in the stack,
Figure 25 Normalized SHG intensity as a function of position in perfectly phase matched, first order quasi-phase matched, and third order quasi-phase matched nonlinear media.
analysis is a scaled dimensionless wave vector mismatch Δs, which is proportional to Δk and inversely proportional to the pump intensity. Rustagi et al. determined that in an ideal stack of plates a relative phase change of Π radians on propagation through each plate is required for proper QPM. Note that this is the same requirement determined in the nondepleted pump regime. However,
Table 35 Frequency Conversion Efficiencies in the Infinite Plane Wave, Nondepleted Pump Approximation for mth order Quasi-Phase Matched Interactions in a Stack of N Plates
the required length of each plate is slightly different. The QPM length requirement for the nth plate is
Ln = 2K (
γn ,) |Δk| (63)
where K( γn) is the complete elliptic integral of the first kind, and γn is the
modulus, determined by the input second harmonic field to the nth plate. For low intensities where Δs 1, the most common experimental situation, γn 2/|Δs|, which yields K(γn) /2 . Then from Eq. (63), Ln /|Δk| = Lc
By contrast, the formulas for SFG and DFG in this same intensity regime are identical to the formulas in the conventional case, given in Section II, but with deff replaced by (2/ )cosΔ ideff, where Δ i is the input phase of the field amplitude, for the sum-or difference-frequency, relative to the nonlinear polarization at each plate. For three waves incident on a conventionally phase matched crystal, the most efficient energy transfer to the desired wave occurs when Δ
i = 0 or Π. More recently, research on QPM has centered around waveguide
technology. Advances in III-V diode laser technology have resulted in commercially available near-infrared diode lasers with single-mode output powers exceeding 100 mW. Materials issues related to developing similar diode lasers in the visible and mid-IR have not been resolved. Hence nonlinear optical devices for frequency conversion with diode lasers have been of considerable interest. With the relatively low output powers of diode lasers, waveguide confinement is necessary for high intensity to achieve useful amounts of frequency-converted radiation. A material such as LiNb03 is attractive because of its reasonably large nonlinear coefficients, its high transparency in the desired wavelength region, its well-developed role in waveguide technologies, and its commercial availability. However, its usefulness is limited by its small birefringence, which is too small for SHG of blue light. It is also too large for the noncritically phase matched DFG of mid-IR radiation. Therefore QPM is being investigated for using these types of materials to achieve efficient frequency conversion in waveguide configurations.