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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 27933–27945
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Towards a versatile active wavelength converter for all-optical networks based on quasi-phase matched intra-cavity difference-frequency generation

Adrián J. Torregrosa, Haroldo Maestre, and Juan Capmany  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 27933-27945 (2013)
http://dx.doi.org/10.1364/OE.21.027933


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Abstract

The availability of reconfigurable all-optical wavelength converters for an efficient and flexible use of optical resources in WDM (wavelength division multiplexing) networks is still lacking at present. We propose and report preliminary results on a versatile active technique for multiple and tunable wavelength conversions in the 1500-1700 nm spectral region. The technique is based on combining broadband quasi-phase matched intra-cavity parametric single-pass difference-frequency generation close to degeneracy in a diode-pumped tunable laser. A periodically poled stoichiometric lithium tantalate crystal is used as the nonlinear medium, with a parametric pump wave generated in a continuous-wave self-injection locked Cr3+:LiCAF tunable laser operating at around 800 nm.

© 2013 Optical Society of America

1. Introduction

In particular, wavelength conversions of input/output wavelengths contained within a spectral region around 1500-1700 nm are of interest for wavelength routing in WDM systems based on standard silica fiber-optic operating in the S, C, L and U low-loss optical bands. Up to date, different techniques have been proposed to construct completely optical wavelength conversion devices transparent to intensity modulation. In particular, nonlinear optical frequency mixing based on the well-known second-order parametric process of difference-frequency generation (DFG) emerges as a promising alternative [1

1. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996). [CrossRef]

]. Formally speaking, the DFG process may be viewed in general system theory as the optical analogy of the heterodyning processes widely used in radio-frequency communication systems. A heterodyne converter [Fig. 1(a)
Fig. 1 (a) Schematic heterodyne frequency converter. (b) Schematic of the compact and versatile wavelength converter proposed.
] requires a local oscillator, a frequency mixer and a filter. An incoming (input) wave at frequency ω2 mixes with a local oscillator at a frequency ω1 and generates converted (output) waves at ω3 = ω1 ± ω2. The filter then selects either ω1 + ω2 (sum-frequency generation, SFG) or ω1 − ω2 (DFG).

In case of DFG optical heterodyning, two optical waves at different frequencies ω1 and ω2 (pump and signal respectively) interact in a nonlinear medium and give raise to a third wave (idler) at the difference-frequency ω3 = ω1 − ω2. The pump, signal, and idler waves, play the role of the local oscillator and of the input and output waves respectively. It is well known from nonlinear optics theory that if the pump wave intensity remains continuous during a second-order the conversion process (or at every time), then the output channel preserves the intensity modulation of the input channel with fidelity (undistorted), provided that the pump wave remains essentially undepleted during the DFG nonlinear interaction process. In the undepleted case, DFG conversion efficiency remains independent of the input signal intensity as it will be shown in (1) [6

6. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. Lett. 127, 1918–1939 (1962).

].

Thus, a versatile reconfigurable non-distorting device where a given input channel may be efficiently converted to an arbitrary output channel is still lacking. Ideally, a set of arbitrary input carriers should be converted to another arbitrary set of output carriers maintaining their original intensity modulation. This requires a tunable local oscillator laser (pump laser in what follows). Also, whilst data speed is in the order of Gigabit/s, routing requires typically reconfiguration times of ~10 milliseconds [10

10. R. Muñoz, R. Martínez, and R. Casellas, “Challenges for GMPLS lightpath provisioning in transparent optical networks: Wavelength constraints in routing and signaling,” IEEE Commun. Mag. 47(8), 26–34 (2009). [CrossRef]

]. Therefore, there are several goals to account for in a versatile wavelength converter. On the one hand, we have to account for high DFG conversion efficiency itself to reduce insertion loss, and ideally through an undepleted pump process to preserve the intensity modulation undistorted. On the other, to account for the possibility of fast enough internal reconfiguration of the device in order to be able to dynamically and arbitrarily achieve a targeted output wavelength to manage wavelength-routing in the network. Ideally, reconfiguration should be governed by an electric signal. As in many cases, one has first to find a suitable technology that allows for the goals, make a proof-of-principle, find evidence that supports the final goal, and then continue with improving and developing practical useful devices. Could such a converting device be realizable? We believe it can.

Figure 1(b) shows a possible implementation of such a versatile DFG modulation-transparent wavelength converter in a compact device. As a proof-of principle, we propose to combine:

- A continuous-wave local oscillator based on a diode-pumped vibronic solid-state laser crystals such as titanium sapphire or the Cr3+-doped colquiriite family (Cr3+:LiSAF, Cr3+:LiCAF and Cr3+:LisGAF) [11

11. S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F6:Cr3+: A Promising New Solid-state Laser Material,” IEEE J. Quantum Electron. 24(11), 2243–2252 (1988). [CrossRef]

]. All these crystals provide broadband emission around 800 nm and therefore allow to build tunable local oscillators in the spectral region of interest. However, keeping an eye on future miniaturization or integration, the latter group presents the advantage of a possible direct pump by low-cost commercially available red laser diodes emitting around 665 nm. In particular, Cr:LiCAF arises as an optimum candidate among colquiriites due to its better spectral match for tunable emission between 720 nm and 840 nm approximately, peak emission cross section around 780 nm, and better thermal properties [11

11. S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F6:Cr3+: A Promising New Solid-state Laser Material,” IEEE J. Quantum Electron. 24(11), 2243–2252 (1988). [CrossRef]

].

- A tuning mechanism in the laser that can change the DGF pump wavelength at the routing reconfiguration speed around 10 ms. Ideally, it should be governed by an electric signal, and should provide linewidth narrowing to the MHz level or better for the DFG pump laser. Self-injection locking [12

12. A. E. Siegman, “Laser injection locking,” in Lasers (University Science Book, 1986), pp. 1129–1170.

] with a piezo-controlled diffraction grating external (coupled) cavity can well account for these requisites [13

13. M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron. 34(7), 1288–1296 (1998). [CrossRef]

,14

14. H. Maestre, A. J. Torregrosa, and J. Capmany, “Intracavity Cr3+:LiCAF + PPSLT optical parametric oscillator with self-injection-locked pump wave,” Laser Phys. Lett. 10(3), 035806 (2013). [CrossRef]

]. The control voltage of the piezo would play the role of Vadj in Fig. 1(b).

- A domain-engineered (poled) ferroelectric crystal for the mixer and filter. The quasi-phase matching (QPM) technique employed in poled second order nonlinear crystals [15

15. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007). [CrossRef]

] can provide efficient nonlinear interactions. In particular, periodically poled ferroelectric crystals like lithium niobate or lithium tantalate have been extensively employed for QPM due to their high nonlinear coefficients and its wide transparency range for nonlinear optical interactions. In this context, domain-engineered patterns allow for multiple-interaction and broadband conversion processes in the same physical crystal, and when designed for DFG they provide a natural filtering for SFG [15

15. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007). [CrossRef]

,16

16. C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. 17(5), 1037–1039 (2005). [CrossRef]

]. In addition, QPM can be electro-optically reconfigured thus providing a way to add some reconfiguration flexibility via an electric control signal [17

17. N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett. 24(23), 1750–1752 (1999). [CrossRef] [PubMed]

,18

18. A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef]

]. This potential reconfiguration is represented by VQPM in Fig. 1(b). Waveguide QPM devices have been also reported which would help in miniaturization [7

7. M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23(13), 1004–1006 (1998). [CrossRef] [PubMed]

,19

19. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24(16), 1157–1159 (1999). [CrossRef] [PubMed]

].

- Intra-cavity (active) conversion because it can lead to high conversion efficiency in CW with an undepleted pump [20

20. R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970). [CrossRef]

, 21

21. J. Capmany, J. A. Pereda, V. Bermúdez, D. Callejo, and E. Diéguez, “Laser frequency converter for continuous-wave tunable Ti:sapphire lasers,” Appl. Phys. Lett. 79(12), 1751–1753 (2001). [CrossRef]

]. Since nonlinear DFG mixing efficiency increases with the power level of the pump wave the overall input/output channel system conversion efficiency can be increased by placing the nonlinear crystal inside the cavity of the DFG pump laser. Because the circulating intra-cavity laser power can exceed the laser output power by some orders of magnitude, only a few percent of the intra-cavity available power suffices to convert the full input channel power available to another output channel and still retain the undepleted pump condition. The DFG undepleted pump power level required for 100% conversion efficiency can then be provided by a much lower power source than in external DFG, i.e., by the power of the diode laser that pumps the local oscillator laser due to the energy stored in the cavity. Further, an advantage of DFG over sum-frequency generation (SFG) and second harmonic generation (SHG) is the possibility of achieving parametric gain which can provide a conversion efficiency in-excess of 100% [6

6. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. Lett. 127, 1918–1939 (1962).

].

Here, we present preliminary results of some intermediate steps towards an ideal conversion device. In particular, we demonstrate a continuous wave (CW) tunable intra-cavity wavelength conversion system that converts multiple input wavelengths to multiple output wavelengths within the spectral region 1500-1700 nm based on single-pass DFG in a periodically poled crystal. The system is pumped with a diode laser. The paper is organized as follows; in section 2 we describe our experimental set-up; in section 3 we present some background on the DFG wave-mixing process efficiency and conversion bandwidth, and particularize for our experimental conditions; in section 4 we present and discuss our experimental results, and in section 5 we summarize the main conclusions from our work.

2. Experimental set-up

The experimental set-up of our preliminary wavelength converting system is shown in Fig. 2(a)
Fig. 2 (a) Experimental configuration of the V-folded cavity for intra-cavity wavelength conversion by single-pass difference frequency generation. (b) Experimental laser tuning curve. Inset: laser beam profile.
. The local oscillator laser (DFG pump laser, or pump laser) uses a two arm V-folded cavity with a quasi-hemispherical geometry in the first arm and a quasi-confocal geometry in the second arm. There are other alternatives [22

22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express 17(16), 14374–14388 (2009). [CrossRef] [PubMed]

], but this configuration allowed us to achieve several goals simultaneously. Firstly, it allows for direct access of the external signal wave to the nonlinear crystal in a collinear single-pass DFG process. Secondly, the quasi-confocal configuration in the second arm produces an additional beam waist of the DFG pump wave in the middle of the second arm to place the nonlinear crystal. Therefore, the signal and pump beams can be tightly focused and spatially overlapped to increase mixing efficiency by collinear tight focusing [23

23. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39(8), 3597–3641 (1968). [CrossRef]

]. Thirdly, it allows for adding an external selective feedback mechanism based on a diffraction grating to perform self-injection locking operation that leads to laser tuning and line width narrowing.

An end-pumped a-cut Cr:LiCAF crystal rod doped with 3 at.% of chromium with plane parallel facets 1.5-mm long and 3-mm in diameter was used as the laser gain medium. The crystal was wrapped around with indium foil and held in a copper plate attached to a thermoelectric cooler that kept the crystal temperature constant at 27°C. The a-cut crystal readily provides polarized laser emission as required for efficient Type-0 QPM mixing (see Section 3). The laser was pumped by a red diode laser at 665 nm. The input facet (mirror M1), was coated for high transmission at 665 nm and high reflection between 775 and 850 nm on the cavity side. The opposite facet was anti-reflection coated for 665 nm and for the 775-850 nm band. A first arm of the cavity is delimited by the input facet M1 and the folding mirror M2, and a second arm defined by the mirror M2 and the main cavity output mirror M3. The resulting V, folds at a small angle of (~20°) degrees in order to keep a small astigmatism in the fundamental cavity mode. Both M2 and M3 are plano-concave spherical mirrors with a radius of curvature (ROC) of 100 mm that provide a second intra-cavity waist approximately at the center of the second arm. Since the pump wave suffers double pass losses per round trip at the folding mirror M2, a high reflectance mirror is required to keep the intra-cavity pump power high. There are two transmitted pump beams in M2 (represented in dotted lines in Fig. 2(a)) and we take advantage of it to monitor the laser output to check self-injection locking operation through a Si-photodiode, and to provide a reference beam to align the external signal along the nonlinear crystal. The folding mirror M2 is coated with a reflectance of R2 = 99.98% in the ~800 nm band on the concave side whereas the flat side was uncoated. Mirror M3 is coated with a reflectance of R3 = 98.25% in the ~800 nm band on the concave side with the flat side uncoated. With this geometry, a first waist of ~60 μm results in the laser crystal, and a second waist of ~30 μm in the middle of the second arm when adjusting the arms lengths to ~96 mm and ~212 mm (first and second arm respectively).

The red pump diode was fiber-coupled and delivered a maximum power of 1.8 W. The resulting output laser power was ~10 mW. The fiber had a 140 μm core diameter and a numerical aperture of 0.45 with an approximate beam quality parameter M2 ~67. This made it difficult to achieve a good beam overlap between the pump and laser beams reducing the overall laser efficiency of the laser [24

24. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988). [CrossRef]

]. Our pump focussing optics (an aspheric lens collimator and a microscope objective) produced an approximate focus diameter of ~200 μm inside the Cr:LiCAF crystal. A future improvement may consist in using single mode or single diode laser emitters as in [22

22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express 17(16), 14374–14388 (2009). [CrossRef] [PubMed]

].

Tuning of the local oscillator was achieved through self-injection locking by collimating the laser output through M3 with a 125 mm focal length lens and coupling to an external cavity based on a diffraction grating mounted in a Littrow configuration. The spectral dependence of the reflectivity of M3 (R3 = 98.25% in the ~800 nm band) controls the feedback ratio, tuning, and efficiency characteristics of the self-injection locking operation. Thus the reflectivity of M3 was chosen to meet a trade-off between enough intra-cavity power for mixing and easy coupling for the self-injection from the externally coupled cavity. The diffraction grating used had 1200 lp/mm (blazed at 26.75° for 750 nm), and had an 80% diffraction efficiency. The first-order diffraction component, which is collinear with the incident beam, is reflected back to the main cavity to perform the injection-locking operation. The zero-order diffracted beam was used as the output and thus the beam direction modifies as the grating is rotated to perform the tuning capability. The output beam direction is controlled by a gold steering mirror. In Fig. 2(b), we show the experimental laser tuning curve in our system. The inset shows the laser beam profile of the laser, which results slightly astigmatic. Concerning the effective reflectivity of the output coupler, the association M3-plus-grating produced an effective reflectivity around 99.75% that retains a high intra-cavity/output power factor as required for efficient nonlinear interaction. In our case the intra-cavity power can then be estimated as Pp ≅ 10 mW/0.0025 = 4W. With a better mode overlap between the 665 nm red pump diode and the Cr:LiCAF fundamental mode values around Pp ~30 W have been already reported [22

22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express 17(16), 14374–14388 (2009). [CrossRef] [PubMed]

].

The Littrow mounting in our set-up provided pump laser line width narrowing down to ~1 nm. It could be replaced by a Littman configuration, and thus the converted (idler) beam would be propagated along a fixed output direction (no steering mirrors would be required), and pump waves could be generated with a narrower spectral width around 1 MHz, and very likely to the sub-MHz range with an improved design [13

13. M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron. 34(7), 1288–1296 (1998). [CrossRef]

]. The standard resource of placing an intra-cavity etalon could further reduce the laser line width if necessary. Alternatively, an intra-cavity birrefrigent plate could be used for laser tuning. However, grating-based tuning can help in providing a fast tuning at the typical network reconfiguration speeds of ~10 ms if its tilt angle is governed by a piezo-electric actuator [18

18. A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef]

].

As the optical mixer, a z-cut periodically poled stoichiometric lithium tantalate (PPSLT) crystal 20 mm long and 2 × 2 mm2 of transverse cross-section was used and placed in the middle of the second arm. The poling period is 22.1 μm with a duty cycle of 0.5 for up and down domains, and had its facets antireflection coated in a small band around ~800 nm and for 1500-1700 nm. The nonlinear crystal was mounted in an oven to be held at a controlled temperature in order to reach the phase matching condition and to reduce possible photorefractive effects. The pump wave generated (790-800 nm) is polarized along the z-axis direction to participate in a QPM-type 0 process (mixing of waves all with extraordinary polarization) with an external signal wave presenting the same polarization, and then taking advantage of the SLT highest nonlinear tensor coefficient d33 = 12.9 pm/V (similar to the case of co-doping with MgO [25

25. I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96(2-3), 423–432 (2009). [CrossRef]

]).

Finally, an external signal wave was created with a home-made tunable erbium doped fiber laser [26

26. H. Maestre, A. J. Torregrosa, C. R. Fernández-Pousa, J. A. Pereda, and J. Capmany, “Widely tuneable dual-wavelength operation of a highly doped erbium fiber laser based on diffraction gratings,” IEEE J. Quantum Electron. 47, 1238–1243 (2011).

] whose output is firstly amplified, partially polarized along the z-axis (parallel to the PPLST crystallographic axis), and finally collimated and focused to a beam radius of ~100 μm into the main cavity through the folding mirror M2 and propagating along the second arm axis. The fiber that delivers the signal to the collimator is single mode for λ > 1280 nm and the signal is polarized using a polarization controller. For simultaneous multiple inputs, other diode lasers are mixed with the tunable signal in a fiber coupler and then amplified in an Er-doped fiber amplifier. The external signal beam is aligned collinear with the laser signal in the second arm by a pair of gold steering mirrors in a periscope configuration, and focused by a lens placed on a longitudinal micrometer translation stage in order to achieve an optimum overlap between both beam waists in the middle of the nonlinear medium. A maximum signal power of 100 mW was available at the output of the collimator.

The laser output from the grating (reflected zero-order) was coupled to a single mode fiber attached to a collimator and fed into an optical spectrum analyser (OSA). In our early experiments we noticed that special care must be taken when aligning the external signal with the pump wave for an accurate collinear interaction and with the collimator axis in order to record spectra with accurate input/output ratios. Any deviation from the collinear condition can make the converted signal reach the collimator (typically of low numerical aperture) out of axis or misaligned with the laser beam and not be correctly coupled to the OSA fiber. A preventive improvement we used (not represented in Fig. 2(a)) was to use a magnifying telescope to check the collinear condition, and then to reverse it for de-magnifying a possible residual misalignment prior to entering the collimator attached to the OSA input fiber. A 10X beam expander was used for this purpose.

3. QPM bandwidth and efficiency

The conversion efficiency in DFG processes is usually defined by the output idler to the input signal power ratio. For collinear interactions among tightly focused Gaussian beams in an undepleted pump approximation it can be modelled as (SI units) [23

23. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39(8), 3597–3641 (1968). [CrossRef]

,27

27. R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).

]:
η=PiPs=16π2deff2LPpε0npnicλsλi2×h(ξ)
(1)
Where Pi, Ps and Pp are the idler, signal and pump powers respectively, deff is an effective nonlinear coefficient of the material which can be made to account also for the wave vector mismatch Δk = kp − (ki + ks) in the interaction, L the length of the nonlinear crystal, np and ns the refractive indices of the nonlinear material for the pump and signal wavelengths respectively, λs and λi the signal and idler vacuum wavelengths respectively, and ε0 and c the dielectric constant and speed of light in vacuum respectively. The last term h(ξ) is a focusing factor (known as Boyd-Kleinmann focusing factor) that lies between 0.8 and 1 for 1 ≤ ξ ≤ 7, where ξ = L/b with L being the crystal length and b the confocal parameter (twice the Rayleigh range) [23

23. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39(8), 3597–3641 (1968). [CrossRef]

]. This simplified approximation does not take into account a possible linear loss in the crystal and assumes the absence of double refraction, otherwise absent when all of the interacting waves have extraordinary polarization, as it will be our case. As it follows from (1), the conversion efficiency is linear with the DFG pump power (laser intra-cavity power in our case), and is independent of the input signal power level for the undepleted pump case. In addition to the photon energy conservation requisite, the global wave-vector mismatch relation required for efficient nonlinear wave-mixing sometimes referred to as “momentum conservation” can be included in (1) by letting deff be a function of the wave-vector mismatch Δk and of the material nonlinear coefficient:
deffdeff(Δk)=1L0Ld*(z)·eiΔk·zdz
(2)
Here d*(z) is the spatial distribution of the effective nonlinear coefficient along the propagation coordinate z once accounted for the polarization of the waves, a fact that is taken into account by using in d* the usual sub-index notation dij proposed by Kleinmann for the components of the nonlinear tensor [27

27. R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).

]. In (2) we assume a collinear interaction and thus have removed the vector notation. Because d* = 0 outside the nonlinear crystal, the integration limits in (2) may be expanded to ± ∞ and (2) gives then (1/L) times the Fourier Transform of the spatial distribution of the nonlinear coefficient in the crystal i.e., deff2(Δk)is (1/L2) times the power spectrum of d*(z), and is limited by the nonlinear crystal length L through Parseval’s theorem [16

16. C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. 17(5), 1037–1039 (2005). [CrossRef]

,29

29. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]

]. In case of birefringent perfect phase matching, d*(z) remains constant along the interaction path and gives the usual efficiency expressiondeff2(Δk)=d*2×sin2(Δk·L/2)(Δk·L/2)2=d*2×sinc2(Δk·L/2). Thus, the nonlinear interaction is only efficient in the vicinity of perfect phase matching (PM), i.e., Δk = 0, with a PM bandwidth in the Δk reciprocal space set by the sinc2 function. In general, we will refer to the deff2(Δk) curve as the PM or QPM efficiency curve or alternatively the QPM tuning curve when normalized. In QPM with ferroelectric crystals d*(z) = d33(z) for all interacting waves polarized parallel to the ferroelectric c-axis and propagating perpendicular to it (Type 0 QPM), and changes sign between ± |d33| (the highest valued diagonal component of the nonlinear tensor) at every domain reversal i.e., at every place in the crystal where the spontaneous polarization changes its “up” or “down” orientation parallel or antiparallel to the ferroelectric + c-axis. In general, d*(z) may be a periodic or aperiodic spatial function along the propagation path in collinear interactions. In case of a periodically poled crystal with a spatial period Λ (length of an up and down domain pair), the equivalent tuning curve for m-order QPM becomes (Δk) = (2d33/mπ)2·sin2(mDπ)·sinc2[(1/2)·(Δk−2π/Λ)·L], where the case m = 1 is referred to as first-order QPM and D is the domain pair duty cycle factor defined as D = x/Λ. Due to even symmetry in the problem, x is the length of any of the up or down domains indistinctly [29

29. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]

]. In our PPSLT crystal the duty cycle factor is D = 0.5. The QPM efficiency curve shape and bandwidth (QPM tuning curve) results then identical to the birefringent case, and set by the crystal length L. It should be apparently clear that the QPM efficiency conditions may be changed (reconfigured) by temperature changes or electro-optic changes in Δk, through the corresponding changes in the refractive indices of the material for the interacting waves (kj = 2πnj/λj). It should also be apparently clear that aperiodic distributions change the shape of the QPM tuning curve and exchange amplitude for bandwidth keeping its area constant due to Parseval’s theorem if the absolute value of d*(z) remains constant along the interaction path. There are some demonstrations of techniques that trade-off QPM bandwidth at the expense of nonlinear effective coefficient by using aperiodically poling patterns such as chirping the domain reversal distribution and others [15

15. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007). [CrossRef]

,16

16. C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. 17(5), 1037–1039 (2005). [CrossRef]

]. In what follows we will refer to QPM tuning curves or efficiency curves and their bandwidth (QPM or conversion bandwidth) indistinctly, whether they are expressed Δk-space or in the corresponding wavelength values of the interacting waves.

One of the requisites for broadband wavelength conversion is to provide enough QPM bandwidth for efficient DFG process. Typically, with periodically poled crystals for SHG the bandwidth is around 1 nm × mm (FWHM) of crystal length with perfect periodical poling [29

29. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]

]. However, for a near-degenerate DFG interaction the conversion bandwidth can be increased considerably by means of a simple technique known as “pump detuning” [30

30. M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and Bandwidth Enhancement of Difference Frequency Generation (DFG)-based wavelength conversion by pump detuning,” Elec. Lett. 35(12), 978–980 (1999). [CrossRef]

]. We illustrate it in Figs. 3
Fig. 3 Theoretical QPM tuning characteristics for the PPSLT crystal (L = 20 mm and Λ = 22.1μm) for different pump wavelengths at room temperature (T = 25.0°C)
and 4
Fig. 4 Temperature optimization in the tunable output conversion of a fixed input channel.
particularized for our conversion system.

Figure 3 shows the simulated relative two-dimensional projection of the QPM tuning curve (multilevel curve) for the DFG processes as a function of the pump wavelength and of the signal and idler wavelengths particularized for our PPSLT crystal at 25 °C. They have been computed from the Sellmeier dispersion relations for lithium tantalate given in [28

28. A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett. 28(3), 194–196 (2003). [CrossRef] [PubMed]

]. The efficiency curve for the SHG of a 1586 nm fundamental wave giving 793 nm is obtained by intersection of a plane perpendicular to the figure represented by the slightly tilted near horizontal line (d) with the multilevel curve. The intersection is represented in inset (d) labeled as SHG. It can be noticed how the QPM bandwidth for this process is around 0.4 nm. However, for a degenerate DFG process pumped at 793 nm with signal and idler at 1586 nm, the efficiency curve is obtained by intersecting the multilevel curve and the plane represented by the vertical line (a). The corresponding relative efficiency curve is represented in inset (a), and gives a FWHM bandwidth around 60 nm. However, if we slightly detune downwards the pump wavelength to the value represented by line (b), the resultant efficiency curve becomes that represented in inset (b), with a FWHM bandwidth around 200 nm. A dip appears at the center of the curve, close to the degenerate condition for that pump (recall the poling period remains constant and that it was optimized for SHG of 793 nm). If the pump is detuned further downwards as to reach the value represented by line (c), then we get a split efficiency curve with a bandwidth around 55 × 2 nm.

In our conversion experiments we set the conditions to operate at room temperature (RT) in a situation similar to that represented in the inset (b) of Fig. 3 which gives the widest conversion bandwidth although not flat in efficiency. However, QPM conditions are sensitive to temperature changes. In Fig. 4 we show the sensitivity predicted by simulation in our efficiency curves when the temperature is raised from RT up to ~50 °C and the signal input is kept constant. This information shows how the QPM efficiency is affected when converting a specific fixed input channel into a tunable output channel in the system. This requires tuning the DFG pump laser (the local oscillator). In the simulated tuning process we started with a 792 nm pump at 25 °C and a 1543 nm input channel and simulated the new QPM conditions when tuning the pump to 793 nm and then to 794 nm, with the output channel shifting from 1627 to 1631 and 1635 nm respectively. A slight decrease in conversion efficiency takes place if the temperature is kept constant, as the output channel deviates from peak conversion efficiency. However, raising the temperature of the PPSLT crystal accordingly, peak conversion efficiency may be recovered as shown in Figs. 4(b) and 4(c). We chose 1543, 1627 and 792 nm because this conversion process matched peak efficiency at RT (25°C).

4. Results and discussion

Under free running operation (no PPSLT inside the main cavity) the pump wave oscillated with a line width of 6 nm (FWHM). When the system was operated under self-injection locking conditions, in the absence of the PPSLT crystal the line width reduced to ~2 nm. When the PPSLT was introduced in the cavity and the laser was optimized in output power a reduction of the power level resulted as a result of the additional loss, and the laser line width got reduced to less than 1 nm. This suggests that a residual reflection in the AR coating created an etalon effect eliminating some of the oscillating axial modes. By extending the second arm to total cavity length of ~308 mm the oscillation threshold at 792 nm was ~1.1 W providing ~10 mW of pump power under self-injection locking for a diode pump power of 1.8 W and the estimated intra-cavity power discussed of ~4 W. A reduction in the laser tuning range took also place as expected from the increase in the intra-cavity loss, as shown in Fig. 2(b).

Figure 5(a)
Fig. 5 Converted wavelengths by an intra-cavity DFG process with a 792 nm pump wavelength (λp) for different signal wavelengths at RT (25°C). (a) Conversion of a tunable input. (b) Conversion of a single input of variable power. The vertical scale in the figures is 5 dB/div.
shows the DFG conversion process for a tunable single input around 1560 nm when the pump laser remains constant at 792 nm. It corresponds to the output spectrum in the conversion system. The center lines in the spectra correspond to the second diffraction order (at 2λp = 1584 nm) of the pump wave and serves as a reference to illustrate the process. An apparent conversion efficiency ~−13 dB follows from the figure. However, one must keep in mind that the real conversion efficiency that is defined as η = Pout / Pin cannot be directly read form the spectra. Because the spectra correspond to the output spectra, the input signal has undergone parametric gain, and its level relative to the output must be corrected as it does not correspond to the input level to the system. Every converted photon created annihilates a pump photon and adds a new photon to the output spectrum of the input wave. Thus, the real level of the input signal must be computed by carefully substracting to the output spectra of the input signal an amount similar to the energy created in the converted output. We estimated it to be around 0.5 dB by numerical integration. Thus, the conversion efficiency is closer to −12.5 dB than to the apparent −13 dB. As it will be discussed later, this conversion efficiency is in reasonable agreement with the conversion efficiency expected by modelling (−9 dB) in our experimental conditions.

Figure 5(a) shows a tunable DFG conversion process with ~20 nm tuning range in the input signal (1545-1565 nm), with conversion to 1605-1625 nm. As in this process we may swap input channels with output channels, we get a practical conversion channel conversion bandwidth of 20 × 2 = 40 nm. This represents the possibility of converting at least 50 International Telecommunication Union standardized channels which are separated by 100 GHz (0.8 nm) [31

31. Telecommunication Standardization Sector of International Telecommunication Union, Recommendation ITU-T G.694.1, “Spectral grids for WDM applications: DWDM frequency grid” (2002).

]. In Fig. 5(b) we show how a single-channel conversion process for different powers of the input channel.

Figure 6
Fig. 6 Tunable wavelength conversion of a single- and two channel inputs by tuning the DFG pump and optimally adjusting the PPSLT temperature between 25 and 50°C.
shows a tunable conversion process for a single-channel and a two-channel input obtained by pump tuning. The smaller conversion efficiency observed in Fig. 6(a) relative to other spectra is due to a worse performance of the pump laser at the moment these spectra were measured as suggested by the lower relative pump power in the spectra. The temperature was adjusted along with pump tuning to optimize output power. Finally, in Fig. 7
Fig. 7 Simultaneous wavelength conversion in the C-band of (a) two input wavelengths at 1550.0 and 1559.3 nm, and (b) three input wavelengths at 1550.6, 1554.5 and 1557.8 nm when a 792 nm pump wave is used at RT (25°C)
we show two- and three-channel simultaneous conversion.

Next, we compare our conversion efficiencies with those predicted by modelling in our experimental conditions, and check the conditions that modelling predicts to achieve 100% conversion efficiency (0 dB) and even parametric gain. Figure 8
Fig. 8 Evolution of the optical intensity of the idler (red) and signal (blue) predicted by modeling for two different intra-cavity pump powers with beam waist sizes of 30, 100 and 100 µm for pump, idler and signal respectively for (a) our working conditions and (b) with higher intra-cavity power leading to parametric gain.
shows the single-pass optical intensity evolution of the signal and idler waves (all assumed Gaussian) obtained with the SANDIA SNLO software [32

32. SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, NM 87185–1423.

] as a function of the crystal length for different focusing conditions and pump power densities, and where linear losses are neglected. Figure 8(a) shows the intensity evolution of the signal and idler waves under the tested experimental conditions: intra-cavity pump power of our 4 W oscillating under self-injection locking operation with a beam waist of ωp ~30 μm located in the center of the PPSLT crystal. The signal wave is also centered in the crystal with a beam waist of ωs ~100 μm. Under these conditions (ours’), the intensity level of the signal wave remains almost constant along the interaction length. A difference of ~9 dB between the intensity level of the signal and the idler waves can be seen at the crystal output. Figure 8(b) represents the same situation if the pump power could be increased to 30 W. It shows that by increasing the intra-cavity power to reasonable values supported by other author’s data [22

22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express 17(16), 14374–14388 (2009). [CrossRef] [PubMed]

], a 6 dB parametric gain can be achieved and the output converted power can therefore equal (100% conversion efficiency) and even exceed the input power.

5. Conclusion

In summary, we report tunable and multiple CW active wavelength conversion in the spectral region of 1500-1700 nm based on single-pass difference frequency generation in an intra-cavity PPSLT crystal. A diode pumped self-injection locked tunable Cr:LiCAF laser (792 ± 4nm) with 4 W of intra-cavity power and spectral width <1 nm has been employed as the pump laser of the DFG nonlinear interaction. Our typical conversion efficiency results ~(−10 dB) are in good agreement with modeling predictions for our intra-cavity laser power ~(−8.9 dB). Full power conversion (0 dB, and even parametric gain) can be reasonably expected by improving the Cr:LiCAF intra-cavity power to realistic values already reported by other authors with this laser crystal (~20-30W). This should be accomplished by using single mode or single emitter red laser diodes at 665 nm and high quality optical components with suitable dielectric coatings or Brewster-angle cut crystals. Also, as discussed in the text, laser spectral widths in the MHz and sub-MHz level for the DFG pump can be reasonably expected for an injection-locked Cr:LiCAF laser. We may also conclude that although periodically poled crystals are useful to provide a significant conversion bandwidth and serve as a proof-of-principle, it can be useful to explore the combined effects of using aperiodically poled crystals and pump detuning to optimize conversion bandwidth and to flatten the conversion efficiency curve in future when working towards a final practical converter device for WDM networks. Thus, we believe it well worth to continue working towards a practical miniaturized active reconfigurable wavelength converter for WDM all-optical Networks based on the system architecture here reported or a similar one.

Acknowledgment

This work was supported by the Ministerio de Ciencia e Innovación under Projects TEC2008-02606 and TEC2011-26842.

References and links

1.

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996). [CrossRef]

2.

J. M. Yates and M. P. Rumsewicz, “Wavelength converters in dynamically reconfigurable WDM networks,” IEEE Commun. Surv. Tutor. 2(2), 2–15 (1999).

3.

K. C. Lee and V. Li, “A wavelength-convertible optical network,” J. Lightwave Technol. 11(5), 962–970 (1993). [CrossRef]

4.

H. S. Hamza and J. S. Deogun, “WDM optical interconnects: A balanced design approach,” IEEE/ACM Trans. Netw. 15(6), 1565–1578 (2007). [CrossRef]

5.

X. Qin and Y. Yang, “Multicast connection capacity of WDM switching networks with limited wavelength conversion,” IEEE/ACM Trans. Netw. 12(3), 526–538 (2004). [CrossRef]

6.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. Lett. 127, 1918–1939 (1962).

7.

M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23(13), 1004–1006 (1998). [CrossRef] [PubMed]

8.

For general aspects of fiber optics communications see G. P. Agrawal, Fiber Optic Communication Systems (John Wiley & Sons, 2002).

9.

S. Walklin and J. Conradi, “Multilevel Signaling for Increasing the Reach of 10 Gb/s Lightwave Systems,” J. Lightwave Technol. 17(11), 2235–2248 (1999). [CrossRef]

10.

R. Muñoz, R. Martínez, and R. Casellas, “Challenges for GMPLS lightpath provisioning in transparent optical networks: Wavelength constraints in routing and signaling,” IEEE Commun. Mag. 47(8), 26–34 (2009). [CrossRef]

11.

S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F6:Cr3+: A Promising New Solid-state Laser Material,” IEEE J. Quantum Electron. 24(11), 2243–2252 (1988). [CrossRef]

12.

A. E. Siegman, “Laser injection locking,” in Lasers (University Science Book, 1986), pp. 1129–1170.

13.

M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron. 34(7), 1288–1296 (1998). [CrossRef]

14.

H. Maestre, A. J. Torregrosa, and J. Capmany, “Intracavity Cr3+:LiCAF + PPSLT optical parametric oscillator with self-injection-locked pump wave,” Laser Phys. Lett. 10(3), 035806 (2013). [CrossRef]

15.

D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. 8(2), 180–198 (2007). [CrossRef]

16.

C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. 17(5), 1037–1039 (2005). [CrossRef]

17.

N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett. 24(23), 1750–1752 (1999). [CrossRef] [PubMed]

18.

A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef]

19.

M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24(16), 1157–1159 (1999). [CrossRef] [PubMed]

20.

R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. 6(4), 215–223 (1970). [CrossRef]

21.

J. Capmany, J. A. Pereda, V. Bermúdez, D. Callejo, and E. Diéguez, “Laser frequency converter for continuous-wave tunable Ti:sapphire lasers,” Appl. Phys. Lett. 79(12), 1751–1753 (2001). [CrossRef]

22.

U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express 17(16), 14374–14388 (2009). [CrossRef] [PubMed]

23.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. 39(8), 3597–3641 (1968). [CrossRef]

24.

W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5(7), 1412–1423 (1988). [CrossRef]

25.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B 96(2-3), 423–432 (2009). [CrossRef]

26.

H. Maestre, A. J. Torregrosa, C. R. Fernández-Pousa, J. A. Pereda, and J. Capmany, “Widely tuneable dual-wavelength operation of a highly doped erbium fiber laser based on diffraction gratings,” IEEE J. Quantum Electron. 47, 1238–1243 (2011).

27.

R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).

28.

A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett. 28(3), 194–196 (2003). [CrossRef] [PubMed]

29.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]

30.

M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and Bandwidth Enhancement of Difference Frequency Generation (DFG)-based wavelength conversion by pump detuning,” Elec. Lett. 35(12), 978–980 (1999). [CrossRef]

31.

Telecommunication Standardization Sector of International Telecommunication Union, Recommendation ITU-T G.694.1, “Spectral grids for WDM applications: DWDM frequency grid” (2002).

32.

SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, NM 87185–1423.

OCIS Codes
(160.2260) Materials : Ferroelectrics
(190.0190) Nonlinear optics : Nonlinear optics
(190.4223) Nonlinear optics : Nonlinear wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 12, 2013
Revised Manuscript: October 13, 2013
Manuscript Accepted: October 31, 2013
Published: November 7, 2013

Citation
Adrián J. Torregrosa, Haroldo Maestre, and Juan Capmany, "Towards a versatile active wavelength converter for all-optical networks based on quasi-phase matched intra-cavity difference-frequency generation," Opt. Express 21, 27933-27945 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-27933


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References

  1. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol.14(6), 955–966 (1996). [CrossRef]
  2. J. M. Yates and M. P. Rumsewicz, “Wavelength converters in dynamically reconfigurable WDM networks,” IEEE Commun. Surv. Tutor.2(2), 2–15 (1999).
  3. K. C. Lee and V. Li, “A wavelength-convertible optical network,” J. Lightwave Technol.11(5), 962–970 (1993). [CrossRef]
  4. H. S. Hamza and J. S. Deogun, “WDM optical interconnects: A balanced design approach,” IEEE/ACM Trans. Netw.15(6), 1565–1578 (2007). [CrossRef]
  5. X. Qin and Y. Yang, “Multicast connection capacity of WDM switching networks with limited wavelength conversion,” IEEE/ACM Trans. Netw.12(3), 526–538 (2004). [CrossRef]
  6. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. Lett.127, 1918–1939 (1962).
  7. M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett.23(13), 1004–1006 (1998). [CrossRef] [PubMed]
  8. For general aspects of fiber optics communications see G. P. Agrawal, Fiber Optic Communication Systems (John Wiley & Sons, 2002).
  9. S. Walklin and J. Conradi, “Multilevel Signaling for Increasing the Reach of 10 Gb/s Lightwave Systems,” J. Lightwave Technol.17(11), 2235–2248 (1999). [CrossRef]
  10. R. Muñoz, R. Martínez, and R. Casellas, “Challenges for GMPLS lightpath provisioning in transparent optical networks: Wavelength constraints in routing and signaling,” IEEE Commun. Mag.47(8), 26–34 (2009). [CrossRef]
  11. S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F6:Cr3+: A Promising New Solid-state Laser Material,” IEEE J. Quantum Electron.24(11), 2243–2252 (1988). [CrossRef]
  12. A. E. Siegman, “Laser injection locking,” in Lasers (University Science Book, 1986), pp. 1129–1170.
  13. M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron.34(7), 1288–1296 (1998). [CrossRef]
  14. H. Maestre, A. J. Torregrosa, and J. Capmany, “Intracavity Cr3+:LiCAF + PPSLT optical parametric oscillator with self-injection-locked pump wave,” Laser Phys. Lett.10(3), 035806 (2013). [CrossRef]
  15. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys.8(2), 180–198 (2007). [CrossRef]
  16. C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett.17(5), 1037–1039 (2005). [CrossRef]
  17. N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett.24(23), 1750–1752 (1999). [CrossRef] [PubMed]
  18. A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef]
  19. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett.24(16), 1157–1159 (1999). [CrossRef] [PubMed]
  20. R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron.6(4), 215–223 (1970). [CrossRef]
  21. J. Capmany, J. A. Pereda, V. Bermúdez, D. Callejo, and E. Diéguez, “Laser frequency converter for continuous-wave tunable Ti:sapphire lasers,” Appl. Phys. Lett.79(12), 1751–1753 (2001). [CrossRef]
  22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express17(16), 14374–14388 (2009). [CrossRef] [PubMed]
  23. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys.39(8), 3597–3641 (1968). [CrossRef]
  24. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B5(7), 1412–1423 (1988). [CrossRef]
  25. I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B96(2-3), 423–432 (2009). [CrossRef]
  26. H. Maestre, A. J. Torregrosa, C. R. Fernández-Pousa, J. A. Pereda, and J. Capmany, “Widely tuneable dual-wavelength operation of a highly doped erbium fiber laser based on diffraction gratings,” IEEE J. Quantum Electron.47, 1238–1243 (2011).
  27. R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).
  28. A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett.28(3), 194–196 (2003). [CrossRef] [PubMed]
  29. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron.28(11), 2631–2654 (1992). [CrossRef]
  30. M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and Bandwidth Enhancement of Difference Frequency Generation (DFG)-based wavelength conversion by pump detuning,” Elec. Lett.35(12), 978–980 (1999). [CrossRef]
  31. Telecommunication Standardization Sector of International Telecommunication Union, Recommendation ITU-T G.694.1, “Spectral grids for WDM applications: DWDM frequency grid” (2002).
  32. SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, NM 87185–1423.

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