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Topic Name: Researchers has demonstrated a highly efficient add-drop filter using a three-dimensional photonic crystal

Category: Computer science & technology

Research persons: Preeti Kohli, Rana Biswas, Gary Tuttle, Ho Kai-Ming

Location: Iowa State University and Ames Laboratory, United States

Details

The Internet is the driver for modern communication, transporting an increasing density of data. Much of this is being carried over optical fibers using wavelength division multiplexing (WDM), in which multiple wavelengths are transported along the same optical fiber. At different points on the fiber it is necessary to pull off (drop) individual wavelength channels for end-users. Simultaneously it is necessary to add data streams into empty wavelength channels. Waveguides in two-dimensional photonic crystals (PCs) and ring resonators have been extensively investigated as all-optical add-drop filters. We show that three-dimensional photonic band gap crystals with complete band gaps can be novel add-drop filters.

We used a microwave-scale layer-by-layer PC that has been extensively developed at Ames Laboratory and Iowa State University with a complete band gap from 11GHz to 12.9GHz, for all directions of wave propagation. The add-drop filter has an entrance waveguide and exit waveguide created by removing rod segments. These waveguides were separated by a dielectric rod of length d (see Figure 1). We created a cavity of length L one unit cell above the waveguide layer. The cavity-waveguide interaction and the crosstalk between the waveguides is controlled by the separation d.
Since all modes carried by the waveguide are within the photonic band gap, there is no leakage of modes to the outside—an inherent problem with both two-dimensional PCs and add-drop filters using ring resonators.

Figure 4 shows the results of transmission measurements for a straight waveguide, two waveguides separated by d=8a without a cavity, and two waveguides with separation d=8a and a cavity with L=0.75a, where a is the rod spacing for the PC. The straight waveguide has a strong transmission band from 11.8 to 12.8GHz. By separating entrance and exit waveguides, the transmission is reduced by >20dB over all frequencies. With the cavity, a narrow transmission peak appears at 12.22GHz (see Figure 4). The peak transmission of this mode is nearly that of the straight waveguide, suggesting excellent coupling. The 12.22GHz mode is the resonant frequency of a single mode cavity of length L =0.75a. We studied the coupling for different cavity sizes (L) and waveguide separations (d). Each cavity has a different resonant frequency. Larger cavities support more than one mode. The larger multimode cavity (shown in Figure 3) of size L=5.5a (and separation d=9a) exhibits three cavity modes with three strong transmission peaks.

Finite difference time domain (FDTD) simulations provide an appealing physical picture. Simulations used a 20-layer PC similar to the one shown in Figure 1, with two waveguide sections coupled by a cavity of length L. Computational constraints necessitated using smaller L and d (d=6a; L=3a) than in the experiments. The frequency response was obtained by exciting the input guide with a pulsed dipole source and simulating the transmitted E fields in the exit guide. Three simulated transmission peaks were obtained similar to those measured,1 indicating resonant cavity modes that couple the input and output streams.

After identifying resonant modes, we obtained a visual understanding by exciting the input guide with a constant frequency source tuned to a resonance (12.5GHz) and simulating the temporal evolution of the fields. Initially (1000Δt, where the time step Δt=2.06ps), large fields exist only in the input waveguide (as shown in Figure 2). As time progresses (3000Δt), the fields grow within the cavity, indicating input waveguide-cavity coupling. At a later time (5000Δt), the intensity gradually builds in the exit guide. Still later (9000Δt), a large excitation of the output guide is accompanied by the excitation of the cavity (see Figure 2). The slow coupling requires >5000 time steps to excite the cavity and then couple to the exit guide.

Waveguides in three-dimensional PCs can couple through defect cavities. The resonant frequency of the cavity can be selected from the input guide and dropped to the output guide. These designs can be scaled down to telecommunications wavelengths (1.5μ). Controlling the geometry of defect cavities can lead to realistic novel add-drop filters for telecommunications applications.

Note for Wavelength-division multiplexing

In fiber-optic communications, wavelength-division multiplexing (WDM) is a technology which multiplexes multiple optical carrier signals on a single optical fiber by using different wavelengths (colours) of laser light to carry different signals. This allows for a multiplication in capacity, in addition to enabling bidirectional communications over one strand of fiber." This is a form of frequency division multiplexing (FDM) but is commonly called wavelength division multiplexing."

The term wavelength-division multiplexing is commonly applied to an optical carrier (which is typically described by its wavelength), whereas frequency-division multiplexing typically applies to a radio carrier (which is more often described by frequency). However, since wavelength and frequency are inversely proportional, and since radio and light are both forms of electromagnetic radiation, the two terms are equivalent.

Note for Finite-difference time-domain

Finite-difference time-domain (FDTD) is a popular computational electrodynamics modeling technique. It is considered easy to understand and easy to implement in software. Since it is a time-domain method, solutions can cover a wide frequency range with a single simulation run.

The FDTD method belongs in the general class of grid-based differential time-domain numerical modeling methods. The time-dependent Maxwell's equations (in partial differential form) are discretized using central-difference approximations to the space and time partial derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is repeated over and over again until the desired transient or steady-state electromagnetic field behavior is fully evolved.

Note for Photonic crystals

Photonic crystals are composed of periodic dielectric or metallo-dielectric (nano)structures that affect the propagation of electromagnetic waves (EM) in the same way as the periodic potential in a semiconductor crystal affects the electron motion by defining allowed and forbidden electronic energy bands. Essentially, photonic crystals contain regularly repeating internal regions of high and low dielectric constant. Photons (behaving as waves) propagate through this structure - or not - depending on their wavelength. Wavelengths of light (stream of photons) that are allowed to travel are known as "modes". Disallowed bands of wavelengths are called photonic band gaps. This gives rise to distinct optical phenomena such as inhibition of spontaneous emission, high-reflecting omni-directional mirrors and low-loss-waveguiding, amongst others.

Since the basic physical phenomenon is based on diffraction, the periodicity of the photonic crystal structure has to be of the same length-scale as half the wavelength of the EM waves i.e. ~200 (blue) to 350 (red) nm for photonic crystals operating in the visible part of the spectrum - the repeating regions of high and low dielectric constants have to be of this dimension. This makes the fabrication of optical photonic crystals cumbersome and complex.

Pictures overview

Figure 1. The PC add-drop filter, with the input and output waveguides separated by a distance d and coupled through a cavity of length L.

Figure 2. E-field intensities from FDTD simulation in the plane containing the input waveguide, the exit waveguide, and the cavity. Simulations are for the resonant frequency of 12.5GHz at 1000, 3000, 5000, and 9000 time steps. The intensity scale is logarithmic.

Figure 3. Measured transmission for a cavity of length L=5.5a (dashed) displaying three resonant frequencies, compared to the straight waveguide and no cavity (d=9a).

Figure 4. Measured transmission for the straight waveguide (solid) compared to transmission for waveguides separated by 9a, with (dotted) and without (dashed) a cavity of L=0.75a. The cavity-induced resonance (arrow) is ∼1dB below the straight guide. 

About Researchers

Preeti Kohli 
Micron 
Manassas, VA

Rana Biswas
Department of Physics and Astronomy, and 
Department of Electrical and Computer Engineering 
Microlectronics Research Center
Iowa State University and Ames Laboratory 
Ames, IA

Gary Tuttle
Department of Electrical and Computer Engineering, and 
Microelectronics Research Center
Iowa State University and Ames Laboratory 
Ames, IA

Ho Kai-Ming
Department of Physics and Astronomy
Iowa State University and Ames Laboratory 
Ames, IA