III-V solar cells dominate the high efficiency charts, but with significantly higher cost. Ultrathin III-V solar cells can exhibit lower production costs and immunity to short carrier diffusion lengths caused by radiation damage, dislocations, or native defects. Nevertheless, solving the incomplete optical absorption of sub-micron layers presents a challenge for light-trapping structures. Simple photonic crystals have high diffractive efficiencies, which are excellent for narrow-band applications. Random structures a broadband response instead but suffer from low diffraction efficiencies. Quasirandom (hyperuniform) structures lie in between providing high diffractive efficiency over a target wavelength range, broader than simple photonic crystals, but narrower than a random structure. In this work, we present a design method to evolve a simple photonic crystal into a quasirandom structure by modifying the spatial-Fourier space in a controlled manner. We apply these structures to an ultrathin GaAs solar cell of only 100 nm. We predict a higher photocurrent for the quasirandom structure (26.2 mA/cm 2 ) than a simple photonic crystal (25.2 mA/cm 2 ). The photocurrent predicted for the quasirandom structure is 84.5% of the photocurrent of an ideal thick device (3 µm), using only 3.3% of the active material.