1. Introduction

Microstructured fibers (MF) continue to attract considerable interest for their unique structure and optical properties which have led to a renewed interest in the study of nonlinear processes in optical fibers, specifically in regards to supercontinuum formation and various mixing and nonlinear frequency conversion processes [1–4]. In a previous paper [5] we have reported about the observation of power-dependent generation of visible radiation by coupling femtosecond pulses at a wavelength of 1.55 microns in a 95 cm segment of a high-Δ (i.e. high-air filling in the cladding) microstructured fiber. Two bands of visible radiation were generated by a combination of temporal pulse splitting of the fundamental pulse followed by Raman self-frequency shifting of one of the split pulses and subsequent third harmonic generation of both frequencies [5]. We expand on the previous results by detailing the dependence of the generated visible radiation on the polarization state of the input pulse coupled into the microstructured fiber. We experimentally observe that the propagation of a pulse of fixed energy, yet polarized along different directions, yields distinct visible components at the output, suggesting a polarization-dependent selectivity for phase-matching according to the input polarization state. These components correspond to the third-harmonic of the fundamental and the self-frequency shifted fundamental. Furthermore, we demonstrate that the third harmonic components, which appear at the output of the MF as higher order modes, are guided in the core of the fiber by comparing the experimentally imaged near-field profile and the calculated mode which verifies the phase matching condition between the fundamental radiation propagating in the fundamental mode and the high-order mode in the visible.

2. Experimental Results

In this set of experiments, a considerably shorter (Z=20 cm) piece of the same microstructured fiber used in previous experiments [5] is employed here. As mentioned above, this fiber is a high-Δ microstructured fiber which consists of a solid silica core of 2.5 microns in diameter, suspended in air by a web of sub-micron silica strands with a cladding diameter of 90 microns and exhibits six-fold symmetry in its structure (an image of this fiber is shown at the end of the paper in Fig. 6). The light coupled into the fiber is generated by an optical parametric oscillator (OPO) that produces ~170 fs pulses (repetition rate of 80 MHz) with average powers up to 250 mW (energies of nanojoules) and operates at a wavelength of λ=1550 nm. The present analysis is performed for low average power values (i.e. up to 25 mW). In this range, the fundamental wavelength λ^FUND=1550 nm is observed to propagate in the fundamental mode through the MF. It must be pointed out that the fiber is not single mode in the range covered by the fundamental wavelength and its self-frequency shifted components (i.e. 1550–1650 nm). The input pulse power is controlled by a λ/2 waveplate and a polarizing cube combination, placed in front of the fiber input. An additional λ/2 waveplate controls the input polarization state to the MF determining the orientation of the linearly polarized light with respect to the MF structure. An intensity transmission analysis as a function of input polarization is performed to assess the principal axes associated with this structure. This reveals two principal polarization directions α and β which are orthogonal to one another. When the input pulses are linearly polarized along one of these two directions, one of two visible modes of different colors is detected at the output. These generated visible frequencies are higher-order modes exhibiting an eight-lobed structure in the far-field and are found to be centered at λ₁=514 nm and λ₂=533 nm (Fig. 1). It has been previously noted [5] that the observed components λ₁ and λ₂ bear a relation to the fundamental such that λ_FUND~ 3λ₁ and λ_F,Shift~ 3λ₂, (or 3ω_FUND~ λ₁ and 3λ_F,Shift ω₂ and where ω_F,Shift is the Raman self-frequency shifted portion of the fundamental). The mechanism for this process was described as temporal splitting of the fundamental pulse followed by Raman-self frequency shift of the split pulse, with subsequent third-harmonic frequency conversion of both pulses as the possible mechanism for the generation of the visible components [5]. Similar fission mechanisms have been described in the analysis of dynamics leading to supercontinum generation [6]. Previous observations of conversion processes to higher order modes date back to early experiments in fibers [7] and have instilled renewed curiosity [4] thanks to the combination of new structures and readily available high-intensity laser sources which make these processes easily observable. However, previous [7] and more recent [8] reports of phase matched guided processes in fibers have been associated to mixing phenomena whereas third-harmonic generation in fibers has been generally reported to be generated in a leaky mode through a Cherenkov-type phase-matching process [9,10].

 

Fig. 1. Far field mode profiles detected at the ouput of the microstructured fiber for polarization states directed along the two previously identified principal axes α and β. The input to the fiber are pulses at λ=1550 nm, τ~170 fs, with maximum average power of 25 mW (for these experiments). The two outputs are centered at (a) λ= 533 nm and (b) λ=514 nm.

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Fig. 2. Plot of modal indices (N=5-25) for λ= 510 nm (black squares), λ= 520 nm (red circles), λ= 530 (green triangles), and modal index for the fundamental as a function of wavelength (black solid line). Phase matching conditions can be identified for the N=21 mode. For further details see text.

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In this case, the mode structure detected experimentally is compared to the calculated pattern of the high order modes supported by this specific geometry of MF. The latter are evaluated by performing modal calculations of the MF with a full vector model based on the supercell plane wave method [11]. The input refractive index profile for the model is a bitmap picture taken from an electron micrograph of the actual fiber employed in these experiments. The material dispersion of silica is taken into account by using the published Sellmeier coefficients. These calculations provide the modal indices and the transverse modal intensities of all of the guided modes of the structure. Using these indices, a comparison can be made between the index of refraction of the fundamental and the modal indices of the higher order modes for the detected wavelength values of the visible components.

 

Fig. 3. Comparison of the experimentally acquired image of the near field profile of the guided λ=514 nm mode and the calculated profile of the N=21 high order mode supported by the MF in that wavelength range.

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The modal indices of the fundamental mode propagating through the microstructured fiber at 1550 nm is n=1.38, whereas higher order modes propagating around 510 nm form a near continuum of decreasing modal indices. Eight-lobed pattern modes whose index of refraction is in the range n=1.38–1.40 indicate the existence of a correctly shaped mode whose index is close to the calculated fundamental mode, thus pointing to a favorable condition for phase matching. It must be observed that the modal indices of high order modes are particularly sensitive to the exact shape and size of the fiber core (which is subject to some uncertainty when using the actual SEM picture of the fiber tip), so it is quite possible that the true index matching in the fiber is better than calculated. This is reflected in the graph by adding error bars (conservatively set at 0.2%) to the calculated indices. The calculated (near-field) mode field pattern for the high-order (N=21) mode is also shown in Fig. 3 and can be seen to follow the experimentally observed far-field profile (see Fig. 1 for comparison). Imaging of the near-field modal profile for the visible light coming out of the microstructured fiber tip was also performed by collecting the output radiation and acquiring the profile on a CCD camera. The comparison between the calculated near-field profile and the experimentally detected profile is illustrated in Fig. 3, and shows very close agreement between the two. This further confirms that the calculated third harmonic higher order mode which is supported by the fiber structure and phase-matched to the fundamental is indeed experimentally observed confirming the existence of a phase-matched and guided third-harmonic process in the MF.

A power dependent spectral analysis is carried out on the fundamental and on the visible harmonics for the two different polarizations. The detected spectra for the fundamental pulse are illustrated in Fig. 4(a,b), whereas the results for the generated visible harmonics are shown in Fig. 5(a,b). These spectra are acquired with an infrared spectral detector (Rees E2000) with sensitivity in the 800–1700 nm range.

A comparison between the spectral features of the fundamental pulse polarized along the direction α (Fig 4a) and the direction β (Fig 4b) shows different details in the spectral dynamics as a function of power but a fundamentally similar behavior: in both cases the spectrum shifts as expected toward longer wavelengths and the magnitude of the shift (~50 nm at P=25 mW) is the same for both input polarization orientations appearing, therefore, independent from the initial polarization. Since the Raman scattering process is an intensity (i.e. pulsewidth) dependent process, this suggests that the dispersion properties are not vastly dissimilar for both polarization states. The visible spectral features are detected by means of a separate spectrometer and acquired with a 16-bit CCD camera. These images and integrated over variable time windows to insure maximum sensitivity.

 

Fig. 4. Detected spectra of the fundamental (λ=1550 nm)radiation at the output of the microstructured fiber as a function of power for linearly polarized light along the directions α and β. The shift at P=25 mW (indicated by the arrow) is the same for both polarization states.

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The collection of spectral results shows a clear difference in dependence of the fundamental input pulse’s polarization state. In the direction α (Fig 5a) a spectral feature centered around λ=514 nm is detected for pulses of average power of 4 mW at 1550 nm. As the power of the fundamental is increased, more light is converted to the visible (with an estimated conversion efficiency of 0.2 % for a 25 mW pump) but only a feature at λ₁=514 nm is observed. The relationship of this component to the fundamental wavelength is consistent with the generation of third harmonic of the fundamental yet no third harmonic from the self-shifted component is observed at these power levels.

When the input pulse polarization is rotated along the direction β (Fig 5b), however, a sharp feature centered at λ₂=534 nm appears for pulses of average powers of 16 mW in addition to the λ₁ component that subsequently vanishes as the power of the fundamental is further increased. Whereas for both polarizations the fundamental shifts to 1600 nm (and beyond for higher input powers, such as the ones described in [5]), the shifted fundamental is converted to third harmonic radiation only when the input pulses linearly polarized along the β direction.

 

Fig. 5. Detected spectra of the visible radiation components at the output of the microstructured fiber as a function of power for both polarization states α and β. The component at 533 nm appears only in one polarization state.

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It must be stated that a combination of the two states (i.e. an input pulse polarized at 45 degrees with respect to the axes α, β generates the two visible components simultaneously, a situation that we most likely encountered in our previous paper [5], where the input polarization state was not being controlled. The polarization-dependent effect is observed here is not lost with varying lengths of fiber. This is most likely due to the fact that the conversion process occurs in the very first centimeters of fiber and thereon the visible components are guided through the remaining length. We have indeed observed the visible radiation generation in segments of just a few centimeters of MF.

 

Fig. 6. Scanning electron microscope image of the fiber tip used in the experiment. Various calibrated measurements performed with the microscope reveal mismatches in the 8 to 10% range between the dimensions indicated as a and b in the Figure, resulting in a slight ellipticity of the core of the microstructured fiber.

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It is also interesting to note that no frequency components that could be attributed to mixing processes [7,8] are detected for the wavelength interval covered by the fundamental and its shifted components (see Figs. 4 and 5). To further probe the detected birefringent behavior, SEM images of the microstructured fiber used were taken to verify the degree of symmetry of the structure. The resultant SEM image is shown in Fig. 6. The calibrated measurements show a slight asymmetry in the core, revealing an effective ellipticity of a solid silica core suspended in air. This mismatch is, however, quite small, yet could contribute to the different behavior seen along the two polarization axes.

3. Conclusions

These results provide an analysis of the nonlinear frequency conversion processes which occur in a high-Δ microstructured fiber when low average power femtosecond pulses at a wavelength of 1550 nm are coupled into it. The conversion of the 1550 nm light into the observed visible components occurs through a phase matched process between the fundamental mode at 1550 nm and high-order modes in the visible. The process is dependent on the linear polarization of the input pulses. This selectivity combined with Raman self-frequency shifting and third harmonic generation, provides a means to generate specific harmonics and therefore a means to control the output’s visible frequency through the input pulse polarization state. The extension of this approach can provide a basis for all-fiber signal control and ultrafast optical switching based on nonlinear phenomena in microstructured fibers.