The other method, employed by various nations including Japan, Italy, Spain and Britain, is to use so-called “jump jets”, fighter jets equipped with vertical thrust equipment. The famous Harrier, now long-retired from British service, is of this type. So is the B version of the F-35 Lightning II.
A jump jet can get airborne after a short unassisted run and benefits from doing this up a “ski jump” ramp. It can lift off vertically, but it can’t carry much if it does this, so a so-called rolling take-off using a ramp is standard practice.
When a jump jet returns to the ship it will have burned fuel and released its weapons, so it will be light enough to come down vertically. This is referred to as Short Take-Off, Vertical Landing (STOVL).
The problem with STOVL jets is that their heavy, bulky vertical thrust equipment means they cannot carry as much fuel and weaponry as a Catobar tailhook plane: they have less range and combat power. Jump jets are also much more expensive, both to buy and to fly.