Two things, in regards to the drawing:
There cannot be a "low impedance connection for all frequencies" that also looks like the drawing. A wire or trace has inductance, the metal part has capacitance to the plane, and the resulting slot between metal parts has resonant frequencies; together, a variety of resonant frequencies results, making a leaky connection (there is poor attenuation overall, and there are myriad pass bands). (If nothing else, realize that at optical frequencies, you can see through the gaps!) Below all these resonances, there is asymptotic attenuation, topping out at whatever the DC resistance dictates.
To an incident wave, mismatch is intended. Can't mismatch more than a ground plane!* The surest way to make an extension of the ground plane is to make a solid connection to the metal part, so that it isn't a part at all! Short of welding it on, any way to keep gaps small will suffice up to a cutoff frequency, hence EMI fingers, gasket, etc. Bolted lap joints covered with conductive tape are also a common choice.
*Well, a metal plane might be a 99.something% effective reflector; there are dielectric mirrors, albeit over modest bandwidths (enough to reflect white light, say) that are 99.999something%, very close to 100%. Close enough that, if you seemingly pinch off a container lined with em, it doesn't become dark due to total internal reflection, oh no... that light still finds a path out!
Typically we only need performance over a modest range of frequencies, say DC to low GHz (most electronics), or mid GHz, or across the 100s of THz (optical shielding), and minimizing transmission is the goal, not necessarily maximizing reflection: absorption is also an option in many cases.
Examples of use cases:
- EMI gaskets/fingers to close metal enclosures around commercial equipment (DC to ~GHz)
- Anti-resonant gaps to seal waveguides, microwave ovens, etc. (λ/2 long contact gap) -- only needs to be good enough for the frequency in question, lower frequencies excluded by below-cutoff waveguide, higher frequencies ignored by other waveguide components (mode-specific coupling loop, filtering at receiver)
- Absorptive materials, anywhere from radar to visible (black): reduces transmission by absorbing instead; whereas reflective surfaces can't be sealed perfectly and accidental internal reflection paths, waveguides, etc. are likely to be created.
Another strategy, by shift of perspective:
Consider a solid block of metal. Stick a circuit down in the middle of it (somehow). It's not communicating with anything, right? Complete short circuit in all directions, surrounded by reference plane, the perfect shield.
Drill a hole into the block, and run a single wire out from the circuit: voila, coaxial cable. This gives you have a port, a point in space through which waves flow in two directions. Nothing gets in or out except for this connection; bandwidth extends as far as this remains an effective waveguide (but for signal quality reasons, we might be wise to filter out or absorb non-TEM00 frequencies, i.e., so the coax still acts like a coax as we usually think of it), and nothing else gets in or out.
Suppose you mill away most of one side, leaving it thin, but still solid. Now it's a sheet metal panel. At frequencies above several skin depths, isolation is still very good (100s dB?), but below there, there is some transmission.
Suppose you cut a slot in the panel. Now there's a visible path in, and at low frequencies, a slot antenna. For frequencies below cutoff (λ/2), it looks like an inductive loop, and has an asymptotic response (down to DC, where the maximum attenuation depends on the resistance around the slot). Above cutoff, there are resonances for all odd multiples, and eventually waveguide modes, then mode breakup as it becomes multiple wavelengths across, relative to the actual width (kerf of the cut) and depth (panel thickness) of the slot.
When we eventually carve this block down to a narrow wire connected to a plate, we've introduced so many slot modes that high frequencies are just wide open (overlapping passbands), and only the lowest-frequency cutoffs remain, including the asymptotic inductive response until DC. Which can also be described in a bottom-up fashion as the panel (with its resonant modes, and capacitance to the main plane) and wire link creating an LC resonator, and other things.
