Metamaterials are artificial engineered structures that can perform unique features because of interaction with electromagnetic waves . These unusual properties such as negative refractive index , perfect absorption , and targeted camouflage  have attracted tremendous interest into the field  and many studies have been done since the pioneering work was published .
As a two-dimensional planar metamaterial form, metasurfaces are also demonstrated remarkable characteristics in various application areas [7–12]. Control and manipulation of the emergent electromagnetic wavefront are one of the significant implementations of the metasurfaces in the optical device technologies . The flat metasurface lenses called as metalenses are candidates to replace conventional bulky spherical lenses which are one of the obstacles to downsizing the modern optical devices .
The traditional lenses control the light propagation path by controlling the phase shift of light continuously using curved surfaces . This spherical shape brings difficulties in the fabrication process and causes aberrations such as spherical and chromatic aberration .
On the other hand, metalenses manipulate the incident light by the control of the local refractive indices  and with that it can reshape the phase, amplitude, and polarization of the light with an ease . Metalenses compose a number of unit-cells called meta-atoms which are nanofins on top of a period of substrate. This configuration makes the fabrication much easier, and it allows the miniaturizing of the optical devices since the array of the meta-atoms is much smaller than conventional lenses .
To mimic the phase profile of the light outgoing from a spherical lens, \(2\pi\) difference should be achieved using nanofins with different radii while the transmission through each unit is kept as high as possible. As a result of the placement of the meta-atoms at the calculated \(\left(x,y\right)\), metalens gains a lens property, and it reshapes the wavefront of the electromagnetic wave to focus on the focal point.
Commonly, the visible region is selected as a working wavelength for the studied metalens. Recently, with the usage of germanium (Ge), metalenses that are working at short wavelength infrared region (SWIR)  and middle wavelength infrared region (MWIR)  are obtained. However, metalenses that are working in long wavelength infrared region need to be studied.
Metalenses which are constructed with metal or dielectric materials are generally passive systems with no dynamic ability . To reach the desired dynamic property, the addition of temperature-sensitive materials is an excellent method. Participation of phase change materials (PCMs) with thermally tunable feature can be an option to bring a tunability to the metalens even after the fabrication . In particular, vanadium dioxide (VO2) with rapid insulator to metal phase change around the temperature of 68 \(℃\) , can be a promising choice to gain control over the focusing and power of the metalens after production.
In this study, Ge based metalens is built to operate at long infrared wavelength. The focusing ability of the proposed metalens is investigated using electric fields along the propagation direction and the focal point. To obtain dynamic featured metalens, VO2 from PCMs is added to the structure. The lens behavior of the PCM based metalens is examined for the different temperature around the critical temperature of the VO2.