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Monolithic Optically Contacted WalkOff-Compensating Structures
(2N-OCWOC)
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Application notes
  1. Birefringence walkoff & deleterious effects
  2. Principle of walkoff-compensation
  3. 2N-OCWOC periodic structure
  4. Benefit in terms of conversion efficiency and beam profile
  5. When to apply for 2N-OCWOC strutures for SHG, DFG, OPO?
  6. Bibliography

  ktp-10-ocwoc

A 10-OCWOC structure made from 1mm thick KTP plates (left) and a 10mm long bulk KTP sample.

1.

What is birefringence walkoff ?

Phase-matching (PM) in three-wave mixing \chi^(2) parametric processes requires that the phase-velocities (vi = c/ni) of the interacting waves are matched. Due to normal material dispersion, this condition can be satisfied only in birefringent nonlinear media (with allowed eigenmode polarizations for the E-fields), along a direction \theta of propagation (PM direction) with respect to the optical cristallo-physical frame. For non-zero PM angle, the "extraordinary" energy or ray path Se (blue, E-field in the plane of figure) walks-off the corresponding wavevector ke (yellow, E-field perpendicular) by a double-refraction  (or walkoff) angle \rho.  This phenomenon results in poor overlap between the interacting rays and elliptic beam shape for the generated e-wave.
pm_i

Representation of PM (in terms of the index ellipsoids) in a birefringent material at an angle \theta from the optic axis (c).

2.

3.


Principle of walkoff compensation

The following figures show how walkoff can be compensated, starting from a bulk element, for type-I and type-II coupling among the 3 interacting waves. The figure can refer for instance to a second-harmonic generation (SHG) of a yellow laser to the blue-UV.

BULK crystal: in type-I coupling, the SH wave is stretched in the walkoff plane, yielding a highly elliptical beam,  while in type-II poor overlap of the two fundamental orthogonally polarized waves limit the interaction length.


 Type-I (ooe)
Type-II (oeo)

bulk-i
Fig. 1a
bulk-II
Fig. 2a
2-OCWOC tandem: the bulk crystal is cut into two halves (N=1), arranged in the WOC configuration and optically adhered (and eventually diffusion bonded). Transverse beam profile re-symmetrization occurs (type-I) together with conversion efficiency enhancement due to the increase in interaction length.

2-ocwoc-i
Fig. 1b
2-ocwoc-ii
Fig. 2b

2N-OCWOC periodic structure                      

8-OCWOC structure: the bulk crystal is cut into 8 plates (N=4) arranged in the WOC configuration. The e-wave is birefringence-guided along the  polarization wave, achieving  full overlap leading to  several times enhanced energy conversion and full SH beam reshaping toward  a  circular Gaussian beam.

Type-I (ooe)
Type-II (oeo)

8-ocwoc-i
Fig. 1c
8-ocwoc-ii
Fig. 2c

4.

Benefit in terms of conversion efficiency and beam profile

For second-harmonic generation (SHG) the power conversion efficiency  of 2N-OCWOC  devices  can be expressed as function of the focusing waist w0 and the walkoff parameter B :


gamma-formula

 with 
B-par

The following figures shows, e.g., the SH efficiency enhancement and transverse beam profile re-symmetrization brought by 2N-OCWOC (N=1 and N=4) with BBO phase-matched for type-I(ooe) SHG of a 570nm dye laser. The case of a struture length Lc = 8mm is considered and compared with the case a a bulk non WOC crystal (yellow curves). For this parametric process, walkoff is as large as \rho=4.8°.

conv-N



green-arrow
 bbo-profile

Tuning curves for Bulk, 2-OCWOC and 8-OCWOC tandems of identical lengths. At optimum phase-mismatch, a x2 enhancement (x7)  is expected  for a 2-plate (8-plate)  tandem as compared with a bulk sample.

Transverse beam shape re-symmetrization in the walkoff  plane, as the pairing number N is increased. The dashed  line corrresponds  to  the  profile in the  walkoff unaffected  direction.


NB: The enhancement in type-II parametric processes is superior to type-I  because the gain in overlap between the two cross-polarized fundamental waves is greater (Fig. 2b).
Experimentally, an efficiency enhancement by x22 into the green has been observed with a 10-OCWOC type-II KTP structure (see picture below) for the SHG at 1064nm.



green-arrow
 conv-eff

ktp-10-ocwoc
Conversion efficiency versus focusing for a bulk KTP (h0), 4-OCWOC (h2) and 10-OCWOC  structure  (h5) , all with Lc=10mm,
The practical design of 2N-OCWOC structures is a very delicate task. In addition to the mechanical processing, it requires the accurate knowledge of the wavelengths involved in the 3-wave mixing process, and a preliminary test of angular phase-matching direction using a test bulk sample, because enhancement depends on how near from normal incidence the structure is designed for.

5.

When to apply for 2N-OCWOC structures ?

These periodic structures are particularly usefull for blue-UV (SHG of visible lasers) and mid-IR generation (DFG or OPOs), because no periodically-poled (PP) materials are available in the extreme range of the optical spectrum.  Due to the low loss at the optical contact boundaries, they can be used inside enhancement resonators (only the end facets need to be AR coated). In the UV, BBO is the only material of choice owing to its largest nonlinearity and transmission among the oxo-borates.  Among the BBO 2N-OCWOC potential applications:

  • cw blue-UV powerful laser sources (200 - 400 nm) for atom cooling and trapping
  • 3rd harmonic generation (THG) using cascaded crystals (OCWOC for the 1st SHG, follwed by the sum-frequency crystal)
  • Optical parametric oscillation with critically phase-matched birefringent NLO crystals (reduced threshold by the walkoff cancellation)
  • Optical Parametric Chirped Pulse Amplification

In the mid-IR, AgGaS2 can be used to cancel the walkoff effect in optical parametric oscillators (OPOs) .
2N-OCWOC structures can also  overcome the aperture limitations of PP materials when high energy pulsed lasers are used, or to lower the oscillation threshold of cw OPOs.

6.

Bibliography

[1] - J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, D. Lupinski, Walkoff-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices, Proc. SPIE 2700 66 (1996).
[2] - J.-J. Zondy, C. Bonnin, D. Lupinski, Second-harmonic generation with monolithic walk-off-compensating periodic structures. I. Theory,  J. Opt. Soc. Am. B 20, 1675 (2003).
[3] - J.-J. Zondy, D. Kolker, C. Bonnin, D. Lupinski, Second-harmonic generation with monolithic walk-off-compensating periodic structures. II. Experiments,  J. Opt. Soc. Am. B 20, 1695 (2003).
[4] - S. Carrasco, D.V. Petrov,  J.P. Torres, L. Torner, H. Kim, G. Stegeman, J.-J. Zondy, Observation of self-trapping of light in walk-off compensating tandems,  Opt. Lett. 29, 382 (2004).
[5] - J. P. Fève, J.-J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, G. Marnier, Optimized blue light generation in optically contacted walkoff-compensated RbTiOAsO4 and KTiOP1-yAsyO4 ,’’ Opt. Commun. 161, 359 (1999).
[6] -  M. Vaupel, A. Maitre, C. Fabre, Observation of pattern formation in an optical parametric oscillator,  Phys. Rev. Lett. 83, 5278 (1999).
[7] - R. F. Wu, P. B. Phua, K. S. Lai, Y. L. Lim, E. Lau, A. Chang, C. Bonnin, D. Lupinski, ‘‘Compact 21-W  2-um intracavity
optical parametric oscillator,’’ Opt. Lett. 25, 1460 (2000).

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