Enhanced solar light absorption in inverse opals via higher-order photonic modes and angular tuning

Higher-order photonic modes have the potential to achieve superior absorption enhancement in inverse opal photocatalysts, beyond conventional blue or red edge slow light modes. This study reports a finite element method, numerical investigation of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>TiO</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> inverse opals with an ultrathin material skeleton and varying diameters of interconnected pores, at different angle of incidence. Both diameter and angle variations are used to tune slow light modes to the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>TiO</b:mi> <b:mn>2</b:mn> </b:msub> </b:math> electronic band edge in the near-UV. In the case of air-filled pores, relevant to gas-phase photocatalysis, for a pore diameter of 240 nm, at normal incidence, the absorption enhancement factor reached a maximum value of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>α</c:mi> <c:mo>=</c:mo> <c:mn>2.07</c:mn> </c:mrow> </c:math> thanks to tuning of the fifth allowed mode of the band structure. By contrast, for pore diameters corresponding to red (blue) edge tuning, an enhancement factor of only <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>α</d:mi> <d:mo>=</d:mo> <d:mn>1.18</d:mn> </d:mrow> </d:math> ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>α</e:mi> <e:mo>=</e:mo> <e:mn>1.97</e:mn> </e:mrow> </e:math> ) could be achieved at normal incidence. Tighter confinement of the fifth mode into the skeleton is responsible for this enhanced performance. At <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msup> <f:mn>45</f:mn> <f:mo>∘</f:mo> </f:msup> </f:math> oblique incidence, tuning of that mode leads to even further enhancement ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>α</g:mi> <g:mo>=</g:mo> <g:mn>2.42</g:mn> </g:mrow> </g:math> ) due to better coupling and light trapping caused by the nonzero in-plane component of the wave vector. In the case of water-filled pores, relevant to liquid-phase photocatalysis, for a pore diameter of 280 nm at normal incidence, the enhancement factor ( <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>α</h:mi> <h:mo>=</h:mo> <h:mn>2.39</h:mn> </h:mrow> </h:math> ) greatly outperforms blue edge tuning ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>α</i:mi> <i:mo>=</i:mo> <i:mn>1.62</i:mn> </i:mrow> </i:math> ) thanks to the tuning of the allowed modes from ninth to 15th of the band structure. We believe our study will offer additional insights into exploiting slow light effects in inverse opals for photocatalysis, and more generally, solar energy conversion applications.