Prior to retiring, Alexander was a successful photographer, noted for his celebrity portraits. For many years he was the official photographer for the New York City Ballet.
Alexander contributed hundreds of original and altered photographs to two of Patrick Dennis's best selling books. Little Me, a mock biography documenting the life of the world's worst actress Belle Poitrine, features more than 150 of Alexander's photographs. Alexander also wrote the novel's preface. Dennis' First Lady: My Thirty Days at the White House told of Martha Dinwiddie Butterfield (Peggy Cass), wife of a robber baron who literally stole the presidency at the turn of the century. Using friends and professional models and actors, Alexander's zany photographs were essential to the novels' success.
For several years he served as Chief Photographer at Andy Warhol's Interview magazine. He was a longtime resident of Saratoga Springs, New York, and was also the life-partner of former New York City Ballet dancer Shaun O'Brien. In the 1940s, Alexander was romantically involved with the dancer and choreographer John Butler.