How does the F-22 Raptor radar reflector work?
The F-22 RCS enhancers size and shape (to some extent), as well as this source for example, suggest it is a Luneburg lens. The Luneburg lens is a device that reflects electromagnetic waves very efficiently back to the source, making it possible for a small device to appear as a big target on a receiver placed at same position as the transmitter (for example a radar).
According to  Wikipedia:

Luneburg lenses are normally layered structures of discrete concentric shells, each of a different refractive index. These shells form a stepped refractive index profile that differs slightly from Luneburg's solution. This kind of lens is usually employed for microwave frequencies, especially to construct efficient microwave antennas and radar calibration standards.

This site further elaborates on the Luneburg lens:

The Luneberg lens is a passive radar augmentation device used to increase the radar reflectivity of a target without the use of additional energy The lens reflector is a sphere in shape, usually composed of concentric dielectric shells. By the proper selection of dielectric constants for each shell, radar energy incident on one of the faces of the lens is focused at a point on the rear surface of the lens. The rear conductive surface reflects radar energy back to the source.
Principal of Operation:
(1) Basically the Luneberg lens is made of concentric shell of polystyrene with varying reflective indices (dielectric constants) from 1 to 2, the highest refractive index being the innermost shell.
(2) A ray passing through the various concentric shell will bend towards normal and then focus at a point. If a metal reflector is placed around the focal point, the ray gets reflected and retraces the same path. This is the principal of Luneberg Lenses
(3) In order to have smooth bending of the ray theoretically, many concentric shells are required. In practice, a few concentric shell are used.
(4)The radar cross section augmentation of the lens is given by the formula( 4∏3R4/4λ )
The RCS is inversely proportional to the squire of the wave length and directly proportional to the 4th power of the radius.&quot;

[sic]  Note: the correct spelling is Luneburg, after Rudolph Lüneburg 
To act as a Luneburg lens, the device cannot be empty. To properly &quot;bend&quot; the incoming and outgoing waves, the sphere must hold some kind of inner refractive structure to make it function properly as a radar reflector over meaningful distances. A single concave spherical layer of reflective material will not achieve this.
It should be noted that the RCS enhancer on F-22 is not spherical in form, but a cylinder with rounded ends. The principle of Luneburg lens could still be applied to the device. And as always, having the inter of net as source, it is totally possible the aforementioned device operates on a different principle. Operating principles of many of the systems on F-22 are not exactly public for obvious reasons... Please feel free to overthrow this answer if better knowledge is available.