The ability to create optical bands occupies nowadays a prominent place in the toolbox of optical engineers. To design a basic one-dimensional photonic crystal with a pass or stop band, it is enough to apply a condition on the optical path inside one period. The problem becomes significantly more complicated when a wide band pass optical filter (WBP-OF) or a specific shaped band pass are needed. Such pass bands are engineered with multi-layered or composed periodic structures. The optimization problem gets even harder when engineering and material constraints are introduced.

In this paper, Hassan et al. formulated this problem based on a method often used to describe the well established optimization problem in the fields of microwaves and integrated circuits: The minimax problem:

min M_f (x̄) and M_f (x̄)=max{f_i (x̄),1 ≤ i ≤ m}

where the function to optimize (minimize) looks at the maximum out of a set of functions. This function, M_f, which encompasses both conditions and constraints, has the basic feature of having discontinuities in its first partial derivatives at specific points. Thus, it is not possible to use simple downhill algorithms that follow the function’s gradient. In essence, what the minimax algorithm does is to split its efforts into two: Horizontally, it attempts to reduce M_f while keeping those functions whose values are close to M_f approximately equal; Vertically, it attempts to decrease the function that is equal to M_f by means of linearization.

To implement this 30 year-old method in the field of photonic optimization, the authors first list in a very rigorous way all the parameters, x̄, and the constrains, f (x̄) , that go into the optimization. They demonstrate its efficiency using two examples. The first corresponds to flattening the ripples of a WBP-OF. For imaging applications, the ripples of the pass band needs to be as small as possible to prevent different wavelength from gathering different amplitudes and phases. In a broad quasi-coherent imaging system such differences can create distortion in the image, where each wavelength produces the image at a different location.

The second example is a shaped spectral filter. Here, the term pass band should not be taken in literally. The maximum transmission does not always need to be the same across all of the past spectrum. One example in which such a shaped filter is needed is that of thermo photo voltaic (TPV) systems. In these systems, the thermal emission is harvested using a photovoltaic cell. Hence, the filter should be optimized by two continuous functions: the thermal emission and the PV specific efficiency curve.

Such strong optimization method can be used for other challenges in photonics and integrated optics. For example, dispersion curves of slow light and hollow waveguides, band gap edges engineering and cavity resonances. By harnessing optimization tools coming from mature engineering fields, the path of the photonic industry looks bright.

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