It is also surprisingly difficult to designate in terms of tropes.
Laura is the story of a supposed dead woman beguiling the detective investigating her "death." The detective, played by Dana Andrew, is drawn originally to her portrait. His adoration expands as he learns more about her personality.
It is NOT love at first sight, at least not as TV Tropes defines the phrase. It is very specifically love towards a (believed to be) dead person that expands as the detective's knowledge of the person increases.
A brief review of one Laura tribute describes the detective as a stalker. This totally misses the point (and is yet another reason people should rewatch classics: context, people!). Look at all the young girls squealing over One Direction or whoever--they are building castles in the sky just as absolutely as the detective, only without his self-awareness.
Which doesn't preclude the obsessive element, especially since the Laura-character is often a troubled, complex individual. The desired one is believed to be permanently unattainable. Yet the detective, admirer, wishes to discover more.
This dissonance explains the fantasy of fans who behave in extreme fashions yet don't cross the line into stalking: their relationship to the unattainable celebrity is part fantasy coupled with a desire to learn more.
Don't ask me--I don't get it.
Anyway, here are some Laura tributes:
"Aquiel," Star Trek: The Next Generation: Geordi becomes more and more enamored with Aquiel, believed to be dead. Geordi also falls in love with the holographic version of Leah Brahms (a plot-line very well-paid off in later episodes) though she is not dead.
"Breaking Point," Numb3rs: Colby Granger becomes more and more fascinated by a kidnapped, possibly dead, investigative journalist.
"An Eye for an Eye," NCIS, Season 2: Tony reflects on the movie Laura while studying a pair of beautiful "disembodied" eyes. Is it possible to fall in love with them? As in many episodes, Tony's supposed chauvinism--his willingness to ask tasteless questions--leads to a larger truth. At a more subtle level, the first Prime Suspect tackles the same idea: the men who supposedly bridle against having a female boss are, yet, worlds away from the deep hatred of women exhibited by the serial killer they are chasing.