Poseidon Energy was likely to have had behind-closed-doors relations with the United States military (parts that would become the Enclave) and was commissioned to develop a new and devastating weapon. Unlike its predecessor, Archimedes I, which was a defense system specifically for HELIOS One, Archimedes II could be utilized offsite, within a limited radius from the HELIOS One collection arrays.
While Father Elijah was still an elder of the Brotherhood of Steel, the Brotherhood found HELIOS One in Nevada. It was not long before Elijah discovered the secrets within the facility, namely Archimedes II. The pre-War technology the Brotherhood sought to preserve and keep out of the hands of wastelanders was often weapons-based, so it was only a matter of time before another party came to investigate their motives with something as seemingly safe as a solar power plant.
The New California Republic set up their headquarters in the Mojave at Camp McCarran in 2275 and took Hoover Dam, but because of their past relations with the Brotherhood, they also came investigating HELIOS One. In 2276, the NCR was able to lay siege to HELIOS in Operation: Sunburst and gain control of the facility, kicking the Brotherhood out and knowledge of Archimedes II with it. So far, the NCR has not been able to unlock the secret of HELIOS as Elijah had, thanks to a Follower of the Apocalypse, Ignacio Rivas, who has kept them in the dark for fear that such a devastating weapon could end up in the wrong hands. As he phrases it, "Some things are best left buried with the old world." Although, the NCR has bigger problems beyond being kept in the dark by Rivas; they hired an incompetent conman, Fantastic, to get the power plant up to code and the security system within HELIOS is currently too dangerous to send soldiers inside, but it's only a matter of time before the NCR (or Caesar's Legion) reaches the Archimedes mainframe.
Before Archimedes II can be utilized, it must be activated by choosing to divert the power of HELIOS One to it at the end of the That Lucky Old Sun quest. Additionally, 24 hours are required to charge the solar arrays to full power. With that, the orbital laser is triggered by allowing two lasers to converge on a target; one is marked by Euclid's C-Finder and another by the beacon located at HELIOS One. By triangulating the distance from the satellite to HELIOS One and the distance from HELIOS One to Euclid's C-Finder, the satellite can precisely mark the point on Earth it must fire upon. Upon the target site, three laser beams converge on the target, followed by a large blue laser beam from the sky which causes massive damage.
Archimedes is a reference to the real world Archimedes, a mathematician, physicist, engineer, inventor, and astronomer in Ancient Greece. He devised the "Archimedes heat ray" which used mirrors to focus sunlight onto approaching enemy ships, causing them to catch fire.
↑The Courier: "You think ARCHIMEDES is a weapon they built here." Ignacio Rivas: "Yes. And the technology they have in this facility is like nothing I've seen. Some of it reminds me of Enclave equipment, but more advanced. A weapon based upon it would be catastrophic, no matter who claimed it. It's no wonder the Brotherhood wouldn't give it up." (IgnacioRivas.txt)
↑The Courier: "What more is there to this place than a power plant?" Ignacio Rivas: "I don't entirely know. Our records on the company that built this place suggest that their dealings were not only in energy, but also in weapons. And I've seen equipment here marked with symbols used by the Pre-War military. Targeting computers. Shock sensors. A codeword comes up repeatedly in the papers I've looked through here. ARCHIMEDES." (IgnacioRivas.txt)
↑Nolan McNamara: "Veronica. I hope-" Veronica Santangelo: "I brought you a present. We unlocked the secret of HELIOS One." Nolan McNamara: "What? Wonderful news!" Veronica Santangelo: "No. It's not. ARCHIMEDES II is an orbital laser. Effective only outdoors in a limited radius and requiring a long recharge." Nolan McNamara: "In the hands of the enemy-" Veronica Santangelo: "They'd be marginally more effective. We lost most of the chapter defending glorified artillery." Nolan McNamara: "We couldn't have known. We fought for what we believed in." Veronica Santangelo: "And nearly died for it. Tomorrow you'd do it all over again, having learned nothing." Nolan McNamara: "Are you trying to shame me?" Veronica Santangelo: "I'm trying to open your eyes. We need to engage the outside world. We can't win without new recruits." Nolan McNamara: "What does the Codex say?" Veronica Santangelo: "A bunch of closed-minded bullshit." Nolan McNamara: "We do not help them, or let them in." Veronica Santangelo: "But-" Nolan McNamara: "We keep knowledge they must never have." Veronica Santangelo: "Give it a chance. For me. I can't stay here and watch us waste away." Nolan McNamara: "I'm sorry." Veronica Santangelo: "We'll die out." Nolan McNamara: "(Sighs) I know." Veronica Santangelo: "Come on. I can't listen to this anymore." (Veronica.txt and NolanMcNamara.txt)
↑The Courier: "Who is Elijah?" Ramos: "Who was Elijah, more like. He was our Elder before McNamara. Bright guy, but just between you and me he was a little off. Our mission is to recover and preserve the technology of the past, but Elijah wanted more. He sought ways to improve upon technology, make it better. When we found HELIOS One, he was like a kid in a candy store. He kept talking about the potential, and a "grand design, never realized." He even insisted we set up our base there, against the objection of nearly every paladin. What followed is a whole other story." (Ramos.txt)
↑The Courier: "The Brotherhood of Steel knew about ARCHIMEDES?" Ignacio Rivas: "I would think you'd know better than I. But perhaps they kept their operation here a secret, even from members of their own order. They weren't here for me to ask, but I doubt they were here for electricity. When the NCR first came here, it was under Brotherhood control. They usually steer clear of one another, but something here changed their minds. The Brotherhood's interest in Pre-War technology has always been in weapons. It's likely they were trying to reclaim ARCHIMEDES when the NCR arrived." (IgnacioRivas.txt)
↑The Courier: "I just do what's necessary to keep the peace." Ignacio Rivas: "That's reassuring, although many who've made that claim to the Followers of the Apocalypse over the years have had less than pure intentions. But if it's really as you say, then take my advice. This installation carries with it dangers that no one here has realized. Take care what you do here, and who you listen to. Some things are best left buried with the old world." (IgnacioRivas.txt)
↑The Courier: "The NCR doesn't know about the weapon?" Ignacio Rivas: "Not yet. By some miracle they've hired an imbecile to try and decipher the systems here. He's spent months working at one console trying to get the solar reflectors to track the sun. What he doesn't know is that the only thing the console controls is the plant's intercom system. I tried to tell him, but he insisted that the largest console had to be the most important. Still, it's only a matter of time." (IgnacioRivas.txt)
↑The Courier: "The NCR asked me to help increase the plant's power output." Ignacio Rivas: "They're playing you for a fool. You'll die in that tower, just like their soldiers did. Why do you think they haven't taken care of this themselves?" (IgnacioRivas.txt)
↑The Courier: "Why would you trust me with this?" Ignacio Rivas: "I'm a man of letters. I'd be torn to pieces by the security system they have in that tower. I'd never reach the mainframe. But eventually the NCR will, or if not them, Caesar's Legion. They will use this place for war. Because the possibility exists you might do anything else, you're the only choice I have." (IgnacioRivas.txt)