Raman-induced frequency shift in CS2-filled integrated liquid-core optical fiber

Optics Communications 318 (2014) 83–87

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Raman-induced frequency shift in CS2-filled integrated liquid-core optical fiber Oscar D. Herrera a,n, L. Schneebeli a,b, K. Kieu a, R.A. Norwood a, N. Peyghambarian a a b

College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA Department of Physics and Material Sciences Center, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany

art ic l e i nf o

a b s t r a c t

Article history: Received 11 November 2013 Received in revised form 13 December 2013 Accepted 17 December 2013 Available online 7 January 2014

We demonstrate an optically tunable frequency shift in an all-fiber based system using a carbon disulfide (CS2) filled integrated liquid-core optical fiber (i-LCOF) and co-propagating pulses of comparable temporal lengths. In 1 m of i-LCOF we were able to shift 18 ps pulses, a full spectral bandwidth at low pump peak powers, using the Raman-induced frequency shift and slow light effects. Numerical simulations of the pulse-propagation equations agree well with the observed shifts. We also analyze the contributions of both the Raman cross-frequency shift and slow light effects to the overall frequency shift. The system is all-fiber based and compact, making it suitable for applications such as a low power wavelength converter. & 2014 Elsevier B.V. All rights reserved.

Keywords: Nonlinear optics Raman effect Fibers Nonlinear optical materials

1. Introduction Stimulated Raman scattering (SRS) is a nonlinear process by which an intense pump beam incident on a medium generates a downward frequency-shifted Stokes beam through molecular vibrations [1]. One manifestation of this nonlinear process is the Ramaninduced frequency shift (RIFS). For a single pulse this process occurs when the pulse experiences a red shift due to its high-frequency components pumping its own low-frequency components. This phenomenon is called a self-frequency shift (SFS). The case of copropagating pulses where the spectral shift is due to the presence of a second pulse is called a cross-frequency shift (CFS) [2–4]. Theoretical investigation of RIFS for single soliton pulses using the moment method and perturbation theory has been conducted in Refs. [5,6], respectively. Similarly, the all-optically induced frequency shift of copropagating picosecond pulses has been investigated in optical fiber through the use of instantaneous Kerr effect [7]. This study showed a tunable frequency shift dependent on the pulse walk-off and crossphase modulation (XPM) without the use of Raman. About 25 ps pulses at 532 nm were created through free-space second harmonic generation by 33 ps pulses at 1064 nm. Wavelength shifts of up to 0.4 nm in 1 m of fiber using 4000 W peak power were observed. These high pump powers were due to the low nonlinear coefficient of silica. Furthermore, SRS and XPM of co-propagating sub-picosecond soliton pulses in silica fiber were investigated in [8]. While the pulse walk-off was neglected and the Raman amplification is negligible,

n

Corresponding author. Tel.: þ 1 520 626 0936. E-mail address: [email protected] (O.D. Herrera).

0030-4018/$ - see front matter & 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.12.041

the CFS of high power pulses increased the frequency shift when compared to single pulse propagation. In addition, the walk-off can be further tuned via the Raman slow light effect and has been theoretically investigated in carbon disulfide (CS2) [9]. In this paper, we investigate the Raman interaction, in particular, the RIFS, of co-propagating pulses in an integrated liquid core optical fiber (i-LCOF) filled with CS2. The Stokes pulse experienced a substantial frequency shift at low pump powers due to the molecular contribution to the XPM and the Raman slow light effect. In our experiment, RIFS is observed by co-propagating a strong 1553 nm picosecond optical pulse with its weak 1729 nm Stokes pulse in a 1-m-long CS2-filled i-LCOF. Tunable red and blue shifts are observed by changing the peak power of the 1553 nm pump pulse. We have also performed numerical simulations of the coupled pulse-propagation equations given by the nonlinear Schrödinger equations (NLSE), which confirm the RIFS results and the role of slow light. Finally, we analyze the nonlinear components of the NLSE to understand their individual contributions to both the temporal delay and the frequency shift. The system is all-fiber based and compact with frequency shifts greater than a pulse bandwidth, exhibiting potential applications as a tunable all-optical wavelength converter, a wavelength selective switch, or an all-optical 1
2 switch.

2. Experiment A schematic of the experimental setup is shown in Fig. 1. A mode-locked (ML) fiber laser with a carbon nanotube saturable absorber (provided by Kphotonics, LLC) generates a 50 MHz pulse

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Fig. 1. The experimental setup used to measure the induced frequency shift of light in a CS2-liquid-core optical fiber Raman amplifier (ML laser – mode-locked fiber laser; PC – polarization controller; FBG – fiber Bragg grating; EDFA – erbium-doped fiber amplifier; i-LCOF – integrated liquid-core optical fiber; WDM – waveguide division multiplexer; VDL – variable delay line; OSA – optical spectrum analyzer). Inset: the optical spectrum of the 1553 nm picosecond pump and the generated Raman signal at 1729 nm.

train at  500 fs pulse duration. A narrow band 1553 nm picosecond pulse train is generated from the ML fiber laser by amplification in an EDFA and spectral filtering from a narrow band fiber Bragg grating (FBG). The FBG filter has a FWHM spectral bandwidth of  0.14 nm that corresponds to  22 ps transform-limited pulse. To generate the signal pulses we used an i-LCOF filled with CS2 to generate the first-order Raman Stokes line which is automatically down shifted from the pump by the Raman shift in CS2 (656 cm  1). The fabrication of the i-LCOF, its use as a Raman medium, and the high transmission losses mainly due to the significant modemismatch at the two gap-splices between the LCOF and the standard optical fiber have been previously discussed [10]. The core diameter of the LCOF is 2 μm with an area of 3:14 μm2 . The inset of Fig. 1 shows the spectrum at the output of the i-LCOF where the generated signal at around 1729 nm is clearly visible. The narrow band picosecond 1553 nm pump is split into two branches [Fig. 1]. The pulses in the first branch, which contain 90% of the average power, enter the i-LCOF filled with CS2 to generate the 1729 nm Stokes signal. The remaining 10% in the second branch is amplified to create the pump for the second i-LCOF (Raman amplifier) using a second EDFA. The length of the first iLCOF is  1 m and it has a transmission of  30% at 1553 nm. Due to the large Raman cross-section of liquid CS2, we observed an impressively low Raman generation threshold pulse energy of only 0.1 nJ. The transform limited temporal width of the 1729 nm signal pulses is  18 ps. Using commercial software Fimmwave 5.1 and the linear refractive index values of CS2, mode profile simulations inside the i-LCOF at the pump and signal wavelengths were calculated and single mode operation was confirmed at both wavelengths [11]. The V # for the pump and Stokes are 2.69 and 2.42, respectively. Similarly, the pump and signal were propagated 1 m and they were effectively single mode. The Raman amplifier is also a 1 m CS2-filled i-LCOF with a transmission of  15%. The loss does not, however, represent a major problem in our experiment, and recent improvements can result in transmissions as high as 64% [12]. Before the Raman amplifier, the pump and signal must be overlapped in time. To achieve that, the pump and signal pulses are first roughly overlapped in time by using a 50 GHz oscilloscope which provides a

precision of 715 ps. Even though the pump and Stokes may not perfectly align with this precision, a part of the pump is present within the Stokes pulse and nonlinear interaction still occurs. A mechanical variable delay line is then used for fine adjustment of the temporal overlap of the pump and signal. For efficient amplification, both the pump and signal must have the same polarization orientation; a fiber polarization controller for the pump is implemented to attain the maximum signal gain. The spectrum is acquired using a highresolution optical spectrum analyzer (OSA). We have also measured the Raman-induced slow light effect by adjusting our experimental setup described in Ref. [13] and using Fourier-transform spectral interferometry. The delays were measured as the change in distance traveled by the Stokes pulse with and without a pump present in the amplifier. The spectra of the Stokes pulse at different input pump peak powers (P0) are plotted in Fig. 2. The pump–Stokes misalignment was   15 ps. The red triangle represents the spectral peak at P0 ¼ 0 W. As the pump power is increased the Stokes0 spectrum begins to experience a frequency shift ðνshift Þ in the negative direction up to a maximum value of  17.85 GHz (P0 ¼2.15 W); this corresponds to  102% of the FWHM of the Stokes0 spectrum. Further increasing P0 introduced a blue shift to the spectrum. This is of great interest as the Stokes spectral shift shows a local minimum unlike the XPM and SPM due to the instantaneous Kerr effect [7]. Fig. 3 displays both the measured νshift (blue circles) and temporal delay caused by slow light (red diamonds) with respect to P0. The maximum Stokes0 delay was 33.1 ps at P0 ¼2.46 W. Both maximum Stokes0 delay and maximum jνshift j appear to be in the same region of P 0  2 W, after which the Stokes0 delay appears to saturate and νshift begins to exhibit a blue shift. Also, the Stokes0 gain maintained a linear growth up to  19 dB (P0 ¼3.54 W) without saturation.

3. Theory In order to understand the Raman-induced frequency shift, we numerically solve the simultaneous propagation of the pump and Stokes pulses along the CS2 filled i-LCOF. The theoretical description based on the NLSE in the slowly varying envelope

O.D. Herrera et al. / Optics Communications 318 (2014) 83–87

P0 = 0.3 W Norm. Int.

Norm. Int.

P0 = 0 W 1 0.5 1729

1729.5 λ (nm)

1730

1 0.5 1729

1729.5 λ (nm)

Norm. Int.

Norm. Int.

1 0.5 1729.5 λ (nm)

1730

1 0.5 1729

1729.5 λ (nm)

1730

P0 = 3.5 W Norm. Int.

Norm. Int.

P0 = 3.2 W 1 0.5 1729

1730

P0 = 2.5 W

P0 = 2.2 W

1729

85

1729.5 λ (nm)

1730

1 0.5 1729

1729.5 λ (nm)

1730

Fig. 2. RIFS of the Stokes spectrum at different pump peak power P0 for a pump–Stokes misalignment of  15 ps. The red triangle represents the spectral peak at P0 ¼0 W. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

35

0

40 0

−15

−10

10

5

0

1

2

3

4

0

P0 (W)

approximation for pump Ap ðz; tÞ and Stokes As ðz; tÞ pulses is given as [8]

β2p ∂2 Ap β3p ∂3 Ap αp ∂Ap ¼ i þ  Ap þ iγ p ð1  f R ÞAp ð
Ap j2 þ 2
As j2 Þ ∂z 2 ∂t 2 6 ∂t 3 2 Z

þ iγ p f R As

1

Z 11 1

hR ðt  t 0 Þ½jAp ðt 0 Þj2 þ jAs ðt 0 Þj2  dt

0

hR ðt t 0 ÞAp ðt 0 ÞAns ðt 0 ÞeiΩR ðt  t Þ dt ; 0

0

ð1Þ



∂As ∂As β2s ∂2 As β3s ∂3 As αs ¼ dwo i þ  As þ iγ s ð1  f R ÞAs ð
As j2 þ 2
Ap j2 Þ ∂z ∂t 2 ∂t 2 6 ∂t 3 2 Z 1 0 þ iγ s f R As hR ðt  t 0 Þ½jAs ðt 0 Þj2 þ jAp ðt 0 Þj2  dt 1 Z1 0 0 þ iγ s f R Ap hR ðt  t 0 ÞAs ðt 0 ÞAnp ðt 0 Þe  iΩR ðt  t Þ dt : ð2Þ 1

1

2

3

P0 (W)

Fig. 3. RIFS (blue circles) and Stokes0 delay (red diamonds) as a function of pump peak power P0 for a pump–Stokes misalignment of  15 ps. Dashed lines are guide for the eyes. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

þ iγ p f R Ap

Stokes delay (ps)

20

shift

(GHz)

−5

ν

(GHz)

15

ν

shift

−10

30

Stokes delay (ps)

25

−5

Fig. 4. Numerical simulations of the RIFS (blue) and the Stokes0 delay (red) for a pump–Stokes misalignment of  15 ps and walk-off parameter of dwo ¼ 14:5 ps=m. The Stokes spectral peak (solid) is also compared to its average location (dashed). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

The active medium is characterized by the dispersion (βj), linear losses (αj), Kerr nonlinearities (γj), and walk-off parameter dwo, where j¼s or p denotes the Stokes or pump, respectively. fR is the fractional contribution of the Raman response to nonlinear polarization and ΩR is the frequency difference between pump and Stokes. Moreover, the Raman response function (hR) is included and characterized through the Raman shift Δν ¼ 656 cm  1 and linewidth (FWHM) δν ¼ 0:7 cm  1 [14]. Even though the pulses are 4 1 ps, the Raman response of CS2 is different than silica fiber therefore we solve Eqs. (1) and (2) with all the Raman terms. The dispersion is computed from a simple step-index model [15,16] and the relevant Sellmeier coefficients [17]. Systematic measurements of linear refractive index as well as the absorption spectra of some interesting nonlinear liquids were also recently reported [11]. As a result, the second-order dispersion for the pump (Stokes) is β 2  105 ps2 =km ð  117 ps2 =kmÞ and the walk-off is given by dwo ¼ 14:5 ps=m inside the LCOF [18]. The nonlinearity γ

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O.D. Herrera et al. / Optics Communications 318 (2014) 83–87

where IðνÞ is the spectrum of the Stokes field. The Stokes0 delay0 s average temporal location was assessed in the same manner. Both average calculations are plotted in Fig. 4 (dashed). It is convenient to extract the average position because it contains more information than the pure peak position and accounts for opposing frequency shifts which lead to strong modifications of the Stokes spectrum for P 0 4 2 W. The computations based on the average positions recover the main features of the experimental observations presented in Fig. 3. In particular, we recognize that the computed RIFS shows a slight initial blue shift followed by a pronounced red shift which is succeeded by a blue shift at around P 0  2 W, compare Fig. 4 (dashed blue line) and Fig. 3 (dashed blue line). It is interesting to note that one can slightly influence the minimum value of the frequency shift and the maximum temporal delay by tuning the initial pump–Stokes misalignment t0 and walk-off parameter dwo (not shown). Fig. 5 shows the average position of the Stokes0 delay and νshift with respect to P0 for the case of a pump–Stokes misalignment of t 0 ¼  30 ps and walk-off parameter of dwo ¼ 10 ps=m. Both the maximum delay and jνshift j increase when compared to the results from Fig. 4. We have previously shown the effects of t0 on the Stokes delay in Ref. [13, Fig. 4]. Similarly the lower dwo may help achieve these higher overall delays and maintain them as seen by the plateauing effect of the delay in Fig. 5. It is difficult to visualize the effect of dwo and t0 on the increased jνshift j without calculating the integrals of Eqs. (1) and (2) because the pulses are of relative spectral size as the Raman linewidth δν of CS2. This means that the Raman gain is not constant throughout the Stokes pulse therefore we must consider all the components in the NLSE, specifically hR. We have also analyzed the effects of the different nonlinear terms in the coupled NLSE to understand their respective contributions to the overall Stokes spectral shift. The nonlinear terms for the pump and Stokes begin on the second line of (1) and (2), respectively. The first two terms in (1) and (2) are given by the instantaneous Kerr-induced contribution to SPM and XPM. The

is fixed such that the Raman gain coefficient g R  6:7
10  11 m=W at the Stokes wavelength. Unlike the g R  2:7
10  11 m=W at the pump wavelength [14], it has been modified to best fit the slope of the measured frequency shift. The fractional contribution of the Raman response fR is 0.89. We set the linear losses to zero because we do not see appreciable absorption at the working wavelengths and consider a fiber of length 1 m. Fig. 4 displays the numerical simulations for both the RIFS and the Stokes0 delay (solid). We have also calculated the centroid of the Stokes spectrum ðνavg Þ due to its asymmetric nature. To do so we define νavg as R

ν  IðνÞ dν νavg ¼ R ; IðνÞ dν

ð3Þ

50 0

ν

20 −10

Stokes delay (ps)

30

−5

shift

(GHz)

40

10

0

1

2

3

P0 (W) Fig. 5. Numerical simulations of the average location for the RIFS (blue) and the Stokes0 delay (red) for a pump–Stokes misalignment of  30 ps and a walk-off parameter of dwo ¼ 10 ps=m. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

7

(GHz)

shift

−5 −10

ν

ν

shift

(GHz)

0

3 1 −1

−15 0

2 P0 (W)

4

0

2 P0 (W)

4

0

2 P0 (W)

4

40

Stokes delay (ps)

40

Stokes delay (ps)

5

30 20 10 0 0

2 P0 (W)

4

30 20 10 0

Fig. 6. The effect of the different nonlinear components of the NLSE on the Stokes pulse RIFS (top) and delay (bottom). The full calculation of the NLSE (solid) is compared with when SPM and XPM (dotted) and Raman amplification (dashed) are set to zero. These values are obtained for a pump–Stokes misalignment of  15 ps and dwo ¼ 14:5 ps=m. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

O.D. Herrera et al. / Optics Communications 318 (2014) 83–87

next two components proportional to jAp ðt 0 Þj2 þ jAs ðt 0 Þj2 (what we refer to as integral 1) are the molecular contribution to SPM and XPM. They are also responsible for the SFS and CFS [7]. The final term proportional to Ap ðt 0 ÞAns ðt 0 Þ [integral 2 of Eq. (1)] or As ðt 0 ÞAnp ðt 0 Þ [integral 2 of Eq. (2)] is responsible for the Raman amplification. We analyze the importance of each nonlinear term within the NLSE. First, we consider the case where only the instantaneous Kerr contributions are included by setting hR to zero. We have observed negligible induced νshift , on the order of MHz, and no Stokes delay. We next consider the effects when integral 1 or integral 2 is independently set to zero. Fig. 6 displays the effects when integral 1 (dotted) or integral 2 (dashed) are set to zero. The full NLSE calculation is also shown (solid). We observe that the Stokes delay is completely dominated by the Raman amplification component (integral 2) of the NLSE [Fig. 6(d), dotted]. This is expected, as this component is solely responsible for the amplification of the Stokes by the pump. Analyzing the νshift of the Stokes field with respect to the molecular contribution of XPM and SPM (integral 1) we obtain a monotonic linear blue shift with respect to P0, see Fig. 6(b), dashed. However, for low pump power, integral 2 dominates leading to Stokes amplification and delay, as well as to a dominant red shift [Fig. 6(b), dotted]. Since the slow-light effects saturate at around 2 W, see Fig. 6(c), and are connected to νshift , we conclude that integral 1, the XPM, then becomes appreciable leading to the observed blue shifting beyond 2 W. One needs the Raman amplification for the Stokes to build up and only then can the XPM play a role. The two components will then compete when increasing P0, thus, observing different regimes of the RIFS [Fig. 6(a)]. This can also be seen when comparing Fig. 4 to Fig. 5 where the maximum slow light delay occurs at a higher P0. The νshift continues to red shift until the maximum delay is reached, after which point the blue shift occurs. Also, in Ref. [13, Fig. 4] the relation between t0 and maximum delay was discussed; it can then be suggested that t0 is a significant factor not only on the maximum delay but also on the maximum jνshift j. Overall, to accurately describe RIFS [Fig. 6(a)], both the molecular XPM and SPM terms (integral 1) and the Raman amplification term (integral 2) must be included. 4. Conclusion In summary, we have demonstrated RIFS with co-propagating picosecond pulses in a CS2-filled i-LCOF. Red or blue frequency shifts are achieved by tuning the pump peak power P0. These

87

frequency shifts are observed at low optical powers due to the high Raman cross-section of liquid CS2. These results agree well with numerical solutions of the NLSE. We saw that the Raman contribution to the XPM (integral 1) enabled higher frequency shifts when compared to the instantaneous Kerr contribution to XPM alone. We have also analyzed the individual contributions of Raman-induced XPM and Raman amplification on both RIFS and Stokes delay. We have concluded that the local minimum of RIFS is due to saturation of the slow light effect where for higher powers molecular XPM becomes dominant. This all-optical fiber system promises potential use as a low power tunable wavelength converter, an on-off switch, or as an all-optical wavelength selective switch.

Acknowledgments This work was supported by the CIAN NSF ERC under Grant #EEC-0812072 and the Air Force Office of Scientific Research COMAS MURI Grant FA9550-10-109558. L.S. wants to thank the Deutsche Forschungsgemeinschaft for financial support through the DFG-project KI 917/2-1.

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