Investigation and development of a high spectral resolution coherent optical spectrum analysis system

Kunpeng Feng; Jiwen Cui; Hong Dang; Shiyuan Zhao; Weidong Wu; Jiubin Tan

doi:10.1364/OE.24.025389

1. Introduction

High resolution optical spectroscopy has always attracted considerable interest due to its extensive applications in optical test and measurement. In recent years, demands of a higher spectral resolution are significantly increasing. For example, the frequency separation between adjacent sub-carriers in an orthogonal frequency domain multiplexing system may be as small as a few tens of MHz [1] and an optical spectrum analysis (OSA) technique of comparable resolution is thus required to test such signals. Similarly, a spectral resolution on the order of several MHz and wide coverage OSA is an essential instrument in the characterization of physics and biochemistry optical sensors [2, 3], optical sources with fine spectrum structures [4, 5], and passive photonic devices [6].

Traditional dispersion spectroscopy, interferometer spectroscopy techniques [7] cannot simultaneously satisfy requirements of spectral resolution and wavelength coverage. Much work has been done on the topic in development of innovation spectroscopy techniques of a high resolution. For example, coherent optical spectrum analysis (COSA) technique was developed in 2002 using a swept optical local oscillator (LO), an electric filters and a balanced photodetector (BPD) to form equivalent swept narrowband filter. It was demonstrated to significantly improve spectral resolution and wavelength coverage upwards to ~100 nm [8]. On the other hand, narrowband spectral filters achieved by nonlinear optics principle, such as stimulated Brillouin scattering (SBS) and four-wave-mixing (FWM), were employed in high resolution OSA [9–12]. SBS-OSA in the benefit of narrowband Brillouin gain spectrum had a high spectral resolution of 80 fm (10 MHz) [9], and several techniques, such as superposition of three Brillouin lines and vector attributes of stimulated Brillouin scattering amplification in standard, weakly birefringent fibers, were utilized to improve its spectral resolution to 3 MHz [10]. Then Brillouin dynamic grating (BDG) is found in FWM effects and a narrowband grating filter of 2.4 MHz was achieved in a 100 m single-mode fiber (SMF) [11]. Yongkang Dong et al. used a swept laser to build a BDG based tunable filter in a 400 m SMF for optical spectrometry and a remarkable high resolution of 0.5 MHz was achieved [12]. However, spectroscopy techniques based on narrowband spectral filters achieved by nonlinear optics principle should utilize fiber of several hundreds meters or even a few tens kilometers which makes them highly sensitive to environment, such as temperature drifts and vibration. Weak nonlinear optics effects lead a low spectral gain or a weak refractive index modulation and the dynamic range of these techniques is much lower than dispersion spectroscopy and COSA technique [8]. Otherwise, lots of optical modulators for nonlinear optics systems make their configurations very complex. Therefore, COSA technique is most appropriate to realize high spectral resolution in any environments due to its high spectral resolution achieved through photoelectric process.

In this paper, COSA technique is thoroughly investigated by building COSA principle which demonstrates operation of COSA and its signal processing in both time and frequency domain. According to COSA principle, resolution bandwidth (RBW) filters are found to have significant influence on the power accuracy and spectral resolution of the OSA results. Much effort is paid to design RBW filters, including center frequency, bandwidth and types of filters. RBW filters are optimized to reduce the power uncertainty of different spectral resolution and satisfy different signal under test (SUT). Finally, simulations and experiments are conducted to verify COSA principle and its excellent capacity in analysis of fine spectrum structures.

2. Principle of COSA system

A schematic diagram of COSA system is illustrated in Fig. 1 [13]. The P polarized mode and S polarized mode of SUT whose spectrum is ready to be characterized are splitted by polarizing beam splitter (PBS) to respectively perform OSA which is benefit of coherent optics principle of COSA technique. COSA can be utilized to analysis the polarized dependent SUT and test their polarizing performance. To achieve spectrum of SUT, the spectra of S and P polarized mode should be squared and added. The SUT of this paper is polarized independent and only P polarized mode is analyzed using COSA. The P polarized modes of swept LO and SUT are combined in a polarization maintaining fiber (PMF) coupler to generate wideband coherent optical signals.

Fig. 1 Schematic diagram of COSA system.

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An arbitrary spectrum of SUT is made up of monochromatic components [14, 15] and COSA principle can be described as analysis of every monochromatic signals. The principle of COSA system is established in three steps: at first, SUT is simplified into a monochromatic signal; then, SUT is modeled as a double monochromatic signal; finally, SUT is an ensemble of complex monochromatic components.

The monochromatic signal can be expressed as Dirac delta function in optical spectrum domain and the electric field $E_{s} = a_{s} \exp (j ω_{s} t + j φ_{s})$ represents monochromatic SUT having an amplitude $a_{s}$ , an optical angular frequency $ω_{s}$ , and an initial phase $φ_{s}$ . The swept LO sweeps at a linear rate $γ$ and its expression for the electric field is $E_{L O} (t) = a_{L O} \exp (j ω_{L O} t + j π γ t^{2} + j φ_{L O})$ , which represents the swept LO having an amplitude $a_{L O}$ , an initial optical angular frequency $ω_{L O}$ , and an initial phase $φ_{L O}$ . SUT and swept LO are combined in a PMF coupler of a coupling coefficient k and the optical intensity at two individual photodetectors of BPD can be written as [8]:

{\begin{cases} i_{A} = k a_{s}^{2} + (1 - k) a_{L O}^{2} + 2 \sqrt{k (1 - k)} a_{s} a_{L O} \cos [(ω_{s} - ω_{L O}) t + π γ t^{2} + (φ_{s} - φ_{L O})] \\ i_{B} = (1 - k) a_{s}^{2} + k a_{L O}^{2} - 2 \sqrt{k (1 - k)} a_{s} a_{L O} \cos [(ω_{s} - ω_{L O}) t + π γ t^{2} + (φ_{s} - φ_{L O})] \end{cases}

The optical signals are converted into photocurrents and then amplified into voltage signals through I/V converting of a trans-impedance amplifier (TIA). Two individual photodetectors of BPD are well-matched and their responsivity difference can be less than 1‰. The voltage signals are subtracted to extract difference terms:

\begin{array}{l} u = R {\underline{(2 k - 1) (a_{s}^{2} - a_{L O}^{2})} + \underline{4 \sqrt{k (1 - k)} a_{s} a_{L O} \cos [(ω_{s} - ω_{L O}) t + π γ t^{2} + Δ φ]}} \\ DC term AC term \end{array}

where,

R

is the responsivity of two individual photodetectors of BPD and

Δ φ = φ_{s} - φ_{L O}

is the initial phase difference of swept LO and SUT.

Equation (2) indicates that the difference voltage signal only has alternating-current (AC) term when coupling coefficient of PMF coupler is 1:1 or $k = 0.5$ , and the proportionality coefficient of AC term reaches its maximum value. Considering the coupling coefficient is not exactly equal to 0.5 in practice, a direct-current (DC) blocking capacitor C is utilized to decrease the residual DC term. So the AC term in Eq. (2) representing the interaction between swept LO and SUT is achieved and can be processed in following modules. The AC term is normalized by omitting its proportionality coefficient for simplification in the discussion and the normalized AC term can characters the interaction between swept LO and SUT. The normalized AC term can be expressed as:

{\tilde{u}}_{A C} (t) = \cos [(ω_{s} - ω_{L O}) t + π γ t^{2} + Δ φ]

$2 π c / ω_{s} = 1550 nm+0 .5 pm$ , $2 π c / ω_{L O} = 1550 nm$ , $γ = 125 GHz/s (1 nm/s)$ and $Δ φ = 0$ is utilized to run the simulation in a time range from 0 to 0.12 ms. Figure 2(a) shows the curve of normalized AC term ${\tilde{u}}_{A C} (t)$ and it is characterized as a linear-frequency-modulation chirp signal. The ${\tilde{u}}_{A C} (ω)$ in frequency domain is achieved by taking Fourier transform of ${\tilde{u}}_{A C} (t)$ and this yields

Fig. 2 Linear-frequency-modulation chirp signal represents the interaction between swept LO and SUT: (a) in time domain and (b) in frequency domain.

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{\tilde{u}}_{A C} (ω) = \frac{1}{\sqrt{2 π γ}} \cos (\frac{ω^{2}}{4 π γ} + \frac{{(ω_{o} - ω_{s})}^{2}}{4 π γ} - \frac{π}{4})

Equation (4) and Fig. 2(b) indicates the form of AC term is Fourier transform invariant which remains the same form in both time and frequency domains. Therefore, the analysis in either time or frequency domain reveals the same signal characteristics. On the other hand, the AC term is a linear-frequency-modulation chirp signal and RBW filter $H (ω)$ in frequency domain can be transformed into a filter envelop function $H (t / γ)$ in time domain when $Δ ω^{2} / 4 π γ > > 1$ wherein $Δ ω$ is the bandwidth of RBW filter, that means the bandwidth of RBW filter is wide enough to contain a few ten periods of chirp signal. The convolution in time domain is thus simplified as below:

y (t) = F^{- 1} [Y (ω)] = {\tilde{u}}_{A C} (t) * h (t) = {\tilde{u}}_{A C} (t) \cdot H (t / γ)

where,

h (t)

is Fourier transform of RBW filter

H (ω)

,

Y (ω) = {\tilde{u}}_{A C} (ω) \cdot H (ω)

and

y (t)

are the output of RBW filter in frequency and time domain, respectively.

A Gauss filter with a center frequency of 3 MHz and a bandwidth of 1 MHz is for example employed as RBW filter and the output of RBW filter in frequency and time domain are illustrated in Figs. 3(a) and 3(b). Then, a RMS power detector which can convert the AC signal into a DC signal representing its instantaneous RMS power $\sqrt{\frac{1}{T} \int_{0}^{T} y^{2} (t) d t}$ is utilized to process the signal filtered by RBW filter and extract its envelop, where T is the integral time of the RMS power detector. T has significant influence on the smooth of the RMS power or envelop. When $T = f_{h}^{- 1}, 5 f_{h}^{- 1}, 10 f_{h}^{- 1}, 15 f_{h}^{- 1}, 50 f_{h}^{- 1}$ , the extracted envelop is shown in Fig. 3(c) where $f_{h}$ is the highest pass frequency of RBW filter. It indicates that the RMS envelop function $S (t)$ in time domain has significant fluctuation when the integral time $T < 10 f_{h}^{- 1}$ ; however, a long integral time $T = 50 f_{h}^{- 1}$ distorts and broadens the shape of envelop; therefore, integral time $T = 10 ~ 15 f_{h}^{- 1}$ is appropriate and a smooth and distortionless envelop can be achieved.

Fig. 3 Signal process procedures of the AC term in Eq. (2) representing the interaction between swept LO and SUT: (a) signal process of a Gauss RBW filter in frequency domain domain, (b) signal process of a Gauss RBW filter in time domain and (c) envelop extraction by a RMS power detector with different integral time.

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The envelop function in time domain is further filtered by video bandwidth (VBW) filter to suppress the noise whose frequency is higher than the spectrum to be scoped. Finally, the OPSD $P_{S U T}$ of SUT is proportional to the integration of the square of RMS envelop function $S (t)$ . Basing Parseval’s theorem, the OPSD $P_{S U T}$ of SUT can be also written in a form of frequency domain as:

P_{S U T} = \frac{1}{2 π} {\int_{- \infty}^{+ \infty} | {\tilde{u}}_{A C} (ω) |}^{2} {| H (ω) |}^{2} d ω = \int_{0}^{t} S^{2} (t) d t

Figures 4(a) and 4(b) explicitly show the phase difference $Δ φ$ changes power of the frequency-domain chirp signal within the passband of the RBW filter. And Eq. (6) indicates that the OPSD $P_{S U T}$ has dependence on the relative phase between swept LO and SUT. The ratio of maximum OPSD error to minimum OPSD by varying the phase oscillating component of integrand kernel function represents the power uncertainty of SUT:

Fig. 4 The dependence the OPSD $P_{S U T}$ on the relative phase between swept LO and SUT: (a) lowpass RBW filter, (b) bandpass RBW filter and (c) relationship between the power uncertainty and the parameters of RBW filter.

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e_{P_{S U T}} = \frac{\max P_{S U T} (Δ φ) - \min P_{S U T} (Δ φ)}{\min P_{S U T} (Δ φ)}

Figure 4(c) shows the relationship between the power uncertainty and parameters of RBW filter. The amplitudes of low frequency components are more easily influenced by the phase difference $Δ φ$ and lowpass RBW filter is not adopted in COSA system. The DC blocking capacitor of BPD also prevents the DC term enter RBW filter and following processing modules. In conclusion, a high center frequency RBW filter helps reduce power fluctuation.

Next, SUT is modeled as $E_{s} = a_{s 1} \exp (j ω_{s 1} t + j φ_{s 1}) + a_{s 2} \exp (j ω_{s 2} t + j φ_{s 2})$ , a sum of double monochromatic signals. The process in time domain of a double monochromatic signal can be analyzed using Eqs. (1)-(3), (5) and (6), as

{\tilde{u}}_{A C} (t) = \cos [(ω_{s 1} - ω_{L O}) t + π γ t^{2} + Δ φ_{1}] + \cos [(ω_{s 1} - ω_{L O}) t + π γ t^{2} + Δ φ_{1}]

Simulation is run when the optical frequency difference of two equal monochromatic signals is 10 MHz, bandwidth $Δ f$ of the Gauss RBW is 1 MHz and its center frequency $f_{0}$ varies from 2 MHz to 4 MHz. Simulation results in Fig. 5 shows that a sufficiently high center frequency leads overlapping between double monochromatic signals. So center frequency of RBW filter limits the spectral resolution and the spectral resolution can be simply estimated as $2 f_{0} + Δ f$ . Considering the power uncertainty results of Fig. 4(c), a highest spectral resolution of 5 MHz with an acceptable low power uncertainty of monochromatic SUT can be achieved with $f_{0} = 2 MHz$ and $Δ f = 1 MHz$ .

Fig. 5 Envelop extracted by RMS power detector of SUT modeled as a double monochromatic signal varying with different center frequency f₀ of RBW filter.

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The power uncertainty of SUT modeled as a double monochromatic signal is calculated in the same way as monochromatic SUT. Basing on Eqs. (1)-(4), the normalized AC term ${\tilde{u}}_{A C} (t)$ in frequency domain can be written as:

{\tilde{u}}_{A C} (ω) = \frac{1}{\sqrt{2 π γ}} {\begin{cases} {\tilde{a}}_{s 1} \exp (- j \frac{ω Δ ω}{2 π γ}) \cos (\frac{ω^{2}}{4 π γ} + \frac{{(ω_{o} - {\bar{ω}}_{s})}^{2}}{4 π γ} + Δ φ_{1}) \\ + {\tilde{a}}_{s 2} \exp (j \frac{ω Δ ω}{2 π γ}) \cos (\frac{ω^{2}}{4 π γ} + \frac{{(ω_{o} - {\bar{ω}}_{s})}^{2}}{4 π γ} + Δ φ_{2}) \end{cases}}

where,

{\bar{ω}}_{s} = (ω_{s 1} + ω_{s 2}) / 2

,

Δ ω = (ω_{s 1} - ω_{s 2}) / 2

,

Δ φ_{1}

and

Δ φ_{2}

represents phase shifts,

{\tilde{a}}_{s 1} = a_{s 1} / a_{0}

and

{\tilde{a}}_{s 2} = a_{s 2} / a_{0}

are normalized amplitudes of a double monochromatic signal.

The integrand kernel function ${| {\tilde{u}}_{A C} (ω) |}^{2} {| H (ω) |}^{2}$ in Eq. (6) representing the phase oscillating component is calculated and expressed as:

{| {\tilde{u}}_{A C} (ω) |}^{2} {| H (ω) |}^{2} = \frac{1}{2 π γ} {| H (ω) |}^{2} [\begin{array}{l} {\tilde{a}}_{s 1}^{2} \sin (\frac{ω^{2}}{2 π γ} + θ_{11}) + {\tilde{a}}_{s 1} {\tilde{a}}_{s 2} \sin (\frac{{(ω - Δ ω)}^{2}}{2 π γ} + θ_{12}) \\ + {\tilde{a}}_{s 1} {\tilde{a}}_{s 2} \sin (\frac{{(ω + Δ ω)}^{2}}{2 π γ} + θ_{21}) + {\tilde{a}}_{s 2}^{2} \sin (\frac{ω^{2}}{2 π γ} + θ_{22}) \end{array}]

where,

θ_{i j}

represents phase difference.

The power uncertainty of double monochromatic SUT can be evaluated by varying the phase differences and with the help of Eqs. (6), (7) and (10). Equation (10) has four terms representing interaction among different spectral components and LO: the first and the last terms are identical to single monochromatic signal as analyzed in Fig. 4(b) and lead to power error described as Eq. (7); the second and the third terms have a frequency shift equal to $Δ ω / 2 π$ which makes the slowly varying part of the chirp signal shown in Fig. 4(a) enter the passband of the bandpass RBW filter when $| Δ ω / 2 π - f_{0} | < Δ f$ . This part similar to DC term suppressed by the DC blocking capacitor and bandpass RBW filter for single monochromatic signal reappears under the condition of double monochromatic SUT with a limited frequency interval. So the power uncertainty is dependent on frequency difference of SUT.

Finally, the form of SUT becomes more complex and an ensemble of variable normalized amplitude ${\tilde{a}}_{s i}$ monochromatic signals. ${\tilde{a}}_{s i}$ represents the OPSD of the optical angular frequency $ω_{s i}$ . The normalized spectrum of SUT is $S (ω_{s i}) = {\tilde{a}}_{s i}^{2} (ω_{s i}) = {[a_{s} (ω_{s i}) / a_{L O}]}^{2}$ . Similar to a double monochromatic signal, the AC term in time domain representing the interaction between swept LO and the ensemble of monochromatic signals can be expressed as:

{\tilde{u}}_{A C} (t) = \int_{- \infty}^{+ \infty} {\tilde{a}}_{s i} (ω_{s i}) \cos [(ω_{s i} - ω_{L O}) t + π γ t^{2} + Δ φ_{i}] d ω_{s i}

Consequently, RBW filter can process the AC term and extract the spectrum $S (ω_{s i})$ of SUT as the way of the double monochromatic signal, however, there is no standalone envelop of single monochromatic signal as indicated by Eq. (5). The OPSD is directly achieved without integration of time-domain envelop as a result of ${\tilde{u}}_{A C} (t)$ in an integral form.

Considering the power uncertainty, the integrand kernel function of ${| {\tilde{u}}_{A C} (ω) |}^{2}$ consists of several terms representing interaction among different spectral components and LO. Similar to Eq. (10), the integrand kernel function term with variable phase difference can be written as:

{| {\tilde{u}}_{A C} (ω, θ_{i j}) |}_{i j}^{2} {| H (ω) |}^{2} = \frac{1}{2 π γ} {\tilde{a}}_{s i} {\tilde{a}}_{s j} \sin (\frac{{[ω + (ω_{s i} - ω_{s j}) / 2]}^{2}}{2 π γ} + θ_{i j}) {| H (ω) |}^{2}

Basing on Eq. (6), the power of complex monochromatic SUT is achieved by spectral integration:

P_{S U T} = \frac{1}{2 π} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} {| {\tilde{u}}_{A C} (ω, θ_{i j}) |}_{i j}^{2} {| H (ω) |}^{2} d ω_{s i} d ω_{s j}

A numerical simulation modified by Monte Carlo method through varying the phase difference and utilizing Eqs. (6), (7) and (13), is run to achieve the power uncertainty of complex monochromatic SUT. However, the power uncertainty of a complex monochromatic SUT with a Gaussian OPSD and using a Gauss RBW filter has a simple and analytical form as [13, 16]:

e_{P_{S U T}} = \frac{\sqrt{γ}}{\sqrt{π \cdot Δ f}} \frac{1}{\sqrt[4]{Δ f^{2} + Δ F^{2}}} \exp (- \frac{2 f_{0}^{2}}{Δ f^{2} + Δ F^{2}})

where,

Δ F

is the bandwidth of SUT’s Gaussian OPSD,

Δ f

and

f_{0}

is the bandwidth and center frequency of a Gauss RBW filter.

Basing on Eq. (14), the relationship between the power uncertainty and the linewidth of SUT is illustrated in Fig. 6. It indicates that a RBW filter with a higher center frequency and a wider bandwidth of RBW filter with a high enough center frequency could reduce the power uncertainty of a wide linewidth of SUT. Therefore, a high center frequency and wide bandwidth of RBW filter is utilized to perform COSA of wide linewidth SUT. Meanwhile simultaneous decrease of spectral resolution has no influence on OSA results of wide linewidth SUT lack of fine spectrum structures. The power uncertainty decreases rapidly with the center frequency $f_{0}$ of RBW filter increasing from 2 MHz to 7.5 MHz, but the changes lower down when the center frequency is higher than 7.5 MHz. On the other hand, the power uncertainty is further reduced through broadening the passband $Δ f$ when $f_{0}$ is sufficiently high. So, two 10th-order Butterworth filters of $f_{0} = 7.5 MHz$ , $Δ f = 10 MHz$ and $f_{0} = 10 MHz$ , $Δ f = 10 MHz$ are chosen as candidate RBW filters. Considering the spectral resolution, a 10th-order Butterworth RBW filter of 7.5 MHz center frequency and 10 MHz bandwidth is finally utilized for 0.2 pm (~25 MHz) medium spectral resolution COSA system.

Fig. 6 Relationship between the power uncertainty of OSA and the linewidth of SUT.

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The principle of COSA is established by analyzing the coherent between swept LO and SUT consisting of single or complex monochromatic signals. A COSA system is proposed to process optoelectronic signals and measure OPSD of SUT. Then, the phase diversity is found to influence the power uncertainty of COSA and the power error is calculated in frequency domain basing on Parseval’s theorem. Considering the power uncertainty and spectral resolution, two RBW filters are designed for high and medium spectral resolution application.

3. Experiment and results

3.1 Experimental setup

The experimental setup of COSA system is as same as the schematic diagram illustrated in Fig. 1. The swept LO is an external cavity tunable laser with a linewidth of 100 kHz. The all-fiber PBS and PMF coupler are made by AFR Company and the working axes are aligned to slow axes of PMF. A switchable gain and bandwidth PDB is Thorlabs PDB450C with coverage of 800-1700 nm. An AC form of PDB450C is utilized and it has a common mode rejection ratio of over 30 dB. The power detector is made by AD8361 which is used for true power measurement and has a working bandwidth up to 2.5 GHz with a good linear response. The integral time of AD8361 can be customized. RBW filters are designed using software named FilterPro and the circuits are built by AD4817 with a high gain bandwidth product of 1 GHz which can ensure that the actual transfer function is as least distortionless as possible. VBW filters are also designed using FilterPro and their circuits are built by OP37 with a medium gain bandwidth product of 63 MHz. The analog signals are digitalized by PCI-1714 made by ADVANTECH with a maximum sampling rate of 10 MHz. Software for acquiring and processing data from PCI-1714, and displaying SUT’s spectrum is embedded on computer.

The wavelength accuracy is guaranteed by a real-time wavelength calibration system consisting of a HCN gas cell and a FP etalon of a 1 pm free spectral range. The interval of calibration wavelength points can be downwards to 1 pm. So the wavelength of optical spectrum analysis system and tunable laser can be connected through this real-time wavelength calibration system and wavelength accuracy can reach 0.5 pm.

3.2 Simulation and verification of COSA principle

Simulation and experimental verification of different RBW filters are conducted. The influence of RBW filter type on the power uncertainty is investigated. The engineering realizable Gauss, Butterworth, Chebyshev filter is chosen as RBW filter but the Bessel filter is not considered because of its worst amplitude-frequency characteristics.

The absolute value of the transfer function of Gauss filter can be expressed as:

H (ω) = \exp (- \ln \sqrt{2} \cdot \frac{{(ω - ω_{0})}^{2}}{{(Δ ω / 2)}^{2}})

where,

ω_{0}

is the center angular frequency and

Δ ω

is the 3 dB bandwidth of Gauss filter.

The absolute value of the transfer function of Butterworth filter can be expressed as:

H (ω) = \frac{1}{\sqrt{1 + {(\frac{ω - ω_{0}}{Δ ω / 2})}^{2 n}}}

where,

n

is the order of Butterworth filter.

The absolute value of the transfer function of Chebyshev filter can be expressed as:

H (ω) = \frac{1}{\sqrt{1 + ξ^{2} T_{n}^{2} (\frac{ω - ω_{0}}{Δ ω})}}

where,

ξ

is the ripple factor,

T_{n}

is the n^th order Chebyshev polynomial.

When SUT is a fiber laser of 1 KHz linewidth and the center frequency of RBW filter is 2 MHz, the power uncertainties of RBW filters of Gauss, Butterworth and Chebyshev filter with different bandwidth are achieved using both simulation and experiment approach. The order of filters are higher, the actual transfer function is more close to that of design. Considering the physical realizability, the order of both Butterworth and Chebyshev filter is chosen to be 10th-order. Figure 7(a) shows the absolute value of the transfer function of three filters. The wavelength of the fiber laser as SUT is 1550 nm and the swept LO sweeps in the range of 1550 ± 0.25 nm. These configurations are used to run the simulation and conduct experiments. The swept LO sweeps 30 times and its spectrum is analyzed by COSA system. The maximum and minimum spectrum power is achieved and the power uncertainty is calculated using Eq. (7). Figures 7(b)-7(d) indicates that simulation results are consistent with the experimental data and the errors may come from the noise and drift of circuits. The error between simulation and experiment of 10th-order Chebyshev RBW filter is larger than the other filters which may be caused by ripples in its passband. Experimental results verify that 10th-order Butterworth RBW filter has a minimum power uncertainty.

Fig. 7 Absolute value of the transfer functions of RBW filters and the power uncertainties of both simulation and experimental results by varying the filter type and bandwidth: (a) absolute value of the transfer function of three filters, (b) power uncertainty of Gauss filter, (c) power uncertainty of Butterworth filter and (d) power uncertainty of Chebyshev filter.

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The spectral resolution is also dependent on the type of RBW filter. SUT modeled as a double monochromatic signal with a frequency difference of 5.5 MHz. Three types of RBW filter have a same center frequency of 2 MHz and bandwidth of 1 MHz. Figure 8 shows the time domain envelops of three RBW filters. It indicate that Gauss filter has a largest overlapping between a double monochromatic signal which leads to a worst spectral resolution and Chebyshev filter has a biggest ripples in the passband which influencs the power uncertainty. Therefore, 10th-order Butterworth filter is appropriately utilized as RBW in COSA system.

Fig. 8 Time domain envelops of a double monochromatic SUT by three RBW filters.

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Basing on the analysis of power uncertainty, the swept velocity of the swept LO determines the period number of chirp signal within passband of RBW filter which influences the power uncertainty. Figure 9(a) shows the relationship between swept velocity and the power uncertainty of monochromatic SUT. It shows that the power uncertainty increases with the swept velocity and also means that the condition $Δ ω^{2} / 4 π γ > > 1$ is close to its limit. In both simulation and experiment, a 10th-order Butterworth filter having a center frequency of 2 MHz and bandwidth of 1 MHz is employed as RBW filter and their results agree with each other.

Fig. 9 Power uncertainty of both simulation and experimental results by varying the swept velocity and linewidth of SUT: (a) relationship between the power uncertainty swept velocity of swept LO and (b) relationship between the power uncertainty SUT’s linewidth.

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Next, the influence of SUT’s linewidth on the power uncertainty is verified. SUT of 1 KHz, 500 KHz, 2 MHz and 10 MHz and a swept fiber laser as LO of 1 KHz is utilized to conduct experiment and run simulation. A 10th-order Butterworth filter of 2 MHz center frequency of and 1 MHz bandwidth is employed as RBW filter. Their results are illustrated in Fig. 9(b) and have a similar trend but the error rapidly increases with SUT’s linewidth. It may be caused by the phase noise and intensity noise of SUT of a wide linewidth.

3.3 OSA of fine spectrum structures

The proposed COSA system is utilized to analyze fine spectrum structures and verify its excellent capacity in analysis of fine spectrum structures. Both narrow laser source and wide amplified spontaneous emission (ASE) source are measured and the results are compared with results by Anritsu OSAer of 30 pm spectral resolution.

A fiber laser of 1 KHz linewidth is employed as a narrow laser source and its intensity modulation signal is analyzed. According to Jacobi-Anger identity, the fiber laser modulated by LiNbO₃ intensity modulator has several peaks and their frequency interval is equal to the modulation frequency. The modulation signal is configured to achieve maximum 1st order peaks and zero 2nd order peaks. A 10th-order Butterworth filter of 2 MHz center frequency of and 1 MHz bandwidth is as RBW filter and a 25 KHz lowpass filter is as VBW filter of COSA system. Results of COSA is illustrated in Fig. 10 and it indicates that a modulation signal of 6 MHz frequency interval (~48 fm in 1550 nm wavelength range) can be distinguished.

Fig. 10 Analysis of intensity modulation signal of narrow laser source: (a) 6 MHz modulation frequency and (b) 9 MHz modulation frequency.

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Nest, ASE spectrum of phase-shift fiber Bragg grating (PS-FBG) is measured. Spectrum of PS-FBG is comparatively wide and the bandwidth can reach ~0.3 nm, however, it has a very narrow notch of ~1 pm in its reflectance spectrum. A 10th-order Butterworth filter of 7.5 MHz center frequency of and 10 MHz bandwidth is as RBW filter and a 5 KHz lowpass filter is as VBW filter of COSA system. Theoretical spectral resolution is 25 MHz (~0.2 pm in 1550 nm wavelength range). The resolution of Anritsu OSAer is 30 pm and bandwidth of VBW filter is 1 KHz. Figure 11 shows the reflectance spectrum and spectral notch structure of PS-FBG measured by both Anritsu OSAer and COSA system. It indicates that reflectance spectrum profiles are same but the result by COSA system has some ripples. It is probably caused by the intensity noise of ASE source and its VBW filter is wider than Anritsu OSAer. However, the spectral notch structures of PS-FBG measured are much different. COSA system gives a much narrow spectral notch which has more spectrum fine information and it is much close to the real spectrum. But the result by Anritsu OSAer only provides a ~32 pm bandwidth notch which is the actual spectral resolution of this OSAer and fine information within the narrow notch is lost.

Fig. 11 Analysis of reflectance spectrum of PS-FBG: (a) result by Anritsu OSAer, (b) fine spectral structure by Anritsu OSAer, (c) result by proposed COSA system and (d) fine spectral structure by proposed COSA system.

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In this section, experimental setup of COSA system is demonstrated. Then RBW filter, the most important module of COSA system, is investigated through simulations and experiments. Considering the power uncertainty and spectral resolution, two 10th-Butterworth filters are chosen to be RBW filters for high and medium spectral resolution COSA system. Finally, the proposed COSA system is utilized to perform OSA and its excellent capacity in analysis of fine spectrum structures is verified through both principle research and experiment.

4. Conclusion

The principle of COSA technique is investigated in detail by building a COSA model which establishes its signal processing in both time and frequency domain. An optoelectronic COSA system is proposed on the foundation of COSA principle and SUT is assumed as a monochromatic signal, a double monochromatic signal and an ensemble of complex monochromatic components to demonstrate the operation of COSA system. Subsequently, RBW filters are found to have significant influence on the power accuracy due to phase diversity and spectral resolution, the two key parameters of COSA. Much effort is paid to design RBW filters, including center frequency, bandwidth and type of filters. Considering power uncertainty, a bandpass RBW filter can reduce the power uncertainty and its passband should be far away from DC, however, the demand spectral resolution limits its center frequency. Simultaneously, the type of filter also has influence on the power uncertainty and spectral resolution. To optimize these two key parameters, a filter of 2 MHz center frequency of and 1 MHz bandwidth (40 fm theoretical spectral resolution) and a filter of 7.5 MHz center frequency of and 10 MHz bandwidth (0.2 pm theoretical spectral resolution) is employed as RBW for high and medium spectral resolution application, respectively. Then, both simulations and experiments are conducted to verify COSA principle. Results show that a 10th-order Chebyshev RBW filter has a minimum spectrum overlapping which is better than Gauss and 10th-order Butterworth RBW filter; however, a 10th-order Butterworth RBW filter has a lowest power uncertainty. 10th-order Butterworth filters are selected to be RBW filter and the power uncertainty of high and medium spectral resolution application is less than 0.5% and 1.2%. Finally, experiments on the OSA of actual spectra using the proposed COSA system are conducted. Experimental results indicate that COSA system can analyze modulation signal of 6 MHz spectral interval and its result of PS-FBG reflectance spectrum has more spectrum fine information than that by a commercial Anritsu OSAer.

It can be concluded that COSA system has an excellent capacity in analysis of fine spectrum structures and has a low power uncertainty. These properties lead to its widely application in the fields of optical communication, physics and biochemistry optical sensors and test of passive photonic devices.

Acknowledgment

Thanks are given to National Natural Science Foundation of China (51575140) for the financial support and Xuelin Jiang for her useful suggestions and experimental assistances.

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Investigation and development of a high spectral resolution coherent optical spectrum analysis system

Abstract

1. Introduction

2. Principle of COSA system

3. Experiment and results

3.1 Experimental setup

3.2 Simulation and verification of COSA principle

3.3 OSA of fine spectrum structures

4. Conclusion

Acknowledgment

References and links

Cited By

Figures (11)

Equations (17)

Optics Express