Miniaturizing optical resonators on-chip offers employing them in lab-on-chip sensing devices, which achieves portability, lower price, and only finger prick sample sizes. However, the chip microfabrication limitation may impose some challenges. Taking the Fabry-Perot cavity, the mirrors ideally should have curved shape in 3D to match the light-beam wave front to achieve good light confinement inside the resonator. But as 3D curvature is challenging to fabricate on-chip, straight mirrors are usually used instead with short cavity lengths to avoid high diffraction loss with the beams' multiple trips between the 2 mirrors. The short length limits the sample space between the mirrors, so it can't accommodate large samples such as some types of biological cells. In previous work, the curvature is divided on 2 plans by using cylindrical mirrors for the horizontal plan confinement, and a fiber-rod-lens for the vertical plan confinement. That scheme achieved good light stability; but the curved mirrors produced side peaks as higher order resonance modes, which put limitation on the sensor range. In this work, a novel design is introduced to overcome this limitation by using straight mirrors instead of curved ones, and use an upright cylindrical lens to confine the light in the transverse direction before the cavity. The novel structure is designed by analytical modeling, and verified by numerical simulations. The cavity lengths are typically of tens of micrometers and can reach hundreds, allowing the fluidic channel to hold large test samples. The chip is fabricated in silicon, then fiber-rod-lenses are simply added post-fabrication.