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Keywords:

  • Integrated optics;
  • laser writing, lithium niobate;
  • nonlinear optics;
  • quasi phase matching

Abstract

  1. Top of page
  2. Abstract
  3. Acknowledgements
  4. References

All optical inscription of quasi phase matching structures in an x-cut LiNbO3 crystal is demonstrated. Quasi phase matching is obtained by periodically lowering the nonlinear refractive index of the crystal using focussed ultrashort pulses. The structures were used to frequency double 1.55 µm light. The converted signal could be enhanced by a factor of 70 with respect to the unmodified material. From these measurement it could be deduced that the nonlinearity has been periodically damped up to 20%.

Within the past years the aim to provide light in any wavelength regime has driven the field of nonlinear optics. Applications range from single frequency sources to broad band parametric frequency conversion. In most cases, second order nonlinearities are exploited for sum and difference frequency generation - with second harmonic generation (SHG) being the most prominent example.

In many applications, the artificial, anisotropic crystal lithium niobate (LiNbO3 ) is used, which has high nonlinear coefficients. In order to achieve efficient photon conversion, the phases of the photons of the incident and of the doubled frequency ω and 2ω have to be matched. Otherwise, back conversion of the second harmonic power inline image to the pump inline image occurs due to the phase mismatch inline image depending on the difference of refractive indices inline image, inline image at the fundamental and second harmonic frequency.

Figure 1(a) displays inline image as a function of propagation length in the nonlinear medium. All curves have been computed by numerically integrating the coupled-amplitude equation for a lossless medium [1]. For the case of perfect phase matching (inline image), the dependence is quadratic (Fig. 1(a), black curve I), for a given mismatch (inline image), back conversion starts to occur at the point where the phase mismatch amounts to π (Fig. 1(a), blue curve IV), thus at a coherence length of

  • display math(1)

In a birefringent crystal, phase matching can be achieved for conversion of ordinary polarized light to extraordinary polarized light, by finding an axis of propagation for which their respective refractive indices are equal. Alternatively, back conversion can be diminished [2] (Fig. 1, curve III) or avoided (Fig. 1, curve II) with quasi phase matching (QPM). Here, the nonlinearity is altered with a period of inline image. Ideally, the sign of the second order nonlinearity d is reversed (Fig. 1(b), green solid line).

image

Figure 1. Second harmonic power over propagation length (in units of inline image) and a sketch of the longitudinal profile of the second order nonlinearity d, the solid line displays domain reversal and the dashed line the investigated periodical lowering of the nonlinearity.

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Usually QPM structures are fabricated by means of electric field poling, where a high voltage is applied to the crystal through a patterned masking layer. This technique is restricted to the d33 component of the nonlinearity, consequently just z-cut crystals can be poled such that the individual domains range through the entire crystal. However, there are certain applications that require the use of x-cut crystals, e. g. electro-optic modulators. At the same time they would benefit from efficient frequency conversion mediated by QPM. While poling of x-cut crystals has been demonstrated with surface electrodes, the reversed domains extended only a few micrometers below the surface [3, 4].

Our aim is to realize a QPM structure that extends far into the volume of an x-cut LiNbO3 wafer. Instead of electric field poling, we use ultrashort laser pulses to structure the crystal. This approach has many benefits. Most importantly, it is more flexible since it does not require any micro structuring technology to lithographically define the respective poling patterns. Additionally, it can easily be combined with ultra-short pulse laser based direct writing of optical waveguides; thus enabling all-optical processing of integrated optical devices. Several functional elements could already be demonstrated with the direct write technique: modulators as well as frequency converters [5] and most recently Bragg reflectors [6]. QPM waveguides however were only demonstrated in crystals that were poled already [7-9]. Mailis et al. demonstrated that the field of a femtosecond UV-laser can induce a domain inversion [10]. Albeit, these modifications were limited to the surface of the z-cut sample.

In this paper, we aim not to switch the sign but to periodically lower the nonlinearity by inline image as sketched in Figure 1(b), red dashed line. This approach has been sucessfully demonstrated on other platforms where domain poling is not possible, e.g. by reducing the nonlinearity of GaAs by ion-implantation [2, 11, 12], by Frozen-in field-induced second order nonlinearity in optical fibers [13] or more recently in the design of a meta-metarial with a QPM periodicity [14]. A Fourier transform of the second order nonlinearity profile yields

  • display math(2)

for the effective second order nonlinearity deff. The efficiency of a QPM structure with lowered nonlinearity is well below that of a poled one, because back-conversion although reduced is allowed (Fig. 1(a), red dashed curve, III). Its conversion efficiency directly depends on how strongly the nonlinearity of the crystal is affected by the modification. Ultrashort pulses can locally alter the crystaline structure of LiNbO3 in two ways. They either raise the extraordinary refractive index (Type I) or destroy the crystaline structure, inducing stress fields (Type II) [15]. Two previous studies addressed how the nonlinearity is affected within fs written modifications. In both a Type I waveguide had been inscribed in a periodically poled LiNbO3 and the decrease of the second order nonlinearity was estimated by measuring the SHG generated within the waveguide and comparing it with the numerically calculated conversion efficiency [7, 8]. Lee et al. measured a substantially decreased normalized conversion efficiency of 0.0003 inline image [7], while Osellame et al. achieved 6.5 inline image and deduced that the second order nonlinearity can be conserved for a certain parameter regime within a Type I modification [8].

The sample used for the experiments here is a congruent LiNbO3 wafer, (MgO, 5mol% doped), 0.5 mm thick, polished as x-cut, with the z-axis of the crystal parallel to the surface (Fig. 2). The maximum second order nonlinearity inline image can be observed for light polarized along the z-axis. For pump light of inline image 1545 nm, the coherence length inline image was determined to be 9.5 µm [16]. In the following we assume that the dispersion for the modified regions is approximately equal and inline image likewise (see Eq. (1)). In the pristine crystal, the losses for the fundamental and second harmonic light were measured to be inline image dB/cm inline image dB/cm for polarizations parallel to the z-axis of the crystal.

image

Figure 2. Schematic of the sample and inscription setup (a), the coordinate system is that of the crystal. The inset (b) outlines the inscription routine of each segment. Inset (c) shows a microscope image of the endfacet of the QPM structure (inscription pulse energy of 650 nJ).

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The structures were inscribed with a cross-bearing translation stage (Aerotech ALS130, bidirectional repeatability of inline image nm) and a regenerative amplifier (Coherent Reg A, operated at 800 nm, 170 fs pulses, repetition rate 100 kHz). Its pulse energy could be continously adjusted up to 750 nJ with a half wave plate and polarizer combination. The light was focussed with a 40 times microscope objective (NA = 0.65) into the sample. We aimed for a period of inline image with a filling factor of 0.5. inline image periods were realized. For each modified volume, the sample was translated with a velocity of 1 mm/s as sketched in the inset of Figure 2. The red part of the arrows indicate where the shutter of the laser was open. Each of these modification lines has an elliptical cross-section with a width of 3–4 µm and 14–16 µm in height. In order to obtain a larger cross-section of overlapping modifications, each modified region consists of seven vertically overlapping 'layers’ of inline image µm spaced lines, which are inline image µm apart. The final structure had a cross-section of inline image µm times inline image µm (Fig. 2(c)). In propagation direction the crystal was inline image mm long. The sample was hence characterized in a free beam setup. The pump laser was a tunable laser (Agilent 8164B) combined with an erbium doped fiber amplifier (EDFA). The system was operated in the pulsed regime with 40 ns pulses at a 166 kHz rate, delivering a peak power of 12 W. The light was coupled into the sample with a lens of 50 mm focal length. Outcoupling was achieved by a microscope objective (40x, NA=0.65).

In the following we describe the results for the QPM structure that has been inscribed with 650 nJ pulses. Although this structures had high propagation losses (inline image dB/cm and inline image dB/cm), a significant conversion could be obtained. Figure 3 shows the beam profiles of fundamental and second harmonic light after passage through the QPM structure. Note that both fundamental and second harmonic light are polarized parallel to the z-axis of the crystal, which clearly distiguishes quasi phase matching from polarization phase matching. While the beam width is conserved, the beam height of the second harmonic light is approximately a third of that of the fundamental. This indicates that the nonlinearity has not been modified homogenously over the cross-section. A possible explanation is that the modification of the non-linearity follows the same graded profile in the x-direction as the darkening (Fig. 2c). Thus, the beam size reduction by SHG is asymmetrically enhanced, because the conversion efficiency is higher in the central region of the structure.

image

Figure 3. Beam profiles of fundamental (a) and second harmonic light (b), double arrows indicating the direction of polarization. The coordinate system is that of the crystal.

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Figure 4 displays the tuning curve at room temperature. QPM and best conversion is obtained at 1545 nm. For comparison, the SHG signal of the pristine crystal is also included (red curve). The conversion efficiency could be enhanced by a factor of up to 70 with respect to the bulk signal.

image

Figure 4. Tuning curves for the inscribed QPM structure and the pristine crystal for comparison.

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Figure 5 shows the power dependence at the phase matched wavelength. In the structure investigated, we did not observe saturation due to pump depletion. Thus, the effective second order nonlinearity can be determined from the quadratic power law

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where η denotes the overal efficiency of the QPM structure and

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is a proportionality constant, which depends on the length of the QPM structure inline image, a loss term inline image and the Boyd-Kleinmann focussing parameter inline image (for the focussing conditions within the experiment) [17, 18]. By inserting the calculated deff and the measured bulk inline image pm/V in Eq. (2), we estimated the contrast of the QPM structure to be inline image. However, this is an upper limit, since our estimate assumes inline image , thus we do not take systematic and statistical errors of fill factor and periodicity into account [19, 20].

image

Figure 5. SHG power vs. input power at the phase matching wavelength.

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QPM structures were also realized with lower and higher pulse energies, but yielded lower or no conversion. This has two reasons: For low pulse energies, the induced modification is primarily a positive index change, which seems to leave the nonlinearity almost untouched [8]. Higher pulse energies result in a partial darkening (Fig. 2(c)), which is not only accompanied by a significant decrease of the second order nonlinearity of up to 20 percent but also by significantly higher losses. Both factors have to be balanced to obtain a QPM structure with good efficiency. While the overall conversion efficiency is low compared to z-cut PPLN or surface poled x-cut PPLN waveguides [3, 4], our approach enables deeply embedding both modulator and frequency converter on a monolithic chip. In combination with current research on femtosecond induced second order nonlinearities in glass [21], QPM with damping domains might pave the way to truly three-dimensional nonlinear devices.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Acknowledgements
  4. References

We like to acknowledge financial support by the German Research Foundation (DFG) under priority program 1157 and the Leibniz program. Jens Thomas is supported by the Carl-Zeiss-Foundation.

References

  1. Top of page
  2. Abstract
  3. Acknowledgements
  4. References