Phase-matched electric-field-induced second-harmonic generation is demonstrated in single-mode germania-doped silica fibers. A periodic second-order nonlinearity is induced by a simple interdigitated electrode structure, which can be rotated to permit phase matching between all propagating modes. The most efficient mode interaction between HE11ω and HE112ω is achieved at 1.064 μm by using a Q-switched Nd+3:YAG laser. In principle, phase matching at any propagating wavelength is possible. This technique could be applied to planar as well as cylindrical waveguides and can be used with many non-χ(2) materials. The asymmetry in the applied electric field enhances the optical-field overlaps between modes of dissimilar orders, and this is also demonstrated. A conversion efficiency of 4.0 × 10−4% has been obtained in unoptimized devices. Device optimization is also discussed.
E. Y. Zhu, L. Qian, L. G. Helt, M. Liscidini, J. E. Sipe, C. Corbari, A. Canagasabey, M. Ibsen, and P. G. Kazansky J. Opt. Soc. Am. B 27(11) 2410-2415 (2010)
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Sensitivity of the Phase-Matching Pitch Λ on the Core Radius a, Core–Cladding Index Difference Δn, and Wavelength λ, for a = 4.0 μm, Δn = 4.5 × 10−3, and λ = 1.064 μm
Mode Interaction
Parameter
LP01ω → LP012ω
LP01ω → LP112ω
∂Δ/∂a
2
5 × 10−3
∂Λ/∂Δn (m)
−10−3
14.55 × 10−6
∂Λ/∂λ (μm/nm)
55 × 10−3
79.4 × 10−3
Phase-match length limited by above parameters (mm) [see Eq. (8)]a
1237
446
Length limited by pitch tolerance alone (mm) (see text)b
90
54.95
δΔn/Δn of 10−3% and δa/a of 10−2% have been used to calculate the data.
A tolerance of ±2.5 × 10−2% assumed.
Table 2
Magnitudes and Phases of the Active χijkl(3)El0 Tensor Elements as a Result of the Components of the Applied dc Electric Field Relative to χxxxx(3)Ex0 and Grouped as in Eqs. (21a) and (21b)a
The subscripts of χ(3) are grouped from terms such as those in Eqs. (18a)–(19b).
Dependent on electrode mark/space ratio, b/c. Values shown assume that the static field components are equal to Ex0.
Table 3
Dimensions of Periodic Electrode Structures Used in Experiments
Mask
Electrode Width, b (μm)
Electrode Space, c (μm)
Pitch, Λ Λ (μm)
A
15.6
4.4
40
B
4.4
15.6
40
C
4.4
11.6
32
Table 4
Measured and Computed Coherence Lengths and Overlap Integrals Ratios for Seven Mode Interactions Are Compared Using Data from Device D1a
LP11ω → LP212ω and LP01ω → LP012ω are coincident in the phase-matched data shown in Fig. 12. The former, weaker interaction was therefore not resolved. LP11ω → LP012ω could not be phase matched because the grating pitch used in the experiment was too large. Interaction LP01ω → LP312ω, could not be measured. a = 4 μm, Δn = 0.0045.
Table 5
Measurement Data on Devices Used in the Experiments
For the computation, values of R have been estimated from measurements of attenuation using oil overlays (see Ref. 32).
Using relation (26). The computed efficiency assumes that all the fundamental wavelength power was in the LP01ω mode, which was not the case.
Tables (5)
Table 1
Sensitivity of the Phase-Matching Pitch Λ on the Core Radius a, Core–Cladding Index Difference Δn, and Wavelength λ, for a = 4.0 μm, Δn = 4.5 × 10−3, and λ = 1.064 μm
Mode Interaction
Parameter
LP01ω → LP012ω
LP01ω → LP112ω
∂Δ/∂a
2
5 × 10−3
∂Λ/∂Δn (m)
−10−3
14.55 × 10−6
∂Λ/∂λ (μm/nm)
55 × 10−3
79.4 × 10−3
Phase-match length limited by above parameters (mm) [see Eq. (8)]a
1237
446
Length limited by pitch tolerance alone (mm) (see text)b
90
54.95
δΔn/Δn of 10−3% and δa/a of 10−2% have been used to calculate the data.
A tolerance of ±2.5 × 10−2% assumed.
Table 2
Magnitudes and Phases of the Active χijkl(3)El0 Tensor Elements as a Result of the Components of the Applied dc Electric Field Relative to χxxxx(3)Ex0 and Grouped as in Eqs. (21a) and (21b)a
The subscripts of χ(3) are grouped from terms such as those in Eqs. (18a)–(19b).
Dependent on electrode mark/space ratio, b/c. Values shown assume that the static field components are equal to Ex0.
Table 3
Dimensions of Periodic Electrode Structures Used in Experiments
Mask
Electrode Width, b (μm)
Electrode Space, c (μm)
Pitch, Λ Λ (μm)
A
15.6
4.4
40
B
4.4
15.6
40
C
4.4
11.6
32
Table 4
Measured and Computed Coherence Lengths and Overlap Integrals Ratios for Seven Mode Interactions Are Compared Using Data from Device D1a
LP11ω → LP212ω and LP01ω → LP012ω are coincident in the phase-matched data shown in Fig. 12. The former, weaker interaction was therefore not resolved. LP11ω → LP012ω could not be phase matched because the grating pitch used in the experiment was too large. Interaction LP01ω → LP312ω, could not be measured. a = 4 μm, Δn = 0.0045.
Table 5
Measurement Data on Devices Used in the Experiments
For the computation, values of R have been estimated from measurements of attenuation using oil overlays (see Ref. 32).
Using relation (26). The computed efficiency assumes that all the fundamental wavelength power was in the LP01ω mode, which was not the case.