NEW YORK — Tingye Li, 81, an electrical engineer whose calculations in the early 1960s helped guide development of the laser and propel the dizzying increase in the speed of fiber-optic communication, died Dec. 27 in Snowbird, Utah.
The cause was a heart attack while he was on a ski trip, his family said. He lived in Boulder.
Lasers were in the early stage of development when Dr. Li and a colleague at Bell Labs, A. Gardner Fox, developed a computer simulation of how lasers produce focused light energy that has transformed fields from medicine to space travel. They reported their findings in a paper published in 1961.
Arno Penzias, a former director of Bell, called their paper a tool kit for subsequent designers of lasers and other optical systems. He said it helped transform the ‘‘wonderful invention’’ of the laser — the word is an acronym for light amplification by stimulated emission of radiation — into ‘‘a practical communications platform.’’
In essence, the researchers provided a mathematical model for how light bounces about inside a laser between two mirrors as it gathers energy, predicting factors like the shape and intensity of light beams. Alan Willner, an electrical engineering professor at the University of Southern California, called the work ‘‘the foundational teaching’’ on the innards of lasers.
“There aren’t many papers that help define a field, but this was one of them,’’ he said.
The research that led to nearly instantaneous communication by light waves was itself snail-like. Dr. Li and Fox had to write their own programs, punching them into decks of cards, for a roomsize computer that was less powerful than a palm-size calculator today. The computer ran the program for two or three hours. A frequent error message meant that the researchers had to scour the cards for a single improperly punched letter, Jeff Hecht wrote in ‘‘Beam: The Race to Make the Laser’’ (2010).
Bell Labs was virtually unchallenged as the largest and most inventive lab in the world, having a hand in many of the 20th century’s most important inventions. Dr. Li — who wrote or helped write more than 100 papers, patents, and books — led research teams at Bell for more than three decades.
Some of their work laid the groundwork for today’s broadband. One area of study helped find ways to use light waves to convey information on optical fiber, rather than copper wire or radio waves. Another team Dr. Li led developed optical amplifiers, which amplify a signal directly, without the need to first convert it into an electrical signal.
Dr. Li was also an early proponent of using the rare metal erbium in the amplifiers.