With a few words from prolific science fiction author Isaac Asimov, the voyage of laser beams through a shark-proof underwater fiber-optic cable began a new era of trans-Atlantic communications.

The cable, thinner than a child's wrist, went into service Wednesday and can carry 40,000 phone calls between the United States and Europe simultaneously, double the capacity of its trans-Atlantic copper-cable predecessors combined.Asimov, author of more than 400 books, spoke the first official words on the cable in a three-way video conference connecting New York, London and Paris.

"Welcome, everybody, to this historic trans-Atlantic crossing - this maiden voyage across the sea on a beam of light," Asimov said at 10:30 a.m. EST, his voice instantly flashed as coded pulses of laser light through the more than 3,500 miles of cable.

In a sign of the voracious demand for communications, the partners in the $361 million project expect the fiber-optic cable to start running out of room by late 1991. That's when a new cable with even greater capacity will go into service.

Fiber-optic service to Japan and the Far East will begin next spring, and other undersea fiber links will reach to the Caribbean and he Mediterranean by the early 1990s.

AT&T said 1988 would be the first year the company handled more than 1 billion calls into and out of the United States.

For residential customers, the new cable, called the TAT-8, will mean a continued decline in the price of trans-Atlantic calls. For businesses, it will mean lower rates and greater capacity for the huge volume of computer data they transmit, especially in areas of finance, travel and tourism.

Ordinary television broadcasts still will be carried by satellite because they would take up too much room on the cable. But the cable's builders expect it to be used for video conferences between offices, with the signals compressed to take up less room.

Lasers have revolutionized phone networks by making it possible to transmit information in the form of rapid pulses of laser light through hair-thin strands of glass known as optical fibers. The lasers transmit information in digital form.

Most long-distance calls within the United States already are carried on optical fibers.

The new cable contains six strands of glass, and two of them are spares. The cable measures 0.8 inch across, except for the sections that are reinforced to guard against shark bites, which are 1.3 inches across.

The first undersea phone cable between the United States and Europe, TAT-1, was built in 1956 and could handle 36 simultaneous calls.