Christi K. Madsen

Optical delay lines based on optical filters

Optical delay lines have some important applications, notably in optical communication systems and in phased arrays. These devices are based on the concept of optical group delay, which, in turn, can be understood as the property of an optical filter. Optical filters are well-understood devices and, in particular, their dispersive properties determine the group delay response. We review these dispersive properties and point out some of the inherent tradeoffs involved in generating large group delay. Fiber Bragg gratings and recent results on optical all-pass filters are used as examples.

Optical all-pass filters for phase response design with applications for dispersion compensation

Lossless all-pass optical filters are introduced, which can approximate any desired phase response while maintaining a constant, unity amplitude response. Architectures using cascade and lattice structures based on ring resonators and cavities defined by reflectors are discussed. Two applications are presented: 1) for fiber dispersion compensation and 2) for compensation of the nonlinear phase response of narrow bandpass optical filters such as thin-film or Bragg grating filters. All orders of dispersion can be compensated in principle, and the filters are periodic so multiple channels can be compensated with a single device. The architectures are very compact compared to alternatives such as chirped Bragg gratings.

Dispersive properties of optical filters for WDM systems

Wavelength division multiplexing (WDM) communication systems invariably require good optical filters meeting stringent requirements on their amplitude response, the ideal being a perfectly rectangular filter. To achieve high bandwidth utilization, the phase response of these filters is of equal importance, with the ideal filter having perfectly linear phase and therefore constant time delay and no dispersion. This aspect of optical filters for WDM systems has not received much attention until very recently. It is the objective of this paper to consider the phase response and resulting dispersion of optical filters in general and their impact on WDM system performance. To this end we use general concepts from linear systems, in particular, minimum and nonminimum phase response and the applicability of Hilbert transforms (also known as Kramers-Kronig relations). We analyze three different classes of optical filters, which are currently being used in WDM systems and compare their performance in terms of their phase response. Finally, we consider possible ways of linearizing the phase response without affecting the amplitude response, in an attempt to approximate the ideal filter and achieve the highest bandwidth utilization.

Integrated all-pass filters for tunable dispersion and dispersion slope compensation

New integrated optical all-pass filters are presented that can be used for tunable dispersion compensation, dispersion slope compensation, and as building blocks in tunable bandpass filters. The dispersion slope compensation capability is demonstrated using ring resonators in /spl Delta/=2% Ge-doped silica planar waveguides. In addition, a tunable four-stage filter with free-spectral range (FSR)=25 GHz, a passband width of 14 GHz (0.56/spl times/FSR), and D=1800 ps/nm is reported.

Efficient architectures for exactly realizing optical filters with optimum bandpass designs

Butterworth, Chebyshev, and elliptic bandpass filter designs are optimal in the sense of band flatness or equiripple characteristics. A new architecture using optical all-pass filters is presented which can realize these designs exactly and efficiently using either ring resonators or reflectors such as Bragg gratings or thin-film interference filters. Design examples are given for a seventh- and eighth-order elliptic filter, and the new architecture is shown to be tolerant to loss. Previously, reflective filters could only approximate optimal responses. An order of magnitude improvement in transition width is demonstrated for an elliptic filter compared to an optimized transmission response for an individual thin-film filter.

General optical all-pass filter structures for dispersion control in WDM systems

All-pass filters (APFs) are devices that allow phase correction or equalization without introducing any amplitude distortion. An optical implementation of such devices is very attractive since they can be used for dispersion compensation. In contrast to other dispersion control devices, optical APFs can correct any order of dispersion. This can be achieved by careful design of multistage APFs to approximate a target phase profile. However, large dispersion is usually narrow band or requires many filter stages. These performance tradeoffs and the general phase properties of optical APFs are reviewed and clarified in the first part of this paper. In the second part, a general design methodology of optical APFs is introduced. We show that any all-pass structure may be constructed from simple N-port devices (such as directional couplers or Mach-Zehnder interferometers) with N-1 outputs fed back to any of the N-1 inputs. The feedback paths may contain delays or further APFs (recursive design). This set of design rules allows for constructing complex all-pass filters of any number of stages starting with very simple elements. We use this technique to demonstrate a number of optical all-pass structures that may be implemented in planar waveguide or using thin-film filter technology.

Integrated resonance-enhanced variable optical delay lines

A wide-tuning-range optical delay line is demonstrated in high (2%) index contrast waveguides. This device integrates four-stage ring resonator all-pass filters (APFs) with cascaded fixed spiral-type delay waveguides; each fixed delay path varies in length by a factor of two from the previous stage. A 2/spl times/2 switch separates each fixed delay and the tunable parts of the delay line. The APF allows for continuous delay tuning. This device enables coherent switching and continuous tuning ranges up to 2.56 ns.

A tunable dispersion compensating MEMS all-pass filter

A tunable dispersion compensating filter based on a multistage optical all-pass filter with a microelectromechanical (MEM) actuated variable reflector and a thermally tuned cavity is described. A two-stage device was demonstrated with a tuning range of /spl plusmn/100 ps/nm, 50-GHz passband and a group delay ripple less than /spl plusmn/3 ps. The device has negligible polarization dependence and is suitable for single or multiple channel compensation. An off-axis, two-fiber package with an excess loss <2 dB/stage avoids the need for a circulator. By cascading four stages, a passband to channel spacing ratio of 0.8 is obtained that allows both 40 Gb/s nonreturn-to-zero (NRZ) and return-to-zero (RZ) signals to be compensated.

General IIR optical filter design for WDM applications using all-pass filters

A general design algorithm is presented for infinite impulse response (IIR) bandpass and arbitrary magnitude response filters that use optical all-pass filters as building blocks. Examples are given for an IIR multichannel frequency selector, an amplifier gain equalizer, a linear square-magnitude response, and a multi-level response. Major advantages are the efficiency of the IIR filter compared to finite impulse response (FIR) filters, the simplicity of the optical architecture, and its tolerance for loss. A reduced set of unique operating states is discussed for implementing a reconfigurable multichannel selection filter.

Optimal dispersion of optical filters for WDM systems

The phase response of optical filters determines their dispersive properties and impacts wavelength-division multiplexing (WDM) system performance. We present a general analysis of the phase response of optical filters used in WDM systems and suggest ways to minimize the detrimental dispersive effects of these filters. Some filters are found to be inherently linear phase filters and in principle are dispersionless. We also show that some filters may be realized for the phase correction of dispersive filters. Experimental system results demonstrate the negative effects of filter dispersion on system performance.