## Abstract

We present an experimental demonstration of an ultrafast all-optical thresholder based on a nonlinear Sagnac interferometer. The proposed design is intended for operation at very small nonlinear phase shifts. Therefore, it requires an in-loop nonlinearity lower than for the classical nonlinear loop mirror scheme. Only 15 meters of conventional (non-holey) silica-based fiber is used as a nonlinear element. The proposed thresholder is polarization insensitive and is good for multi-wavelength operation, meeting all the requirements for autocorrelation detection in various optical CDMA communication systems. The observed cubic transfer function is superior to the quadratic transfer function of second harmonic generation-based thresholders.

© 2007 Optical Society of America

## 1. Introduction

All-optical signal processing is an important part of modern optical communications. Development of ultrafast communication systems, working beyond the limit of today’s electronics, demands simple, effective and cheap all-optical elements for data processing. For example, an optical thresholder, among other required devices, is an essential part of systems based on Code Division Multiple Access (CDMA) in the optical domain. It is used for detection of the code autocorrelation peak and filtering out the undesired cross-correlation.

Various schemes have been proposed for amplitude discrimination, including using of Semiconductor Optical Amplifiers (SOAs) [1], spectral broadening in holey fiber [2], supercontinuum generation in dispersion-flattened fiber [3], and second harmonic generation in Periodically Poled Lithium Niobate (PPLN) [4]. However, several limitations apply to all these techniques. The speed of SOA-based devices is intrinsically limited by the carrier lifetime in heterostructures, while the other devices mentioned are based on nonlinear spectral transformation with subsequent spectral filtering, which implicitly assumes using a single wavelength. Also, spectral transformation requires relatively large nonlinear phase shifts in the nonlinear element.

We propose using a modified Nonlinear Optical Loop Mirror (NOLM), which is in fact a nonlinear Sagnac interferometer. Using a NOLM for switching and pulse shaping was first investigated in 1988 [5]. Later, modified versions of the NOLM with in-loop amplifiers or asymmetric loss [6] were introduced. Recently, the use of an in-loop directional attenuator [7] was proposed. However, these schemes remain quite impractical because they typically consist of kilometers of nonlinear fiber.

We introduce a novel modification which lowers the required nonlinear phase shift and therefore the length of nonlinear element (or required power). To allow precise and independent control of amplitudes of interfering waves we suggest using a tunable directional attenuator. It is made of only standard commercially available components (see the device section below) and does not noticeably increase the cost of the setup, but provides significant advantages over standard NOLM-based devices. To understand these advantages we describe the theory underlying the operation of NOLM in the next section. The remainder of the paper presents experimental results obtained with the proposed thresholder and discussion of possible applications of the novel NOLM design.

## 2. Theoretical background

The complete theory of NOLM was developed in late 80s (see e.g. [8]). Here we will focus on the small nonlinear phase shift regime, in order to point out the effects which distinguish the design of our thresholder.

The main idea of the NOLM-based thresholder is to exploit the intensity-dependent nonlinear phase shift in order to change the transmittance *T* — the ratio of output power to the launched power: *T* = *P _{out}*/

*P*. This effect causes the thresholder to behave nonlinearly with input power. To achieve effective thresholding, we would like to have complete destructive interference of the counterpropagating waves at the output port. This means that the waves’ amplitudes at the output port must be equal, and their phases opposite, if there is no nonlinear phase shift. To be more realistic, we assume that there are small errors in both phase and amplitude. Assume that one wave would give output power

_{in}*kP*in the absence of another wave (without interference), and the other wave — (

_{in}*k*+δ)

*P*so δ is the amplitude mismatch. The phase difference between these two waves is equal to φ = π + φ

_{in}_{e}+ φ

_{NL}, where φ

_{e}is the initial phase error and φ

_{NL}= Γ

*P*is a nonlinear phase shift proportional to the input power. When two waves interfere, the output power takes the form

_{in}$$\phantom{\rule{4em}{0ex}}={P}_{\mathrm{in}}\left[2k+\delta -2\sqrt{k\left(k+\delta \right)}\mathrm{cos}\left({\phi}_{e}+{\phi}_{\mathrm{NL}}\right)\right].$$

We are interested mainly in the case of small intensity error, i.e. δ ≪ *k*, and small nonlinear and error phases, i.e. φ_{e},φ_{NL} ≪ 1. Finding the Taylor series expansion up to the first non-vanishing term, the resulting expression for the output power is

Now as the term φ_{NL} depends on the input power, we substitute φ_{NL} = Γ*P _{in}* into Eq.(2):

So at small φ_{NL} the output of the thresholder is described by three terms which are linear, quadratic, and cubic with input power. Simple analysis shows that the linear term dominates at ${\phi}_{\mathrm{NL}}\lesssim \frac{1}{2}\sqrt{{\phi}_{e}^{2}+\frac{{\delta}^{2}}{4{k}^{2}}}$, and at ${\phi}_{\mathrm{NL}}\lesssim \sqrt{{4\phi}_{e}^{2}+\frac{{\delta}^{2}}{4{k}^{2}}}$ the cubic term becomes dominant. The quadratic term shows up only as a transition between the linear and cubic dependences. This behavior can be explained quite simply: at low phase shifts the transmittance *T* does not depend on the launched power because of the phase and amplitude errors, which allows some non-zero transmittance. So in this regime the output power is proportional to the input power, i.e. the device behaves just as a linear attenuator. When the nonlinear phase shift becomes strong enough to overcome both phase and amplitude mismatches (φ_{e} and δ), we may neglect these two parameters. In that case the ratio of output and input amplitudes is proportional to the nonlinear phase shift. So the ratio of powers, i.e. *T*, grows as a square of phase shift, resulting in a cubic transfer characteristic. In most situations, the cubic curve is steep enough to eliminate small signals and pass through big ones, that is, to perform thresholding. For example, thresholders based on a second harmonic generation in PPLN have only a quadratic transfer curve, which is inferior to the cubic one observed in our study.

Summarizing, we conclude that the low-power behavior of the NOLM depends strongly on the precision of the initial balance of the loop. So one should carefully eliminate both phase and amplitude errors to perform thresholding at low input power. Therefore, an addition of precise in-loop amplitude control is beneficial for lowering the required power.

## 3. Experimental demonstration

#### 3.1. Device description

The experimental setup was designed to meet all the necessary tunability requirements which were already discussed. The basic schematic of the setup is shown in Fig. 1. To maximize the non-linear parameter Γ we use an asymmetric 90/10 fiber coupler, so most of the input energy is delivered directly to the nonlinear fiber in a single direction. The relative phase of the interfering waves is controlled by the standard polarization controller. Since a 90/10 coupler was used, the ratio of output powers in a conventional NOLM scheme would be approximately 1:100. To make them equal we use a directional element consisting of a tunable isolator. This tunable isolator is, in fact, a standard polarization-independent optical isolator that can be tuned by applying an external magnetic field. Most optical isolators which are sensitive to a magnetic environment can be used here. Adjusting the magnetic field strength, we have obtained the required 20dB attenuation in a single direction with the ability of precise tuning. Although such a tunable isolator may introduce an additional undesired nonlinear phase shift, none of our experiments showed any indication of it. Therefore, even if this effect exists, it is small and we can describe it as a slight perturbation of the phase error parameter.

Another key element of the setup is the nonlinear element. We use 15.5m of commercially available highly Ge-doped silica-based fiber with ∆*n* = 0.043. The measured nonlinear coefficient at λ = 1550nm is γ= (9±1)W^{-1}km^{-1}. The fiber loss at the same wavelength is 2dB/km and can be neglected. The resulting nonlinear coefficient of NOLM, after taking into account the splitting ratio of the coupler and splice losses, is a quite modest value of Γ = 0.1W ^{-1}. The measured chromatic dispersion of the nonlinear fiber is *D* = (-55 ± 5)ps/nm ∙ km, i.e. it is in the region of normal dispersion.

To measure the transfer characteristics of the proposed thresholder, we used an erbium-doped fiber-based Mode-Locked Laser (MLL), which produces optical pulses at a wavelength of 1.55μm. We used two different repetition rates: 622MHz for observation of high-peak power behavior, and 10GHz corresponding to an OC-192 data rate in a telecommunication system. The measured pulse width is the same (within precision of the measurement, which is better than 10%) for both repetition rates and is equal to 2.2ps FWHM under the assumption of a sech^{2} pulse profile. In all experiments we used an Erbium-Doped Fiber Amplifier (EDFA) with a maximum output power of about 300mW, directly connected to the input of the thresholder. All power measurements were conducted in points “in” and “out” (Fig. 1) with a standard average power meter.

#### 3.2. Thresholder transfer function

The transfer function was measured by varying the input power. This was achieved by adjusting the pump current of the EDFA. It is important to note that the measured spectrum and pulsewidth after the EDFA does not depend on the pump current for power levels used in the experiments. Therefore, the EDFA, working as a linear device, only serves for adjusting the input power of the thresholder.

In order to present the results of measurements with pulsed MLL signals in universal power units, which do not depend on the repetition rate and pulse profile, we scaled both the experimentally measured mean input and output power by a normalization constant that we will define. A theoretically predicted transfer function for the case of zero phase and amplitude errors goes to zero at φ_{NL} = 2π and touches the in-phase interference line at φ_{NL} = π as follows from Eq.(1). The experimentally observed dependence does not reach these points, but still shows similar behavior. We found the point of the maximum measured transmittance and ascribed a nonlinear phase shift of π to it. Also, from the known nonlinear coefficient of the fiber used in the setup we calculated the required input CW power which would produce the same nonlinear phase shift of π and called it the effective peak power for this particular point of maximum transmittance. This procedure defined the normalization constant, which is the ratio between measured mean power and effective pulse power. The same value was used for normalization of all other data points. For the higher repetition rate of MLL this constant was scaled proportional to the rate (16 times), since the same procedure could not be used again due to insufficient peak power at higher repetition rate. The fact that after such normalization the data is in agreement with our measurements conducted with CW light (see later in text) justifies this normalization method.

At the same time the actual peak power was calculated from the measured mean power and the measured pulse autocorrelation under the assumption of a sech^{2} intensity profile. The actual peak power appears to be 1.7 times higher than the effective peak power defined above. This is reasonable because an effective power includes an overall nonlinear response for the whole pulse. Such an integral response is weaker than the maximal peak response, corresponding to the actual peak power. Also, the deviations from the ideal sech^{2} pulse profile may contribute to this peak-to-effective power ratio.

The results of the transfer function measurement after power scaling at both axes are plotted in Fig. 2. It shows a highly non-linear behavior of the transfer function at low powers (inset), which we propose to use for signal thresholding, and also the usual transfer characteristic of NOLM [8] at higher powers (main plot).

Using a low repetition rate MLL we were able to get up to 100 watts in effective peak power, but as we showed before, large powers are not necessary for thresholder operation, since one can utilize even very small phase shifts. To be able to see a detailed low-power limit, we plot the same data in logarithmic coordinates in Fig. 3. Also, we again plot the output power upper limit, which scales linearly with the input power. The line at the right shows a slope with actual cubic dependence that we predict theoretically for the thresholder. The measured data demonstrates good agreement with the theoretical prediction: at nonlinear phase shift φ_{NL} smaller than 0.05 it grows linearly with the input power, and at φ_{NL} ≳ 0.1 the cubic dependence is observed up to φ_{NL} ≈ 1.

Previously, we demonstrated that the low-power linear transmission region is a consequence of the error offset of either the phase or amplitude of the interfering waves. In spite of having a full phase and amplitude control in the experiment, there is still an error of the order of 0.1 radian, which limits the range of available power for thresholding. Presumably, it is connected with the spectral width of the input light. The nearly transform-limited optical pulses from our MLL have a spectral width of δγ ≈ 1.3nm, so different spectral components may interfere under different conditions, resulting in some overall phase/amplitude error.

To support this statement we have conducted a series of measurements with a continuous wave laser, which has a much narrower spectral width of less than 0.1nm. To obtain a sufficient peak power, we modulate the laser to obtain a 1:8 duty cycle pulse train with a repetition rate of 311 MHz. Since these pulses have an almost rectangular profile, their effective peak power is the same as the actual power, calculated from the measured mean power and known duty cycle. The obtained data are shown in Fig. 3 with CW markers. The observed transfer function for CW light has the same behavior as expected, and matches the data obtained with the pulsed laser.

A simple comparison of the CW and MLL curves in Fig. 3 shows that the CW light has the broader region of slope-3 dependence, which starts at a nonlinear phase shift of as low as 0.04 radians. In general, CW light requires less power and has broader dynamic range. We also experimentally observed that an initial interferometer misalignment has a quite similar effect on the transfer function as a broadening of the incident spectrum. That also demonstrates that a broad spectrum introduces an overall error phase offset. Therefore, a narrower spectral width of the input light benefits the proposed thresholder scheme by taking advantage of a small φ_{NL} operation. Nevertheless, as will be shown later in the applications section, the thresholder performs satisfactory even for broad spectral widths of the order of 10 nm.

#### 3.3. Applications

To demonstrate thresholder operation in a more realistic environment, we set up several experiments that imitate the use of the proposed device in optical CDMA communication systems.

Figure 4 shows the discrimination of high pulses at a single wavelength, as may be advantageous for detection of an autocorrelation peak in a coherent optical CDMA system [9]. The original input signal here is a modulated pulse train of the MLL at 10GHz. It should be noted that the actual pulse width is much smaller than it appears on the plot, since all the measurements were limited by the 30GHz oscilloscope bandwidth. The obtained thresholded output signal is shown in the same figure along with the calculated third power of the input signal. Good suppression of the weak pulses as well as an agreement with the expected cubic-transformation law are observed.

Another experiment was made with incoherent optical CDMA signals [10]. The testbed used contains 4 transmitters with different CDMA codes, generating pseudo-random traffic. Each code consists of 3 pulses of different wavelengths in different time chips. The bit rate of each channel is 2.5Gb/s (OC-48). The wavelength separation between adjacent light frequencies is 5 nm, resulting in 10nm of total span. A more detailed description and schematic of the testbed is given in [10]. All 4 signals were combined together and passed through a decoder, which matches to one of the transmitters. The resulting autocorrelation peak with cross-correlation noise is shown in Fig. 5A. This signal was then amplified to a mean power of 150mW and passed through the thresholder. The resulting eye-diagram is also shown in the Fig. 5B. We observe significant suppression of the cross-correlation, which potentially allows use of slower and cheaper electronics for signal detection. Although the initial signal can be detected with fast enough detector and electronic thresholder (sufficiently faster than the bit rate), if a slower detector is used its response time becomes longer and it integrates the signal over a longer period; so the cross-correlation signal, which has higher total energy than the autocorrelation peak itself, adds more interference. If a characteristic time of detector becomes comparable with the bit period the cross-correlation signal will dominate and will disrupt a communication. However, the optically thresholded signal has sufficiently lowered energy of cross-correlation and still can be detected. Thus optical thresholding can potentially increase the achievable speed of optical CDMA communication.

The data and clock recovery module used in our experiment is unable to lock into the initial signal, however it works with the optically thresholded signal. The error rate (< 10 ^{-11}) measured with the 2^{15} -1 pseudo-random bit sequence indicates error-free transmission. It should be said that a much faster electronic receiver with bandwidth of more than 12GHz can detect the initial signal as well, which is also demonstrated in experiment and is consistent with the discussion above.

Another important characteristic of thresholding for systems applications is polarization in-sensitivity. Effects of polarization were observed in the same setup after introducing a polarization scrambler in all 4 channels. The resulting output eye-diagram is shown in Fig. 5C. Polarization scrambling adds some amplitude noise to the thresholded signal, but does not worsen the suppression of the cross-correlation. Also, it does not disrupt the error-free transmission. Moreover, if the time scale of polarization change is in the millisecond range or slower, this amplitude jitter may be reduced by subsequent amplification in the standard erbium amplifier due to gain saturation phenomena.

## 4. Discussion

The proposed scheme of a nonlinear Sagnac interferometer with a tunable directional element may find other possible applications for ultra-fast all-optical signal processing, since it adds the possibility of fine amplitude tuning to the well-known NOLM scheme [5].

To achieve superior thresholding characteristics, we combined the idea of a directionally attenuated NOLM [7], which increases an effective nonlinear coefficient introducing a strong asymmetry into the loop, with the idea of fine amplitude equalization of interfering waves, which effectively lowers the required nonlinear phase shift. A combination of these two ideas allows to use a nonlinear element with sufficiently lower nonlinear coefficient than in the classical NOLM scheme. The demonstrated use of conventional silica-based fiber as a nonlinear element simplifies the setup and reduces its cost. However, other nonlinear elements may be used to achieve further reduction in the required optical power. The nonlinear refraction index of silica (2.2 × 10^{-20}m^{2}/W, [11]) is relatively low compared to other glasses, such as lead-silicate (*n*
_{2} ≈ 2 × 10^{-19}m^{2}/W, [12]), chalcogenide As_{2}S_{3}-based (*n*
_{2} ≈ 4 × 10^{-18}m^{2}/W, [13]) and bismuth-oxide (*n*
_{2} ≈ 1.1 × 10^{-18}m^{2}/W, [14]). Therefore, non-silica based fibers can potentially be used in the proposed thresholder scheme to increase the in-loop nonlinearity.

The tunable directional element may also be beneficial for NOLM-based all-optical switches, where the amplitude equalization may help to decrease the required control pulses power in a similar way, and also for other Sagnac interferometer-based optical fiber devices.

## 5. Conclusion

We have proposed and experimentally demonstrated an all-optical thresholder based on a modified NOLM. Our scheme is much more power-efficient than the classical NOLM. This in turn lowers the requirement of having a strong nonlinearity in the loop. The experimentally demonstrated thresholder is based on only 15 meters of conventional silica-based fiber, and is built with only standard commercially available components. The measured transfer characteristic is very close to the theoretically predicted third-power law, and therefore the proposed thresholder is more efficient than second harmonic generation-based thresholders that have quadratic transfer function. The demonstrated capability of multiwavelength broad spectrum operation and the low polarization sensitivity make it suitable for application in optical CDMA and similar systems requiring all-optical peak detection. The proposed scheme may also be used with other nonlinear elements, such as non-silica-based optical fibers, for further reduction of required input power.

We would like to thank Yury and Olga Polyansky for help and useful discussions.

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