Fig. 1. (a) Traditional GVMM upconversion (δ≠0) in bulk birefringent-phase-matching (BPM) crystal has an extremely short interaction length, resulting in low efficiency for the frequency conversion of ultrashort pulses. (b) GVM upconversion (δ=0) in a PPLN thin film with a wide bandwidth, supporting ultrashort pulse upconversion. Lc is the coherence length. (c) Diagram of birefringent-phase matching of a negative uniaxial crystal. θm is the phase-matching angle between optical axis c and wave vector k. (d) Scheme of QPM by offering a reciprocal vector G. (e) The efficiencies of SHG for different phase-matching types.

Fig. 2. Simulated QPM period (2Lc) as a function of the fundamental wavelength for different types of upconversions. GVM occurs at the extreme of the dispersion curve, in which case it exists in three kinds of upconversion, as marked as points A (1.490, 18.0), B (1.505, 6.5), and C (1.515, 4.0).

Fig. 3. (a) BBO: central wavelengths of δ=0 and Δk=0 as a function of θm. δ=0 and Δk=0 simultaneously only occur at θm=19.84°, as inserted in (a). At other angles, only one matching type can be satisfied. (b) PPLN thin film: central wavelengths of δ=0 and Δk=0 as a function of the thickness of the film. Δk=0 can always be satisfied under the same condition when δ=0 if given a proper QPM period. Insert: two specific examples that show that δ and Δk equal zero at the same time, when h=30  μm at λ=2.7  μm (nearly bulk) and h=700  nm at λ=1.515  μm, respectively.

Fig. 4. (a) SEM image of the endface of the sample. A 700-nm-thick PPLN thin film is sitting on a SiO2 layer with a LN substrate. (b) Observed light confinement and top view of the periodic QPM structure. The direction of the periodic structure has a 8° angle-off with the x axis. (c) Diffraction pattern of PPLN thin film, which indicates the grating structure on the interface of PPLN and SiO2. (d) Simulated intensity distributions of fundamental and second-harmonic waves with TM mode.

Fig. 5. (a) Measured normalized SHG power as a function of fundamental wavelength. The upconversion bandwidth is 9 nm (1.125 THz) for a 4-cm-long crystal. (b) Linear relationship between SHG power and the square of input FF power at wavelength of 1530 nm and temperature of 24.1°C. (c) Recorded upconversion bandwidth for a 2-cm-long crystal, which is 15 nm (1.875 THz). (d) Experiment and simulation upconversion bandwidths as functions of crystal length.