This paper presents the concept of an optical transmitter based on optical arbitrary waveform generation (OAWG) capable of synthesizing Tb/s optical signals of arbitrary modulation format. Experimental and theoretical demonstrations in this paper include generation of data packet waveforms focusing on (a) achieving high spectral efficiencies in quadrature phase-shift keying (QPSK) and 16 quadrature amplitude modulation (16QAM) modulation formats, (b) generation of complex data waveform packets used for optical-label switching (OLS) consisting of a data payload and label on a carrier and subcarrier, and (c) repeatability and accuracy of duobinary (DB) data packet waveforms with BER measurements. These initial demonstrations are based on static OAWG, or line-by-line pulse shaping, to generate repeated waveforms of arbitrary shape. In addition to experimental and theoretical demonstrations of static OAWG, simulated results show dynamic OAWG, which involves encoding continuous data streams of arbitrary symbol sequence on data packet waveforms of arbitrary length.
©2009 Optical Society of America
High capacity optical transmission systems incorporate techniques such as chromatic dispersion (CD) compensation, and high spectral efficiency modulation formats in order to meet the increasing demands of telecommunication systems. The primary enabler for implementing modulation formats with more bits per symbol is the digital coherent receiver . Introduced within the past 5 years, this concept measures and digitizes the full field information while also post-compensating for transmission impairments offline. Likewise, combining intensity and phase modulators (or in-phase/quadrature-phase (I/Q) modulators), which directly map electrical voltages to the intensity and phase (or real and imaginary) parts of the optical field, with fast electrical arbitrary waveform generation has enabled generation of data in advanced modulation formats with transmission impairment pre-compensation . Multi-tone coherent communication techniques such as orthogonal frequency division multiplexing (OFDM) [3,4] and coherent wavelength division multiplexing (CoWDM) [5,6] improve spectral efficiency and dispersion tolerance by placing orthogonal subcarriers extremely close to each other. This paper discusses a promising technology, coherent optical arbitrary waveform generation (OAWG) [7–13], which is capable of generating THz bandwidth ultra-high capacity data of any modulation format, including OFDM or an entire CoWDM spectrum, by using low-speed (≤40 GHz) electronics.
Figure 1 shows the operation principle of OAWG for two cases; Fig. 1(a) shows static OAWG [7,9] where each line of an optical frequency comb (OFC) is independently controlled by static amplitude and/or phase modulations (Mi), and Fig. 1(b) shows dynamic OAWG where each line of an optical frequency comb undergoes intensity and/or phase modulations (Mi(t)) at frequencies up to the comb frequency spacing [12,14,15]. A chip scale implementation of OAWG operates by first separating the individual comb lines of an OFC onto different spatial locations using a high-resolution spectral demultiplexer with GHz channel spacing. Next, each modulator operates at a practical electrical bandwidth (≤ 20 GHz) whose maximum frequency corresponds to the demultiplexer channel spacing, and is not dependent on the number of comb lines. A second multiplexer then coherently combines the modulated comb lines potentially producing THz bandwidth waveforms while only requiring modest individual modulator modulation rates.
Integrated chip-scale OAWG becomes practical with the development of high-resolution arrayed-waveguide gratings  and fast electro-optic amplitude and phase modulators  within the same platform. Many applications for custom THz bandwidth arbitrary waveforms exist including light detection and ranging (LIDAR), coherent control of both chemical reactions and quantum mechanical wave packets, and the generation of high-speed data in advanced modulation formats [2,10,16]. An application of particular interest for next generation optical networks, and the focus of this paper, is a format-agile and high-capacity communications transmitter based on OAWG (OAWG transmitter) that can generate Tb/s rate data packet waveforms. In addition, complex modulation formats can be implemented using an OAWG transmitter to realize ultra-broadband OFDM [3,4] or an entire CoWDM spectrum [5,6] independent of the OFC comb line spacing.
This paper is organized as follows: Section 2 presents the static OAWG principle and algorithm. Section 3 presents a chip-scale experimental implementation of static OAWG to produce repetitive data packets in a variety of modulation formats with up to ~1 Tb/s capacity. Eye diagrams and a bit-error-rate (BER) curve generated from the experimental data corroborate the efficacy of this technique. Section 4 discusses a dynamic OAWG algorithm, which enables the generation of waveforms with durations much longer than an OFC period. Section 5 concludes by providing an outlook towards a next generation optical transmitter based on OAWG.
2. Static OAWG transmitter
An arbitrary communications transmitter based on static OAWG requires an optical frequency comb generator (OFCG), a waveform shaper and digital signal processing (DSP). Figure 1(a) illustrates the static OAWG schematic and principle. The OFCG produces an OFC, which is a set of frequency modes with constant frequency spacing that serves as the waveform input to the waveform shaper device. The waveform shaper controls the intensity and phase of each line to create a shaped data packet waveform of length 1/fr that repeats at the OFC frequency spacing, fr. The DSP algorithm determines the intensity and phase settings for each comb line necessary for the waveform shaper device to generate the data packet waveform in the desired modulation format. Such a transmitter can generate a repetitive arbitrary waveform that appears as a desired bit sequence in any modulation format at discrete symbol rates, which are multiples of the OFC comb spacing, fr. The lower symbol rate limit is determined by fr, while the upper symbol rate limit is determined by the OFC bandwidth. Data rates in excess of 1 Tb/s are achieved when the product of the spectral bandwidth and the spectral efficiency surpasses 1 Tb/s. The generated waveform can also be precompensated for CD of an expected fiber transmission distance.
2.1 Optical Frequency Comb Generator
An OFC is a set of n optical frequency comb lines with an exact frequency spacing of fr, with a coherent and stable phase relationship for a total bandwidth of B = n fr. Figure 3(a,b) shows a 40 GHz OFC. Ideally, the OFCG for OAWG applications should be capable of independently controlling its center wavelength, frequency spacing, fr, and the total number of comb lines, n. An ideal comb source has a stable frequency spacing, stable absolute frequency, and stable relative phase among the comb lines. Additionally, it is convenient if the OFC's spectral phase and intensity are constant across its entire bandwidth. The time domain representation of such a comb source is a short pulse with its full-width-at-half-maximum (FWHM) approaching 1/B and 1/ fr as its repetition period.
Figure 2 shows the OFCG used for the static OAWG experiments in Section 3. The OFCG involves heavy sinusoidal phase modulation of a tunable, narrow-linewidth single-frequency laser to create many (~40 or more) sidebands. Additional amplitude modulation can flatten the spectrum . Alternatively, with proper control of RF1, RF2 and VBIAS, a single dual-electrode Mach-Zehnder modulator (DEMZM) can simultaneously perform amplitude and phase modulation. Combining the signals from PM1 and PM2 produces a flat amplitude frequency comb spectrum [7,18–20]. PM3 and PM4 can further increase the number of comb lines to 60. Following , all RF signals are from the same source (HP 83752A) and the relative RF phases and amplitudes are set to produce a maximally flat and broad frequency comb. Propagation through standard single mode fiber (SSMF) compresses the pulse by removing the quadratic component of the spectral phase. In our experiments, the OFC is set to either 10 GHz or 40 GHz (Fig. 3(a,b)) by changing the RF frequency. The generated frequency combs have several central modes at > −3 dBc and outside modes at > −20 dBc, which is acceptable due to the spectral profiles of the desired data packet waveforms (e.g. Figure 3(c)).
2.2 Waveform shaper
The waveform shaper creates shaped data packet waveforms from a comb source through static OAWG, also known as line-by-line pulse shaping [7,8]. According to Fig. 1(a), the waveform shaper first demultiplexes the comb source and places each comb line onto a separate output waveguide or spatial location. Next, each comb line is individually modulated in both intensity and phase (Fig. 1(c)). Finally, the modulated comb lines are multiplexed onto a single spatial location or waveguide forming the shaped waveform. Figure 3 shows an example of a 9-bit 360 Gb/s  on-off keying (OOK) packet waveform created with a waveform shaper using static OAWG. Figure 3(a,b) depicts the input comb source spectrum and time domain while Fig. 3(c,d) shows the shaped waveform spectrum and time domain.
In this paper, experiments utilized a 10 GHz waveform shaper with 64 wavelength channels  and a 40 GHz waveform shaper with 128 wavelength channels . Both waveform shapers are integrated devices based on the silica platform with demultiplexers and multiplexers implemented with arrayed-waveguide gratings (AWGs). Shaped data packet waveforms are measured using cross-correlation frequency-resolved optical gating (XFROG) , and a single-shot (SS) technique [21,22]. XFROG is a phase sensitive measurement technique that averages over many repeated waveforms, and thus is useful as a diagnostic tool for static OAWG waveform measurements. T The single-shot technique is based on four-quadrature spectral interferometry (FQSI) using balanced coherent detection, which enables near quantum limited measurements. Other single-shot techniques, such as those based on single-shot XFROG geometries exist , but rely on nonlinear interactions between gate and reference pulses. In this paper, the OFC served as the reference pulse for both XFROG and SS-FQSI measurements.
2.3 Static OAWG DSP algorithm
There are two distinct DSP algorithms; 1) data packet specification DSP (Fig. 4 ) and 2) OAWG modulation DSP. Data packet specification DSP determines the desired data packet waveform from an input bit-sequence. OAWG modulation DSP determines the intensity and phase modulations necessary for a waveform shaper to create the data packet waveform.
Figure 4 shows the data packet specification DSP algorithm applied to the creation of 8-bit  CD precompensated OOK and quadrature phase-shift keying (QPSK) packet waveforms (Fig. 4(f,g)) of duration 1/ fr. The algorithm begins by defining a train of unit impulses (i.e. delta functions) evenly spaced within the data packet waveform time window (1/ fr), with the intensity and phase of each unit impulse set to one modulation format symbol. In the case of 1 bit/symbol modulation formats, such as OOK, duo binary (DB) and differential phase shift keying (DPSK), the number of symbols is equal to the number of bits within the time window. In order to maintain the same bit-rate for multi-level modulation formats, such as QPSK (2 bits/symbol) and 16 quadrature amplitude modulation (16QAM) (4 bits/symbol), the number of symbols is equal to the number of bits within the specified time window divided by bits/symbol. Figure 4(b) shows the resulting symbol trains for the OOK and QPSK waveforms with the corresponding discrete Fourier transforms shown in Fig. 4(c).
Figure 4(a) shows a raised cosine modulation filter (a type of Nyquist filter) , which is band-limited in the frequency domain. The impulse response of the raised cosine filter defines the shape of each bit. The β-rolloff factor of the raised cosine filter is a measure of the bandwidth beyond the Nyquist bandwidth of S/2. The bandwidth (B) of the raised cosine filter is dependent on the β-rolloff factor according to B = (1 + β)S/2, where 0 ≤ β ≤ 1. Raised cosine filters with lower β-rolloff factors have greater amounts of time domain ripple due to the more boxlike spectrum, while raised cosine filters with higher β-rolloff factors have significantly reduced time domain ripple at the expense of a greater bandwidth requirement. Another property of Nyquist filters is zero intersymbol interference (ISI) at adjacent symbol locations.
Next, the temporal shape of each symbol is defined by applying a raised cosine filter to the ideal symbol train. Figure 4(d) shows filtered spectra for OOK, using β-rolloff factors of 1 and 0, and QPSK, using a β-rolloff factor of 1, symbol trains. Figure 4(e) shows the corresponding filtered time domain OOK and QPSK waveforms. At this point, CD precompensation can be incorporated into the discrete spectral profile of the specified waveform packet by applying the inverse of the transmission link transfer function to the filtered symbol train spectrum. Figure 4(f) shows the CD precompensated filtered spectrum and Fig. 4(g) shows the resulting CD precompensated filtered time domain OOK and QPSK waveforms. Similarly, compensation for other system or device filtering effects can be included. The number of comb lines per symbol required to create the filtered symbol train is the bandwidth of the modulation filter divided by the symbol rate, S.
At this point, the static OAWG modulation DSP algorithm determines the intensity and phase modulator settings necessary for a pulse shaper to create the fully defined data packet waveform. The intensity and phase of each comb line in the spectrum of the target data packet waveform are used to generate the low frequency (≪ fr) or constant modulations for static OAWG.
3. Static OAWG communication applications experiments
An OAWG transmitter can generate any waveform within its effective modulation bandwidth (i.e., the product of the number of wavelength channels and fr). This section shows several experimental examples of static OAWG including the ability to modulate data with high spectral efficiency (greater than 2 bits/s/Hz) in advanced modulation formats , the creation of optical-label switching (OLS) data packet waveforms consisting of a data payload and label on a carrier and subcarrier, respectively, and measurements of the repeatability and accuracy of 50-bit duobinary (DB) data packet waveforms with BER measurements. Figure 5 shows the experimental arrangement for generating and characterizing the data waveform packets.
3.1 Spectrally efficient data modulation
An OAWG transmitter has the capability to generate data packet waveforms in any modulation format, including OOK and spectrally efficient multi-level QPSK and 16QAM. As an example, several experiments were performed utilizing a 10 GHz comb source with 40 comb lines for a total bandwidth of 400 GHz, and a 10 GHz OAWG device . A raised cosine filter with a β-rolloff factor of 0 enabled maximization of spectral efficiency for OOK and QPSK waveforms. The 16QAM waveform used a β-rolloff factor of 0.5 as a compromise between spectral efficiency, and a wider opening in the eye diagram.
Figure 6(a) shows the target and measured spectra for a 40-bit 400 Gb/s NRZ-OOK repetitive data packet waveform with a spectral efficiency of 1 bit/s/Hz. Figure 6(b) depicts the corresponding time domain waveform. The measured data closely resembles the target data in both the spectral and time domains. Note that in the time domain the data packet waveform has many different peak heights, but the ‘1’ level at each symbol location is constant. Figure 6(c,d) shows ideal and calculated eye diagrams of the OOK data packet waveform. There is a noticeable spread in the ‘1’ and ‘0’ levels in the measured eye diagram due to shaping errors, but the eye indicates potential for receiver detection and thresholding.
Figure 7(a,b) depicts the target and measured spectra and time domain waveforms for an 80-bit 800 Gb/s QPSK data packet with a spectral efficiency of 2 bits/s/Hz. The measured data closely matches its target in both domains. Figure 7(c,f) shows the target and measured constellation diagrams generated by selecting a 0.5 ps window around the center of each symbol. Figure 7(d,e,g,h) shows real and imaginary eye diagrams of the target and measured data. Both real and imaginary axis eye diagrams are necessary to resolve the four QPSK symbols. The two amplitude levels at the center of each bit period are clearly visible. The calculated real and imaginary eye diagrams in Fig. 7(f,g) are clearly open.
Figure 8 shows a 120-bit 1.2 Tb/s 16QAM shaped data wave-form packet with a spectral efficiency of 3 bits/s/Hz. The waveform has rapid line-by-line variations in the spectral do-main. Additionally, the data packet in the time domain has 16 different symbols that must be accurately specified. Considering the complexity of the waveform, spectral shaping errors will have large impact on the ability to threshold the 16QAM data. Although most of the measured spectral lines are within 0.02 radians of their target values, the measured time domain packet as seen in Fig. 8(b) has noticeable differences to the target. Figure 8(c,d) shows the target and measured constellation diagrams. Inaccuracies in waveform shaping resulted in a blurring of the modulation format symbols and several errors in the measured data constellation diagram. Figure 8(e) shows a constellation diagram of the measured data after correction for all spectral phase errors in the shaped waveform, which results in no symbol errors compared to Fig. 8(d). The potential for high spectral efficiencies and thus higher bitrates foreshadows single channel data rates at greater than 1 Tb/s with further improvement to the waveform shaping accuracy.
3.2 Optical label switching (OLS)
OLS is a promising technology for implementing next generation, all optical packet switching networks . OLS processes payloads all-optically while allowing both optical and electrical processing of labels through all-optical label extraction and rewriting. Among the many optical labeling schemes, subcarrier multiplexed labeling facilitates relatively simple all-optical extraction and rewriting. Recent OLS systems have implemented double-sideband sub-carrier multiplexing (DSB-SCM)  and carrier-suppressed subcarrier multiplexing (CS-SCM) labeling schemes , in which labels are encoded on spectral components on lower and upper subcarriers. However, conventional techniques for subcarrier modulation bandwidth have limited the label data rate.
Demonstrations of an arbitrary transmitter based on OAWG resulted in the generation of complex OLS packets with 10-bit 100 Gb/s payloads and 4-bit 40 Gb/s labels within a 100 ps duration using OOK and phase-shift keying (PSK). Experiments utilized a 10 GHz comb source with 31 comb lines for a total bandwidth of 310 GHz, and a 10 GHz waveform shaper. Example cases of OLS packets were generated with 10-bit  100 Gb/s payloads and 4-bit  40 Gb/s labels in NRZ-OOK and NRZ-PSK modulation formats. The DSP followed the data specification DSP algorithm in Fig. 4 separately for both the payload and label, and then utilized the DSB-SCM labeling method with a sub-carrier frequency of ± 130 GHz to create the OLS packets.
Figure 9(a) shows the measured and target OOK packet spectrum. The payload exists in the baseband while the label lies in the two sidebands. Figure 9(b) shows the corresponding time domain OLS data packet waveform. Small deviations between the measured and target spectra resulted in time domain waveform errors. Using a computer program, the payload and label spectra were extracted (windowed) from the packet spectrum. Figure 9(c,d) shows the corresponding time domain payload and label data packet waveforms. Each OOK bit is clearly defined with an extinction ratio >13 dB between ‘1’ and ‘0’ levels for both the payload and label.
Figure 10(a) presents the measured and target PSK packet spectrum. The measured spectral intensity and phase closely match the target values, which yields a time domain OLS data packet waveform with minimal errors (Fig. 10(b)). Figure 10(c,d) shows the extracted time domain payload and label data packet waveforms. There is a noticeable π-phase change between ‘0’ and ‘1’ bits. The intensity minima are a result of using the raised cosine modulation filter.
3.3 OAWG transmitter BER analysis
A measure of fidelity and stability of an OAWG transmitter consists of examining repeated measurements of a 100 ps, 50-bit duobinary (DB) waveform at 500 Gb/s with a bandwidth of 490 GHz. Figure 11(a) shows the measured intensity of the example 50-bit DB waveform defined using a raised cosine modulation filter with β-rolloff factor of 0 for increased spectral efficiency. A 10 GHz comb source with 49 comb lines for a total bandwidth of 490 GHz, in conjunction with a 64 channel 10 GHz OAWG device, produced the shaped waveforms. The repetitive 50-bit DB waveform was measured 500 times at various power levels using SS-FQSI [21,22]. As mentioned earlier, SS-FQSI is a true single-shot measurement technique which does not require a periodic signal waveform. Each measurement retrieves the complete amplitude and phase of the signal with near quantum-limited sensitivity, thereby making it possible to measure the statistics of optical waveform fluctuations.
Figure 11(b) shows a simulated eye diagram of the 100 ps, 50-bit DB target waveform at 500 Gb/s, with a power level of 60,000 photons, without any noise or waveform shaping errors. The spread of the rising and falling edges, and 1’s level broadening, is a result of significant time domain ripple introduced by the low β-factor of the raised cosine modulation filter. Figure 11(c) depicts an eye diagram generated from 500 SS-FQSI measurements of 50-bit DB waveforms at 500 Gb/s with a power level of 60,000 photons at the receiver. The eye opening in Fig. 11(c) is much smaller than the ideal eye in Fig. 11(b) due to waveform shaping errors in the frequency domain and system noise, but the general trend of the histogram follows the ideal eye in Fig. 11(b).
Most waveform shaping errors are due to inaccuracies in adjusting the spectral amplitude and phase of each comb line to their target values. Since these errors vary on a mode-by-mode basis, they appear as a noise signal in the time domain which is evenly distributed across the entire temporal window. This leads to an interesting effect when the waveform is viewed as time-domain intensity data. The apparent distortions are larger where there is energy (e.g., ‘1’ level) and less where there is little or no energy (e.g., ‘0’ level). This arises due to the coherent interference between the noise signal and the target waveform . This is indicated in the eye diagrams as much larger variance in the ‘1’ level than the ‘0’ level. If the static OAWG packet has fewer 1’s than 0’s the data packet would have less distortion due to shaping errors because there would be more signal power per bit but the same noise power per bit. However, if the data packet is measured in the field domain, the noise equally spreads amongst each symbol level.
Figure 11(d) shows a BER curve calculated from the measured data at various power levels. The BER was determined by comparing the target pattern against 500 single-shot acquisitions of the repetitive data packet, for a total of 25,000 bits at each power level. The highest power level of 60,000 photons (−11.14 dBm) achieved a BER < 10−5 (error-free for 25,000 bits), thus indicating potential for a sufficiently fast receiver to successfully detect a 500 Gb/s data waveform generated with an OAWG transmitter.
4. Dynamic optical arbitrary waveform generation
The experimental data presented shows the generation of repetitive waveforms with up to 490 GHz bandwidth using silica based photonic light-wave circuits (PLCs) and static modulations on an OFC. For example, the high spectral efficiency 16QAM packet has a data rate of 1.2 Tb/s, but still repeats the same 120 bits every 100 ps (OFC period). To create data packet waveforms suitable for use in real networks it is necessary to switch the modulations rapidly (on the order of fr) to create an extended data packet with a duration much longer than an OFC period. Figure 12 shows the rapid modulations, known as dynamic OAWG, which generate sidebands on each comb line that can undergo significant filtering when combined with a spectral multiplexer (Fig. 1(b)). A time domain approach (temporal slice OAWG) has already been discussed by . Here we discuss a spectral domain approach (spectral slice OAWG) to determine the necessary comb line modulations, which is compatible with spectral multiplexers.
Spectral slice OAWG determines the comb line modulations in the spectral domain needed to construct each spectral slice of the extended duration waveform. Spectral slice OAWG DSP proceeds as follows: 1) the extended duration waveform spectrum is computed and divided into spectral slices. Figure 12(a) shows the time domain of the extended duration data packet consisting of four 100 ps OFC periods. Figure 12(b) shows the spectrum of the extended duration data packet waveform divided into 10 GHz wide band-limited spectral slices. 2) Each spectral slice is pre-emphasized for spectral filtering introduced by the multiplexer. 3) Then, the necessary comb line modulations are the inverse Fourier transform of each spectral slice, which are centered on the comb lines. Figure 12(c) shows the time domain modulations of each comb lines required to generate the corresponding spectral slice. 4) Fig. 12(d) shows a gapless spectral multiplexer used to combine the modulated comb lines to generate the extended duration waveform. The gapless spectral multiplexer enables combination of the modulated comb lines without distortion. The modulations shown in Fig. 12(c) assume I/Q modulators (Fig. 1(d)). Unlike an intensity and phase modulator, an I/Q modulator maps the electrical modulations directly to the real and imaginary parts of the optical field, which matches the electrical bandwidth requirement to the spectral slice bandwidth. Figure 12(d) shows a simulation of a gapless AWG multiplexer similar to the arbitrary filter AWG multiplexer in .
The comb line modulations determined by spectral slice OAWG are band-limited and do not have overlapping spectra. Therefore, the comb line modulations are compatible with two key objectives: first, the electronics operate at the spectral slice bandwidth (comb line spacing) and second, gapless spectral multiplexers can be used. Spectral slice OAWG DSP allows for practical and straightforward generation of extended duration data packets making the dynamic OAWG feasible.
In this paper, we proposed, and demonstrated through proof-of-principle experiments using static OAWG, the viability of an OAWG-based transmitter for next generation optical networks. This transmitter is transparent to modulation format and is bandwidth scalable by shaping additional comb lines, limited only by the number of channels in the waveform shaper. Additionally, we showed the capability of a static OAWG transmitter to create repetitive, high spectral efficiency data packet waveforms, create complex OLS data packet waveforms, and achieve error free BER. Further improvements in pulse shaping fidelity should allow generation of data packet waveforms with high spectral efficiencies in excess of 3 bits/s/Hz and error-free operation at lower signal power levels. The true potential of a high-speed OAWG-based transmitter is realized when combined with the spectral slice OAWG technique. This combination overcomes the repetitive waveform limitation of static OAWG and may facilitate the generation of long duration Tb/s data packet waveforms while only using GHz rate I/Q modulators. Currently, work is in progress to realize integrated GHz rate modulators and high-resolution AWGs in InP , enabling dynamic OAWG to become a reality. Additionally, work is in progress to detect infinite duration waveforms by means of optical arbitrary waveform measurement (OAWM), in which each spectral slice is coherently detected using low speed electronics .
The authors would like to thank Jay Lowell, Erich Ippen, Bill Jacobs, and Enrique Parra for their constant encouragements and enlightening discussions. This work was supported in part by DARPA and SPAWAR under OAWG contract HR0011–05–C–0155.
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