Your better bet, with a smaller (but still huge) lens (or series of mirrors that form the equivalent of a lens), would be to put the equipment inside the orbit of Venus, keep it synchronous with Mars orbit (this requires fuel; which you might be able to accomplish mostly with solar power; e.g. accelerating atoms to near light speed using electromagnets and emitting them as propellant).
Then your lens can focus light on Mars (planet wide, not to a point!).
Venus is 0.72 AU (Earth is 1.0 AU) and Mars is 1.52 AU from the Sun. Mercury is 0.39; so put your equipment about 0.5 AU from the sun (47 million miles).
The formula for the area of a sphere is $4\times \pi \times radius^2$. So at 1.5 AU vs 0.5 AU, the $4\times \pi$ cancels out, and the ratio of areas is $\frac{0.5^2}{1.5^2}=0.111$, a factor of 9. This means, at this distance, the light that finally reaches Mars occupies 1/9 the area of the disk of Mars. If you wish to double that light; you need a lens (or mirror arrangement) collecting twice as much: But that collection area is roughly the area of a circle, whose area is computed as $2\times \pi \times radius^2$; so you only need to increase the diameter of the mirror by $\sqrt{2}=1.41$ to double the light reaching Mars. (Mirror arrangements can mimic lenses, it is what we do in a reflecting telescope.)
This is still big: Mars diameter is 4212 miles, radius 2106 miles, so the disk has an area $\pi \times 2106^2$ is about 14 million square miles. A Ninth of that would be 1.55 million sq mi; or a disk of radius 702 miles. To double that light, you need a disk of radius 992 miles; or round it up to 1000.
Getting closer to the sun reduces the size requirement, but I am not sure how close you can get to the sun without melting the mirrors and equipment. I'm pretty sure NASA already has materials sturdy enough to serve at 0.5 AU; but if not, invent some fictional materials; it would not be implausible.
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The surface area here is quite large; but there is no requirement it be constructed in one piece, or all at once. There are many advantages to building such a construct in pieces. We need 3 million square miles of mirror; but we can engineer this as three million devices of one square mile each. In a disk form this would have a perimeter of 3.545 miles; on Earth I routinely walk that far, for exercise, in about 75 minutes. A square mile is a manageable area, if you are weightless.
Can we manufacture 3 million such devices? Look at how many cars, refrigerators, houses, TVs and cell phones we have manufactured. If the motivation is there, then the answer is yes; especially since most of this is probably a paper-thin shell of reflecting surface, and the real "device" is probably just the size of a gymnasium for a basketball court.
Advantages.
- Greater safety and resilience. The devices can be spread out over a very large area and be widely separated, by hundreds or thousands of miles, making them difficult to attack or sabotage.
- Configurability. Individual mirrors can be turned to reflect light past Mars, to reduce the amount of extra light reaching Mars.
- Repairability. A single device, if broken or off-target, is catastrophic. In three million parts, a single broken mirror reduces output by $\frac{1}{3,000,000}$ and is unnoticeable, it can be repaired when you get to it.
- Gradual construction. I presume these would be manufactured in space, from asteroid material. They could be manufactured over the course of a few decades, and be deployed as finished: For three million devices, that would be just 411 per Earth day; a fast rate but not implausible (and of course you keep the space factory going afterwards, manufacturing replacements or backups or additional capture area).
- 3-D occupation. The mirrors do not have to be all joined together, as long as they all focus light on the target. Say they are spread over 15 degrees of the radius. For a 0.5 AU (=radius 47 million miles); that would be an arc of 12.3 million miles (say MM). Devices could positioned in a slab 12MM x 12MM and in layers about 6MM deep. This is $8.64\times 10^{20}$ cubic miles; allowing each of the 3,000,000 devices a cube about 66,000 miles on a side all to itself. Remember each is only one square mile of reflective surface; and it is 66,000 miles to the next one. This exact configuration is just for a back of the envelope computation to get the scale right; but clearly we can afford plenty of room to maneuver within the grid for the space-faring workmen, or even the factory itself. It need not be crowded, and no out of control ship, or asteroid, is going to "take out" a large number of our mirrors. And since they are maneuverable themselves, perhaps they can pull in their mirrors (roll them in; or close up like a flower) to avoid any debris they detect would hit their mirror.
The surface area is large, but I think a manageable engineering project for a Martian colony; and it can be engineered for great resilience, and be highly resistance to terrorism or sabotage or accidental destruction. An added function beyond warming Mars: Solar power from close to the sun could be harvested to drive lasers, aimed at Mars orbital receivers, that eventually transfer power to the planet. Because your terraforming equipment and atmosphere generators will also demand giant amounts of energy.
