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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 14 — Jul. 15, 2013
  • pp: 17122–17130
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Control of the properties of micro-structured waveguides in lithium niobate crystal

Huseyin Karakuzu, Mykhaylo Dubov, and Sonia Boscolo  »View Author Affiliations


Optics Express, Vol. 21, Issue 14, pp. 17122-17130 (2013)
http://dx.doi.org/10.1364/OE.21.017122


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Abstract

We study numerically depressed-index cladding, buried, micro-structured optical waveguides that can be formed in a lithium niobate crystal by femtosecond laser writing. We demonstrate to which extent the waveguiding properties can be controlled by the waveguide geometry at the relatively moderate induced refractive index contrasts that are typical of the direct femtosecond inscription.

© 2013 OSA

1. Introduction

The combination of excellent electro-optical, acousto-optical and nonlinear optical (χ(2)) properties, as well as its wide transparency window, make lithium niobate (LiNbO3) an attractive host material for applications in integrated nonlinear optics [1

1. T. Suhara and M. Fujimura, Waveguide Nonlinear-Optic Devices (Springer-Verlag, 2003) [CrossRef] .

]. The majority of such applications require manufacture of optical waveguides (WGs) to confine light propagation in reduced volumes, thus reaching high light intensities. As one of the most efficient techniques for three-dimensional volume micro-structuring of transparent dielectrics, the femtosecond (fs) laser inscription method [2

2. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003) [CrossRef] .

, 3

3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

] has been widely applied to fabricate optical WGs in numerous optical materials, including optical crystals [4

4. A. M. Streltsov, “Femtosecond-laser writing of tracks with depressed refractive index in crystals,” in Conference on Laser Micromachining for Optoelectronic Device Fabrication , A. Ostendorf, ed., Proc. SPIE 4941, 51–57 (2003) [CrossRef] .

11

11. F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser & Photon. Rev. doi: [CrossRef] (2013).

], ceramics, glasses and polymers. The possibility of inscribing arbitrarily shaped WGs in the bulk of various crystals has allowed for new geometrical degrees of freedom in the design of integrated optical devices. Buried integrated laser sources, nonlinear-frequency converters, amplifiers, single-photon detectors and other devices have already been achieved based on this technology [3

3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

, 11

11. F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser & Photon. Rev. doi: [CrossRef] (2013).

].

While any transparent material being irradiated by fs laser pulses with an energy at or above a certain threshold becomes absorbing, this occurs only in the vicinity of the focal point. This fact allows precision modification of the material refractive index (RI) by translating the sample continuously along a certain three-dimensional path. Such a procedure can lead to the creation of isolated air holes or voids [12

12. S. Juodkazis, M. Sudzius, V. Mizeikis, H. Misawab, E. G. Gamaly, Y. Liu, O. A. Louchev, and K. Kitamura, “Three-dimensional recording by tightly focused femtosecond pulses in LiNbO3,” Appl. Phys. Lett. 89, 062903 (2006) [CrossRef] .

, 13

13. S. Juodkazis and H. Misawa, “Laser processing of sapphire by strongly focused femtosecond pulses,” Appl. Phys. A 93, 857–861 (2008) [CrossRef] .

], pearl chains [14

14. R. Graf, A. Fernandez, M. Dubov, H. J. Brueckner, B. N. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87, 21–27 (2007) [CrossRef] .

], and also continuous, smooth tracks that are suitable for low-loss light guiding [15

15. T. Allsop, M. Dubov, V. Mezentsev, and I. Bennion, “Inscription and characterization of waveguides written into borosilicate glass by a high-repetition-rate femtosecond laser at 800nm,” Appl. Opt. 49, 1938–1950 (2010) [CrossRef] [PubMed] .

]. The positive RI contrasts between exposed and unexposed areas that are typically induced by direct fs writing in optical glasses [3

3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

] can be up to an order of magnitude higher than those of optical fibres [15

15. T. Allsop, M. Dubov, V. Mezentsev, and I. Bennion, “Inscription and characterization of waveguides written into borosilicate glass by a high-repetition-rate femtosecond laser at 800nm,” Appl. Opt. 49, 1938–1950 (2010) [CrossRef] [PubMed] .

]. Continuous, smooth tracks can also be inscribed in various crystal materials [3

3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

,5

5. I. Bennion, M. Dubov, I. Khruschev, A. Okhrimchuck, and A. Shestakov, “Laser inscription of optical structures in crystals,” Patent WO 2005040874 A2 (2005), http://www.google.com/patents/WO2005040874A2.

,6

6. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG: Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30, 2248–2250, (2005) [CrossRef] [PubMed] .

,11

11. F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser & Photon. Rev. doi: [CrossRef] (2013).

,16

16. A. G. Okhrimchuk, V. K. Mezentsev, H. Schmitz, M. Dubov, and I. Bennion, “Cascaded nonlinear absorption of femtosecond laser pulses in dielectrics,” Laser Phys. 19, 1415–1422 (2009) [CrossRef] .

,17

17. A. Okhrimchuk, V. Mezentsev, A. Shestakov, and I. Bennion, “Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses,” Opt. Express 20, 3832–3843 (2012) [CrossRef] [PubMed] .

], featuring reduced RI in the central area of the track and slightly increased RI in the surrounding region [18

18. J. Burghoff, S. Nolte, and A. Tünnermann, “Origins of waveguiding in femtosecond laser-structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007) [CrossRef] .

]. Single tracks in crystals may exhibit waveguiding properties, but guidance occurs only in the surrounding areas of residual stress left within the material by the laser beam passage [3

3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

]. On the other hand, by writing multiple tracks with a reduced RI around the unmodified volume of material it is possible to produce a depressed-index cladding with the central volume serving as the core of a WG [4

4. A. M. Streltsov, “Femtosecond-laser writing of tracks with depressed refractive index in crystals,” in Conference on Laser Micromachining for Optoelectronic Device Fabrication , A. Ostendorf, ed., Proc. SPIE 4941, 51–57 (2003) [CrossRef] .

6

6. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG: Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30, 2248–2250, (2005) [CrossRef] [PubMed] .

,10

10. Q. An, Y. Ren, Y. Jia, J. R. Vázquez de Aldana, and F. Chen, “Mid-infrared waveguides in zinc sulfide crystal,” Opt. Mater. Express , 3, 466–471 (2013) [CrossRef] .

,12

12. S. Juodkazis, M. Sudzius, V. Mizeikis, H. Misawab, E. G. Gamaly, Y. Liu, O. A. Louchev, and K. Kitamura, “Three-dimensional recording by tightly focused femtosecond pulses in LiNbO3,” Appl. Phys. Lett. 89, 062903 (2006) [CrossRef] .

], whereby the mechanical stress has minor influence on the WG modes. The simplest type of depressed-index cladding consists of only two parallel tracks positioned close to each other [3

3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

, 18

18. J. Burghoff, S. Nolte, and A. Tünnermann, “Origins of waveguiding in femtosecond laser-structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007) [CrossRef] .

]. But such a WG structure does not allow for control over the waveguiding properties. On the other hand, due to geometric flexibility, the depressed cladding may consist of a fairly large number of arbitrarily arranged tracks confining the flexibly large and shaped core guiding area [17

17. A. Okhrimchuk, V. Mezentsev, A. Shestakov, and I. Bennion, “Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses,” Opt. Express 20, 3832–3843 (2012) [CrossRef] [PubMed] .

]. Depressed-cladding WGs have been demonstrated to achieve light propagation with good mode confinement at different wavelengths, and low propagation losses as compared with directly written, single-track WGs [5

5. I. Bennion, M. Dubov, I. Khruschev, A. Okhrimchuck, and A. Shestakov, “Laser inscription of optical structures in crystals,” Patent WO 2005040874 A2 (2005), http://www.google.com/patents/WO2005040874A2.

, 6

6. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG: Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30, 2248–2250, (2005) [CrossRef] [PubMed] .

, 10

10. Q. An, Y. Ren, Y. Jia, J. R. Vázquez de Aldana, and F. Chen, “Mid-infrared waveguides in zinc sulfide crystal,” Opt. Mater. Express , 3, 466–471 (2013) [CrossRef] .

, 17

17. A. Okhrimchuk, V. Mezentsev, A. Shestakov, and I. Bennion, “Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses,” Opt. Express 20, 3832–3843 (2012) [CrossRef] [PubMed] .

, 19

19. L. Dong, W. Wong, and M. E. Fermann, “Single mode propagation in fibers and rods with large leakage channels,” Patent US 2013/0089113 A1 (2013), http://www.google.co.uk/patents/US7787729.

]. It has also been proved that depressed-cladding WGs in nonlinear crystals can achieve enhanced-efficiency second-harmonic generation as compared with stress-induced WGs [20

20. N. Dong, F. Chen, and J. R. Vázquez de Aldana, “Efficient second harmonic generation by birefriengent phase matching in femtosecond laser inscribed KTP cladding waveguides,” Phys. Status Solidi: Rapid Research Lett. 6, 306–308 (2012) [CrossRef] .

, 21

21. Y. Jia, J. R. Vázquez de Aldana, C. Romero, Y. Ren, Q. Lu, and F. Chen, “Femtosecond-laser-inscribed BiB3O6 nonlinear cladding waveguide for second-harmonic generation,” Appl. Phys. Express 5, 072701 (2012) [CrossRef] .

].

In this paper, we study numerically depressed-cladding, buried WGs that can be formed in a z-cut LiNbO3 crystal by fs laser writing, in a pursuit of establishing how experimentally accessible parameters, such as the number, position and size of the cladding tracks, and the RI contrast between the low-index cladding structure and the core guiding region, can be used for achieving control over the propagation constants of modes with different polarizations, hence the conditions for (quasi-) phase matching in a WG geometry. A similar approach has already been used for controlling the waveguiding properties of micro-structured optical fibres (MOFs) [22

22. F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres (Imperial College, 2012).

24

24. G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflatteend chromatic dispersion with low losses,” Opt. Lett. 28, 989–991 (2003) [CrossRef] [PubMed] .

], where tracks with a reduced RI are naturally formed during the fibre drawing process. The results presented in this paper are relevant to various applications. These include optical parametric amplifiers with a small footprint based on WGs in χ(2)-nonlinear materials, ultrafast, synchronously-pumped single-photon (quantum) sources and detectors realized as WG-based, frequency-conversion modules, all-optical wavefront generators and pulse shapers, and mid-infrared (IR) integrated optical components.

2. Waveguide packing geometry and methodology

For this study, we modeled depressed-cladding WG structures with a hexagonal shape. This is a fairly commonly used WG shape, which has already been well studied in the case of isotropic materials such as MOFs [24

24. G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflatteend chromatic dispersion with low losses,” Opt. Lett. 28, 989–991 (2003) [CrossRef] [PubMed] .

]. The depressed cladding was formed by a finite number of rings of regularly spaced, cylindrical tracks whose centers were arranged hexagonally, as shown in Fig. 1. These tracks can be written in a LiNbO3 crystal by direct fs laser irradiation using a transverse inscription geometry [3

3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

]. In Fig. 1 we also show the microscopic image of a top view of an example WG that we have fabricated in LiNbO3 crystal with a high-repetition-rate fs laser system, revealing smooth, high-contrast tracks, without any coloring. In our modeling, the reduced RI of the tracks was assumed to be a real value, uniform across the cross section of a track, and polarization- and wavelength-independent. Note that this might not be the case in practical scenarios, especially under arbitrary fs laser irradiation protocols. Indeed, direct measurements of the ultrafast dynamics of the dielectric permittivity of glass materials [25

25. A. V. Turchin, M. Dubov, and J. A. R. Williams, “3D reconstruction of the complex dielectric function of glass during femtosecond laser micro-fabrication,” Opt. & Quantum Electron. 42, 873–886 (2011) [CrossRef] .

] revealed that irradiation by high-repetition-rate fs laser can generate changes in both real and imaginary parts of the permittivity, especially for long irradiation times or high laser pulse energies. Importantly, fs-written tracks in crystals possess a complex geometry and include volumes of material with increased and decreased RIs [6

6. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG: Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30, 2248–2250, (2005) [CrossRef] [PubMed] .

]. However, the change of RI, averaged across the cross section of each track, has always negative sign. Key parameters that were varied in the numerical model were extracted from experiments (the results will be published elsewhere). They include the track size d, the track spacing or pitch a, the RI contrast between the cladding and core regions δn, and the number of track rings or depressed-cladding layers Nr. On the other hand, in this work we did not explore different symmetries, more complex topologies or tiling, and disorder. Some of such examples can be found in [19

19. L. Dong, W. Wong, and M. E. Fermann, “Single mode propagation in fibers and rods with large leakage channels,” Patent US 2013/0089113 A1 (2013), http://www.google.co.uk/patents/US7787729.

].

Fig. 1 Left: cross section of modeled depressed-cladding WG with two rings of tracks, and ellipsoid of indices for LiNbO3 host. Right: top microscopic view of example microstructured WG fabricated in LiNbO3 by high-repetition-rate fs laser.

LiNbO3 is a class 3m, negative uniaxially birefringent crystal, suitable for both type I and type II (quasi-) phase matching [26

26. D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer-Verlag, 2005).

]. In this study we considered a z-cut LiNbO3 wafer, with the larger surfaces perpendicular to the z axis of the coordinate system, coincident with the optical axis of the crystal (Fig. 1). Light was assumed to propagate along the y axis. The Sellmeier expansions for the indices of 5 mol.% magnesium oxide (MgO) doped LiNbO3 were taken from [27

27. D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol.% magnesium oxide-doped lithium niobate,” J. Opt. Soc. Am. B 14, 3319–3322 (1997) [CrossRef] .

].

Equations (1) and (2) were solved using the COMSOL simulation software based on the finite element method to find out the complex effective RIs no,eeff of the modes of the structure for the two orthogonal polarization states x and z. The wavelength was varied in the transparency window of 5% MgO-doped LiNbO3. In the numerical simulations, a perfectly matched layer (PML) absorber was used to truncate the computational domain and, thus, minimize the effect of boundary reflections. We chose a circular PML surrounding the cross-section of the WG structure and isotropic in its absorption, defined by [29

29. Y. Tsuji and M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18618–623 (2000) [CrossRef] .

]
nPML(r)=no,eikmax(rrinL)2,rin<rrin+L
(3)
where r is the polar radial coordinate, rin and L are the respective inner radius and thickness of the PML, and kmax is the maximum absorption value, which was assumed to be wavelength-independent. Special care was given to the choice of the parameters of the PML and the computational mesh. Indeed, the PML must have sufficiently large kmax to provide an adequate level of absorption and be wide enough to guarantee a small absorption gradient across its extent. In [30

30. A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys. 230, 2369–2377 (2011) [CrossRef] .

], the computational error was estimated to scale down with the PML’s thickness approximately as 1/L8. The mesh size must be a few times smaller than the wavelength being used to ensure good accuracy of the results. In our simulations, we set kmax = 0.05 and L = 40μm, and we mapped the computational domain with an automatically configured, triangle mesh with the minimum size 0.003μm in the core of the domain and the relative growth rate 1.1. The maximum mesh size at the periphery of the domain was of the same order of magnitude as the shortest wavelength in use (0.3μm). The same mesh was used for all wavelengths in the range being studied. Optimized PML and mesh parameters led to a maximum error of approximately 10−10 dB/cm in the computed confinement losses L. During the wavelength scanning, the most compact, Gaussian-like mode was selected using the criterium of ’minimum effective mode area’.

3. Results and discussion

Fig. 2 Real parts of effective RIs for O and E waves as a function of wavelength for a depressed-cladding WG with two rings of tracks, Nr = 2. The O and E RIs of the unmodified material are also shown. WG parameters are: d = 1.6μm, a = 2μm, δn = −0.05.

In Fig. 3 we show the variation of the key WG quantities: WG dispersion DW and confinement loss L, as a function of both wavelength and track spacing for a WG with two rings of tracks. The pitch a was varied from 2 to 7μm, whereas other WG parameters were kept the same as in Fig. 2. A noticeable trend in the dispersion curves is that the dispersion changes introduced by the WG are more pronounced for smaller a. These changes, however, are not big enough to affect the total dispersion of the structure significantly. Note that at the shorter wavelengths the depressed cladding can effectively confine the modes in the core guiding region. Guidance becomes worse at longer wavelengths, hence the modes behave like ’leaky modes’. Because of such a leakage at the longer wavelengths, none of the resonance features which would be expected due to the periodicity of the structure, can be observed. Moreover, band-gap resonances could be observed for this structure at wavelengths three or four times larger than the pitch, which fall outside the wavelength range used in our study. Our simulations also show that the change of the pitch in itself does not extend the spectral range where the loss figures for the modes are acceptably low. We assume here 1dB/cm to be an acceptable loss level for technological applications.

Fig. 3 Left: WG dispersion DW for O wave, and right: confinement losses for O and E waves as a function of wavelength for a depressed-cladding WG with two rings of tracks with various pitches. The material dispersion Dmat is also shown. Other WG parameters are: d = 1.6μm, δn = −0.05.

The influence of the RI contrast of tracks on the WG dispersive and loss properties is illustrated by Fig. 4. There δn was varied from −0.02 to −0.05. It is clear that larger RI contrasts expand the wavelength region where the values of geometric loss are acceptably low, even with only two rings of tracks. The wavelength region where the WG contribution to the total dispersion is not negligible becomes also wider, though the dispersion changes due to the WG remain small.

Fig. 4 Left: WG dispersion DW for O wave, and right: confinement losses for O and E waves as a function of wavelength for a depressed-cladding WG with two rings of tracks of various RI contrasts. The material dispersion Dmat is also shown. Other WG parameters are: d = 1.6μm, a = 2μm.

A general fact that emerged from our study is that control over the waveguiding properties is better for compact cladding structures with small-sized and densely packed tracks with the largest possible RI contrasts. Figure 5 highlights the more interesting scenario that can be achieved with a varying number of cladding layers. The RI contrast was set to δn = −0.01 in these simulations. As can be seen from Fig. 5, while the dispersion changes due to the WG become increasingly more pronounced with increasing Nr, the overall effect of adding rings 3–7 on the dispersion properties of the structure is little. On the other hand, importantly, adding further rings of tracks can reach much better control over the losses even at the relatively moderate RI contrasts that are currently technologically feasible. As Fig. 5 shows, adding rings 3–7 results in an extension of the spectral range where the confinement losses in both O and E polarizations are below 1dB/cm to the wavelengths near 2μm, and in a reduction of the losses in both polarizations by more than three orders of magnitude near the telecommunication wavelength λ = 1.55μm. This is an important result for any practical applications of such WG structures. We would like to note, however, that the figures reported here include only confinement losses showing the limitations that are due to the confinement by a micro-structured WG. In practice the total losses of the modes propagating in the structure will always be higher because of various factors, including: material absorption induced by fs irradiation, scattering losses due to irregularities (non-smoothness) of the cladding tracks, and imperfect positioning of the tracks which would increase the leakage of modes out of the guiding region.

Fig. 5 Left: WG dispersion DW for O wave, and right: confinement losses for O and E waves as a function of wavelength for a depressed-cladding WG with varying number of track rings. The material dispersion Dmat is also shown. Other WG parameters are: d = 1.6μm, a = 2μm, δn = −0.01.

As it was shown by Renversez et al. [24

24. G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflatteend chromatic dispersion with low losses,” Opt. Lett. 28, 989–991 (2003) [CrossRef] [PubMed] .

] in the case of MOFs, a natural strategy to achieve low losses with fewer tracks or, equally, to extend the spectral range of low-loss operation of the WG structure, is to allow the track diameter to differ from one ring to another with the exterior rings that have large tracks. This design concept is illustrated in Fig. 6, which shows the variation of the confinement losses in the O and E polarizations with wavelength for a seven-ring structure with different track diameters. The track diameter of the innermost ring was arbitrarily set to d1 = 1μm, and the diameter of subsequent rings was increased linearly up to the maximum value d7 = 2.2μm for the outermost ring. Such a variation of the track size can be easily realized in practice by changing the energy of the irradiating fs laser pulses from one ring to another. Note, however, that this would entail a slight change in the induced RI contrast since also the latter depends on the pulse energy. The pitch was a = 2.5μm, and the RI contrast was δn = −0.01 in these simulations. One can see from Fig. 6 that, compared to the usual WG structure made of tracks of identical diameter (Fig. 5), this WG design allows us to expand the diapason of low-loss operation for both O and E polarizations into the mid-IR spectral region. Optimization of these WG geometries should enable further expansion of their low-loss operational spectral range.

Fig. 6 Left: confinement losses for O and E waves as a function of wavelength for depressed-cladding WG with seven rings of tracks, Nr = 7, with different diameters d = 1 – 2.2μm. Other WG parameters are: a = 2.5μm, δn = −0.01. The losses for seven rings of identical diameter are also shown (extracted from Fig. 5). Right: cross section of modeled WG structure.

An important issue that should be addressed here relates to the practical feasibility of the investigated WG structures. As mentioned previously, there are experimental limitations on the magnitude of the RI contrasts that can be reached for smooth tracks in crystals. Thus, to provide WG structures that display low-loss operation over a wide spectral range, the most viable solution is to write a fairly large number of rings of tracks, possibly with different sizes. These requirements on the number of rings make high-repetition-rate fs laser inscription the preferred micro-fabrication technique, as high-repetition-rate fs systems can enable up to four orders of magnitude quicker fabrication than the low-repetition-rate ones [15

15. T. Allsop, M. Dubov, V. Mezentsev, and I. Bennion, “Inscription and characterization of waveguides written into borosilicate glass by a high-repetition-rate femtosecond laser at 800nm,” Appl. Opt. 49, 1938–1950 (2010) [CrossRef] [PubMed] .

]. For example, for a propagation length of 10 centimeters in a WG with seven rings (around 200 tracks) the total length of the inscribed lines would amount to approximately 20 meters. Clearly, if one uses a kHz fs system (with a typical sample translation speed of 10 to 100μm/s, or of 500μm/s by use of astigmatic beam inscription [16

16. A. G. Okhrimchuk, V. K. Mezentsev, H. Schmitz, M. Dubov, and I. Bennion, “Cascaded nonlinear absorption of femtosecond laser pulses in dielectrics,” Laser Phys. 19, 1415–1422 (2009) [CrossRef] .

]), the fabrication time required on a single structure may exceed 60 hours, whereas a high-repetition-rate system can do the job in less than an hour.

4. Conclusions

We have shown numerically the feasibility of controlling the guiding properties of depressed-index cladding WGs that can be formed in a LiNbO3 crystal by high-repetition-rate fs laser writing, by exploiting the WG geometric and structural characteristics. Our study ranged over the parameter space: track size, spacing, number of rings, and RI contrast, that is accessible experimentally. As we saw, the relatively moderate RI contrasts that are feasible by use of current fs micro-fabrication technology mean that geometric WG parameters have little control over the chromatic dispersion properties of the WG. On the other hand, the number of track rings revealed to play a major role in the control of the geometric losses. Importantly for technological applications, we have shown that for the typical induced RI contrast −0.01, increasing the number of rings from two to seven results in an extension of the spectral range where the confinement losses in both O and E polarizations are acceptably low (below 1dB/cm) to the wavelengths near 2μm, and in a reduction of the losses in both polarizations by more than three orders of magnitude near the telecommunication wavelength λ = 1.55μm. We have also shown that WG designs with track diameters that differ from one ring to another [24

24. G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflatteend chromatic dispersion with low losses,” Opt. Lett. 28, 989–991 (2003) [CrossRef] [PubMed] .

] can further expand the spectral region of low-loss operation into the mid-IR range. Similarly, these designs would allow us to achieve low losses with fewer tracks. In view of the requirements imposed by losses on the number of rings, high-repetition-rate fs lasers would advantageously be used to fabricate the WG structures studied in this paper. We plan to develop optimization procedures and design principles for micro-structured WGs in LiNbO3 that are tailored to specific applications in a future work.

Acknowledgments

We would like to thank Dr. Vladimir Mezentsev, Prof. Keith Blow (Aston University) and Prof. Ivan Avrutsky (Wayne State University, Detroit, MI, USA) for fruitful discussions. We also acknowledge support from the Leverhulme Trust (grant RPG-278).

References and links

1.

T. Suhara and M. Fujimura, Waveguide Nonlinear-Optic Devices (Springer-Verlag, 2003) [CrossRef] .

2.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77, 109–111 (2003) [CrossRef] .

3.

R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012) [CrossRef] .

4.

A. M. Streltsov, “Femtosecond-laser writing of tracks with depressed refractive index in crystals,” in Conference on Laser Micromachining for Optoelectronic Device Fabrication , A. Ostendorf, ed., Proc. SPIE 4941, 51–57 (2003) [CrossRef] .

5.

I. Bennion, M. Dubov, I. Khruschev, A. Okhrimchuck, and A. Shestakov, “Laser inscription of optical structures in crystals,” Patent WO 2005040874 A2 (2005), http://www.google.com/patents/WO2005040874A2.

6.

A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG: Nd3+ crystal by femtosecond laser writing,” Opt. Lett. 30, 2248–2250, (2005) [CrossRef] [PubMed] .

7.

J. Thomas, M. Heinrich, J. Burghoff, S. Nolte, A. Ancona, and A. Tüennermann, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 2799178, (2007) [CrossRef] .

8.

J. Burghoff, H. Hartung, S. Nolte, and A. Tünnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A 86, 165–170 (2007) [CrossRef] .

9.

S. Campbell, R. R. Thomson, D. P. Hand, A. K. Kar, D. T. Reid, C. Canalias, V. Pasiskevicius, and F. Laurell, “Frequency-doubling in femtosecond laser inscribed periodically-poled potassium titanyl phosphate waveguides,” Opt. Express 15, 17146–17150 (2007) [CrossRef] [PubMed] .

10.

Q. An, Y. Ren, Y. Jia, J. R. Vázquez de Aldana, and F. Chen, “Mid-infrared waveguides in zinc sulfide crystal,” Opt. Mater. Express , 3, 466–471 (2013) [CrossRef] .

11.

F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser & Photon. Rev. doi: [CrossRef] (2013).

12.

S. Juodkazis, M. Sudzius, V. Mizeikis, H. Misawab, E. G. Gamaly, Y. Liu, O. A. Louchev, and K. Kitamura, “Three-dimensional recording by tightly focused femtosecond pulses in LiNbO3,” Appl. Phys. Lett. 89, 062903 (2006) [CrossRef] .

13.

S. Juodkazis and H. Misawa, “Laser processing of sapphire by strongly focused femtosecond pulses,” Appl. Phys. A 93, 857–861 (2008) [CrossRef] .

14.

R. Graf, A. Fernandez, M. Dubov, H. J. Brueckner, B. N. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B 87, 21–27 (2007) [CrossRef] .

15.

T. Allsop, M. Dubov, V. Mezentsev, and I. Bennion, “Inscription and characterization of waveguides written into borosilicate glass by a high-repetition-rate femtosecond laser at 800nm,” Appl. Opt. 49, 1938–1950 (2010) [CrossRef] [PubMed] .

16.

A. G. Okhrimchuk, V. K. Mezentsev, H. Schmitz, M. Dubov, and I. Bennion, “Cascaded nonlinear absorption of femtosecond laser pulses in dielectrics,” Laser Phys. 19, 1415–1422 (2009) [CrossRef] .

17.

A. Okhrimchuk, V. Mezentsev, A. Shestakov, and I. Bennion, “Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses,” Opt. Express 20, 3832–3843 (2012) [CrossRef] [PubMed] .

18.

J. Burghoff, S. Nolte, and A. Tünnermann, “Origins of waveguiding in femtosecond laser-structured LiNbO3,” Appl. Phys. A 89, 127–132 (2007) [CrossRef] .

19.

L. Dong, W. Wong, and M. E. Fermann, “Single mode propagation in fibers and rods with large leakage channels,” Patent US 2013/0089113 A1 (2013), http://www.google.co.uk/patents/US7787729.

20.

N. Dong, F. Chen, and J. R. Vázquez de Aldana, “Efficient second harmonic generation by birefriengent phase matching in femtosecond laser inscribed KTP cladding waveguides,” Phys. Status Solidi: Rapid Research Lett. 6, 306–308 (2012) [CrossRef] .

21.

Y. Jia, J. R. Vázquez de Aldana, C. Romero, Y. Ren, Q. Lu, and F. Chen, “Femtosecond-laser-inscribed BiB3O6 nonlinear cladding waveguide for second-harmonic generation,” Appl. Phys. Express 5, 072701 (2012) [CrossRef] .

22.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres (Imperial College, 2012).

23.

T. P. White, R. C. McPhedran, C. M. de Sterke, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 488–490 (2001) [CrossRef] .

24.

G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflatteend chromatic dispersion with low losses,” Opt. Lett. 28, 989–991 (2003) [CrossRef] [PubMed] .

25.

A. V. Turchin, M. Dubov, and J. A. R. Williams, “3D reconstruction of the complex dielectric function of glass during femtosecond laser micro-fabrication,” Opt. & Quantum Electron. 42, 873–886 (2011) [CrossRef] .

26.

D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer-Verlag, 2005).

27.

D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol.% magnesium oxide-doped lithium niobate,” J. Opt. Soc. Am. B 14, 3319–3322 (1997) [CrossRef] .

28.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, CA, 1989).

29.

Y. Tsuji and M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18618–623 (2000) [CrossRef] .

30.

A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys. 230, 2369–2377 (2011) [CrossRef] .

OCIS Codes
(130.3730) Integrated optics : Lithium niobate
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(220.4000) Optical design and fabrication : Microstructure fabrication
(230.7370) Optical devices : Waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: June 4, 2013
Revised Manuscript: July 1, 2013
Manuscript Accepted: July 2, 2013
Published: July 10, 2013

Citation
Huseyin Karakuzu, Mykhaylo Dubov, and Sonia Boscolo, "Control of the properties of micro-structured waveguides in lithium niobate crystal," Opt. Express 21, 17122-17130 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-14-17122


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References

  1. T. Suhara and M. Fujimura, Waveguide Nonlinear-Optic Devices (Springer-Verlag, 2003). [CrossRef]
  2. S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A77, 109–111 (2003). [CrossRef]
  3. R. Osellame, G. Cerullo, and R. Ramponi, eds., Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics 123 (Springer-Verlag, 2012). [CrossRef]
  4. A. M. Streltsov, “Femtosecond-laser writing of tracks with depressed refractive index in crystals,” in Conference on Laser Micromachining for Optoelectronic Device Fabrication, A. Ostendorf, ed., Proc. SPIE4941, 51–57 (2003). [CrossRef]
  5. I. Bennion, M. Dubov, I. Khruschev, A. Okhrimchuck, and A. Shestakov, “Laser inscription of optical structures in crystals,” Patent WO 2005040874 A2 (2005), http://www.google.com/patents/WO2005040874A2 .
  6. A. G. Okhrimchuk, A. V. Shestakov, I. Khrushchev, and J. Mitchell, “Depressed cladding, buried waveguide laser formed in a YAG: Nd3+ crystal by femtosecond laser writing,” Opt. Lett.30, 2248–2250, (2005). [CrossRef] [PubMed]
  7. J. Thomas, M. Heinrich, J. Burghoff, S. Nolte, A. Ancona, and A. Tüennermann, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett.91, 2799178, (2007). [CrossRef]
  8. J. Burghoff, H. Hartung, S. Nolte, and A. Tünnermann, “Structural properties of femtosecond laser-induced modifications in LiNbO3,” Appl. Phys. A86, 165–170 (2007). [CrossRef]
  9. S. Campbell, R. R. Thomson, D. P. Hand, A. K. Kar, D. T. Reid, C. Canalias, V. Pasiskevicius, and F. Laurell, “Frequency-doubling in femtosecond laser inscribed periodically-poled potassium titanyl phosphate waveguides,” Opt. Express15, 17146–17150 (2007). [CrossRef] [PubMed]
  10. Q. An, Y. Ren, Y. Jia, J. R. Vázquez de Aldana, and F. Chen, “Mid-infrared waveguides in zinc sulfide crystal,” Opt. Mater. Express, 3, 466–471 (2013). [CrossRef]
  11. F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser & Photon. Rev. doi: (2013). [CrossRef]
  12. S. Juodkazis, M. Sudzius, V. Mizeikis, H. Misawab, E. G. Gamaly, Y. Liu, O. A. Louchev, and K. Kitamura, “Three-dimensional recording by tightly focused femtosecond pulses in LiNbO3,” Appl. Phys. Lett.89, 062903 (2006). [CrossRef]
  13. S. Juodkazis and H. Misawa, “Laser processing of sapphire by strongly focused femtosecond pulses,” Appl. Phys. A93, 857–861 (2008). [CrossRef]
  14. R. Graf, A. Fernandez, M. Dubov, H. J. Brueckner, B. N. Chichkov, and A. Apolonski, “Pearl-chain waveguides written at megahertz repetition rate,” Appl. Phys. B87, 21–27 (2007). [CrossRef]
  15. T. Allsop, M. Dubov, V. Mezentsev, and I. Bennion, “Inscription and characterization of waveguides written into borosilicate glass by a high-repetition-rate femtosecond laser at 800nm,” Appl. Opt.49, 1938–1950 (2010). [CrossRef] [PubMed]
  16. A. G. Okhrimchuk, V. K. Mezentsev, H. Schmitz, M. Dubov, and I. Bennion, “Cascaded nonlinear absorption of femtosecond laser pulses in dielectrics,” Laser Phys.19, 1415–1422 (2009). [CrossRef]
  17. A. Okhrimchuk, V. Mezentsev, A. Shestakov, and I. Bennion, “Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses,” Opt. Express20, 3832–3843 (2012). [CrossRef] [PubMed]
  18. J. Burghoff, S. Nolte, and A. Tünnermann, “Origins of waveguiding in femtosecond laser-structured LiNbO3,” Appl. Phys. A89, 127–132 (2007). [CrossRef]
  19. L. Dong, W. Wong, and M. E. Fermann, “Single mode propagation in fibers and rods with large leakage channels,” Patent US 2013/0089113 A1 (2013), http://www.google.co.uk/patents/US7787729 .
  20. N. Dong, F. Chen, and J. R. Vázquez de Aldana, “Efficient second harmonic generation by birefriengent phase matching in femtosecond laser inscribed KTP cladding waveguides,” Phys. Status Solidi: Rapid Research Lett.6, 306–308 (2012). [CrossRef]
  21. Y. Jia, J. R. Vázquez de Aldana, C. Romero, Y. Ren, Q. Lu, and F. Chen, “Femtosecond-laser-inscribed BiB3O6 nonlinear cladding waveguide for second-harmonic generation,” Appl. Phys. Express5, 072701 (2012). [CrossRef]
  22. F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres (Imperial College, 2012).
  23. T. P. White, R. C. McPhedran, C. M. de Sterke, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett.26, 488–490 (2001). [CrossRef]
  24. G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflatteend chromatic dispersion with low losses,” Opt. Lett.28, 989–991 (2003). [CrossRef] [PubMed]
  25. A. V. Turchin, M. Dubov, and J. A. R. Williams, “3D reconstruction of the complex dielectric function of glass during femtosecond laser micro-fabrication,” Opt. & Quantum Electron.42, 873–886 (2011). [CrossRef]
  26. D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer-Verlag, 2005).
  27. D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol.% magnesium oxide-doped lithium niobate,” J. Opt. Soc. Am. B14, 3319–3322 (1997). [CrossRef]
  28. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, CA, 1989).
  29. Y. Tsuji and M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol.18618–623 (2000). [CrossRef]
  30. A. Oskooi and S. G. Johnson, “Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media,” J. Comput. Phys.230, 2369–2377 (2011). [CrossRef]

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