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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A theoretical study of RF-photonic channelizers using four architectures formed by active integrated filters with tunable gains is presented. The integrated filters are enabled by two- and four-port nano-photonic couplers (NPCs). Lossless and three individual manufacturing cases with high transmission, high reflection, and symmetric couplers are assumed in the work. NPCs behavior is dependent upon the phenomenon of frustrated total internal reflection. Experimentally, photonic channelizers are fabricated in one single semiconductor chip on multi-quantum well epitaxial InP wafers using conventional microelectronics processing techniques. A state space modeling approach is used to derive the transfer functions and analyze the stability of these filters. The ability of adapting using the gains is demonstrated. Our simulation results indicate that the characteristic bandpass and notch filter responses of each structure are the basis of channelizer architectures, and optical gain may be used to adjust filter parameters to obtain a desired frequency magnitude response, especially in the range of 1–5 GHz for the chip with a coupler separation of ∼9 mm. Preliminarily, the measurement of spectral response shows enhancement of quality factor by using higher optical gains. The present compact active filters on an InP-based integrated photonic circuit hold the potential for a variety of channelizer applications. Compared to a pure RF channelizer, photonic channelizers may perform both channelization and down-conversion in an optical domain.

RF photonics technology extending from coaxial cable replacement in RF communication links to signal processing in an optical domain, has recently led to higher efficiency, less complexity, and lower cost than conventional electronic systems, especially at high microwave and millimeter wave frequencies [

Many optical channelizer approaches have been attempted. The optical filter is a key element for the realization of a photonic channelizer. Tunable frequency response filters are becoming strongly desired for exploiting the full bandwidth available. State of the art photonic channelizers are based on optical filter banks that are implemented via various filtering techniques, including free-space diffraction grating [

In this work, four different two-dimensional (2D) active filter architectures are proposed, which may all be considered building blocks for photonic channelizers. Gains are incorporated in these structures to reduce net loss and to provide tunability by emphasizing or de-emphasizing certain frequency components. In addition to gain elements, all four architectures consist of nano-photonic couplers (NPCs) that are interconnected by multi-quantum well (MQW) InP ridge waveguides. The architectures make use of two- and four-port couplers and differ by their respective the structural layout.

In the signal processing domain, three different functions are fundamental to filter operation. The first function is the ability to split signals into different paths or branches. Optically, this function is achieved by the use of photonic couplers. A coupler is capable of splitting different incoming signals into a number of different waveguides. Practically, splitting of the signal involves a different scaling factor for each output signal. For example, in the case of a two-port coupler, an incoming signal is split into two different waveguides with two different transmission and reflection scaling factors. The second function of a filter is its ability to combine or sum different combinations of incoming signals. Again, photonic couplers may accomplish this task by the coupling of different signals from different waveguides into a single waveguide. The resultant signal could be either a direct summation of the different signals combinations or cancellation among some combinations depending on the phase of incoming signals. The third function that filters provide is the introduction of time delay between summing and splitting nodes. A true time delay may be provided by length of waveguide between adjacent couplers. This may be realized by the inducing of semiconductor optical amplifiers (SOAs). SOAs not only provide device tunability but necessarily introduce true time delays [

The couplers design method proposed here is based on a concept of frustrated total internal reflection, which achieves a compact and efficient way of controlling signal reflection and transmission coefficients [

Section 2 illustrates network diagrams of the four photonic channelizer architectures. Section 3 presents how these channelizers are fabricated on InP-based wafers using conventional microelectronics processing techniques. Section 4 describes how the channelizers are modeled with a state space modeling approach, and how the transfer functions at each port may be derived using a Z-transform technique. Section 5 is devoted to the analysis and discussion of simulation results for the four architectures based on three sets of parameters with high transmission, high reflection and completely symmetric parameters. Optical gain may be used to adjust filter parameters to obtain a desired magnitude response, especially in the frequency range of 1–5 GHz. The spectral response of a structure III device is measured as a function of different injection currents. Conclusions drawn from the simulation and experimental results are given in Section 6.

The network diagrams of ^{−1} represents a unit sample delay that is equivalent to a time delay of

A network diagram of a structure based entirely on two-port couplers is shown in ^{th} and 6^{th} order) and two feed-forward paths from the input to any output. In total, the structure I consists of 6 two-port couplers, and seven SOAs waveguides. The two-port couplers may couple a signal into multiple waveguides in which the signal is amplified by injection of different currents for different gains. Hence, the possibility of shaping up the frequency response by tuning SOA gains becomes a key step in the design process.

^{th} order with 2^{nd}, 4^{th}, 6^{th}, 8^{th}, 10^{th}, 12^{th}, and 14^{th} order loops. Notice that the second order loops can only be created by using four-port couplers that stem from two consecutive back reflections. Therefore, a single second order loop exists in this structure since only a single waveguide exists between the two four-port couplers in the middle. This becomes of special importance when the case of a channelizer design is discussed with high reflection parameters.

For the network diagram of the third architecture shown in ^{th} order with even order feedback loops ranging from 2^{nd} to 8^{th} order. Notice that the existence of four 2^{nd} order loops is due to having four consecutive back reflections. This allows a great range of tuning options for poles and zeros of the system.

For the fourth architecture, ^{th} order with a total of nine outputs.

Physically the four structures of photonic channelizers shown above may be realized on MQW epitaxial InP wafers. The experimental work here represents a photonic circuit with a highly integrated architecture. The InP epitaxy provides SOA regions between these nano-photonic couplers. These SOAs provide the delay and the broad gain bandwidth for optical signal processing. The speed of these amplifiers provides tremendous agility to the photonic integrated circuit.

The MQW epitaxial structure on 2” Si-doped InP wafers is commercially available from nLight Corporation. The active region consists of three 7.0 nm compressively-strained GaInAsP QWs separated by two 10.0 nm tensile-strained GaInAsP barriers. To fabricate these SOAs on the wafers, ridge waveguides are defined using conventional photolithography and reactive ion etching. High aspect ratio etching of coupler trenches in InP is conducted by focused ion beam patterning and an HBr-based inductively coupled plasma chemistry [

As an example,

This section is concerned with the modeling of the four proposed architectures. The main objective of the modeling is to develop a unified method for deriving transfer functions and evaluating the stability of the structures. The state space modeling approach offers a comprehensive analysis of the systems’ internal states which in turn results in better analysis of the filter’s behavior and stability. State space representations [^{n}^{m}^{p}_{i}

In general, the number of states is determined by the number of waveguides in two-port coupler structures and twice the number of waveguides in four-port coupler structures. Given an arbitrary labeling scheme for inputs, outputs, and the states as shown in

The corresponding state space matrices for each architecture are given in the

Once the state space matrices are derived, the transfer function matrix is given by:

The transfer function matrix is independent of numbering of the internal states. The (^{th}^{th}^{th}^{th}^{th}^{th}^{th}^{−1}. Then one computes the standard inner product of the resulting vector with ^{th}_{ij}_{ij}

System stability has many definitions and types. Traditionally, in the digital signal processing domain, stability is defined as a system in which a bounded input gives a bounded output. The desirable attribute of bounded input-bounded output stability (BIBO) is equivalent to asymptotic stability in the absence of pole-zero cancellations in the following sense: if the system’s transfer matrix is proper (

Assuming coupler separation of ∼9 mm by InP waveguides with a refractive index of 3.2, a sampling time of _{s}_{s}

In general the state space modeling approach can readily handle imperfections such as lossy couplers. The four-port couplers simulated here are symmetric and without loss, yielding three conditions for energy conservation, based on equal magnitudes of total incident time-average Poynting vectors and total reflected and transmitted time-average Poynting vectors [

Again, the eigenvalues of computed _{7}).

Once the device is fabricated, gains are the only elements that may change the filter’s spectral characteristics. Hence, different manufacturing conditions are considered, and the gains adaptation capabilities are examined. In the design examples below three different sets of parameters are assumed that physically represent three specifications of trench width. Specifically, cases of high transmission, high reflection, and completely symmetric parameters, shown in table [

Structure I with two feed-forward paths and two feedback loops may only yield a basic channelizer where the range of frequencies for which the notch/resonator peak may be relocated is considered to be limited. More complicated structures with more signals paths (higher order) may result in a more comprehensive channelizer design with more frequency bands. For this reason, the second structure that benefits from the use of 2 four-port couplers is considered for providing a more complicated signal path and a higher order filter. The output ports may also have the same characteristics of bandpass and notch responses as shown in structure I. However, more frequencies can be precisely separated and controlled by adjusting gains. Characteristics of different channelizers may be obtained by using different gain values.

Next we examine a structure that consists entirely of four-port couplers. The single loop structure has a total of eight bi-directional ports with four waveguides connecting the couplers. Therefore, a total of four gains from SOAs may be used to tune the device. Using the same parameters as in structure II (high transmission) similar results are obtained as shown in

Let us consider a different manufacturing scenario where a high reflectivity or a wide trench width resulting in low transmission parameters is assumed. In this case the device becomes more sensitive to gain values since the high reflectivity means that the structure may behave like a ring resonator. Mathematically, the poles of the system are greatly affected by the reflection and the scattering coefficients only, due to the absence of transmission coefficients in feedback loops. Thus, transmission components could only affect zeros. That is, the higher the reflection/scattering coefficients, the greater the poles magnitude. However, this may cause stability issues if the gains are not properly chosen. Hence, it is important to investigate the asymptotic stability for cases of high reflectivity as it does not take high gain values for the system to become unstable. This fact explains the high gain values that the device can handle in cases of high transmission parameters. Still with slightly low gain values, a higher dynamic range is achieved than with the case of unity gains. The output ports have notch filters with different notch frequency locations, as shown in

Another potential application is to explore the resulting frequency responses from switching off some of the gains in the structure. Generally, a higher order filter may be preferred over lower order filters to achieve better performance. However, the higher order structure implies a higher number of SOAs which may degrade the optical signal to noise ratio. Therefore, the lower order structures may still be the designer’s first choice for some cases that require simple frequency separation channels with a moderate dynamic range. It is thus useful to obtain a lower filter order through the switching property of SOAs. Specifically, an obvious resonator behavior may be obtained by switching off _{2} and _{4} in ^{th} order where the feedback loops become more dependent on reflection coefficients. In particular, an all-pole system is exhibited by some of the output ports when switching off _{2} and _{4}. The primary role of the gains is to push the poles as close as possible to the unit circle. All the output port responses have the same behavior which is very similar to a sharp resonator. Therefore, only frequencies with

Structure IV is obtained by extending structure III with two additional four-port couplers in the vertical direction. The frequency responses of all outputs can be either bandpass with wide passbands or notch filters with different notch locations. The increased number of gain stages allows for a variety of tunability of notch locations.

A variety of different notch locations are obtained by using a combination of parameters with and without gains. The choice of the off gain modifies the layout of the structure. _{5}, _{6}, and _{7} results in the same structure with only 4 four-port coupler elements. The major setback for going from a more dense structure to a lower one is the complete loss of some output port signals. For example, switching off the gain stages _{5}, _{6}, and _{7} leads to the loss of outputs 4, 5, 8 and 9. That is, the scaled structure will have less output than that of structure III itself. The dynamic range achieved using structure IV is considered to be the highest among all four structures. This results from a large pool of poles and zeros of the system.

It is practical to consider a manufacturing case with symmetric parameters in which an incoming signal is coupled equally in four different directions. In the symmetric case, the gains have an increased role in shaping frequency response by breaking up the symmetry.

From the previous simulation results we may conclude that structure IV offers the most comprehensive frequency tuning options. A variety of frequency bands may be separated within the free spectral range for structure IV. While structure I may provide a proper dynamic range, its ability to distinguish different frequencies within the free spectral range is very limited. This is a direct result from the simple signal flow and the limited number of poles and zeros that the structure provides. Significant improvements are noted when migrating to structures II and III.

Modeling of the proposed structures through the state space approach is very practical and may provide solutions for accurate analysis of the system’s asymptotic stability. The sparse nature of the ^{th} order, with 16 input/outputs. With any arbitrary labeling scheme, filling in these state space matrices is easily obtained by using simple algorithms. Also, the expanded systems may still be reduced to the original system block, if needed, using the switching property of the SOAs.

_{1}, _{2}, _{3}, and _{4} gain stages, respectively. As the total applied current is increased, the quality factor of the device is improved significantly, as shown in

This indicates that the quality factor is controllably tuned by application of an optical gain by current injection. Similar results are also obtained from an optical tapped-delay-line microwave signal processor filter, and its passband width may be tuned by controlling the gain of an active erbium-doped fiber [

A theoretical study of RF-photonic channelizers with four architectures formed by active integrated filters with tunable gains is presented. The four proposed architectures vary in the structural layout and internal nano-photonic coupler formations, (either two-port or four-port). The behavior of the nano-photonic coupler is experimentally based on the phenomenon of frustrated total internal reflection. These photonic channelizers may be fabricated in one single semiconductor chip on MQW epitaxial InP wafers using conventional microelectronics processing techniques.

A state space modeling approach is used to derive the transfer functions and analyze the stability of these filters, and the

As a starting point, the measurement of spectral response shows the enhancement of quality factor for a structure III type device by using higher injection currents that provide higher optical gains. These compact active filters on integrated photonic circuits with MQW InP-based technology hold considerable potential for channelizer applications. Fabrication of a photonic channelizer with coupler separation of ∼9 mm for a 10 GHz sampling frequency is currently underway. Simulation results shown here will be studied.

The authors gratefully acknowledge the support of the Defense Advanced Research Project Agency (DARPA) through grant HR0011-08-1-005.

State space matrices for each structure are extracted from the two basic sets of equations in (1).

Network diagram of structure I. Transmitted, _{i}^{−1} represent unit delay (blocks), and _{i}

Network diagram of structure II. Transmitted, _{i}^{−1} represent unit delay (blocks), and _{i}

Network diagram of structure III. Transmitted, _{i}^{−1} represent unit delay (blocks), and _{i}

Network diagram of structure IV. Transmitted, _{i}^{−1} represent unit delay (blocks), and _{i}

Schematic setup for spectral response measurements of the photonic channelizer devices (EDFA: erbium-doped fiber amplifier, PC: polarization controller, DUT: device under test, LDD: laser diode driver, TEC: thermoelectric cooler, OSA: optical spectrum analyzer). Inset: A custom designed submount and circuit board assembly for device testing.

Frequency response for structure I using low transmission parameters.

Dynamic range for frequencies (ω = _{1}) in structure I.

Frequency response for structure II using high transmission parameters. Different notch locations are observed.

Frequency response for structure III using high transmission parameters. A high dynamic range is achieved.

Frequency response for structure III using high reflection parameters.

Frequency response of output 4 for structure III with some unused gains, resulting in a resonator behavior.

Frequency response for structure IV using high transmission parameters.

Frequency response for structure IV using high transmission parameters.

Frequency response for structure IV using high transmission parameters with different combination of unused gains.

Frequency response using symmetric parameters for structure IV. Solid lines represent output signals with gains. Dashed lines represent output signals with unity gains.

_{1}, _{2}, _{3}, and _{4} gain stages. _{1}, _{2}, _{3}, and _{4} gain stages. _{o}

Coupler coefficients used for the three proposed manufacturing cases.

Design | ||||
---|---|---|---|---|

High transmission | 0.4 | −0.4 | 0.2 | 0.8 |

High reflection | 0.4 | −0.4 | 0.8 | 0.2 |

Symmetric | 0.5 | −0.5 | 0.5 | 0.5 |