Optical Frequency Comb Generator for Coherent

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Abstract—This paper presents a theoretical analysis and an experimental demonstration of an optical comb generator. Based on the recirculating frequency ...
Optical Frequency Comb Generator for Coherent WDM System in Tb/s Applications Daniel Moutinho Pataca and Fábio Donati Simões

Mônica de Lacerda Rocha

Optical Transmission Group CPqD Foundation Campinas, Brazil {pataca, fsimoes}@cpqd.com.br

Electrical Engineering Department Engineering School of São Carlos, University of São Paulo São Carlos, Brazil [email protected]

Abstract—This paper presents a theoretical analysis and an experimental demonstration of an optical comb generator. Based on the recirculating frequency shifting technique, it targets high capacity applications that require high spectral efficiency and dispersion resilient transmission, such as optical orthogonal frequency division multiplexing (OFDM). The generator relies on the use of coherent and orthogonal multi-carrier (Coherent WDM) that makes use of a single laser source (seed). As far as we know, the theoretical model described here is presented for the first time. We experimentally demonstrate the generation of 26 comb lines with optical signal to noise ratio from 25 to 35 dB, in a spectral window of ~ 4 nm. The theoretical analysis prediction has shown excellent agreement with the experimental results. Keywords: Coherent WDM; comb generator; high capacity optical transmission; optical orthogonal frequency multiplexing; recirculating frequency shifting; superchannel.

I.

INTRODUCTION

According to ITU (International Telecommunication Union) statistics, by the end of 2010 one third of the world's population was of Internet users. The number of people online has doubled in the last five years and of the 226 million new Internet users that have come online, more than two thirds are from developing countries, where the development rate is higher. The ITU report suggests that 71% of people in western countries were online by the end of 2010, compared to just 21% in developing countries, implying that broadband may represent a transformational technology that can be used to spur development [1]. A projection of such high demand, starting from access networks, spreads the need for disruptive technologies until the trunk networks. This trend is confirmed by the fact that technologies for 100 Gb/s have been standardized in both context, Ethernet (IEEE 802.3 standard) and Optical Transport Network, (ITU G.709 recommendation), and transmission equipment with 100G interfaces are commercially available [2]. Following the Internet traffic growth, of about more than 50% over the year, the use of optical transmission systems at rates exceeding 100 Gb/s per channel is expected for the next generation trunk lines [3]. The main challenge for the research on systems running at rates exceeding 100 Gb/s is to demonstrate, by means of different modulation and reception techniques, the optical transmission at rates tending to 400 Gb/s and 1 Tb/s over long distances (hundreds of kilometers). As the system capacity increases, the challenges become more severe and the alternatives for addressing them become more complex.

Unfortunately, it is usual that the proposed solutions add new problems as side effects that will also need to be addressed. In general, those challenges are related to methods of generating and receiving new modulation formats, to broadband and low noise optical amplification techniques and to the combat of noise and distortion, generated in the transmitter and receiver, in combination with linear and nonlinear propagation effects. Considering that the available optical amplifier bandwidth is fixed (typically ~ 5 THz) and that the demand for accommodating IP traffic grows exponentially, an important premise of the new generation systems is to guarantee the spectral efficiency increase, for each optical channel, in comparison to channels generated by more traditional technologies. Besides the technical difficulties associated to high spectral efficiency, the transmission reach which is physically feasible also represents an important requirement, which then sets up a scenario with constraints and commitments. In such a context, this article presents a theoretical analysis and the experimental development of an optical comb generator, based on the Recirculating Frequency Shifting (RFS) technique [4], which can be used, in association with other modulation formats, in transmitters and receivers of high-capacity systems. Those comb generators produce a set of mutually orthogonal optical signals, which reduces the interference between channels in WDM systems. Unlike traditional WDM, the system proposed here reduces the need for guard bands between channels making more efficient use of the available optical bandwidth. The paper is organized as follows: section 2 presents a brief description of the state of the art regarding optical transmitters for systems operating at transmission rates higher than 100 Gb/s per channel. Section 3 and 4 present a theoretical analysis and the experimental investigations of the optical comb generator, respectively. Finally, section 5 presents the conclusions. II. OPTICAL GENERATORS FOR HIGH CAPACITY SYSTEMS Historically, in the first optical systems, the capacity increase was achieved by increasing the transmission rate: a technique that was limited by the available electronics speed and by fiber propagation impairments. In a second phase, after the development of WDM and optical amplifiers, the capacity upgrade was also achieved by increasing the number of channels. Such approach was limited by the available bandwidth of optical amplifiers and by interference between

adjacent channels, establishing a compromise between channel spacing and spectral density. Nowadays, different techniques have been developed targeting the spectral efficiency increase, among them, various modulation formats, techniques for reducing the fiber propagation constraints, new Forward Error Correction (FEC) techniques and an increase of channel count [1 - 2]. Such increase on the number of channels may be obtained from the reduction of interferences between them by using mutually orthogonal optical carriers [5]. In wired and wireless systems, orthogonal frequency division multiplexing (OFDM) is a multi-carrier transmission technique which can be used to combat radio frequency (RF) microwave multipath fading and to improve the speed of the signals [4]. The optical equivalent technology of RF OFDM, i.e. optical OFDM, has become a promising technique for high spectral efficiency and dispersion resilient transmission, where the generation of optical multi-carrier sources represents a paramount issue. In multi-carrier transmission, besides the orthogonality aspect, it is necessary to have frequency-locked carriers, in order to take advantage of OFDM for high spectral efficiency. One of the techniques that enable transmission of several Tb/s per fiber relies upon the use of coherent and orthogonal multi-carrier (Co-WDM) that makes use of a single laser source with high aggregate capacity and exploits parallel processing techniques, with moderate speeds per carrier and high spectral efficiency. Such high bit rate signal, produced from a single laser, comprising multiple carriers locked in frequency and modulated in a synchronous mode, is known as superchannel. In this signal, the interference between the orthogonal modulated carriers can be eliminated by controlling the phase of adjacent channels. It has been shown that a channel, among several others, can be detected, with minimum penalty caused by interference between channels, when the following conditions are met [5] • carrier separation is equal to the symbol rate of each modulated carrier, • symbols, in modulated carriers, are aligned in time, • the transmitter bandwidth is large enough to accommodate the carriers, • appropriate sample rate and anti-aliasing filtering are applied. An important feature of the superchannel signal is that the bigger the number of carriers the smaller should be the difference between the frequency separation (between carries) and the symbol transmission rate of each one. That means, it is crucial to generate stable carriers, without variation of the frequency interval between them and with same transmission rate for each one. Among many techniques used for generating superchannel signals, three may be highlighted: • Cascade of Mach-Zehnder modulators (MZM) commonly used to generate signals with two to eleven carriers; its limitation is the small number of generated carriers, which is determined by the MZMs electro-optic bandwidth and by the maximum amplitude of the driver signal [6]. • Recirculating Frequency Shifting, RFS - based on the frequency conversion produced by single side band

modulation, allows the generation of great number of highly stable carriers [7]. • Discrete mode laser (DM) driven by a sine wave – similar to gain switching in semiconductor lasers resulting in phase locking at the output. Its main advantages are simplicity and low cost [8]. The optical source presented in this paper is based on the RFS technique, where the optical signal, generated by a laser source, is shifted, in frequency, within a recirculation loop. The so-called Comb-Generator (CG) is the basic unit of the whole transmitter and consists of a singlemode laser, a 2x2 optical coupler, a double Mach-Zehnder (MZ) optical modulator , an optical amplifier (Erbium-doped fiber amplifier, EDFA), to compensate for the loop losses, and an optical filter, for limiting the number of generated carriers and the level of amplified spontaneous emission noise within the loop, as illustrated in Fig.1. According to the figure, an optical signal (coming from a laser source), is continuously injected into the loop through one of the coupler input ports, and circulates on the loop. After each round trip part of the signal outputs the loop and part returns to it.

Figure 1. Schematic diagram of a comb generator.

In the loop, the optical modulator is optically controlled by a polarization controller and electrically driven by two RF sine waves. Its biasing points are adjusted in such a way to generate a single side-band suppressed carrier signal (SSB-SC), which is than amplified and filtered. The action of the filter is crucial as it limits the optical noise and cuts off the optical carriers that exceed its bandwidth. Note that the filter output is added to the signal coming from the laser and inputs the loop again. At each round trip, the optical modulator shifts the signal spectrum in a frequency equal to the RF frequency applied to it. After many round trips, the circulating signal spectrum is shifted to outside of the filter bandwidth, thus limiting the number of comb lines at the generator output. III.

THEORETICAL ANALYSIS

An optical OFDM transmitter modulates the optical carriers generated by the CG. Those optical channels must have special characteristics of spacing, phase, power and optical signal to noise ratio (OSNR) in order to allow transmission with negligible penalties. The spacing between carriers is given by the frequency of the RF signal applied to the modulator [7]. The phase of the carriers comes locked to the phase of the laser used as a seed. To determine the spacing between carriers at the CG output, the frequency, f0, of the seed signal is related to its wavelength λ0, by:

This work has been sponsored by Funttel (Finep) and Fapesp (grant 06/04546-4)

λ0 = c f 0

(1)

where c is the free space light velocity. When the optical carrier crosses a MZ adjusted for providing a positive wavelength shift, Δλ, i.e. towards the lower side band (SSB-SC LSB), its optical frequency is shifted by the RF frequency, fm, applied to the modulator. This way, the new optical frequency becomes:

λ 0 + Δλ = c ( f 0 − f m )

(2)

The wavelength of the n-th line is then given by:

λ ( n ) = λ 0 + n Δλ

(3)

The carrier wavelength variation becomes:

Δλ = (c f 0 − f m ) − c f 0 For f0 >> fm, (4) may be simplified to:

Δλ ≅ c ⋅ f m f 0

2

(4) (5)

Δλ ≅ λ 0 f m c

(6)

The spacing between optical carriers generated in the CG is related to the modulation frequency applied to the RF modulator according to (6). From (3) and (6) we get: λ (n) = λ0 {1 + [(n ⋅ λ0 ⋅ f m ) c]}

(7) In a simplified view, the optical transmission reach is limited by two main constrains: propagation distortions and OSNR degradation. As the CG is, basically, a generator of optical carriers that will be modulated and transmitted, a special attention should be given to the OSNR of each comb line. Thus, to optimize the CG operation it is necessary to know the signal and noise level of each carrier. Those parameters will be analyzed in a way that it will be possible to determine each carrier OSNR at the generator output. First, some assumptions are made. The coupling ratio of the optical coupler is 50%, its attenuation is αco, and its transmittance is the inverse of the attenuation. The MZ modulator attenuation is represented by αm. The optical amplifier (EDFA) presents a small signal gain that saturates it, thus its output power, under saturation condition, is given by PA and its noise figure is represented by NF. The optical filter presents a transmittance of αF, within the optical transmission bandwidth, B0, which is limited by its initial and final wavelengths λini and λf, respectively. Outside this band, the filter presents infinity attenuation. Furthermore, the optical gain and attenuation values of all devices in the loop are constant as a function of the optical wavelength. As indicated in Fig. 1, a cw optical signal (seed), with input power Pin and wavelength λ0, is applied at the CG input. That signal, combined in the 50/50 coupler with other signals already presented in the ring (λ1, ... ,λn), is divided in two equal parts, Pout and P1. Therefore, n

Pout = P1 = ∑ Pλi

(8)

i =0

where Pout exits the ring and P1 re-enters it. The CG input signal, measured at the coupler output is given by:

(9)

In Fig. 1, the signal power P4 comprises line components at λ1 to λn, which are limited in band by the filter bandwidth. The total power at the coupler input is then given by: n

P4 = ∑ Pλi

(10)

i =1

The value of P4 is defined by PA, αF and B0. Each time all channels complete a round trip, they are wavelength shifted according to the frequency applied to the MZ. The comb lines are generated in the loop after each round trip until being limited by the ring bandwidth, which is defined by the amplifier and the filter. That means, when a line exceeds the optical band limit, it is cut off. Thus, at each round trip, a new line is introduced by the seed laser, centered in λo, and a line, centered in λn+1, is cut off. The value of P4 thus becomes: ⎛ n P4 = (PA α F )⋅ ⎜ Pλi ⎜ ⎝ i =1



By substituting (1) into (5), it comes: 2

Pλ 0 = Pin α co



n +1

∑ Pλ ⎟⎟ i

i =1



(11)

The number, N, of lines which comprise the signal with power P4, spectrally limited between λ1 and λf, is given by:

(

)

N = λ f − λ Δλ

(12) where Δλ is the wavelength shift caused by the frequency shift fm and is given by (6). Therefore,

[(

N ≅ c. λ f − λ1

)] (λ20 ⋅ f m )

(13) Considering that all lines generated in the CG are power balanced, the value of Pin may be given by:

Pin = P4 N = PA (α F ( N + 1) ) (14) Under those conditions, the CG output power, Pout, is then:

Pout = [( N ⋅ Pin ) α co ] = ( N ⋅ PA ) [α F α co ( N + 1)]

(15)

Each line power, at the CG output, is thus given by:

Pλ 0 = Pλ1 = ... = PλN = PA [α F α co ( N + 1)

(16)

Once the power of the exiting comb lines has been calculated, their individual OSNR can be estimated from the noise level of each line. The accumulated noise of each line comes from two different sources. The first one is the laser, itself, and the second is the optical amplifier inside the loop. In this analysis, the CG input signal is assumed to have negligible noise, since the seed laser presents very high OSNR (typically, superior to 45 dB at a resolution of 0.1 nm). By the other side, the amplifier spontaneous emission (ASE) noise generated by the EDFA, per state of polarization, may be written as [9]: PASE = 0.5 ⋅ h ⋅ f ⋅ B0 ⋅ [(G ⋅ NF ) − 1]

(17) where h is the Planck constant (6,6260755.10-34 J/s), f is the signal frequency, B0 is the optical bandwidth, G is the amplifier gain and NF is its noise figure. The modulator, operating in single side band suppressedcarrier (SSB-SC) mode, eliminates one of the states of

polarization that travels through it. Therefore, the existence of an accurate polarization control inside the loop is assumed. At each round trip an ASE level is inserted by the amplifier and is also frequency shifted by the modulator. Therefore, the noise which is generated by the amplifier at the lower frequencies of the optical filter bandwidth, is shifted an amount of fm and, in the next round trip, it will be added to the noise generated by the amplifier, at that frequency. The process continues successively until the frequency shift is large enough to fall outside the filter bandwidth. From (17), we notice that for constant gain and noise figure, the noise power, per frequency unit, introduced at each round trip, is nearly constant inside the filter bandwidth. To calculate the noise power which is inserted at each round trip, the optical filter bandwidth, B0, is divided in intervals equal to fm. Assuming C-band operation (1530 to 1560 nm) and taking as reference its central wavelength (1545 nm), any spectral variation within this band results in less than 1% of variation in relation to the absolute wavelength value. Therefore, as a simplification, λini, λf and λ0 may be represented by λ and, for a signal with bandwidth equivalent to fm, the noise power becomes: PASE (m) = {(m + 1) ⋅ h ⋅ c ⋅ f m [(G ⋅ NF ) −1]} (2 ⋅ λ ) (18) where m is the round trip number, starting from m = 0, when the EDFA output signal has not been shifted, yet, by the modulator. The OSNR generated in the loop must be high enough to not cause additional impact on the OSNR degradation during the optical fiber propagation. That leads to an OSNR threshold for the comb lines, at the CG output, which is dependent on the system transmission characteristics, as well as on channel bit rate and modulation format. Determining the OSNR value, once each channel signal power and noise level are known, becomes trivial. Since this kind of measurements are usually made with an optical spectrum analyzer (OSA), it is necessary to define an optical bandwidth over which the noise power is considered, once it is, differently from the comb lines, continuously distributed over the spectrum. An OSA operates according to its monochromator resolution, therefore, in (19) the optical bandwidth will be the OSA resolution, r. The noise power expression than becomes:

[

(

PASE (m) = (m + 1) ⋅ h ⋅ c 2 ⋅ r ⋅ [(G ⋅ NF ) −1] 2 ⋅ λ3

The OSNR of each line depends on, among other parameters, the spectral slice width where the line is located. Thus, it is necessary to know the signal power and the noise level on that wavelength range. The seed wavelength, λ0, may be located inside or outside the optical filter bandwidth [λini to λf] or even in an outside spectral slice shifted of fm. Therefore, the CG noise level may start to accumulate in a region without comb lines. The value of m, for each line, depends on the modulation frequency hop (fm), the optical filter bandwidth start frequency (λini), the seed wavelength (λo) and the round trip number (n) that the seed wavelength performs before exiting the CG. From (7), it may be written as:

{[

][(

m = n ⋅ (λ0 λini )2 + c ⋅ λ0 − λini λ2ini ⋅ f m

)]}

(23) The OSNR at the CG output is the same of that at the amplifier output. By substituting (7) in (13) and putting the result in (16), it is possible to determine each channel power at the amplifier output, Pλ, by:

[

(

Pλ = PA ⋅ λ2 ⋅ f m c λ f − λ0

)]

(24) Finally, the OSNR for each comb line, from 0 to N, is obtained from (24) and (22) by: OSNR(n) =

2 ⋅ PA ⋅ λ5 ⋅ f m (m + 1) (λ f − λ0 ) [(NF ⋅ α F ⋅ α co ⋅ α m ) − 1]⋅ h ⋅ c3 ⋅ r

(25)

where the wavelength for lines m and n comes from (23). IV.

EXPERIMENTAL DEVELOPMENT

Figure 2 shows the experimental set-up used in the assembly and characterization of the optical comb generator. For the generation of multiple carriers, we used a recirculating loop comprising a 40 Gb/s lithium niobate modulator, typically used for differential quadrature phase shift keying (DQPSK) modulation, with extinction ratio superior to 22 dB, two optical amplifiers (EDFAs) and one wavelength selective switch (WSS) as a filter. The light source feeding the loop is a distributed feedback (DFB) laser centered at 1551.81 nm.

)]

(19) The wavelength λ, inside B0, corresponds to the initial spectrum slice at the CG output and is given by: λ (m ) = λini [1+ ((m ⋅ λini ⋅ f m ) c )] (20) The amplifier gain, G, under saturation condition, is a function of its maximum output power, PA, and of the signal input power. In that case, the amplifier input power will be a function of the output power and of the transmittances related to the devices placed between the EDFA output and input. This way, the gain parameter, G, may be written as:

G = α F α coα m By taking (21) into (19) we get:

{

PASE ( m ) = ( m + 1) ⋅ h ⋅ c 2 r ⋅ [( NF ⋅ α F ⋅ α co ⋅ α m ) − 1] 2λ3

(21) Figure 2. Experimental setup.

}

(22)

A tunable RF generator was used to feed the DQPSK modulator with a 20 GHz RF signal. This electrical signal was split into two and the phase of one was 90º delayed in relation

to the other, in a way to guarantee the SSB-SC modulation. The RF driver amplifiers present electrical bandwidth of 40 GHz and output power of 19 dBm. Figure 3 shows the DFB spectrum at the modulator output, taken before closing the loop. With different adjustments of the RF levels and DC biasing it was possible to suppress the fundamental carrier (1551.81 nm) and the upper sideband frequency, keeping only the lower sideband. From the figure we may also observe the presence of higher order harmonics, caused by nonlinearities of the modulator transfer curve.

V.

CONCLUSION

We have presented a theoretical model which can be used as a system design tool. It allows the OSNR optimization, based on practical parameters, in a coherent comb generator (CG) that makes use of a single laser source (seed) and is based on the recirculating frequency shifting techniques. Such CB has been experimentally implemented and demonstrated the generation of 26 comb lines with optical signal to noise ratio ranging from 25 to 35 dB, in a spectral window of ~ 4 nm. The experimental results validate the theoretical model by showing excellent agreement with the theoretical prediction. Unlike traditional WDM, the system proposed here reduces the need for guard bands between channels making more efficient use of the available optical bandwidth, which is suitable for Tb/s application. As far as we know, the theoretical model described here is presented for the first time.

Figure 3. Seed signal spectrum after the SSB-SC modulation.

Figure 4 shows the measured and simulated comb generator output spectrum. As can be seen, we obtained 26 carriers separated by 20 GHz with an OSNR ranging from 25 to 35 dB and a variation in amplitudes inferior to 3 dB. The reduction in the signal to noise ratio between the first and last carrier is due to the accumulation of noise at every turn along the loop, caused by the generation of ASE in optical amplifiers. We also may notice that the simulation results were very close to the measured values, thus validating and demonstrating the accuracy of our theoretical model. Figure 5 summarizes the results, presenting the theoretical and experimental values of OSNR for each carrier generated at the CG. Again, the experimental results are very close to those obtained from the analytical method, except for those carriers with signal to noise ratio superior to 35 dB. The reason for that is the limitation of the optical spectrum analyzer for resolving the carriers at this wavelength spacing.

Figure 5.Theoretical and measured OSNR for each comb line.

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[9] Figure 4. Theoretical and experimental comb generator output spectrum.

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