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Tunable Second Harmonic Generation in a Nd3 + -Doped Fiber Laser Using a LiNbO3-Integrated Mach–Zehnder
OPTICAL FIBER TECHNOLOGY ARTICLE NO.
4, 83]90 Ž1998.
OF970235
Tunable Second Harmonic Generation in a Nd 3 +-Doped Fiber Laser Using a LiNbO 3-Integrated Mach – Zehnder Pascal Mollier, Henri Porte, Benoit Grappe, Jerome ´ ˆ Hauden, and Jean-Pierre Goedgebuer Laboratoire d’Optique P.M. Duffieux, UMR CNRS 6603, Institut des Microtechniques de Franche-Comte´ (IMFC), Uni¨ ersite´ de Franche-Comte, ´ 25 030 Besancon Cedex, France Received July 8, 1997; revised October 24, 1997
We report on a tunable neodymium-doped fiber laser using an intracavity lithium niobate-integrated tuner. The device is a low-voltage asymmetric LiNbO 3 Mach]Zehnder interferometer working as a tunable spectral filter. Laser emission occurs simultaneously at two wavelengths, l0 s 1088 nm and l2 s 544 nm, due to the nonlinear properties of the crystal. The lasing wavelengths are tuned over ranges of 12 nm in the infrared and 6 nm in the green region with tuning rates of 0.25 and 0.12 nmrV, respectively. Q 1998 Academic Press
1. INTRODUCTION
Doped-fiber lasers are widely developed because of their low laser threshold, their good efficiency, and their large spectral gain that allows tuning ranges of several nanometers. Wavelength tunable lasers already have been built using intracavity filters, in particular with Nd3q-doped fiber. Tunability of fiber lasers is usually achieved by tilting or rotating optical components such as gratings or stacks of birefringent plates w1, 2x. In order to avoid mechanical adjustments of the wavelength one can use electrooptic tuners with tunable semiconductor lasers as described previously w3x. Such tuners can be built with bulk electrooptic components. They, however, require high driving voltages. To overcome this drawback, we propose here the use of an intracavity LiNbO 3-integrated tuner featuring a low driving voltage. Several types of LiNbO 3-integrated filters have been previously reported. For instance, Heismann w4x has described such an integrated optics tuner based on a Ti:LiNbO 3 TErTM mode converter working as a wavelength filter. 83 1068-5200r98 $25.00 Copyright Q 1998 by Academic Press All rights of reproduction in any form reserved.
84
MOLLIER ET AL.
For several years, there has been a great interest in rare-earth-doped-integrated devices. In particular, neodymium-diffused LiNbO 3 lasers and amplifiers have been demonstrated. For example, Amin demonstrated the tunability of such a laser using a Y-junction channel waveguide obtained by titanium indiffusion into a Nd:LiNbO3 substrate. In this case the tunability is 2.3 nm for voltages over the range y25 to 25 V w5x. We describe in this paper a new configuration of a tunable fiber laser based on the use of a Ti:LiNbO 3-imbalanced Mach]Zehnder interferometer ŽMZI. w6, 7x. This type of filter allows a wide tunable range. Demonstration of infrared wavelength tunability is achieved with a Nd3q-doped fiber. Moreover, we show that due to the nonlinear properties of lithium niobate, the device can also work as a tunable frequency doubler, by second harmonic generation in the visible. We describe first the basic setup, the configuration of the integrated tuner, and the principle of operation. Then we report the main results obtained with this system.
2. PRINCIPLE OF OPERATION
Figure 1 shows the experimental configuration. The laser cavity consists of a 3-m-long Nd3q-doped fiber ŽFIBERCORE. linked to the electrooptic integrated tuner. The latter is an imbalanced Mach]Zehnder interferometer integrated in a Z-cut lithium niobate substrate. Both the input face of the doped fiber and the output face of the integrated tuner are coated with dielectric multilayer mirrors ŽTiO 2rSiO 2 .. The reflectivity is greater than 99% for the first mirror and 90% for the output one in a spectral range of 200 nm at the 1.1 m m wavelength. In the green region, the reflectivity of the two mirrors is 20%. The pump beam is an unpolarized 818-nm-wavelength laser diode. To avoid photorefractive effect into the lithium niobate substrate, the pump beam is first launched into the doped fiber core, using a microscope objective. Indeed, the main part of the power pump is absorbed in the doped fiber. The transmitted laser beam is collimated with a lens. The lasing emission, centered at the 1088 nm wavelength corresponding to the maximum of fluoroescence of Nd3q doped fiber, results from oscillations of the light between the two mirrors. Thus, the integrated device works as an intracavity tuning element. The waveguide pattern of the latter consists of two Y-junctions linked together by a straight arm of length L1 and a bent arm of length L2 . The electrodes induce a vertical electric field EZ in both waveguide arms of the MZI, when a voltage VZ is applied.
FIG. 1. Experimental setup of the tunable fiber laser using a LiNbO 3 -integrated tuner.
TUNABLE SECOND HARMONIC GENERATION
85
The principle of operation is the following. In order to achieve simultaneously electrooptic tunability and second harmonic generation ŽSHG. the polarization of light in the cavity is controlled to excite the TE-mode of the waveguide corresponding to the ordinary refractive index n 0 . The total OPD Žoptical path difference., D s D 0 q D mŽ VZ ., introduced between the two arms of the intracavity electrooptic two-wave interferometer is the sum of a static OPD, D 0 s n 0 Ž L2 y L1 ., and a voltage-dependent one, D mŽ VZ . < D 0 , given by D m Ž VZ . s
1 2
r 13 n30 g TE
VZ d
Ž L 2 q L1 . ,
Ž 1.
where r 13 s 8.6 pmrV is the electrooptic coefficient of lithium niobate, g TE is the overlap coefficient between the electric field, EZ s VZ rd, and the optical field. d is the electrode gap. The resulting half-wave voltage, corresponding to the TE-mode, is Vl r2 s
l0 d r 13 n30 g TE
Ž L 2 q L1 .
.
Ž 2.
It can be shown that the one-pass spectral relative transmission of the intracavity tuner can be expressed as T Ž l. s
1 2
1 q cos
2p
ž ž l
D0 q
l0 VZ 2Vl r2
//
.
Ž 3.
According to relation Ž3., the one-pass spectral transmission of such a filter features pseudo-periodic transmission peaks, with a free spectral range ŽFSR. related to the OPD of the filter by FSR f
l20 D0
,
Ž 4.
where l0 is the central wavelength of the fluoroescence spectrum of the Nd3qdoped fiber. Laser emission occurs at wavelengths l that correspond to constructive interference at the output of the MZI, i.e., D 0 q l0 VZ r2Vl r2 s m l, where m is an integer. In this laser configuration, the emission spectrum of the pumped Nd3q-doped fiber laser is centered at l0 s 1088 nm with a bandwidth of D l s 12 nm. Wavelength tuning is carried out by varying the OPD introduced by the MZI. D 0 is chosen such that there is only one transmission peak of the filter inside the spectral gain curve of the laser; i.e., FSR f l20rD 0 G D l, yielding in this case D 0 f 100 m m w3x. As a voltage VZ is applied to the tuner, the total OPD changes linearly. Hence, the emitted wavelength is shown to be expressed as
lŽ VZ . s l0 q a VZ ,
Ž 5.
where l 0 s D 0rm, and a s d lrdV s FSRr2Vl r2 , expressed in nmrV, represents the tuning rate.
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MOLLIER ET AL.
The required voltage to tune the wavelength over the whole spectral gain curve is 2Vl r2 . In this configuration, the tunability is achieved on adjacent modes of the cavity by mode hopping. The tunability of the fundamental wavelength being defined, we discuss now the nonlinear behavior of the tuning. Second harmonic generation can be obtained into lithium niobate waveguide by polarization mode coupling through the nonlinear optical coefficient d 31 s 5.8 pmrV. The expression for the SHG efficiency ignoring depletion of the fundamental field is given by w7x
hs
Pv 2 Pv 0
s
2 8p 2 d 31
Pv 0 L2
nv 0 nv 2 c « 0 l20
Seff
j sin c 2
D kL
ž / 2
,
Ž 6.
where Pv 0 and Pv 2 are optical powers of fundamental field and the second harmonic one, respectively; L is the interaction length; Seff is the effective surface of interaction; j is the overlap coefficient between the fundamental and the second harmonic fields; c s 3 = 10 8 msy1 ; and « 0 s 8.85 = 10y1 2 Frm. D k is the wave vector mismatch, given by w8x D k s kv 2 y 2 kv 0 s
4p
l0
Ž nv 2 y nv 0 . .
Ž 7.
The phase mismatch can typically be cancelled using the natural birefringence of the crystal. The phase-matching condition corresponds to nv 0 s nv 2 ; this requires that the fundamental and the second harmonic be orthogonally polarized. In lithium niobate, which is a positive single axis birefringent crystal with large nonlinear susceptibility, the SHG can especially be obtained with natural birefringence dispersion of the material. In our case, the waveguide orientation Žalong the Y-axis, on a Z-cut substrate . is such that the TE-polarized emission of the Nd3q-doped fiber at l0 s 1088 nm is phase-matched to a TM-polarized second harmonic at l2 s 544 nm into the waveguides. In the phase-matching conditions, i.e., nv 0 s nv 2 , the conversion efficiency can be expressed from Eq. Ž6. as
hs
2 Pv 0 L2 8p 2 d 31
nv2 0 c « 0 l20
Seff
j.
The theoretical estimation of conversion efficiency is h s 0.024%, with Seff s 15.5 m m2 , L s 35 mm Žcorresponding to the interaction length., and considering j s 0.18 Žcomputed with the optogeometric parameters of the waveguide.. The spectral transmission of the integrated MZI is such that when a transmission peak is centered at v 0 , another one is centered at v 2 s 2 v 0 . For guided waves, phase-matching tolerances of SHG are larger than in bulk configurations. Indeed, the effective index of an optical guided wave has a value intermediate between the substrate index n s and the maximum index at the surface of the guiding region n s q D n. The total phase-matching range can be determined by constructing a diagram which represents the area delimited by n TE Ž l., w n s q D n x TE Ž l., n TM Ž lr2., w n s q D n xTM Ž lr2. w9x. Typically for a Ti:LiNbO 3 waveguide, the phase-matching conditions are respected in a 20 to 30 nm range. Consequently, the LiNbO 3 device
TUNABLE SECOND HARMONIC GENERATION
87
can also be used as an intracavity frequency doubler. When the fundamental wavelength is tuned, the phase-matching condition remains fulfilled and the generated second harmonic is tuned in the same way. From Eqs. Ž2. and Ž4., one can see that the values of the FSR and the half-wave voltage of the tuner for the second harmonic are, respectively, one quarter and one half of those for the fundamental wave. Thus, the tuning range of the second harmonic is half the tuning range of the fundamental wavelength. This is also the case for the tuning rate.
3. EXPERIMENTAL RESULTS
The MZI tuner is designed to generate an OPD of about 100 m m. As n TE f 2.23 is the effective index of the TE-propagation mode at l 0 s 1088 nm, the optogeometric parameters of the waveguides were defined with a length L1 s 2 cm for the straight arm and a length L2 s 2.0045 cm for the curved arm designed with a bend radius of R s 4.22 cm. The 5-m m-wide waveguides were diffused from a 50-nmthick electro-beam-evaporated titanium layer. The diffusion process was performed at 10208C for 8 h in a wet-oxygen atmosphere to prevent the waveguides from LiO 2 out-diffusion. The Cr]Au:electrodes, 50 and 250 nm thick, respectively, were etched by a photolithographic process over a 150-nm-thick SiO 2 buffer layer. The electrodes were patterned over the waveguides in a 2-cm-long push]pull configuration. The width of each electrode is 20 m m and the gap is d s 10 m m. The waveguide is monomode at 1.08 m m and only the TE mode is supported. At 0.544 m m, the waveguide is multimode for both TM and TE polarizations. The effective half-wave voltage was measured to be 17 V. The value of the OPD introduced by the MZI was assessed from the spectral transmission of the filter using the broadband fluorescence of the 818-nm-pumped Nd3q-doped fiber as a source before the deposition of the mirrors. Figure 2 shows the spectral transmission thus obtained. The measured FSR of the channeled spectrum is 11 nm,
FIG. 2. Experimental channeled spectrum produced by the imbalanced Mach]Zehnder interferometer ŽTE mode.: FSR s 11 nm. The dashed lines mark the limits of the laser gain curve of bandwidth D l s 12 nm.
88
MOLLIER ET AL.
corresponding to an experimental OPD D 0 s 108 m m. This value is slightly greater than the optimal value of 100 m m. The losses introduced by the tuner in the cavity for a round trip are g s y6 dB, and the threshold is obtained for a 42-mW-absorbed pump power. Without a tuner, the threshold was obtained for an absorbed pump power of 10 mW. With a tuner, the output laser power is 1 mW for an absorbed pump power of 82 mW, yielding a 2.5% laser efficiency. The spectrum analysis of the emitted beam is reported in Figure 3. Multimode laser emission occurs at the wavelength corresponding to the maximum of gain, with a full width at half maximum ŽFWHM. of 0.8 nm. The laser emission is TE-polarized. The transmitted optical spectrum of the second harmonic is displayed in Fig. 4, showing the SHG occurs mainly in the TM-mode. The SH optical power transmitted by the laser is measured to be equal to 1 mW. Taking into account the power of the fundamental field stored inside the laser cavity, about 9 mW, and the 90% reflectivity of the output mirror, we estimate that the experimental conversion efficiency is h s 0.011% mW. This result is smaller than the theoretical one because of a weaker overlap coefficient j and a slight velocity mismatch, Ž nv y nv . f 10y5 . The total length of the cavity is 3.5 m, and the longitudinal 2 0 mode, spacing is 0.11 pm. As a driving voltage ranging between 0 and 36 V Žcorresponding to 2Vl r2 . is applied to the tuner, wavelength is tuned by mode hopping. The tuning curves are shown in Fig. 5. The variation of emitted wavelength versus applied voltage is linear and the tuning ranges are 11 and 5.5 nm for l0 s 1088 nm and l2 s 544 nm. The variations of output power, over the tuning range for l0 s 1088 nm, are smaller than 1 dB, which corresponds to a variation of laser efficiency less than 0.5%. For the SH, these variations are not significant. The presence of two simultaneously emitted wavelengths is due to the nonoptimized FSR of the filter resulting in two adjacent transmission peaks inside the gain curve of the laser. Work is in progress to increase the tuning range up to optimized value of 12 nm. The slopes of the curves in Fig. 5 indicate experimental tuning rates of 0.25 and 0.12 nmrV for l0 s 1088 nm and l 2 s 544 nm. The wavelength can be tuned over the FSR up to 1 kHz, which corresponds to a tuning speed of 11 nmrms and 5.5 nm for, respectively, l 0 s 1088 nm and l2 s 544 nm.
FIG. 3. Transmitted optical spectrum of the laser beam at 1088 nm. The emission is mainly TE-polarized.
TUNABLE SECOND HARMONIC GENERATION
89
FIG. 4. Transmitted optical spectra of the second harmonic. Dashed lines, TE-polarization; continuous line, TM-polarization.
4. CONCLUSION
In conclusion, we have reported on a LiNbO 3-integrated imbalanced Mach] Zehnder interferometer used as a tunable filter in a Nd3q-doped fiber laser. With this system that involves no mechanical motion, we have shown that a tuning range of 12 nm around 1.088 m m can be obtained with a tuning rate of 0.25 nmrV. This tuner can be used with other types of fiber lasers, especially with erbium-doped fibers. Work is in progress to increase the selectivity of the filter by cascading
FIG. 5. Emitted wavelength versus driving voltage: Ža. second harmonic, l s 544 nm; Žb. fundamental wavelength, l s 1088 nm.
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MOLLIER ET AL.
several MZIs with increasing path differences Ž D 0 , 2D 0 , 4D 0 , ??? .. The device can be used as an intracavity nonlinear element for SHG in the case of a Nd3q-doped fiber laser. The SH emission is observed without any photorefractive damage and a 0.12 nmrV tuning rate was measured. This work consists of the first demonstration of such an hybrid tuning fiber laser using a LiNbO 3-integrated component linked with a doped fiber laser. Different ways will be investigated to improve the efficiency of frequency doubling. For instance, an optimization of opto-geometric parameters of the waveguide can be realized to improve the overlap between the fundamental beam and the SH. This opens the way to new solid-state and tunable lasers built with a doped fiber and integrated optics technology, working in the visible region of the spectrum with possible extension to shorter wavelengths. The generation of shorter wavelengths, from a signal at l s 1.55 m m, for example, could be achieved by the use of quasi-phase-matching section of the waveguide obtained by ferroelectric domain inversion. This approach could be extend to integrated doped planar waveguide. In this case, the main interest is the realization of a very compact laser source.
ACKNOWLEDGMENTS This work was supported by the Ministere et de la Recherche. ` de l’Enseignement Superieur ´
REFERENCES w1x L. Reeckie, R. J. Mears, S. B. Poole, and D. N. Payne, ‘‘Tunable single mode fiber lasers,’’ IEEE J. Lightwa¨ e Technol., vol. 4, 956 Ž1986.. w2x L. P. Alcock, A. I. Fergusson, D. C. Hanna, and A. C. Tropper, ‘‘Tunable continuous-wave neodymium-doped monomode-fiber laser operating at 0.900]0.945 and 1.0701.135 m m,’’ Opt. Lett., vol. 11, 709 Ž1986.. w3x J. P. Goedgebuer, S. Gurib, and H. Porte, ‘‘Single frequency electro-optical tuning of an extended cavity laser diode at 1500 nm wavelength,’’ IEEE J. Quantum Electron., vol. QE28, 1414 Ž1992.. w4x F. Heismann, R. C. Alferness, L. L. Bhul, G. Eisenstein, S. K. Korothy, J. J. Veselka, L. W. Stulz, and C. A. Burrus, ‘‘Narrow-linewidth, electro-optically tunable InGaAsP-Ti:LiNbO 3 extended cavity laser,’’ Appl. Phys. Lett., vol. 51, 164, Ž1987.. w5x J. Amin, M. Hempstead, J. E. Roman, and J. S. Wilkinson, ‘‘Tunable coupled-cavity waveguide laser at room temperature in Nd-diffused Ti:LiNbO 3 ,’’ Opt. Lett., vol. 19, 1541 Ž1992.. w6x M. J. Ahmed and L. Young, ‘‘Proposed interferometric filters,’’ Appl. Opt., vol. 19, 3051 Ž1980.. w7x H. Okayama and M. Kawahara, ‘‘Tunable filters with extended tunability,’’ Jpn. J. Appl. Phys., vol. 31, 1628 Ž1992.. w8x A. Yariv, ‘‘Quantum Electronics,’’ 3rd ed., Wiley, New York, 1989. w9x M. De Micheli, J. Botineau, S. Neveu, P. Sibillot, D. B. Ostrowsky, and M. Papuchon, ‘‘Extension of second harmonic phase-matching range in lithium niobate guide,’’ Opt. Lett., vol. 8, 116 Ž1983..
4, 83]90 Ž1998.
OF970235
Tunable Second Harmonic Generation in a Nd 3 +-Doped Fiber Laser Using a LiNbO 3-Integrated Mach – Zehnder Pascal Mollier, Henri Porte, Benoit Grappe, Jerome ´ ˆ Hauden, and Jean-Pierre Goedgebuer Laboratoire d’Optique P.M. Duffieux, UMR CNRS 6603, Institut des Microtechniques de Franche-Comte´ (IMFC), Uni¨ ersite´ de Franche-Comte, ´ 25 030 Besancon Cedex, France Received July 8, 1997; revised October 24, 1997
We report on a tunable neodymium-doped fiber laser using an intracavity lithium niobate-integrated tuner. The device is a low-voltage asymmetric LiNbO 3 Mach]Zehnder interferometer working as a tunable spectral filter. Laser emission occurs simultaneously at two wavelengths, l0 s 1088 nm and l2 s 544 nm, due to the nonlinear properties of the crystal. The lasing wavelengths are tuned over ranges of 12 nm in the infrared and 6 nm in the green region with tuning rates of 0.25 and 0.12 nmrV, respectively. Q 1998 Academic Press
1. INTRODUCTION
Doped-fiber lasers are widely developed because of their low laser threshold, their good efficiency, and their large spectral gain that allows tuning ranges of several nanometers. Wavelength tunable lasers already have been built using intracavity filters, in particular with Nd3q-doped fiber. Tunability of fiber lasers is usually achieved by tilting or rotating optical components such as gratings or stacks of birefringent plates w1, 2x. In order to avoid mechanical adjustments of the wavelength one can use electrooptic tuners with tunable semiconductor lasers as described previously w3x. Such tuners can be built with bulk electrooptic components. They, however, require high driving voltages. To overcome this drawback, we propose here the use of an intracavity LiNbO 3-integrated tuner featuring a low driving voltage. Several types of LiNbO 3-integrated filters have been previously reported. For instance, Heismann w4x has described such an integrated optics tuner based on a Ti:LiNbO 3 TErTM mode converter working as a wavelength filter. 83 1068-5200r98 $25.00 Copyright Q 1998 by Academic Press All rights of reproduction in any form reserved.
84
MOLLIER ET AL.
For several years, there has been a great interest in rare-earth-doped-integrated devices. In particular, neodymium-diffused LiNbO 3 lasers and amplifiers have been demonstrated. For example, Amin demonstrated the tunability of such a laser using a Y-junction channel waveguide obtained by titanium indiffusion into a Nd:LiNbO3 substrate. In this case the tunability is 2.3 nm for voltages over the range y25 to 25 V w5x. We describe in this paper a new configuration of a tunable fiber laser based on the use of a Ti:LiNbO 3-imbalanced Mach]Zehnder interferometer ŽMZI. w6, 7x. This type of filter allows a wide tunable range. Demonstration of infrared wavelength tunability is achieved with a Nd3q-doped fiber. Moreover, we show that due to the nonlinear properties of lithium niobate, the device can also work as a tunable frequency doubler, by second harmonic generation in the visible. We describe first the basic setup, the configuration of the integrated tuner, and the principle of operation. Then we report the main results obtained with this system.
2. PRINCIPLE OF OPERATION
Figure 1 shows the experimental configuration. The laser cavity consists of a 3-m-long Nd3q-doped fiber ŽFIBERCORE. linked to the electrooptic integrated tuner. The latter is an imbalanced Mach]Zehnder interferometer integrated in a Z-cut lithium niobate substrate. Both the input face of the doped fiber and the output face of the integrated tuner are coated with dielectric multilayer mirrors ŽTiO 2rSiO 2 .. The reflectivity is greater than 99% for the first mirror and 90% for the output one in a spectral range of 200 nm at the 1.1 m m wavelength. In the green region, the reflectivity of the two mirrors is 20%. The pump beam is an unpolarized 818-nm-wavelength laser diode. To avoid photorefractive effect into the lithium niobate substrate, the pump beam is first launched into the doped fiber core, using a microscope objective. Indeed, the main part of the power pump is absorbed in the doped fiber. The transmitted laser beam is collimated with a lens. The lasing emission, centered at the 1088 nm wavelength corresponding to the maximum of fluoroescence of Nd3q doped fiber, results from oscillations of the light between the two mirrors. Thus, the integrated device works as an intracavity tuning element. The waveguide pattern of the latter consists of two Y-junctions linked together by a straight arm of length L1 and a bent arm of length L2 . The electrodes induce a vertical electric field EZ in both waveguide arms of the MZI, when a voltage VZ is applied.
FIG. 1. Experimental setup of the tunable fiber laser using a LiNbO 3 -integrated tuner.
TUNABLE SECOND HARMONIC GENERATION
85
The principle of operation is the following. In order to achieve simultaneously electrooptic tunability and second harmonic generation ŽSHG. the polarization of light in the cavity is controlled to excite the TE-mode of the waveguide corresponding to the ordinary refractive index n 0 . The total OPD Žoptical path difference., D s D 0 q D mŽ VZ ., introduced between the two arms of the intracavity electrooptic two-wave interferometer is the sum of a static OPD, D 0 s n 0 Ž L2 y L1 ., and a voltage-dependent one, D mŽ VZ . < D 0 , given by D m Ž VZ . s
1 2
r 13 n30 g TE
VZ d
Ž L 2 q L1 . ,
Ž 1.
where r 13 s 8.6 pmrV is the electrooptic coefficient of lithium niobate, g TE is the overlap coefficient between the electric field, EZ s VZ rd, and the optical field. d is the electrode gap. The resulting half-wave voltage, corresponding to the TE-mode, is Vl r2 s
l0 d r 13 n30 g TE
Ž L 2 q L1 .
.
Ž 2.
It can be shown that the one-pass spectral relative transmission of the intracavity tuner can be expressed as T Ž l. s
1 2
1 q cos
2p
ž ž l
D0 q
l0 VZ 2Vl r2
//
.
Ž 3.
According to relation Ž3., the one-pass spectral transmission of such a filter features pseudo-periodic transmission peaks, with a free spectral range ŽFSR. related to the OPD of the filter by FSR f
l20 D0
,
Ž 4.
where l0 is the central wavelength of the fluoroescence spectrum of the Nd3qdoped fiber. Laser emission occurs at wavelengths l that correspond to constructive interference at the output of the MZI, i.e., D 0 q l0 VZ r2Vl r2 s m l, where m is an integer. In this laser configuration, the emission spectrum of the pumped Nd3q-doped fiber laser is centered at l0 s 1088 nm with a bandwidth of D l s 12 nm. Wavelength tuning is carried out by varying the OPD introduced by the MZI. D 0 is chosen such that there is only one transmission peak of the filter inside the spectral gain curve of the laser; i.e., FSR f l20rD 0 G D l, yielding in this case D 0 f 100 m m w3x. As a voltage VZ is applied to the tuner, the total OPD changes linearly. Hence, the emitted wavelength is shown to be expressed as
lŽ VZ . s l0 q a VZ ,
Ž 5.
where l 0 s D 0rm, and a s d lrdV s FSRr2Vl r2 , expressed in nmrV, represents the tuning rate.
86
MOLLIER ET AL.
The required voltage to tune the wavelength over the whole spectral gain curve is 2Vl r2 . In this configuration, the tunability is achieved on adjacent modes of the cavity by mode hopping. The tunability of the fundamental wavelength being defined, we discuss now the nonlinear behavior of the tuning. Second harmonic generation can be obtained into lithium niobate waveguide by polarization mode coupling through the nonlinear optical coefficient d 31 s 5.8 pmrV. The expression for the SHG efficiency ignoring depletion of the fundamental field is given by w7x
hs
Pv 2 Pv 0
s
2 8p 2 d 31
Pv 0 L2
nv 0 nv 2 c « 0 l20
Seff
j sin c 2
D kL
ž / 2
,
Ž 6.
where Pv 0 and Pv 2 are optical powers of fundamental field and the second harmonic one, respectively; L is the interaction length; Seff is the effective surface of interaction; j is the overlap coefficient between the fundamental and the second harmonic fields; c s 3 = 10 8 msy1 ; and « 0 s 8.85 = 10y1 2 Frm. D k is the wave vector mismatch, given by w8x D k s kv 2 y 2 kv 0 s
4p
l0
Ž nv 2 y nv 0 . .
Ž 7.
The phase mismatch can typically be cancelled using the natural birefringence of the crystal. The phase-matching condition corresponds to nv 0 s nv 2 ; this requires that the fundamental and the second harmonic be orthogonally polarized. In lithium niobate, which is a positive single axis birefringent crystal with large nonlinear susceptibility, the SHG can especially be obtained with natural birefringence dispersion of the material. In our case, the waveguide orientation Žalong the Y-axis, on a Z-cut substrate . is such that the TE-polarized emission of the Nd3q-doped fiber at l0 s 1088 nm is phase-matched to a TM-polarized second harmonic at l2 s 544 nm into the waveguides. In the phase-matching conditions, i.e., nv 0 s nv 2 , the conversion efficiency can be expressed from Eq. Ž6. as
hs
2 Pv 0 L2 8p 2 d 31
nv2 0 c « 0 l20
Seff
j.
The theoretical estimation of conversion efficiency is h s 0.024%, with Seff s 15.5 m m2 , L s 35 mm Žcorresponding to the interaction length., and considering j s 0.18 Žcomputed with the optogeometric parameters of the waveguide.. The spectral transmission of the integrated MZI is such that when a transmission peak is centered at v 0 , another one is centered at v 2 s 2 v 0 . For guided waves, phase-matching tolerances of SHG are larger than in bulk configurations. Indeed, the effective index of an optical guided wave has a value intermediate between the substrate index n s and the maximum index at the surface of the guiding region n s q D n. The total phase-matching range can be determined by constructing a diagram which represents the area delimited by n TE Ž l., w n s q D n x TE Ž l., n TM Ž lr2., w n s q D n xTM Ž lr2. w9x. Typically for a Ti:LiNbO 3 waveguide, the phase-matching conditions are respected in a 20 to 30 nm range. Consequently, the LiNbO 3 device
TUNABLE SECOND HARMONIC GENERATION
87
can also be used as an intracavity frequency doubler. When the fundamental wavelength is tuned, the phase-matching condition remains fulfilled and the generated second harmonic is tuned in the same way. From Eqs. Ž2. and Ž4., one can see that the values of the FSR and the half-wave voltage of the tuner for the second harmonic are, respectively, one quarter and one half of those for the fundamental wave. Thus, the tuning range of the second harmonic is half the tuning range of the fundamental wavelength. This is also the case for the tuning rate.
3. EXPERIMENTAL RESULTS
The MZI tuner is designed to generate an OPD of about 100 m m. As n TE f 2.23 is the effective index of the TE-propagation mode at l 0 s 1088 nm, the optogeometric parameters of the waveguides were defined with a length L1 s 2 cm for the straight arm and a length L2 s 2.0045 cm for the curved arm designed with a bend radius of R s 4.22 cm. The 5-m m-wide waveguides were diffused from a 50-nmthick electro-beam-evaporated titanium layer. The diffusion process was performed at 10208C for 8 h in a wet-oxygen atmosphere to prevent the waveguides from LiO 2 out-diffusion. The Cr]Au:electrodes, 50 and 250 nm thick, respectively, were etched by a photolithographic process over a 150-nm-thick SiO 2 buffer layer. The electrodes were patterned over the waveguides in a 2-cm-long push]pull configuration. The width of each electrode is 20 m m and the gap is d s 10 m m. The waveguide is monomode at 1.08 m m and only the TE mode is supported. At 0.544 m m, the waveguide is multimode for both TM and TE polarizations. The effective half-wave voltage was measured to be 17 V. The value of the OPD introduced by the MZI was assessed from the spectral transmission of the filter using the broadband fluorescence of the 818-nm-pumped Nd3q-doped fiber as a source before the deposition of the mirrors. Figure 2 shows the spectral transmission thus obtained. The measured FSR of the channeled spectrum is 11 nm,
FIG. 2. Experimental channeled spectrum produced by the imbalanced Mach]Zehnder interferometer ŽTE mode.: FSR s 11 nm. The dashed lines mark the limits of the laser gain curve of bandwidth D l s 12 nm.
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corresponding to an experimental OPD D 0 s 108 m m. This value is slightly greater than the optimal value of 100 m m. The losses introduced by the tuner in the cavity for a round trip are g s y6 dB, and the threshold is obtained for a 42-mW-absorbed pump power. Without a tuner, the threshold was obtained for an absorbed pump power of 10 mW. With a tuner, the output laser power is 1 mW for an absorbed pump power of 82 mW, yielding a 2.5% laser efficiency. The spectrum analysis of the emitted beam is reported in Figure 3. Multimode laser emission occurs at the wavelength corresponding to the maximum of gain, with a full width at half maximum ŽFWHM. of 0.8 nm. The laser emission is TE-polarized. The transmitted optical spectrum of the second harmonic is displayed in Fig. 4, showing the SHG occurs mainly in the TM-mode. The SH optical power transmitted by the laser is measured to be equal to 1 mW. Taking into account the power of the fundamental field stored inside the laser cavity, about 9 mW, and the 90% reflectivity of the output mirror, we estimate that the experimental conversion efficiency is h s 0.011% mW. This result is smaller than the theoretical one because of a weaker overlap coefficient j and a slight velocity mismatch, Ž nv y nv . f 10y5 . The total length of the cavity is 3.5 m, and the longitudinal 2 0 mode, spacing is 0.11 pm. As a driving voltage ranging between 0 and 36 V Žcorresponding to 2Vl r2 . is applied to the tuner, wavelength is tuned by mode hopping. The tuning curves are shown in Fig. 5. The variation of emitted wavelength versus applied voltage is linear and the tuning ranges are 11 and 5.5 nm for l0 s 1088 nm and l2 s 544 nm. The variations of output power, over the tuning range for l0 s 1088 nm, are smaller than 1 dB, which corresponds to a variation of laser efficiency less than 0.5%. For the SH, these variations are not significant. The presence of two simultaneously emitted wavelengths is due to the nonoptimized FSR of the filter resulting in two adjacent transmission peaks inside the gain curve of the laser. Work is in progress to increase the tuning range up to optimized value of 12 nm. The slopes of the curves in Fig. 5 indicate experimental tuning rates of 0.25 and 0.12 nmrV for l0 s 1088 nm and l 2 s 544 nm. The wavelength can be tuned over the FSR up to 1 kHz, which corresponds to a tuning speed of 11 nmrms and 5.5 nm for, respectively, l 0 s 1088 nm and l2 s 544 nm.
FIG. 3. Transmitted optical spectrum of the laser beam at 1088 nm. The emission is mainly TE-polarized.
TUNABLE SECOND HARMONIC GENERATION
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FIG. 4. Transmitted optical spectra of the second harmonic. Dashed lines, TE-polarization; continuous line, TM-polarization.
4. CONCLUSION
In conclusion, we have reported on a LiNbO 3-integrated imbalanced Mach] Zehnder interferometer used as a tunable filter in a Nd3q-doped fiber laser. With this system that involves no mechanical motion, we have shown that a tuning range of 12 nm around 1.088 m m can be obtained with a tuning rate of 0.25 nmrV. This tuner can be used with other types of fiber lasers, especially with erbium-doped fibers. Work is in progress to increase the selectivity of the filter by cascading
FIG. 5. Emitted wavelength versus driving voltage: Ža. second harmonic, l s 544 nm; Žb. fundamental wavelength, l s 1088 nm.
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several MZIs with increasing path differences Ž D 0 , 2D 0 , 4D 0 , ??? .. The device can be used as an intracavity nonlinear element for SHG in the case of a Nd3q-doped fiber laser. The SH emission is observed without any photorefractive damage and a 0.12 nmrV tuning rate was measured. This work consists of the first demonstration of such an hybrid tuning fiber laser using a LiNbO 3-integrated component linked with a doped fiber laser. Different ways will be investigated to improve the efficiency of frequency doubling. For instance, an optimization of opto-geometric parameters of the waveguide can be realized to improve the overlap between the fundamental beam and the SH. This opens the way to new solid-state and tunable lasers built with a doped fiber and integrated optics technology, working in the visible region of the spectrum with possible extension to shorter wavelengths. The generation of shorter wavelengths, from a signal at l s 1.55 m m, for example, could be achieved by the use of quasi-phase-matching section of the waveguide obtained by ferroelectric domain inversion. This approach could be extend to integrated doped planar waveguide. In this case, the main interest is the realization of a very compact laser source.
ACKNOWLEDGMENTS This work was supported by the Ministere et de la Recherche. ` de l’Enseignement Superieur ´
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