1. Introduction

In the past decade, the subject of narrowband optical parametric amplification (NB-OPA) by degenerate four-wave mixing (FWM) [1–8] has been studied thoroughly in optical fibers. Among the applications of NB-OPA are widely tunable filters, wavelength converters, slow light devices and tunable optical parametric oscillators at mid-infrared wavelengths. In NB-OPA, the pump is positioned in the normal dispersion regime and phase matching is obtained only for a signal at large detunings by a balance between dispersion parameters of different orders. The spectral position and width of the phased matched region are determined by, and are very sensitive to the pump detuning from the zero dispersion wavelength. Most reported NB-OPA experiments operated at 1550nm and used dispersion shifted fibers with lengths of hundreds of meters.

In semiconductor waveguides, the optical mode is confined to very small volumes and hence the nonlinearity is large. There has been extensive research on FWM and parametric amplification in Silicon waveguides of different kinds [9–13]. Silicon waveguides are limited by two photon absorption (TPA) at 1550nm and hence, use very large pump powers. Hydrogenated silicon [11] has also been attempted as a means to overcome TPA but those devices tend to be unstable. Operation at 2050 − 2350nm avoids TPA and has also been demonstrated [9]. Waveguides with simple designs exhibit only anomalous dispersion and therefore narrowband parametric interactions are not possible.

Photonic Crystal Waveguides (PCWs) offer enhanced characteristics compared to both fibers and simple semiconductor waveguides due to the ability to fashion different optical properties of the propagating modes by changing the geometric design [10,14]. By using a high band-gap semiconductor such as Ga_0.5In_0.5P, two photon absorption is avoided at 1550nm. By employing slow mode propagation, nonlinear functionalities are vastly enhanced [10]. Such a devices have already shown superb parametric efficiency when the pump was positioned in the anomalous dispersion regime [15, 16] where a gain of 11dB was measured with a pulsed pump having a peak power of less than 1W.

A new generation of dispersion engineered PCWs avails a dispersion function with two or more zero crossings, and wide spectral ranges of both normal and anomalous dispersion regimes [17]. The dispersion is controlled by the holes radius together with an asymmetric shift of the two inner most rows of holes. Such devices can be used for NB-OPA, as predicted by simulations [18–21].

We report here the first experimental demonstration of NB-OPA in a PCW whose loss and dispersion spectra are shown in Fig. 1(a). The Photonic Crystal structure is that of air holes patterned in a hexagonal grid on a 180nm thick suspended Ga_0.5In_0.5P membrane. The waveguide is 1.5mm long and has tapered mode converters at the input and output facets designed to increase coupling efficiency as seen in the inset of Fig. 1(a). The periodic constant is a = 482nm and the innermost rows of holes were shifted by T = 0.15a asymmetrically. From measurements of the PCW group index spectrum n_g(ω), we evaluated the dispersion profile β (ω) with a Taylor series (around λ_c = 1545nm) consisting of 31 coefficients. Losses were extracted from transmission spectrum measurements with a white light source. Intrinsic losses are unfortunately high in the normal dispersion regime and hence the overall FWM efficiency is reduced. Moreover, the transmission spectrum exhibits random features of increased losses, probably due to disorder and non-uniformity of the PCW that includes small cavities which are distributed randomly along the waveguide.

 

Fig. 1 (a) Spectra of the fitted linear dispersion coefficient β₂ (blue trace and left axis) and measured loss coefficient α_dB (green trace and right axis). The inset shows the edge of the PCW with a mode converter. (b) Map of the parametric gain coefficient g in units of mm⁻¹. The dashed lines mark the two zero dispersion wavelengths.

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In order to predict the pump and signal wavelengths that avail NB-OPA, we evaluated the parametric gain coefficient g for degenerate FWM as in [19]:

For an asymmetric shift ratio [17] T/a = 0.15 the fitting parameters used in all following calculations are: A = 1.17μm⁻³, B = −40.16μm⁻¹, C = 0.502 and λ₀ = 1540.5nm. With XPM and FWM the effective overlap integral I_{e f f} is evaluated using a geometric mean of I_SPM(λ_m):

Here the wavelengths λ_m are in increasing order; of course with degenerate FWM λ₂ = λ₃.

The pump-signal wavelengths combinations for which g² > 0 are depicted in the two dimensional map shown in Fig. 1(b) for a 650mW CW pump, with color scaling for the value of g given in units of mm⁻¹. Pump wavelengths in the normal dispersion regime, roughly between 1547nm and 1561nm (dashed lines mark the zero dispersion wavelengths) are phase-matched with widely detuned signals by balancing dispersion parameters of different orders.

2. Experimental setup and measurements

The experimental setup is described in Fig. 2. A pulsed laser with a repetition rate of 20MHz serves as the pump and a continuous wave (CW) tunable laser source (TLS) is the probe. The spectrum of 14ps wide pump pulses from the laser is filtered so that the pulses are broadened to T_{e f f} = 35ps. The pump and probe are combined at a ratio of 80:20 before being transmitted in free-space to a lens collimator which couples the field to the PCW. An anti-reflection coated polarizer aligns the field with the TE polarization mode of the PCW. A beam-splitter taps off 12% of the input beam for monitoring. The waveguide output is coupled to a single mode fiber which feeds an optical spectrum analyzer.

 

Fig. 2 Experimental setup. Light is coupled into and out of the PCW by free-space beams (red lines), which are coupled to optical fibers (blue lines).

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A careful calibration of the experimental setup allowed to determine the input and output coupling losses which were found to be 2dB and 2.5dB respectively. Two pump wavelengths in the normal dispersion regime, 1547.9nm and 1549.6nm, were chosen and the peak power inside the PCW was kept around 650mW. Larger pump powers were not used in order to stay far from the relatively low optical damage threshold of these waveguides. Unlike in conventional semiconductor waveguides where the damage occurs at the front facet, here the damage threshold is determined by the propagation mode and the pulse width. For pulses wider than 10ps, it was found to be 1 − 2W.

An optical spectrum analyzer (OSA) measured the average spectra of the idler wave generated by FWM. Since the pump pulse train had a duty cycle of RT_{e f f} = 0.0007, the observed idler power was lower by 31.5dB compared to its true peak value. The CW probe average power inside the waveguide was 1.1mW; its wavelength was placed on either side of the pump and tuned over a range of several nanometers (in steps of 0.05nm and 0.1nm respectively for the short and long wavelength pumps) according to the map of Fig. 1(b). The entire spectrum was recorded as presented in Fig. 3(a) and 3(b) for each pump, respectively. The pump pulse shape at the input is shown in the inset of Fig. 3(a).

 

Fig. 3 Measurements of output spectra with a pulsed pump and a CW probe. Different probe-pump detunings generate idlers at appropriate different wavelengths, depending on pump wavelength: (a) λ_p = 1547.9nm ans (b) λ_p = 1549.6nm.

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The narrowband nature of the response is clearly seen. For probe wavelengths near the pump, no idler is generated since phase matching conditions are satisfied in a NB-FWM process at large detunings from the pump. For the pump at 1547.9nm, phase matching is obtained at a detuning of about 6nm while for the pump at 1549.6nm, which is spectrally located farther from the shortest zero dispersion wavelength and is hence deeper in the normal dispersion region, it is close to 13nm. This is a characteristic of NB-FWM where a small change in pump wavelength yields a large change in the detuning for which phase matching occurs [3].

The FWM efficiency is defined as the ratio between the average idler output power and the input probe power. These were evaluated by integration of idler and signal spectra and considering the duty cycle of the pulse train. Thus the data of Fig. 3(a) and Fig. 3(b) of the output spectra can be summarized in Fig. 4 for the two pump wavelengths (blue and red dots). Though the parametric conversion efficiency is not large, the change in the spectral position where phase matching takes place and the dependence on detuning of the gain spectral width are clearly seen. Larger efficiencies may be obtained with lower propagation losses, with a waveguide design in which scattering losses at long wavelength are lower and by improving the membrane structure so that larger poump powers can be tolerated. The latter requires improvements in the waveguide surface properties as well as better thermal management. As the pump shifts to longer wavelengths, the 3dB bandwidth of the conversion efficiency reduces from 1.7nm to 1nm for large probe-pump detunings. The conversion ratio values are moderately low due to increased losses at longer wavelengths.

 

Fig. 4 Conversion efficiency obtained from M-SSFT simulations (solid curves) and from measurements (dots) as a function of probe-pump detuning for a pump at 1547.9nm (blue) and 1549.6nm (red).

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Concurrently, the M-SSFT model [23] was used to simulate the propagation of the pump pulse and a CW probe along the 1.5mm long PCW. The dispersion and losses which are depicted in Fig. 1(a), together with the nonlinear modeling of the interaction [22] were used to describe the optical medium while the input powers and pulse shape were the same as in the experiments. The blue and red solid curves in Fig. 4 represent the calculated conversion efficiency (calculated from the average power of the idler pulse) with pump wavelengths of 1547.9nm and 1549.6nm, respectively. We believe that the differences between the measured results and the simulations stem from distributed defects along the waveguide that contribute not only to the random features in transmission spectrum but also to variations in mode distributions. These can be translated to variations in propagation parameters along the propagation axis, similar to an effect encountered in imperfect optical fibers [24, 25]. Partial phase matching is consequently obtained for a wider range of probe-pump detunings and thus the overall measured efficiency spectrum is wider than the calculated one. Additionally, at some wavelengths the efficiency is higher than predicted since the modified mode distributions enhance the nonlinearity at those specific wavelengths. The conversion efficiency is larger for positive probe-pump detunings with λ_p = 1549.6nm. This is in agreement with the theory of ref [21] which predicts this asymmetry when losses are larger on the pump Stokes side.

To conclude, we have demonstrated, for the first time, NB-OPA in a semiconductor waveguides. The specially designed PhC waveguide with two zero dispersion wavelengths has a wide normal dispersion regime where a pulse pump was placed. A CW probe yields a pulsed idler for a very narrow pump-signal detuning range. The principles of NB-OPA studied previously in optical fibers were applied now successfully to PCWs offering numerous possibilities for implementing chip-scale devices such as narrow band amplifiers, optically tuned filters and tunable parametric oscillators.