respect to a conventional combiner. These improvements have a huge effect on e.g. the power budget in passive optical networks, where a large number of splitting stages are required. The Mach-Zehnder interferometers were realized in the InP/InGaAsP semiconductor material system, which is perfectly suitable for the integration of the photonic integrated circuits for the telecommunication applications. In order to realize both active components (such as e.g. SOAs) and passive components (such as e.g. waveguides, couplers), an active-passive integration technique was applied. This integration was realized in a close cooperation between JDS Uniphase Eindhoven and the COBRA Research Institute. It employs a three-step metal-organic vapor-phase epitaxy regrowth process. The quantum dot material was grown within the COBRA Research Institute. Our MZIs use a ridge waveguide design, for which a reactive ion etching process was developed in the COBRA cleanroom. As a result of photonic integration our integrated Mach-Zehnder interferometers have very small dimensions: less than a square millimeter.

Linear and nonlinear optical absorption coefficients and refractive index changes in asymmetrical Gaussian potential quantum wells with applied electric field

Intersubband optical absorption coefficients and refractive index changes in modulation-doped asymmetric double quantum well

Gain and phase dynamic characteristics in the compressive, unstrained and tensile strained InGaAs-InGaAsP quantum well (QW) semiconductor optical amplifiers (SOAs) are theoretically investigated via a detailed model. Based on the calculation of energy band structure, the effects of compressive and tensile strain on the differential gain and the derivative of refractive index change are investigated. It is demonstrated that the compressive strained QW SOA shows the fastest gain recovery rate and the largest phase change. That is because the SOA has the characteristics of the largest differential gain and the smallest derivative of refractive index change. In addition, the ultrafast recovery process due to the carrier heating effect can be enhanced significantly in the tensile strained QW SOA.

The amplification of super-Gaussian pulses in a system of bit rate 40 Gb/s with duty cycle 0.5 by traveling-wave semiconductor optical amplifier (TW-SOA) is investigated. The carrier wavelength of the super-Gaussian pulse is 1550 nm. Simulative results related to pulse broadening due to nonlinear self-phase modulation (SPM) phenomenon are analyzed and compared. This paper analyses the issues of super-Gaussian pulse and spectrum distortion in semiconductor optical amplifiers (SOA). It is shown that the amplified super-Gaussian pulse shapes and their spectra are depended on the length of SOA and compared the results with the published work.

This paper presents the development of several multilayer feed-forward artificial neural network (ANN) models aimed at the simulation and parametrization of semiconductor optical amplifiers (SOAs). In the direct approach, it is assumed that the SOA physical parameters are known, and the ANNs can reproduce the results of detailed SOA models up to 20 times faster. In the inverse approach, it is assumed that the SOA is a grey-box with a known model but unknown parameters, and the ANNs infer the SOA model parameters from the input-output data. These results provide efficient surrogate models to represent SOAs in future digital twins for on-line optimization of ultra-wide band transmission systems that employ the SOA as the repeater element.

This study explores how hydrostatic pressure, temperature, incident light intensity, and structural parameters modulate optical absorption coefficients and refractive index changes in GaAs/Al0.3Ga0.7As spherical quantum dots under the screened cosine Kratzer potential. We use the Nikiforov-Uvarov method to solve the Schrödinger equation to determine the relevant wave functions and energy levels. And using iterative method and density matrix theory, we derived analytical expressions for the optical absorption coefficients and refractive index changes. The results of the numerical analyses demonstrate that both the structural parameters of the quantum dots and the external environmental factors significantly influence the optical absorption coefficients and refractive index changes, with varying degrees of impact. It is particularly noteworthy that these factors are extremely important for modulating the peak amplitude and resonance peak position of the optical absorption coefficients and refractive index changes, providing important theoretical basis for us to deeply understand and modulate the nonlinear optical properties of quantum dots.

A theoretical model is presented to analyze the noise suppression characteristics in cross-gain-compression (XGC)-based regenerators, where an optical bandpass filter (BPF) is cascaded after a semiconductor optical amplifier (SOA). Analytical expressions of variance are obtained for in-phase and quadrature noises after SOA and after filter. The result shows that the physical mechanism behind XGC-based noise suppression is that gain change in the SOA is out of phase with the input power fluctuation, which leads to a negative cross-correlation term in the expression of in-phase noise variance at SOA output. On the other hand, nonlinear phase noise introduced by refractive index change in the SOA will contributes to quadrature noise, which is proportional to the square of the linewidth enhancement factor ~ αN2. It is proposed that a slightly blue-shifted optical BPF can convert phase/quadrature noise-related frequency chirp into amplitude fluctuation that can cancel a part of the amplitude fluctuation after SOA, thus lead to further reduction of in-phase noise. This mechanism can be used to alleviate the negative effect of SOA-induced nonlinear phase noise and enhance the overall noise suppression performance of XGC-based regenerators, which is experimentally and numerically demonstrated at 10 Gbit/s.

We have numerically analyzed nondegenerate four-wave mixing (FWM) among short optical pulses in a semiconductor optical amplifier (SOA) by the finite-difference beam propagation method (FD-BPM). We used the nonlinear propagation equation taking into account gain spectrum dynamic gain saturation which depends on carrier depression, carrier heating, and spectral hole-burning, group velocity dispersion, self-phase modulation, and two-photon absorption. To analyze FWM in an SOA, the evolution in time and spectral domain of two input optical pulses with different frequencies during propagation was calculated. From this simulation, it has become clear that the method me used here is a very useful technique for simulating FWM characteristics in SOA's. We also found that the wavelength dependence of the gain is crucial if the detuning is larger than 1 THz.

Four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) has several important features, such as, high speed and high FWM conversion efficiency as well as optical demultiplexing (DEMUX) (Mecozzi et al., 1995; Mecozzi & Mrk, 1997; Das et al., 2000). The are several applications of FWM in SOAs for all-optical devices, such as, wavelength converters (Vahala et al., 1996), optical samplers (Inoue & Kawaguchi, 1998), optical phase conjugators (Kikuchi & Matsumura, 1998) and optical multiplexers/demultiplexers (Kawanishi et al., 1997; Kawanishi et al., 1994; Morioka et al., 1996; Uchiyama et al., 1998; Tomkos et al., 1999; Kirita et al., 1998; Buxens et al., 2000) have been demonstrated for optical communication systems. When a pulse of a time-multiplexed signal train (for example, a probe pulse) and a pump pulse are injected simultaneously into an SOA, gain and refractive index in the SOA are modulated and an FWM signal is generated by the modulations. Thus, we can obtain a demultiplexed signal as an FWM signal at the output of SOA. All-optical demultiplexing has been experimentally demonstrated up to 200 Gbit/s (Morioka et al., 1996). Tomkos et al., (Tomkos et al., 1999) suggested a number of ways to improve the performance of the dual-pump demultiplexer at 40 Gbit/s as follows; adjustment of the input wavelengths at the peak gain wavelength of the SOA under saturation conditions, the use of higher pump power at the input of the device, or/and the use of pulsed pumps with short pulsewidths. For the higher bit-rate, the overlap of the input to the FWM signal pulses may appear both in the time and spectral domain. The pattern effect may also appear in the FWM signal due to the slow components of the optical nonlinearities in SOAs (Saleh & Habbab, 1990). These effects degrade the usefulness of the FWM in SOAs as a practical DEMUX device in optical network/ communication systems. Therefore, it is very important to analysis the optical DEMUX characteristics based on FWM in SOAs for the ultrafast multi-bit input optical pulses.

Due to the limitations of measurement equipment and the influence of factors such as the environment and target, measurement errors may occur during the data acquisition process of airborne LiDAR bathymetry (ALB). The refractive index of water is defined as the propagation ratio of the speed of light waves in a vacuum to that in water; this ratio influences not only the propagation speed of the laser pulse in water but also the propagation direction of the laser pulse entering water. Therefore, the influence of refractive index changes in water on the ALB errors needs to be analyzed. To this end, the principle of ALB is first briefly introduced. Then, the calculation method for the refractive index of water is described with Snell’s law and an empirical formula. Finally, the influence of refractive index changes on ALB errors is analyzed using the derived formula at the water–air interface and in the water column. The experimental results showed that in a constant elevation of 50 m for a bathymetric floor, the refractive index changes in water caused by temperature, salinity, and depth are less than 0.001. The maximum bathymetric error and maximum planimetric error caused by the refractive index changes at the water–air interface are 0.036 m and 0.015 m, respectively. The ALB errors caused by refractive index changes in the water column are relatively low, and the water column does not need to be layered to calculate the ALB errors. The influence of refractive index changes in water on the ALB error is minimal, accounting for only a small proportion of all bathymetric errors. Thus, it is necessary to determine whether the effect of the ALB error due to refractive index changes in water needs to be corrected based on the accuracy requirements of the data acquisition. This study and analysis can provide a reference basis for correcting ALB errors.

In this work, Silicon oxide (SiO2) nanoparticles, graphene oxide nanosheet (GO) and GO–SiO2 nanohybrid composites have been synthesized. The role of GO concentration in the starting solution was investigated and correlated to the morphological, structural and optical properties of the studied samples. The structural studies for nanohybrid composites showed that by increasing GO:weight ratio from 0.5 to 2.0, not only does the SiO2 crystalline phase change from cubic to orthorhombic, but the structure of GO also transformed to RGO. The related FESEM images indicate that GO sheets are well-covered by SiO2 nanoparticles with very small grain size and that the accumulation of nanoparticles on each sheet has a high density. Linear Optical measurements showed two optical band gaps of [Formula: see text][Formula: see text]eV and 5.3[Formula: see text]eV for SiO2 nanoparticles, and band gap value of 4.15[Formula: see text]eV for GO nanosheets, which it reduces to 3.3[Formula: see text]eV after formation of the nanohybrid composite with GO: SiO2 weight ratio of 2.0. The nonlinear optical properties of GO–SiO2 with different weight ratio are measured using Z-scan technique. The results showed that the nonlinear refractive index of SiO2 and GO nanoparticles and nanohybrid composite (0.5:1,1:1,2:1) ([Formula: see text]–[Formula: see text]) changed and has a negative sign. It was observed that the nonlinear refractive index changes in different ratios of compounds. Experimental results show that after the formation of the composite, the nonlinear refractive index shows a significant increase in the presence and effectiveness of the GO.

We present a phenomenological model of subpicosecond pulse evolution in semiconductor laser amplifiers, which includes carrier heating effect, gain dispersion, gain saturation, and three kinds of self-phase modulations (SPM). The results obtained from this model are applied to and found to agree very well with experimental measurements of spectral distortions and time-resolved gain on a semiconductor laser amplifier with 460-fs and 2-ps input pulses. The device parameters that are used to match the experimental results are within a reasonable range, either suggested by previous experiments or by published calculations, The results show that the evolution of the pulses and their spectra is sensitively dependent on the input pulse shape and on a variety of time domain and frequency domain amplitude and phase shaping effects. Matching the theory to the experimental data suggests that among the possible causes of the carrier heating two-photon absorption (TPA) is the most important. This effect of TPA needs to be included to properly account for the observed dependence of the carrier heating gain reduction on the pulse length. By examining separately the contribution of the corresponding terms, we also prove the importance of SPM due to the carrier heating and to the instantaneous nonlinear index in shaping the output spectrum. We compare our model with Agrawal's theory, which is valid for pulses of tens of picosecond duration, and find large differences for subpicosecond pulses. For 2-ps pulses, on the other hand, the differences are fewer and less dramatic. The good agreement of the new model with experiments will now allow diagnostics and predictions of pulse evolution in semiconductor optical amplifiers from the picosecond to the subpicosecond range.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Gain and phase dynamics induced by ultra-short pulse in semiconductor optical amplifiers operating in counter-propagating scheme are numerically investigated by employing a field propagation model. The numerical model accounts for the carrier depletion, carrier heating, spectral hole burning and gain dispersion. Propagating schemes have significant influences on gain and phase dynamics, especially for the ultrafast dynamics. Compared to the co-propagating, the counter-propagating causes reduced ultrafast dynamics in gain and phase dynamics. Relatively slow saturation processes in gain dynamics are observed. Analysis results show the drive currents and active lengths of semiconductor optical amplifiers are the main factors influencing the slow saturation processes.