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TUHH OEM: Photonic Crystals

Photonic Crystals

Introduction

Photonic crystals are materials with periodically distributed refractive index variation. Photonic crystals can inhibit light propagation in certain directions due to the photonic band gap effect similar to the band gap effect for electrons in crystal structures. Due to the complicated production of 3D photonic crystals, an alternative of a 2D slab structure was proposed [1] were light in the vertical direction is confined by the total internal reflection [2]. The property of the photonic band gap effect can be used to guide light along line-defects [3] and to confine light in cavities [4] (see Fig 1a and 1b).

Fig1a Fig1b
Fig. 1a: Field distribution of a mode in a line-defect waveguide. Fig. 1b: Field distribution of a mode in a hetero waveguide cavity where middle section has slightly different periodicity as sections on the left and right [5].

Through recent years substantial optimization of photonic crystal properties was achieved. The propagation losses in line-defect waveguides were decreased to several decibels per centimeter [6]. Their dispersion properties were thoroughly investigated, demonstrating light slower as 0.01 speed of light [7] and slow light with vanishing dispersion. [8] The quality factor of the photonic crystal cavities increased substantially reaching one million [5,9]. Different concept appeared for tunable optical buffers based on photonic crystal waveguides [7,10] and cavities [11], as well as concepts for modulators based on slow light mode in photonic crystal waveguides. [12] Due to the property of photonic crystals to isolate light and transmit electric current between the holes, slotted photonic crystal waveguides are proposed [13].

Goals

The photonic crystal research in the institute for Optical and Electronic Materials is concentrated on the slow light effects in silicon line-defect waveguides as well as on tunable cavities in silicon and polymer photonic crystals. The electro optical tuning is achieved by functionalizing silicon photonic crystals with nonlinear polymers as cladding material or slot filling.

The goal for the slow light waveguides is the realization of silicon line-defect waveguides with tunable time delay in the order of 1 nanosecond and tunable dispersion of several hundred picoseconds per millimeter. Periodical and chirped waveguides will be investigated in respect for their bandwidth, time delay, dispersion and tunability. Low voltage electro-optical modulators are going to be achieved with modulation frequency around 100 GHz. These modulators are based on slow light line-defect waveguides in Mach-Zehnder interferometers and on resonant photonic crystal cavities by the electro-optical shift of the phase shift or resonance frequency correspondingly. High Q photonic crystal cavities functionalized with polymers can be also used for tunable time delay.

Results

The original concept for electro-optical modulation was based on polymer photonic crystal cavities [14–18] by modulating directly the refractive index of polymer slab [19; 20]. The exact position of the resonance can be trimmed by the UV exposure of the polymer [21].It was demonstrated that omnidirectional band gap can be achieved in polymer photonic crystals [22] and low refractive index substrate can be used to maintain vertical confinement [23; 24]. The integration with silicon photonics was set as a next step.

By introducing a 100 nm wide slot filled by organic nonlinear optical material into a silicon photonic crystal defect waveguide an optical field enhancement in the nonlinear material can be achieved (Hybride Silizium-Polymer-Nanophotonik). By slightly varying the lattice constant a heterostructure is formed that acts as a resonant cavity (see Fig. 2a). By applying an external electric field to the slotted region the resonance frequency of the cavity is shifted (see Fig. 2b).

Fig2a Fig2b
Fig. 2a: Field profile of a heterostructure cavity formed in a slotted photonic crystal waveguide. Fig. 2b: Transmission spectrum shift of a PhC heterostructure cavity due to refractive index modulation in the slotted region.

A concept for dispersionless slow light waveguides was proposed [25] with group index 50 and bandwidth of 700GHz (see Fig. 3a). At the same time concepts for large positive and negative dispersion were developed [26] with dispersion of 200 ps/nm/mm. An efficient approximation for chirped photonic crystal structures was demonstrated [27] and a double stage coupling to slow light waveguides with transmission intensity more than 95% was designed (see Fig. 3b).

The calculations were performed using the Finite Integration Method of CST, Darmstadt. [28] Some other simulations were done with Transfer Matrix Method, MIT Photonic-Bands [29] and CAvity Modeling FRamework (CAMFR) [30].

Fig3a Fig3b
Fig. 3a: Wavenumber, group velocity and dispersion of the optimized dispersionless line-defect waveguide. Fig. 3b: Efficient coupling to slow light through double transition

References

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  28. http://www.cst.com
  29. http://ab-initio.mit.edu/mpb
  30. http://camfr.sourceforge.net