It exists
The ABL doesn't burn through a missile, or disintegrate it. Rather it heats the missile skin, weakening it and causing failure due to flight stresses. If proven successful, a fleet of seven Boeing 747s with the ABL system would be constructed. In operation they would be divided between two combat theaters.one of these loitering at the Sea of Japan ad pretty much most of NK missiles will be shot down.
From wiki
While designed mainly for use against tactical ballistic missiles (TBMs), which are shorter ranged and move slower than ICBMs, the ABL has more recently been considered for possible use against ICBMs during their boost phase. This would be more challenging since the longer range of ICBMs would limit the ability of the ABL to reach them. By contrast, tactical ballistic missiles are fired from closer range; hence, the ABL could more easily intercept them without overflying hostile territory. However, some liquid fueled ICBMs have thinner skins than TBMs, so they would be easier to damage. Also, the boost phases of ICBMs are much longer, which gives more time to track and fire on them. But, in general, the ABL would likely be less effective against ICBMs.
A 2003 report by the American Physical Society on National Missile Defense found that if the ABL achieves its design goals it could be successful against liquid fueled ICBMs at a range of up to 600 km. However, its effective range against tougher solid fueled ICBMs would only be 300 km--likely too short to be useful in many scenarios.
Intercept sequence
The ABL system uses infrared sensors to initially detect the missile. Then three lower power tracking lasers calculate the missile's course and speed, aimpoint, and measure atmospheric turbulence. Atmospheric turbulence deflects and distorts light, so the measured turbulence is used by the ABL adaptive optics system to compensate. After that the main laser is fired for 3 to 5 seconds from a turret located on the aircraft's nose, causing the missile to break up in flight near its launch area. The ABL is not designed to intercept TBMs in the terminal, or descending phase. Thus the ABL must be within a few hundred kilometers of the missile launch point.
Operational considerations
The ABL uses chemical fuel similar to rocket propellant to generate the high power laser. Current plans call for sufficient laser fuel for about 20 laser shots. If a more difficult target such as an ICBM required a longer duration "dwell time" to disable, this would decrease the number of available shots before refueling the laser. If less difficult targets such as shorter range TBMs required less dwell time, possibly 40 laser shots could be made without refueling. The ABL aircraft must return to base and land to reload more laser fuel. Preliminary operational plans call for the ABL to be protectively escorted by fighter and possibly electronic warfare aircraft. The ABL aircraft would likely fly a figure eight pattern near suspected launch sites for long periods, awaiting an intercept target. A figure eight pattern prevents the aircraft from having to turn away from the target area as long as the orbit is designed such that both turns are towards the target area. It can be refueled in flight, staying aloft for long periods. The goal would be to stay over friendly territory and fire inward across hostile territory to intercept the missile.