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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 11 — May. 28, 2007
  • pp: 6717–6726
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Tunable dispersion-tolerant picosecond flat-top waveform generation using an optical differentiator

R. Slavík, Y. Park, and J. Azaña  »View Author Affiliations


Optics Express, Vol. 15, Issue 11, pp. 6717-6726 (2007)
http://dx.doi.org/10.1364/OE.15.006717


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Abstract

We study the influence of dispersive propagation on picosecond flat-top pulses, which are generated using long period fiber grating (LPG)-based optical differentiators. We suggest an extremely simple scheme to compensate for the dispersion-induced flat-top pulse distortion; this scheme is based on proper tuning the LPG coupling strength. As this coupling strength may be changed via LPG axial straining, the demonstrated device can be tuned to compensate for different levels of the dispersion in a very easy and straightforward fashion. This allows for very fine flat-top pulse shape adjustment, even after propagation through a relatively long section of dispersive optical fiber. In the experimental demonstration reported here, the dispersion tolerance of 1.8-ps flat-top pulses propagating through a standard telecom fiber (SMF-28) was increased from ≈2 m to ≈18 m, giving a 9-fold improvement.

© 2007 Optical Society of America

1. Introduction

The generation of ultrashort pulses with flat-top temporal intensity profiles is highly desired for a range of non-linear optical switching and frequency conversion applications that are of particular interest in ultrahigh-bit-rate fiber optics communication systems [1–4

1. J. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings,” IEEE Photon. Technol. Lett. 14, 203–205 (2002). [CrossRef]

]. The most usual way to obtain short flat-top pulses is based on temporal re-shaping of a short optical pulse generated by a mode-locked laser (e.g., of Gaussian or Sech2 shape) using a linear filtering stage [5

5. P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol. 19, 746–752 (2001). [CrossRef]

, 6

6. L. Qian, A. M. H. Wong, S. A. Neata, and X. Gu, “Simple and efficient optical pulse shaping: new algorithm and experimental demonstration,” Conference on Lasers and Electro-Optics (CLEO) 2006, Long Beach, CA, USA. Paper JWB-33.

]. One of the main challenges in handling short flat-top pulses in a practical experiment is that their optical spectral bandwidth is considerably wide (the bandwidth may be up to several times larger compared to, e.g., a Gaussian pulse of the same duration) and thus these pulses are very sensitive to dispersion. This becomes critical for flat-top pulses suitable for 160–640 Gbit/s systems with the corresponding timeslot durations of 6–1.5 ps. The bandwidth of such flat-top pulses can reach several THz - these extremely-high-bandwidth pulses are severely distorted even when propagated through sub-meter lengths of a standard telecom fiber. In practice, however, it is necessary to deliver the flat-top pulses from their generation stage to the specific location where they are going to be used, preferably through the standard telecom fiber. This implies the need for additional, preferably tunable, dispersion control that would allow for fine tuning to obtain the optimum flat-top waveform shape at the fiber output. However, existing compensation techniques either lack fine tunability (e.g., dispersion compensating fibers) or are designed for signals of much smaller bandwidth (e.g., Fiber Bragg gratings, Gires-Turnois etalons) and/or considerably increase complexity of the system (reflection-operated chirped Bragg gratings, prism-based dispersers, etc.). Another drawback is that they may give rise to additional, detrimental non-linear effects (e.g., dispersion compensating fibers).

Recently, we reported a novel method for flat-top pulse generation that is based on optical differentiation of an input Gaussian-like optical pulse [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

]. Our optical differentiator was implemented using a long period fiber grating (LPG) [8

8. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699 [CrossRef] [PubMed]

]. We showed that this scheme allowed for highly energetically efficient generation of flat-top waveforms with the flat-top pulse duration tuning ability [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

]. In this report we investigate how flat-top pulses generated using this new filtering scheme are affected by chromatic dispersion. Further, we show that the dispersion-induced distortion can be pre/post compensated by a proper adjustment of the LPG coupling strength. As the coupling strength may be practically changed via simple LPG straining, the demonstrated device can be tuned to compensate for different levels of dispersion in a very easy and straightforward fashion, allowing for very fine flat-top pulse shape adjustment, even after propagation through a relatively long section of dispersive optical fiber. We emphasize that this is a unique capability of this recently reported LPG-based flat-top pulse generation technique, which is not present in any of the previously proposed flat-top pulse re-shaping methods [5

5. P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol. 19, 746–752 (2001). [CrossRef]

], [6

6. L. Qian, A. M. H. Wong, S. A. Neata, and X. Gu, “Simple and efficient optical pulse shaping: new algorithm and experimental demonstration,” Conference on Lasers and Electro-Optics (CLEO) 2006, Long Beach, CA, USA. Paper JWB-33.

]. Finally, we provide a detailed physical explanation of this unique feature; in particular, we show that the proposed dispersion compensation mechanism is predominantly based on variations of the LPG phase characteristics, more specifically on variations of the value of the phase jump across the LPG resonance, which are induced by the LPG coupling strength tuning. The same concept could be easily generalized to obtain similar functionality with other differentiator implementations (e.g., using two arm interferometers [15

15. Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first and higher-order differentiators based on interferometers,” Opt. Lett. 32, 710–713 (2007). [CrossRef] [PubMed]

]).

2. Theoretical analysis

In this section, we briefly review the principle of the flat-top pulse generation based on optical differentiation [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

]. Subsequently, we study how this flat-top pulse is distorted by the first-order chromatic dispersion and how this degradation can be compensated by a proper modification of the coupling strength characteristics of the fiber LPG.

2.1 Effect of dispersive propagation

In [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

] it was shown that an optical differentiator with the spectral transfer function of -j(ω - ω 0), where ω 0 is the central frequency of the optical differentiator (frequency of zero transmission), can re-shape a transform-limited input optical pulse of real temporal envelope (spectrally centered at ωcar) into an optical pulse of temporal envelope v(t) (centered at the same carrier frequency ωcar) as follows:

v(t)u(t)t+j(ωcarω0)u(t),
(1)
v(t)2u(t)t2+(ωcarω0)2u(t)2,
(2)

In this notation, the average time delay induced by the LPG is not considered. From (1) and (2), it is obvious that for ωcar = ω 0 the device operates as an optical differentiator. However, for ωcarω 0, |v(t)|2 consists of the sum of the differentiated waveform and the original waveform, with a relative weight given by the detuning factor (ωcar-ω 0)2. When |u(t)|2 is a temporally symmetric pulse (like a Sech2 or a Gaussian), the differentiated pulse is a symmetric double-pulse [8

8. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699 [CrossRef] [PubMed]

]. By properly adjusting the detuning factor (ωcar-ω 0)2, the valley in between the two peaks of the double-pulse (differentiated waveform) can be completely filled with the contribution coming from the second term of the right side of (2) (which has the shape of the original pulse u(t)) leading to the formation of a single flat-top pulse [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

].

In the presence of the first-order chromatic dispersion D, the original, transform-limited waveform u(t) changes to:

u(t)dispw(t)exp(jDt2),
(3)

where w(t) is a real (transform-limited) function. For example, for u(t) Gaussian, w(t) is also of Gaussian shape of longer duration. As a result, Eq. (1) can be re-written as:

v(t)disp(w(t)exp(jDt2))t+j(ωcarω0)w(t)exp(jDt2),
(4)

and in terms of intensity,

v(t)disp2w(t)t2+w(t)2((ωcarω0)2Dt)2.
(5)

By comparing (5) with (2) we see that besides u(t) being replaced by w(t), the so-called detuning factor has been modified to ((ω car-ω 0)-2Dt)2, which depends on the time variable due to the presence of the introduced term Dt. This term is odd-symmetric in t (i.e. it is negative for t<0 and positive for t>0 with the same absolute value for ±|t|), thus inducing an asymmetric distortion in the otherwise temporally symmetric output pulse waveform. It is worth noting that the term Dt does not cause the mentioned asymmetric distortion in (5) when the device is operated as an optical differentiator, which corresponds to (ωcar-ω 0)=0.

The dispersion-induced flat-top waveform distortion predicted by (5) can be better illustrated by numerical simulations. Through all our numerical analyses, we consider an input pulse generated by a mode-locked laser (with Sech2 intensity temporal shape) with a full-width at half of maximum (FWHM) time duration of 1.8 ps and a central (carrier) optical wavelength of 1550 nm. We assume an ideal differentiator with a spectral transfer function ∝-j(ω-ω 0). Further, we assume a value of the differentiator-pulse detuning (ωcar-ω 0)2 that fills 90% of the gap between the two peaks of the differentiated waveform (double-pulse), i.e. the generated flat-top consists of two peaks with a 10% valley in between them. Although the pulse can be ideally flat-top (valley of 0%) [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

], the chosen value allows for a better visualization of the principle of operation. Fig. 1 shows the temporal profile of the pulse generated at the differentiator output after propagation through different lengths of a standard telecom fiber (SMF-28, dispersion of 0.023ps2/m, Corning Inc.) when the central wavelength of the pulse is shorter than the central wavelength of the differentiator (ωcar -ω 0>0). As predicted by (5), the amplitude of the leading-edge peak of the flat-top pulse (occurring at t<0) decreases as the chromatic dispersion increases while the opposite tendency is observed for the trailing-edge peak of the flat-top pulse (occurring at t>0). When considering the opposite sign of the dispersion, -D, (5) predicts that the situation is inverted in time (the leading-edge peak increases in intensity while the trailing-edge peak decreases in intensity as the pulse propagates through the dispersive fiber). Obviously, as evidenced by (5), when the pulse carrier wavelength is longer than the central wavelength of the differentiator (ωcar -ω 0 <0), the induced asymmetric waveform distortion follows the opposite trend as that described above.

Fig. 1. Temporal characteristics of the generated flat-top pulse with an ideal differentiator, ωcar>ω0, for different levels of dispersion experienced by the pulse (represented in lengths of the SMF-28 fiber of 0 m (black), 3 m (red), 6 m (blue), and 9 m (green)).

2.2 Principle of LPG tuning for counterbalancing the effect of the dispersion

Here, we provide a brief heuristic analysis that predicts that the dispersion-induced distortion of a flat-top pulse generated with an LPG-based optical differentiator [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

] could be compensated by properly adjusting the coupling strength of the LPG. The physics behind this interesting feature is further investigated is Section 2.3.

H(ω)[cos(κL)+(ωω0)sin(κL)]exp(jβL),
(6)

where κ is the LPG coupling coefficient, α is a constant, L denotes the grating length, κL is the coupling strength, and β is the core mode propagation constant. In order to implement an optical differentiator, the LPG must be set to operate in the full-coupling condition (cos(κL)=0, giving κL = π/2 within multiples of 2π) [9

9. M. Kulishov and J. Azaña, “Long-period fiber gratings as ultrafast optical differentiators,” Opt. Lett. 30, 2700–2702 (2005). [CrossRef] [PubMed]

]. Now, let us consider a slight detuning Δκ in the LPG coupling coefficient with respect to the value for which κL = π/2. Considering the first two terms of the corresponding Taylor series, we can use the following approximations

cos(κL)ΔκL,sin(κL)1,
(7)

and rewrite (6) as

H(ω)[ΔκL+(ωω0)]exp(jβL).
(8)

For the sake of simplicity, we will first consider zero detuning between the input pulse carrier frequency ωcar and the filter central frequency ω 0; in this case, the filtering operation in the temporal domain is given by

v(t)αu(t)t+ΔκLu(t).
(9)

We recall that u(t) and v(t) are the complex temporal envelopes of the input and output optical pulses (both spectrally centered at ωcar). The key aspect of (9) is that there is no phase difference between the two terms on the right hand side, so the output intensity includes an interference term:

v(t)2α2u(t)t2+ΔκLu(t)2+2αΔκLu(t)tu(t).
(10)

In deriving (10), a transform-limited input optical pulse (with real temporal envelope) has been assumed. Further assuming that this input pulse is also temporally symmetric (e.g. Gaussian or Sech2), the last term in (10) exhibits temporal odd symmetry (i.e. it is negative for t<0 and positive for t>0 with the same absolute value for ±|t|), thus inducing a temporally asymmetric waveform distortion similar to that caused by the dispersion (see discussions above). This odd symmetry comes from the differentiated waveform (∂u(t)/∂t) that consists of two pulses that have identical temporal field profiles (inverted in time), but are phase shifted by π. This π-phase shift implies that the field intensities of the two pulses are of opposite signs [8

8. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699 [CrossRef] [PubMed]

]. As a result, (10) indicates that depending on the sign of Δκ, the leading-edge peak of the generated optical pulse will exhibit a higher intensity (Δκ>0) or a lower intensity (Δκ<0) than that of the trailing-edge peak.

When considering (i) a finite detuning of the pulse carrier frequency ωcar from the filter central frequency ω 0 and (ii) the effect of dispersive propagation, we obtain an equation that includes two asymmetry terms – one that is associated with the pulse dispersive propagation (present in (5)) and another one that is associated with the effect of LPG coupling strength tuning (present in (10)):

v(t)disp2α2w(t)t2+Δκ2L2w(t)2+2αΔκLw(t)w(t)t+α2((ωcarω0)2Dt)2w(t)2
(11)

By a proper choice of the sign and magnitude of Δκ, the two asymmetry terms in (11) can, to a certain degree, cancel each other out. In this way, the dispersion-induced waveform asymmetry could be compensated by a proper tuning of the LPG coupling strength (to operate outside the full-coupling condition). As will be shown, our numerical simulations and experimental results show that the dispersion-induced waveform distortion can be counterbalanced almost entirely using this simple mechanism even in the presence of a significant amount of the dispersion.

2.3 Discussion

The cos(κL) term of the LPG spectral transfer function in (6) influences predominantly the phase filtering characteristics close to the LPG resonance wavelength, as shown in Fig. 2. Thus, any variation of the LPG coupling strength around its full-coupling value will essentially affect the value of the phase jump induced by the LPG filter across its resonance frequency. We will show in what follows that this phase jump is actually the key factor in providing the above anticipated dispersion compensation feature of the LPG filter.

Fig. 2. Phase (a) and magnitude (b) variation of the LPG spectral transfer function; LPG length: 70 mm, period 530 μm. The LPG coupling strength κ was adjusted to achieve LPGs resonant transmission (in intensity) of -30 dB (red), -20 dB (blue) and -16 dB (green). The dashed curves are for undercoupled and dotted for overcoupled LPGs. Situation for LPG in full coupling condition is shown as black, solid line. For simplicity, only the extreme values are shown in plot (b) – the characteristics of overcoupled and undercoupled LPGs of identical resonant transmission are almost identical.

To confirm this claim, we considered a notch filter that has a spectral transfer function with the amplitude identical to that of an ideal optical differentiator (i.e. linear spectral amplitude variation with zero transmission at the filter’s central frequency) but with a phase variation having an arbitrary jump across the filter central frequency. The time waveform obtained at the output of this notch filter is shown in Fig. 3, where we considered ωcar = ω 0 (same conditions as for the analytical study presented above, Eq. (9) and (10)). The results present in Fig. 3 can be understood by considering the spectral characteristics of the filtered pulse. The output pulse spectrum consists of two adjacent spectral lobes that are formed by filtering the input symmetric (single-lobe) pulse spectrum with the considered notch filter. The corresponding temporal waveform is the result of the temporal beating between these two spectral lobes. The temporal beating period is inversely proportional to the spectral distance of the two spectral lobes; the duration of the entire waveform is then given by the pulse bandwidth (more precisely by the inverse Fourier transform of any of the two pulse spectral lobes). Typically, only two or three temporal periods are visible, Fig. 3. The relative phase between the two pulse spectral lobes, which is set by the phase jump at the filter central frequency, determines the temporal features of the generated beating waveform. For instance, in the case of a phase jump value of π, the destructive interference between the two spectral lobes occurs just at the center of the time envelope and, as a result, a temporally symmetric waveform that consists of two time lobes with the same amplitude (the exact differentiation) is obtained [8

8. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699 [CrossRef] [PubMed]

], Fig. 3(c). However, for a zero phase jump, the constructive interference occurs at the center of the envelope and we obtain a symmetric temporal waveform consisting of the main peak and two smaller sidelobes, Fig. 3(c). It is also straightforward to understand the situation when the phase jump is decreased (Fig. 3(a)) or increased (Fig. 3(b)) from the value of π: simply, the position of destructive interference is moved to longer (Fig. 3(a)) or shorter (Fig. 3(b)) times, which, following the time envelope of the entire beating waveform (shown in Fig. 3), results in the leading- edge peak amplitude increase (Fig. 3(a)) or decrease (Fig. 3(b)), while the trailing-edge peak follows just the opposite trend. This behavior is in excellent agreement with that predicted by (10) when the LPG coupling strength is changed around its full-coupling value; we reiterate that this is expected considering that the LPG coupling strength tuning affects predominantly the value of the phase jump induced by the LPG filter across its resonance (central) frequency, as shown in Fig. 2.

Fig. 3. Temporal characteristics of the input pulse that passed through the filter that has the ideal differentiator’s magnitude transfer response having various levels of the phase jump (shown in the Fig.) across the filter central frequency. The envelope of the beating signal is shown for illustration.

As anticipated above, the potential dispersion in the system could be ‘pre-compensated’ by introducing a suitable phase jump (different from π) across the central frequency of the optical differentiator filter, e.g. by properly tuning the LPG coupling strength, during the flattop pulse re-shaping process. Specifically, an introduction of a phase jump smaller than π (Fig. 3(a)) across the differentiator’s central frequency will generate an asymmetrically distorted flat-top pulse with the leading-edge peak of higher amplitude than that of the trailing-edge peak. During the dispersive propagation through a conventional telecom fiber, the amplitude of the leading-edge peak is expected to decrease while the amplitude of the trailing-edge peak is expected to increase (assuming that ωcar>ω0, see results in Fig. 1); in this way, at a certain fiber propagation distance, the original asymmetric distortion (at the pulse re-shaper output) will be almost fully compensated resulting in the optimum flat-top pulse shape.

Our predictions have been first confirmed by numerical simulations. Fig. 4 shows the results of our numerical analysis considering (a) the ideal optical filter of Fig. 3 and (b) the simulated LPG filter with characteristics shown in Fig. 2. First, we observe that the performance of both filters is almost identical, fully confirming our central hypothesis that the value of the phase jump at the filter’s center frequency is the key parameter providing the dispersion-compensation feature. Fig. 4 shows that the dispersive propagation through up to ≈7.5 meters of SMF-28 fiber can be almost fully compensated (the flat-top waveform can be made almost identical to that obtained at the pulse re-shaper output) by properly tuning the phase jump across the filter’s center frequency. Specifically, in order to compensate the dispersion introduced by 7.5 meters of SMF-28 fiber, the filter’s phase jump needs to be reduced to 0.75π (the corresponding LPG filter has a resonant transmission of -20 dB). When a longer section of SMF-28 is used (e.g. 15 m in the example shown), the flat-top shape may be still obtained (for phase jump of 0.5π or LPG resonant transmission of -16 dB), however, a certain level of distortion is already apparent.

Fig. 4. Temporal characteristics of the flat-top pulse generated with a filter that has magnitude response identical to an ideal differentiator and a constant phase response with a jump across its central frequency (π, black, 3/4π, blue, and π/2, red, respectively) (a) and with full-coupled/undercoupled LPG with characteristics shown in Fig. 2 (for -20 and -16 dB) (b). The dispersion experienced by the pulse (represented in lengths of the SMF-28 fiber) is adjusted to obtain the desired flat-top temporal waveform.

3. Experiments and discussion

The LPG used in our proof-of-concept experiments was made in a standard telecom fiber (SMF-28, Corning Inc.) using the point-by-point technique with a CO2 laser [11

11. I. Bralwish, B. L. Bachim, and T.K. Gaylord, “Prototype CO2 laser-induced long-period fiber grating variable optical attenuators and optical tunable filters,” Appl. Opt. 43, 1789–1793 (2004). [CrossRef]

]. Specifically, the used fiber LPG was 70 mm long, with a period of 530 μm, which corresponds to coupling into the 3rd odd cladding mode at the resonance wavelength of 1550 nm. The measured and predicted field magnitude responses are shown in Fig. 5. We see that the predicted resonance dip is slightly narrower than that experimentally achieved; however, the shape of the spectral response of the realized LPG filter is very close to the theoretical predictions, especially the linear spectral dependency around the resonance wavelength.

Fig. 5. Calculated (dash red) and measured (solid blue) spectral characteristics of the used LPG that was 70 mm long with period of 530 μm when adjusted for full coupling. The solid, green line shows the spectral power density of the used short pulse (measured with resolution of 1 nm) with central wavelength adjusted for optimal flat-top pulse generation.

To quantify the ability of our tunable dispersion-compensation technique, we define ‘critical dispersion’ as the amount of dispersion that causes the ‘maximum acceptable’ deviation from the optimum (dispersion-less) flat-top waveform. Obviously, the ‘maximum acceptable’ deviation depends on the specific application. Here, we consider that the ‘maximum acceptable’ deviation is of 10% in the power intensity (5% in the field intensity), which means that the maximum intensity difference across the flat-top part of the generated pulse cannot exceed 10%. In our particular demonstration, this corresponds to 2 m of SMF-28 fiber. Considering that we were able to counter-balance the dispersion induced by 18 meters of SMF-28, we demonstrated compensation ability of 9 critical dispersions.

Fig. 6. Waveforms at the output of the LPG filter adjusted to obtain flat-top waveform (a); situation shown in (a) after adding 18 meters of SMF-28 standard telecom fiber (b); and situation from (b) after re-adjusting the filter coupling strength and filter-input pulse detuning to recover the flat-top waveform (c). Calculated data shown as dashed red; measured as solid black.

6. Conclusions

We have investigated how (sub-)picosecond flat-top optical pulses generated using a recently reported linear pulse re-shaping scheme based on ultrafast differentiation [7

7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

] are affected by first-order chromatic dispersion. The predominant effect is a temporally asymmetric waveform distortion, which becomes more noticeable for higher dispersion amounts. Further, we have demonstrated that this dispersion-induced distortion can be compensated for by properly adjusting the LPG coupling strength. We have shown that this interesting property is mostly due to the change in the phase shift across the LPG spectral resonance which is induced by the LPG coupling strength variation. As the LPG coupling strength may be practically changed via simple axial straining of the fiber LPG, the demonstrated device can be tuned to compensate for different levels of dispersion in an extremely simple and practical fashion, thus allowing for a very fine flat-top pulse shape adjustment, even after propagation through a relatively long section of a dispersive optical fiber. Specifically, in the experiment reported here, we increased the acceptable level of residual dispersion in the pulse shaping system by nearly one order of magnitude. We believe that besides its intrinsic physical interest, the newly reported, unique feature of a LPG-based flat-top pulse shaper could be very useful for practical optical switching applications based on the use of flat-top waveforms, particularly in ultrahigh-bit-rate optical communication systems.

Acknowledgments

This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) through its Strategic Grants Program and by the Grant Agency of AS, Czech Republic, contract KJB200670601 and Czech Science Foundation (102/07/0999).

References and links

1.

J. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, “All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings,” IEEE Photon. Technol. Lett. 14, 203–205 (2002). [CrossRef]

2.

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4.

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6.

L. Qian, A. M. H. Wong, S. A. Neata, and X. Gu, “Simple and efficient optical pulse shaping: new algorithm and experimental demonstration,” Conference on Lasers and Electro-Optics (CLEO) 2006, Long Beach, CA, USA. Paper JWB-33.

7.

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating,” Opt. Express , 14, 12671–12678 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-26-12670 [CrossRef]

8.

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699 [CrossRef] [PubMed]

9.

M. Kulishov and J. Azaña, “Long-period fiber gratings as ultrafast optical differentiators,” Opt. Lett. 30, 2700–2702 (2005). [CrossRef] [PubMed]

10.

R. Slavík, “Extremely deep long-period fiber grating made with CO2 laser,” IEEE Photon. Technol. Lett. 18, 1705–1707 (2006). [CrossRef]

11.

I. Bralwish, B. L. Bachim, and T.K. Gaylord, “Prototype CO2 laser-induced long-period fiber grating variable optical attenuators and optical tunable filters,” Appl. Opt. 43, 1789–1793 (2004). [CrossRef]

12.

L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995). [CrossRef]

13.

Y. Park, F. Li, and J. Azaña, “Characterization and optimization of optical pulse differentiation using spectral interferometry,” IEEE Photon. Technol. Lett. 18, 1798–1800 (2006). [CrossRef]

14.

R. Slavík and F. Todorov, “Tuning of long-period fibre gratings written by CO2 laser with the resonant transmission below -45 dB,” Electron. Lett. , 43, 16–18 (2007). [CrossRef]

15.

Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first and higher-order differentiators based on interferometers,” Opt. Lett. 32, 710–713 (2007). [CrossRef] [PubMed]

OCIS Codes
(060.2430) Fiber optics and optical communications : Fibers, single-mode
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(230.1950) Optical devices : Diffraction gratings
(320.5540) Ultrafast optics : Pulse shaping
(320.7080) Ultrafast optics : Ultrafast devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 22, 2007
Revised Manuscript: May 11, 2007
Manuscript Accepted: May 11, 2007
Published: May 16, 2007

Citation
R. Slavik, Y. Park, and J. Azaña, "Tunable dispersion-tolerant picosecond flat-top waveform generation using an optical differentiator," Opt. Express 15, 6717-6726 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-11-6717


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References

  1. J. H. Lee, P. C. The, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical modulation and demultiplexing systems with significant timing jitter tolerance through incorporation of pulse shaping fiber Bragg gratings," IEEE Photon. Technol. Lett. 14, 203-205 (2002). [CrossRef]
  2. F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, "All-optical pulse reshaping and retiming systems incorporating pulse shaping fiber Bragg grating," J. Lightwave Technol. 19, 746-752 (2001).
  3. L. K. Oxenlowe, M. Galili, A. T. Clausen, and P. Jeppesen, "Generating a square switching window for timing jitter tolerant 160Gb/s demutiplexing by the optical Fourier transform technique," Proc. of the 32nd European Conference on Optical Communication (ECOC 2006), Cannes, France, September 2006. Paper We2.3.4.
  4. L.K. Oxenlowe, M. Galili, H.C.H. Mulvad, P. Jeppesen, R. Slavík, J. Azaña, Y. Park, "Using a newly developed long-period grating filter to improve the timing tolerance of a 320 Gb/s demultiplexer," Conference on Lasers and Electro-Optics (CLEO 2007), Baltimore, Maryland, USA, May 2007. Paper CMZ5. [CrossRef]
  5. P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, "Rectangular pulse generation based on pulse reshaping using a superstructured fiber Bragg grating," J. Lightwave Technol. 19, 746-752 (2001). [CrossRef]
  6. L. Qian, A. M. H. Wong, S. A. Neata, and X. Gu, "Simple and efficient optical pulse shaping: new algorithm and experimental demonstration," Conference on Lasers and Electro-Optics (CLEO) 2006, Long Beach, CA, USA. Paper JWB-33.
  7. Y. Park, M. Kulishov, R. Slavík, and J. Azaña, "Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber grating," Opt. Express,  14, 12671-12678 (2006). [CrossRef]
  8. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, "Ultrafast all-optical differentiators, " Opt. Express 14, 10699-10707 (2006). [CrossRef] [PubMed]
  9. M. Kulishov and J. Azaña, "Long-period fiber gratings as ultrafast optical differentiators," Opt. Lett. 30, 2700-2702 (2005). [CrossRef] [PubMed]
  10. R. Slavík, "Extremely deep long-period fiber grating made with CO2 laser," IEEE Photon. Technol. Lett. 18, 1705-1707 (2006). [CrossRef]
  11. I. Bralwish, B. L. Bachim, and T.K. Gaylord, "Prototype CO2 laser-induced long-period fiber grating variable optical attenuators and optical tunable filters," Appl. Opt. 43, 1789-1793 (2004). [CrossRef]
  12. L. Lepetit, G. Chériaux, and M. Joffre, "Linear technique of phase measurement by femtosecond spectral interferometry for applications in spectroscopy," J. Opt. Soc. Am. B 12, 2467-2474 (1995). [CrossRef]
  13. Y. Park, F. Li, and J. Azaña, "Characterization and optimization of optical pulse differentiation using spectral interferometry," IEEE Photon. Technol. Lett. 18, 1798-1800 (2006). [CrossRef]
  14. R. Slavík and F. Todorov, "Tuning of long-period fibre gratings written by CO2 laser with the resonant transmission below -45 dB," Electron. Lett.,  43, 16-18 (2007). [CrossRef]
  15. Y. Park, J. Azaña, and R. Slavík, "Ultrafast all-optical first and higher-order differentiators based on interferometers," Opt. Lett. 32, 710-713 (2007). [CrossRef] [PubMed]

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