Method of and apparatus for generating tunable coherent radiation by noncollinear phase-matched sum-difference frequency optical mixing

Apparatus for generating tunable coherent radiation at a frequency .omega..sub.sd by noncollinear nonlinear four-photon sum-difference frequency optical mixing, that comprises:

• means generating a first laser beam, a second laser beam, and a third laser beam of frequencies .omega..sub.1, .omega..sub.2 and .omega..sub.3, respectively, so that .omega..sub.sd = .omega..sub.1 + .omega..sub.2 - .omega..sub.3 ;
• a nonlinear medium positioned to receive the beams which are directed upon the nonlinear medium in a noncollinear configuration to generate the sum-difference frequency radiation as an output from the nonlinear medium, said nonlinear medium having a third order nonlinearity;
• the first beam being directed upon the nonlinear medium, the second and third beams being directed at certain angles to the first beam and to at least a substantial part of the same portion of the nonlinear medium excited by the first beam, the beams being mixed in said portion of nonlinear medium to provide said sum-difference frequency .omega..sub.sd ;
• and means adjusting the angle between the first and second beams as well as the angle between the first and third beams to achieve the phase matching necessary for efficient generation of the radiation at the said sum-difference frequency .omega..sub.sd.

A method of generating tunable coherent radiation at frequency .omega..sub.sd by noncollinear nonlinear N-photon sum-difference frequency mixing using p laser beams that comprise:

• generating a plurality of laser beams of frequencies .omega..sub.1, .omega..sub.2 . . . .omega..sub.p such that
• .omega..sub.sd = (n.sub.1 .omega..sub.1 + n.sub.2 .omega..sub.2 + . . . n.sub.i .omega..sub.i) - (n.sub.i+1 .omega..sub.i+1 + n.sub.i+2 .omega..sub.i+2 + . . . n.sub.i+j .omega..sub.p),
• wherein .omega..sub.1, .omega..sub.2 . . . .omega..sub.1, .omega..sub.i+1, .omega..sub.i+2 . . . .omega..sub.p represent frequencies of input laser beams to-be-mixed, n.sub.1, n.sub.2 . . . are positive integers and satisfy the relationships
• (n.sub.1 + n.sub.2 . . . n.sub.i) .gtoreq. 2,
• (n.sub.i+1 + n.sub.i+2 . . . n.sub.i+j) .gtoreq. 1, and
• n.sub.1 + n.sub.2 +. . . n.sub.i + n.sub.i+1 . . . n.sub.p = N-1;
• directing the beam at the frequency .omega..sub.1 upon a nonlinear optical medium, said nonlinear optical medium having an (N-1)th order nonlinearity and small absorption coefficients at the frequencies .omega..sub.1, .omega..sub.2 . . . .omega..sub.p ;
• directing the laser beams at the frequencies .omega..sub.2 . . . .omega..sub.p at some certain angles and to at least a substantial part of the same portion of the nonlinear optical medium excited by the beam at the frequency .omega..sub.1, the beams being mixed in the nonlinear optical medium to provide the sum-difference frequency .omega..sub.sd ;
• and adjusting the angle between the beams to achieve the phase matching necessary for efficient generation of the sum-difference frequency .omega..sub.sd.

A system for generating tunable coherent radiation at frequency .omega..sub.sd by noncollinear nonlinear N-photon sum-difference frequency mixing using p laser beams that comprises:

• means generating a plurality of p laser beams of frequencies .omega..sub.1, .omega..sub.2 . . . .omega..sub.p such that
• .omega..sub.sd = (n.sub.1 .omega..sub.1 + n.sub.2 .omega..sub.2 + . . . n.sub.i .omega..sub.i) - (n.sub.i+1 .omega..sub.i+1 + n.sub.i+2 .omega..sub.i+2 + . . . n.sub.p .omega..sub.p),
• wherein .omega..sub.1, .omega..sub.2 . . . .omega..sub.i, .omega..sub.i+1, .omega..sub.i+2 . . . .omega..sub.p represent frequencies of input laser beams to-be-mixed, n.sub.1, n.sub.2 . . . are positive integers and satisfy the relationships
• (n.sub.1 + n.sub.2 . . . n.sub.i) .gtoreq. 2,
• (n.sub.i+1 + n.sub.i+2 . . . n.sub.p) .gtoreq. 1, and
• n.sub.1 + n.sub.2 + . . . n.sub.i + n.sub.i+1 . . . n.sub.p = N-1;
• a nonlinear medium positioned to receive the beams which are directed upon the nonlinear medium in a noncollinear configuration to generate the sum-difference frequency radiation as an output from the nonlinear medium, said nonlinear medium having an (N-1)th order nonlinearity, the beam at the frequency .omega..sub.1 being directed upon the nonlinear medium, the beam at frequency .omega..sub.2 and any further beams being directed at certain angles to the beam at the frequency .omega..sub.1 and to at least a substantial part of the same portion of the nonlinear medium excited by the beam at the frequency .omega..sub.1, the beams being mixed in said portion of nonlinear medium to provide said sum-difference frequency .omega..sub.sd.