40 Gb/s CAP32 short reach transmission over 80 km single mode fiber

Yuliang Gao; Qunbi Zhuge; Wei Wang; Xian Xu; Jonathan M. Buset; Meng Qiu; Mohamed Morsy-Osman; Mathieu Chagnon; Feng Li; Liang Wang; Chao Lu; Alan Pak Tao Lau; David V. Plant

doi:10.1364/OE.23.011412

1. Introduction

The capacity of access networks must evolve as the proliferation of more bandwidth intensive services has been provided such as streaming Internet video, video on demand and cloud-based storage and computing. With accessibility to optical phase and polarization, coherent transceivers supporting 100 Gb/s per channel are widely available for commercial deployment. However, it is not likely for coherent techniques to be used in short reach communications as the IQ modulator, optical hybrid and local oscillator not only increase cost but also footprint and, as a result, impede system integration. Instead, intensity modulation-direct detection (IM-DD) techniques are widely favored for the short reach scenario. Numerous such schemes have been investigated including pulse amplitude modulation [1,2], direct detection orthogonal frequency-division multiplexing/discrete multi-tone modulation [3,4] and carrier-less amplitude/phase modulation (CAP) [5–7].

Among these techniques, CAP modulation is an attractive candidate since it doesn’t require a complex mixer and a radio frequency (RF) source for down conversion [8]. Neither does it need the discrete Fourier transform (DFT) therefore the use of high speed digital-to-analog converter (DAC) can be avoided in commercial products. Recently, many CAP systems with large capacities have been reported in the literature, such as a CAP16 system achieving bit rates up to 40 Gb/s [5]. However, single-band CAP systems have stringent requirements for flat channel frequency responses [9]. Multiband CAP technique (MultiCAP) is proposed to mitigate the impact of channel responses by carefully manipulating the modulation formats and power loading on each sub-band [10–12]. However, considerable power penalties can still be observed for the sub-bands near the feeding dips when the transmission distance is longer than 40km [10]. Thus, the CD induced non-flat in-band frequency response, also called the power fading effect (PFE), is considered as a critical limiting factor to system capacity and maximum reach. On the other hand, single-side band (SSB) techniques have been introduced to avoid the cut-off effect [10]. However, to generate an optical SSB signal requires an additional sharp optical filter precisely aligned with half of the signal sideband. Otherwise, an IQ modulator or specially designed transmitter is required to perform the Hilbert transform [13]. Another alternative is pre-compensating CD at the transmitter (Tx) [14] which requires high speed DACs where simple transmitter architecture of CAP systems such as analogue implementation cannot be adopted [15]. On the other hand, we have presented various receiver digital equalization techniques to compensate for PFE [6, 8, 9]. However, one drawback of traditional transversal receiver equalizers is that they introduce extra noise to the recovered signal also known as noise enhancement [16]. Furthermore, the maximum reach for previous 40 Gbit/s CAP systems is still not more than 40 km even with the aid of digital signal equalization techniques.

In this paper, we first theoretically and numerically investigate the PFE in CAP systems. Then we propose the use of degenerate four-wave mixing (DFWM) to mitigate PFE. In particular, we find that by using properly adjusted launched powers the DFWM in the fiber link can effectively reduce the phase shift introduced by CD and thus alleviate fading effects. Experiment results show that at the optimum launch power in our system produces a 60 km reach over single mode fiber (SMF) at the 7% FEC threshold of 3.8 × 10⁻³ [17]. In addition, we evaluate the performance of the decision feedback equalizer (DFE) in such a frequency-selective optical channel. It is shown that the DFE equalizer provides superior tolerance to the CD-induced PFE compared with a linear equalizer (LE), and thereby, the maximum reach is further extended to 80 km which is twice the longest reach for a single carrier 40 Gbit/s CAP system reported to date at the wavelength of approximately 1530 nm.

2. Operating principle

2.1 Carrier-less amplitude and phase modulation

CAP signal can be generated using two orthogonal shaping filters g_I(t) and g_Q(t). The impulse responses of the two filters form a Hilbert pair, expressed as [6]

g_{I} (t) = f (t) \cdot \sin (2 π f_{c} t)

g_{Q} (t) = f (t) \cdot \cos (2 π f_{c} t),

where f(t) is the baseband square-root raised-cosine shaping filter, the roll-off factor is set to be 0.1in this paper, f_c is the carrier frequency. The in-phase and quadrature symbols a_n and b_n are first sent into g_I(t) and g_Q(t), respectively. The two filtered signals are then added together to generate the electrical CAP signal as shown in Fig. 1. The transmitted signal can be expressed as

s (t) = \sum_{n = - \infty}^{\infty} [a_{n} g_{I} (t - n T) - b_{n} g_{Q} (t - n T)],

where a_n and b_n denotes the in-phase and quadrature components, n is the symbol index, and T is the symbol period. At the receiver side, the signal r(t) after the photodetector (PD) is first passed through the two matched filters which are the time reverse of g_I(t) and g_Q(t) to separate the in-phase and quadrature components

Fig. 1 Schematic structure of CAP modulation and demodulation.

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r_{I} (t) = r (t) * g_{I} (- t)

r_{Q} (t) = r (t) * g_{Q} (- t) .

Then, an adaptive filter updated by least mean square algorithm is used to equalize channel distortion before the final data decision.

2.2 Chromatic dispersion induced power fading and degenerate four-wave mixing

After transmission, each frequency of the signal has experienced a different phase shift. This results in a PFE after direct detection. To evaluate the CD-induced PFE, the fiber is modeled as an all-pass filter with a transfer function given by

H (f) = e^{- j π D \frac{λ^{2}}{c} L f^{2}},

where f is the frequency offset from the optical carrier, D is the chromatic dispersion, λ is the optical wavelength, L is the length of the fiber and c is the speed of light in vacuum. The optical signal at the output of the fiber, E(t), is then given by

E (t) = \sqrt{A + s (t)} * h (t),

where A represents the DC bias and h(t) is the inverse Fourier transform of H(f). At the PD, the optical signal is captured by the square-law detection

r (t) = {| \sqrt{A + s (t)} * h (t) |}^{2} .

The signal can be expanded into Taylor series on the square-root term. The detected signal can be expressed as

r (t) = [(\sqrt{A} + \frac{s (t)}{2 \sqrt{A}} - \frac{s^{2} (t)}{8 A^{3 / 2}} + ...) * h (t)] \cdot {[(\sqrt{A} + \frac{s (t)}{2 \sqrt{A}} - \frac{s^{2} (t)}{8 A^{3 / 2}} + ...) * h (t)]}^{*} .

After expanding Eq. (9), the detected electrical signal can be expressed as

r (t) = A + \frac{s (t) \otimes h (t)}{2} + \frac{s * (t) \otimes h * (t)}{2} - \frac{s^{2} (t) \otimes h (t)}{8 A} - \frac{{(s * (t))}^{2} \otimes h * (t)}{8 A} + ...,

where the operation

\otimes

stands for convolution and the superscript * is conjugation. In Eq. (10), the first term is the DC component. The second and third terms are the linear outputs of interest obtained by convoluting signal s(t) with the channel response h(t). The rest are regarded as the noise induced by the interaction of the detector nonlinearity and fiber CD. Note that these noise terms can be considered sufficiently small when bias level A is set to be much larger than signal s(t) [18]. Then, the linear terms can be further simplified since the CAP signal is real valued, (i.e., s(t) = s*(t)). Thus, Eq. (10) can be simplified as

r (t) \approx A + s (t) * \frac{h (t) + h^{*} (t)}{2} = A + s (t) * h_{e q} (t),

where the equivalent transfer function H_eq(f) is

H_{e q} (f) = \frac{e^{j π D \frac{λ^{2}}{c} L f^{2}} + e^{- j π D \frac{λ^{2}}{c} L f^{2}}}{2} = \cos (π D \frac{λ^{2}}{c} L f^{2}) .

To validate Eq. (12), a simulation has been conducted on a 40 Gbit/s CAP32 system. Fiber nonlinearity is first turned off to focus on the CD impact. The RF spectral density of r(t) is shown in Fig. 2 for different transmission distances. The dashed lines display the squared equivalent transfer function |H_eq(f)|² obtained in Eq. (12). The solid curves represent the simulated RF spectrum with various transmission distances. Note that all the simulation results in this section are obtained using data sets of 2¹⁶ symbols. One can see that the high frequency components start to experience a cut-off effect as the distance is increased above 40km. When the distance is 60 km and 80 km, power dips can be observed at 8.4 GHz and 7.3 GHz respectively which agree well with the analytical transfer function H_eq(f).

Fig. 2 RF spectrum of received 40 Gbit/s CAP32 signals with different transmission distances. Solid lines are the RF spectrum. Dashed lines represent the analytical transfer function obtained in Eq. (12). L denotes the fiber length.

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To study the DFWM, the nonlinear Schrodinger equation in the absence of polarization effects is given by [19,20]

i \frac{\partial E (z, t)}{\partial z} + i \frac{α}{2} E - \frac{1}{2} β_{2} \frac{\partial^{2} E}{\partial t^{2}} + γ {| E |}^{2} E = 0,

where E(z,t) denotes the optical field propagating in the fiber,

γ

is the fiber nonlinearity coefficient, z is the transmission distance, t is time,

α

is the coefficient for fiber loss and

β_{2}

is the dispersion of group velocity.

Assuming that three random frequency components are located at $f_{p}, f_{q}, f_{r},$ , then the FWM component produced by these frequencies will be located at the frequency of $f_{g} = f_{p} + f_{q} - f_{r}$ , and the generated FWM product can be described as [21]

E_{F W M, g} = i γ E_{p} E_{q} E_{r}^{*} \frac{\exp [(- α + i Δ β) z] - 1}{i Δ β - α},

where E_p, E_q and E_r are the optical fields of any three random frequency components in the system, E_FWM,g represents the optical field of the FWM product at frequency

f_{g}

.

Δ β = β_{p} + β_{q} - β_{r} - β_{g}

denotes the phase mismatching term, where

β_{i} (i = p, q, r, g)

is the propagation constant for the carrier at frequencies

f_{p}, f_{q}, f_{r}, f_{g}

. In the CAP system, the DC component is usually much larger than other signal components and thus the DC involved degenerated FWM product contributes the majority of the entire nonlinear effect.

In this case, the most significant DFWM products are caused by the interaction of the DC component, which means E_p and E_q both equal to the optical carrier, and one signal frequency component E_r in the signal sideband. The degenerated FWM component that is located on the frequency f can be expressed as

E_{F W M} (f) = i γ E^{2} (0) E^{*} (- f) \frac{\exp [(- α + i Δ β) z] - 1}{i Δ β - α},

where

E_{F W M} (f)

is the FWM product generated by the signal component at frequency –f. For an intensity modulated signal, the spectrum on one sideband is the Hermitian conjugate of the spectrum component on the other side (e.g.,

E (f) = E^{*} (- f)

). Thus, the signal with DFWM can be written as

\begin{array}{l} E_{t o t a l} (f) = E (f) + E_{F W M} (f) \\ = {1 + i γ E^{2} (0) \frac{\exp [(- α + i Δ β) z] - 1}{i Δ β - α}} \cdot E (f) . \end{array}

Therefore, each frequency experiences both phase and amplitude changes depending on the $Δ β$ value of its corresponding $E_{F W M} (f)$ . This term introduces a nonlinear phase rotation to each frequency component that is opposite to the phase shift induced by CD. To illustrate the interaction between CD and FWM, the optical phase shift $Δ φ$ is obtained by Eq. (17)

Δ φ (f) = \arg (E_{o u t} (f) / E_{i n} (f)),

where

E_{i n} (f)

and

E_{o u t} (f)

are the optical fields at frequency f before and after 80 km SMF transmission. Figure 3 shows the simulation results of the optical spectrum and phase shift

Δ φ (f)

at various launch powers. Different from Fig. 2, both the CD and fiber nonlinearities are considered. At frequency of 8.5 GHz, 1.55, 1.67, 2.00 and 2.12 rad phase shifts are observed respectively for 10, 12, 14 and 15dBm launch power cases. The launch power in the linear case is 0 dBm. For the 10dBm launch power case, the phase shift is almost identical to the linear transmission where only CD is considered. However, the phase rotation is reduced by 0.57 rad for the 15 dBm launch power case. Also, the π/2 phase shift point (i.e., the dip frequency in RF spectrum) is significantly increased by 1.15GHz indicating effective mitigation of the PFE. As can be noticed, the power density function is quite flat over the whole optical spectrum. Thus, the phase shift introduced by self-phase modulation and cross-phase modulation effects should be identical for different frequency components. Since we only care about the relative phase-shift differences for different frequency components and the minimum phase shift will be set to zero for comparison. Thus, the phase shift in Fig. 3 is only contributed by DFWM.

Fig. 3 Optical power spectrum at Tx and phase shift after 80 km SMF transmission for a 40 Gbit/s CAP32 signal with various launch powers. Fiber nonlinearity effects are turned off in the linear transmission case. The LP is launch power.

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Figure 4 shows the simulation results of the RF spectrum of the CAP32 signal after direct detection with various launch powers. It can be seen that the CD-induced power fading effect is mitigated with increased launch power. The power dip is increased from 7.49 GHz to 8.18 GHz for the launch power of 0 dBm and 9 dBm respectively. When the launch power is increased to 12 dBm, no power dip is observed in the RF spectrum anymore. Thus, it can be concluded that the degenerate FWM is effective for the CD-induced power fading mitigation in IM-DD systems. Here, the DFWM induced phase shift is obtained in a single-carrier system. If wavelength-multiplexing CAP (WDM-CAP) technique is incorporated, multiple power peaks should be observed in the optical spectrum as shown in [10]. With such multiple wavelengths carriers, inter-channel FWMs will not accumulate because the phases of different carriers are uncorrelated and the CD-induced walk-off between different WDM channels will destroy the phase-matching condition. Thus, for a WDM-CAP system, only intra-channel FWM should be considered and similar phenomenon should be expected.

Fig. 4 RF spectrum of received 40 Gbit/s CAP32 signals with different launch powers.

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3. Experimental results

Figure 5 shows the experiment setup of the CAP32 system. At the transmitter side, the bit sequence is mapped onto in-phase and quadrature components a_n and b_n, respectively. Then, the coded sequence is up-sampled by a factor of four in order to match the operating rate of the shaping filters that follows. After in-phase/quadrature component separation, the two signals are sent into two shaping filters. The filter center frequency $f_{c}$ is given by $(1 + α) \cdot B / 2 + Δ f$ . Here, the roll-off factor $α$ is 0.1, B is symbol rate and $Δ f$ is the 100 MHz frequency offset. Then, the signal is pre-emphasized to mitigate the DAC analog frequency response using the method in [22]. Two high speed Micram DACs with 6 bit resolution together with two field-programmable gate array (FPGA) boards are used to generate the 8 Gbaud CAP32 RF signal at a sampling rate of 32 GSa/s. It should be noted that this is only a proof of concept experiment and the high-speed DAC can be replaced by two electrical filters in the future commercially available products. The output power from laser is 12 dBm. The output amplitude after the electrical amplifier is 400 mV peak-to-peak and is used to drive an intensity modulator (IM) whose $V_{π}$ and bandwidth are 5V and 33GHz respectively. Since external modulator is incorporated for the data loading, phase or frequency chirp effect will be mitigated in the laser output to focus on the interaction between CD and DFWM effect. Contrarily, if a directed modulated laser is adopted for data modulation, a frequency chirp will be introduced to the output signal. The dominant linear part of the chirp is equivalent to a CD induced chirp term [20] which will not affect the PFE compensation from DFWM. The residual small nonlinear chirp will slightly degrade the PFE compensation due to the unbalanced phase distortion on the sidebands on different sides of the central frequency. However, the DFWM effect is still helpful in compensating the CD induced PFE. The modulated signal is then boosted to compensate for the insertion loss of the PC and the IM. Then, a variable optical attenuator (VOA) is used to adjust the launch power from 0 dBm to 15dBm. After the fiber link, another VOA is used to keep the received power to be constant even the launch power has been changed. The signal is then detected by a wide bandwidth 10 GHz PD with a sensitivity of −25dBm. In the end, $1.6 \times 10^{5}$ CAP32 symbols are sampled by an oscilloscope at a sampling rate of 80 GSa/s for offline processing.

Fig. 5 Schematic of the 40 Gbit/s CAP32 experiment setup. DAC: digital-to-analog converter; VOA: variable optical attenuator; SMF: single mode fiber; T-T BPF: tunable bandwidth and tunable central wavelength bandpass filter; PD: photo detector; Rx: receiver; BER: bit error rate.

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For the offline processing, the captured signal is first resampled to 4 samples per symbol. Then, two time-reversed of matched filters g_I(t) and g_Q(t) filters comparing with the transmitter are used to separate the in-phase and quadrature signals. These signals are subsequently down-sampled to 2 samples per symbol and processed by the digital equalizer to compensate for the channel distortions. In such a frequency-selective channel, decision feedback equalizer (DFE) can be used for the data equalization to alleviate the noise enhancement effect [16]. A transversal LE is also studied for comparison. To achieve a fair comparison, both equalizers have the same tap length, step size and are both updated with least mean square algorithm. Figure 6 shows the block diagram of DFEwhere y(n) is the input signal, d(n) is the transmitted symbol, $\hat{d} (n)$ is the data decision and e(n) is the error signal. The feedforward and feedback equalizers are denoted as C(z) and F(z) whose tap spaces are $T_{s} / 2$ and $T_{s}$ , respectively. The input is first equalized by a 30-tap forward equalizer C(z). Since the channel response is not flat as shown in Fig. 2, the linear channel equalizer will over-amplify the noise at the fading dips which is also known as the noise enhancement effect [16]. To mitigate its impact, another 5-tap feedback equalizer F(z) can be enabled for estimating the enhanced noise $n (n)$ by looking into the difference between C(z)’s output and data decisions. The final output of the DFE is obtained by subtracting the equalized signal of the forward equalizer from the equalized output of the feedback equalizer. In commercialized realization of our scheme, phase-lock-loop or QAM receivers [12] should be adopted for clock-jitter compensation. However, the timing jitter is sufficiently small in our experiment so we rely on the DFE to compensate for the timing jitter [23].

Fig. 6 Schematic diagram of decision feedback equalizer. For linear equalization, only the forward equalizer C(z) is used while both forward equalizer C(z) and feedback equalizer F(z) are enabled for decision feedback equalization. y(n): input signal; C(z): transfer function of forward equalizer; F(z): transfer function of feedback equalizer; d(n): transmitted symbol; $\hat{d} (n)$ : data decision; e(n): error signal.

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First, bit error rates (BERs) versus different launch powers for 40 km, 60 km and 80 km transmission links have been studied. Figure 7(a) shows the 40 km transmission result for LE and DFE. In order to maintain a fixed sensitivity, the received power for all points displayed are kept at −10dBm using the VOA. The optimum launch power in Fig. 7(a) is 6 dBm for both LE and DFE as the fading effect is not severe enough while the dominant distortion comes from the fiber nonlinearity. The DFE increases the BER from 10⁻⁴ at 6 dBm to 8 × 10⁻⁴ at 15 dBm. For the LE, the BER increases from 2.4 × 10⁻⁴ at 6dBm to 1.7 × 10⁻³ at 15dBm. Figure 7(b) experimentally demonstrates that the power fading effect has been mitigated and the high frequency components are elevated, as predicted by the simulations in Fig. 4.

Fig. 7 (a) Launch power versus BER (b) RF power spectrum after 40 km SMF transmission. LE: linear equalizer; DFE: decision feedback equalizer.

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In the 60 km transmission, larger launched powers are required to mitigate the PFE and the optimum launch power is increased to 9 dBm for DFE and 12 dBm for LE as can be seen in Fig. 8(a). The 3 dB difference is because DFE has a superior tolerance to power fading. The received power is kept at −10dBm for all the test cases. At high launch powers, we note that the performance difference between the two techniques becomes smaller. This is because the high frequencies are over amplified by DFWM, and therefore nonlinear noise becomes dominant. Thus, a balance has to be struck between PFE and fiber nonlinearities. The optimum BER obtained using DFE is 2 × 10⁻⁴ at 9 dBm launch power while the optimal BER for LE is 7.8 × 10⁻⁴ at 12 dBm. We also observe that the high frequency components are enhanced with increased launch power in Fig. 8(b).

Fig. 8 (a) Launch power versus BER (b) RF power spectrum after 60 km SMF transmission. LE: linear equalizer; DFE: decision feedback equalizer.

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Figure 9(a) shows the 80 km transmission result for LE and DFE. The optimum power is increased to 12 dBm and 14 dBm for DFE and LE respectively because a larger FWM effect is required to mitigate the severe PFE existing at this reach. The optimum BER for DFE is 10⁻³ at a launch power of 12 dBm while the optimum BER for LE is 4.5 × 10⁻³ at 14 dBm. Although the optimum launch power of 12 dBm is much larger compared to long-haul transmission cases, it is still an acceptable value in short reach communication systems [10]. The received power is set to be −10dBm. From Fig. 9(b), we note that the fading dip is more severe compared to the 40 and 60 km cases and thus requires a higher launch power beyond 14 dBm. However, this introduces too much nonlinear noise and even with the optimum launch power of 14 dBm, LE still cannot achieve a 7% FEC threshold of 3.8 × 10⁻³.

Fig. 9 (a) Launch power versus BER (b) RF power spectrum after 80 km SMF transmission. LE: linear equalizer; DFE: decision feedback equalizer.

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Figure 10 shows the received power versus BER for (a) 40 km, (b) 60 km and (c) 80 km fiber links. For the 40 km link, the optimum launch power of 6 dBm is chosen and the required received power at BER of 3.8 × 10⁻³ are −15.22 dBm for DFE and −14.75 dBm for LE with a power penalty of 0.47 dBm. For the 60 km transmission, the launch power is 9 dBm to mitigate PFE and the required received power are −13.41 dBm and −12.82 dBm for DFE and LE, respectively, resulting in a 0.59 dBm power penalty. For the 80 km transmission, the optimum launch power of is set to be 12 dBm and the required received power for DFE at BER threshold of 3.8 × 10⁻³ is −11.83 dBm. However, LE cannot achieve a FEC threshold of at the maximum received power of −10 dBm. As a conclusion, using the DFWM and DFE to mitigate the CD-induced PFE we successfully transmit a 40 Gb/s CAP32 signal over 80 km distance with a received power of −11.83 dBm at the BER threshold of 3.8 × 10⁻³.

Fig. 10 BER versus the received signal power for (a) 40 km, (b) 60 km and (c) 80 km SMF transmissions. LE: linear equalizer; DFE: decision feedback equalizer.

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4. Conclusion

We studied the chromatic dispersion CD-induced PFE in short reach IM-DD CAP systems. DFWM is found to be beneficial to mitigate this effect. The inter-relationship between power fading and DFWM is theoretically studied and verified through simulation. Also, we have experimentally demonstrated a 40 Gbit/s CAP32 transmission over 40 km, 60 km and 80 km SMF fiber links. To recover the distorted signal, both traditional LE and DFE are fully investigated and their robustness with respect to CD-induced PFE is experimentally verified. With optimized launch power, traditional LE can achieve a BER threshold of 3.8 × 10⁻³ for 40km and 60km transmission at received powers of −14.75 dBm and −12.82 dBm, respectively. For DFE, 40 km, 60 km and 80 km transmission can be achieved with received powers of −15.22, −12.82 and −11.83 dBm.

Acknowledgments

The authors would like to acknowledge the support of the Hong Kong Government General Research Fund (GRF) under project number PolyU 152079/14E.

References and links

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40 Gb/s CAP32 short reach transmission over 80 km single mode fiber

Abstract

1. Introduction

2. Operating principle

2.1 Carrier-less amplitude and phase modulation

2.2 Chromatic dispersion induced power fading and degenerate four-wave mixing

3. Experimental results

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (10)

Equations (17)

Optics Express