Igor Koltchanov

Four-wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching

Four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) is an important tool for frequency conversion and fast optical switching in all-optical communication networks. We review the main applications of SOAs as nonlinear optical components. Concentrating on FWM, we define general parameters that are of relevance for signal processing applications. We show, how basic experiments and general simulation procedures can be used to determine optimum operating conditions for the intended applications. Besides a comprehensive investigation of FWM among continuous waves, we present new experimental results on FWM with picosecond optical pulses. A comparison of both reveals a different behavior and demonstrates that new optimization criteria and advanced theoretical models have to be applied for the case of short optical pulses. Moreover, we discuss the possibility to extract the dynamical SOA parameters from our experiments.

Noise analysis of frequency converters utilizing semiconductor-laser amplifiers

This paper deals with a general problem concerning semiconductor-laser amplifiers used for frequency conversion. The amplified spontaneous emission (ASE) of a saturated amplifier is investigated experimentally and theoretically. An analytical solution accounting for the spatial dependence of the inversion parameter as well as the spectral dependence of the ASE is derived. Hence, the results can be applied to arbitrary saturation conditions and frequency shifts. Our theory is applied to frequency converters based on four-wave mixing and is found to be in good agreement with both the numerical results and the experimental data. In order to quantify the performance of a frequency converter, a noise figure is defined and shown to be strongly dependent on the frequency detuning and the power of the input waves.

Multiple signal representation simulation of photonic devices, systems, and networks

Photonic systems design requires simulation over a wide range of scales; from wavelength-sized resonances in lasers and filters, to interactions in global networks. To design these global systems, while considering the effects of the smallest component, requires sophisticated simulation technology. We have developed the Photonic Transmission Design Suite, which includes five different signal representations, so that the details of device performance can be efficiently considered within a large network simulation. Alternatively, a design can be studied using a coarse signal representation before switching to a detailed representation for further refinement. We give examples of the application of these representations, and show how the representation of a signal is adapted as it propagates through a system to optimize simulation efficiency.

Gain dispersion and saturation effects in four-wave mixing in semiconductor laser amplifiers

This paper addresses four-wave mixing (FWM) in semiconductor laser amplifiers from the point of view of a propagation problem. The gain dispersion effect, i.e., the difference of the gain factors for the pump, probe and signal waves is shown to be significant in the case of large detunings >1 THz. It is given an analytical solution of the FWM problem including gain dispersion and saturation effects. Considering the saturation behaviour, it is shown that the linear gain factors for the different waves and the nonlinear susceptibilities associated with the different nonlinear effects must be characterized by different carrier densities at transparency. A comparison of our theory with a numerical model, with previous approaches and with experimental data is given.

Analytical theory of terahertz four‐wave mixing in semiconductor‐laser amplifiers

Four‐wave mixing in bulk semiconductor‐laser amplifiers is investigated for detunings up to 3 THz. Gain dispersion, i.e. the difference of the gain factors for pump, probe and signal waves as well as saturation effects are found to play a significant role in four‐wave mixing with large detunings. To properly describe the saturation behavior, it is assumed that both differential gain and carrier density at transparency are different for different waves. Also, the nonlinear susceptibilities associated with different nonlinear effects are characterized by different dependencies on the carrier density. Generally, the carrier densities at the zero points of the nonlinear susceptibilities (if any) and those of the linear gain factors do not coincide. An analytical solution including these issues is given and a comparison with experimental data is presented.

Time-and-frequency-domain modeling (TFDM) of hybrid photonic integrated circuits

This work addresses the efficient modeling of hybrid large-scale photonic integrated circuits (PICs) comprising both, active and passive sub-elements. We describe a new modeling approach, the time-and-frequency-domain modeling (TFDM) that improves accuracy, memory requirements and simulation speed in comparison with traditional pure timedomain method. In TFDM, clusters of connected linear PIC elements are modeled in frequency domain, while interconnections between such clusters and non-passive PIC elements are modeled in the time domain. Behavioral models of the fundamental building blocks of PICs are presented and combined in several application examples showing the robustness of the entire modeling framework for PICs.

Efficient design of photonic integrated circuits (PICs) by combining device- and circuit- level simulation tools

This work addresses a versatile modeling of complex photonic integrated circuits (PICs). We introduce a co-simulation solution for combining the efficient modeling capabilities of a circuit-level simulator, based on analytical models of PIC sub-elements and frequency-dependent scattering matrix (S-matrix) description, and an accurate electromagnetic field simulator that implements the finite element method (FEM) for solving photonic structures with complicated geometries. This is exemplified with the model of a coupled-resonator induced transparency (CRIT), where resonator elements are first modeled in the field simulator. Afterwards, the whole structure is created at a circuit level and statistical analysis of tolerances is investigated.

Design of complex large-scale photonic integrated circuits (PICs) based on ring-resonator structures

The exponentially growing number of components in complex large-scale Photonic Integrated Circuits (PICs) requires the necessity of photonic design tools with system-level abstraction, which are efficient for designs enclosing hundreds of elements. Ring-resonators and derived structures represent one example for large-scale photonics integration. Their characteristics can be parameterized in the frequency-domain and described by scattering matrix (S-matrix) parameters. The S-matrix method allows time efficient numerical simulations, decreasing the simulation time by several orders of magnitude compared to time-domain approaches yielding a better modeling accuracy as the number of PIC elements increases. We present the modeling of optical waveguides within a sophisticated design environment using application examples that contain ring-resonators as fundamental structure. In the models, the two orthogonally polarized guided modes are characterized by their specific index and loss parameters. Systematic variation of circuit parameters, such as coupling factor or refractive index, allows a comfortable design, analysis and optimization of many types of complex integrated photonic structures.

Design of Optical Access Systems using Computer Modeling

We present numerical techniques that allow efficient modeling of the transport of broadband services over fiber-optic links in access networks using various technologies. Application examples of Hybrid Fiber Coax (HFC), Radio-over-Fiber (RoF) systems and 10-Gb/s Ethernet transport over multimode fiber are provided to demonstrate the value of simulation during the R&D and deployment phases of product introduction.

Unrepeated Raman-amplified transmission of 28 Gbaud PM-16QAM over 300 km enabled by digital nonlinear pre-compensation

We demonstrate the effectiveness of digital nonlinear pre-compensation for Raman-amplified transmission of single-carrier 28 Gbaud PM-16QAM. Our simulation results show that by applying transmitter side digital backpropagation and carefully selecting forward and backward Raman pump powers, unrepeated transmission over 300 km can be achieved.