We present a filter design formalism for the synthesis of coupled-resonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators. We describe a method for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators. The designs of Butterworth and Bessel CROW filters are demonstrated as examples.

Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs)

In this paper, a bandpass transmission filter realized in phase-shifted waveguide gratings based on photonic crystals (PCs) is proposed. Phase-shift regions each composed of one period of photonic crystal (PC) waveguide are incorporated into PC waveguide gratings. The magnitudes of the phase-shifts are modified by involving small changes in the size of the border rods in the phase-shift regions. Using standard coupled-mode theory and finite-difference time-domain (FDTD) method, we show that by properly choosing the magnitudes of phase-shifts and the lengths of waveguide gratings, a flat-top and sharp roll-off response with a narrow bandwidth is theoretically and numerically achieved by the designed filter. A further analysis shows that the center frequency of the transmission band can be changed by altering the magnitude of the phase-shift and the response performance exhibits relaxed sensitivity to the phase-shift variation. As a specific application, we theoretically demonstrate a third-order Chebyshev bandpass filter based on compound phase-shifted PC waveguide gratings. The filter performance is suitable for dense wavelength-division-multiplexed (DWDM) optical communication systems with a channel spacing of 100-GHz.

Bandpass filters based on phase-shifted photonic crystal waveguide gratings

Photonic Crystal Narrow Band Filters Using Biperiodic Structures

A new type of compact three-port circulator with flat-top transmission band (FTTB) in a two-dimensional photonic crystal has been proposed, through coupling the cascaded magneto-optical resonance cavities to waveguides. The coupled-mode theory is applied to investigate the coupled structure and analyze the condition to achieve FTTB. According to the theoretical analysis, the structure is further optimized to ensure that the condition for achieving FTTB can be satisfied for both cavity-cavity coupling and cavity-waveguide coupling. Through the finite-element method, it is demonstrated that the design can realize a high quality, nonreciprocal circulating propagation of waves with an insertion loss of 0.023 dB and an isolation of 23.3 dB, covering a wide range of operation frequency. Such a wideband circulator has potential applications in large-scale integrated photonic circuits for guiding or isolating harmful optical reflections from load elements.

Compact photonic crystal circulator with flat-top transmission band created by cascading magneto-optical resonance cavities.

A multichanneled filter based on a branchy defect in a microstrip photonic crystal is proposed. By introducing a branchy structure across the defect region, multiple defect modes will appear inside the photonic gap, leading to the multichanneled filtering phenomenon. In comparison with the conventional multichanneled filters, the proposed structure is more compact and tunable as far as the device volume and fabrication are concerned. The microwave experiment results are found in agreement with simulation results.

Multichanneled filter based on a branchy defect in microstrip photonic crystal

In this paper, a general methodology for the design of higher order coupled resonator filters in photonic crystals (PCs) is presented. In the proposed approach, the coupling between resonators is treated as though it occurs through a waveguide with an arbitrary phase shift. The coupling through the waveguide is analyzed theoretically, based on the coupled-mode theory in time. The derived theoretical model suggests a way to extend an equivalent circuit approach, previously demonstrated with a certain value of a phase shift, to the higher order filter design with an arbitrary phase shift. The validity of the proposed approach is confirmed by the design of a third-order Chebyshev filter having a center frequency of 193.55 THz, a flat bandwidth of 50 GHz, and ripples of 0.3 dB in the passband. The characteristics of the designed filter are suitable for wavelength-division-multiplexed (WDM) optical communication systems with a 100-GHz channel spacing. The performance of the designed filter is numerically calculated using the two-dimensional (2-D) finite-difference time-domain (FDTD) method.

Higher order optical resonant filters based on coupled defect resonators in photonic crystals

We have designed photonic crystal based bandpass filters whose characteristics are suitable for WDM communication system. The filters consist of coupled point defect resonators in two-dimensional photonic crystal. The frequency response of coupled resonators has been analyzed by the coupling of modes in time, from which the design parameters for the coupled resonator filters have been extracted. For the appropriate choice of the design parameters, each resonator is treated as a lumped L-C resonance circuit, and from the analogy between the equivalent circuit and the standard L-C filter circuits, the design parameters are simply determined from the table for general filter circuit design. Based on the determined design parameters, a photonic crystal based filter has been designed and its performance has been calculated using the finite-difference time-domain method. The designed filter shows a pass band of 50GHz and 0.5 dB in-band ripple, which is suitable for typical WDM communication systems with 100GHz channel spacing.

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Dong-Soo Park

Papers

Higher order optical resonant filters based on coupled defect resonators in photonic crystals

Photonic Crystal Based Bandpass Filter Design for WDM Communication Systems