A DFB-SOA Based Optical Vector Network Analyzer for Characterization of Bandpass Optical Devices

Abstract

In this paper a novel optical vector network analyzer (OVNA) utilizing a distributed feedback semiconductor optical amplifier (DFB-SOA) is introduced. The proposed OVNA is implemented by converting the transmission response of the optical device under test (ODUT) into the electrical domain. The main principle of the OVNA is predicated on the optical carrier restoration facilitated by the wavelength-selective amplification attribute of the DFB-SOA. The implemented OVNA effectively determined the transmission spectrum of an optical filter possessing a passband of 9-GHz bandwidth, achieving a commendable resolution of 25 MHz in the measurement process. The dynamic range of the OVNA can be broadened by adjust the driven current under the DFB-SOA. Additionally, the detection range of our system can be expanded through the utilization of broadband optoelectronic devices. Furthermore, the OVNA possesses considerable potential for integration onto a single chip.

1. Introduction

Optical Vector Network Analyzers (OVNAs) are indispensable tools for the precise measurement and comprehensive characterization of optical devices. Utilizing an OVNA, we can acquire both phase and magnitude responses, which facilitate the design and enhancement of optical links. Traditional OVNAs are fundamentally implemented through the use of interferometers or modulation-based phase shifts [1,2,3]. Nevertheless, the inherent lack of stability and the comparatively coarse tuning resolution of the wavelength-scanning laser constraints the precision of measurements to an extent that it falls short of the requirements for comprehensive spectrum characterization of high-Q optical components [4,5,6,7]. To address the issue at hand, researchers have introduced an OVNA that utilizes optical single sideband (OSSB) modulation. This technique effectively converts the transmission spectrum of the ODUT from the optical domain to the electrical domain, as detailed in references [8,9,10,11,12,13,14,15]. Correlated with the benefits of the extraordinary high-frequency tuning capabilities of the electrical vector network analyzer (EVNA), the OVNA utilizing OSSB modulation can attain measurement resolutions in the range of several kHz or even less. Typically, to quantify the transmission response of an ODUT, it is essential that the optical carrier possesses a robust energy level capable of beating with the sidebands, which encapsulate the alterations inherent to the ODUT’s transmission response. Nevertheless, the OVNA employing OSSB modulation is ill-suited for bandpass optical components, as the optical carrier frequency migrates beyond the transmission bandwidth of the ODUT, resulting in substantial attenuation. In order to achieve spectral characterization of ODUTs featuring bandpass responses, several methods have been proposed recently. An OVNA capable of quantifying both passband and stopband characteristics is presented [16]. The optical carrier is preserved and unaltered, while the sideband is separately allocated to delineate the passband of the ODUT, through the bifurcation of the carrier and sideband onto two distinct channels. Due to the differential phase shifts experienced by the carrier and sidebands across channels, this OVNA exhibits heightened sensitivity to environmental fluctuations. Consequently, the acquisition of reliable phase response using this approach is challenging. An OVNA design that enhances measurement precision for bandpass response evaluation is established, as referenced in [17]. By employing four distinct measurement stages, an enhanced resolution and a minimized error in the measurements are achieved. Nonetheless, the incorporated Brillouin-assisted optical carrier processor results in the OVNA being both exorbitantly priced and intricate.

In our previous work, we introduced an OVNA that employs a distributed-feedback semiconductor optical amplifier (DFB-SOA) [18]. The DFB-SOA is a DFB laser operating below the lasing threshold, which could exhibit dual functionality as both an optical filter and an optical amplifier concurrently [19,20]. The optical-to-electrical conversion of the ODUT’s spectrum is effectuated through the implementation of our proposed OVNA. Initially, the optical carrier undergoes modulation via an EVNA utilizing a phase modulator prior to its injection into the ODUT. Subsequently, the lower sideband traverses the optical spectrum that is intended for measurement in the ODUT, concurrent with a marked reduction in the optical carrier and the accompanying undesired sidebands. In the DFB-SOA, the primary optical carrier experiences significant amplification, whereas no appreciable gain is observed for the sidebands. Eventually, the optical carrier with enhanced power beats with the scanning sideband within the photodetector, resulting in the generation of a microwave signal. This signal coherently transports the transmission response of the ODUT, which is subsequently received and spectrally characterized by an EVNA. By utilizing a cascaded DFB-SOA with an ODUT, our proposed OVNA maintains the optical carrier, enabling the measurement of optical components with bandpass response characteristics. In this paper, the operating principle of the proposed DFB-SOA based OVNA is mathematically analyzed in detail. The experimental validation of our proposed OVNA is established through spectral analysis of an optical bandpass filter. The experimental results indicate that the proposed DFB-SOA based OVNA is capable of accurately assessing the ODUT utilizing a bandpass response, achieving a superior measurement resolution of 25 MHz. The dynamic range of the proposed system in relation to the driven current of the DFB-SOA is also investigated. Additionally, the detection range of our system can be expanded through the utilization of broadband optoelectronic devices. Furthermore, the OVNA we have introduced is highly suitable for integration into a microchip platform.

2. Operating Principle

The schematic of the proposed DFB-SOA based OVNA is presented in Figure 1 and Figure 2. An optical carrier, produced via a tunable laser source (TLS), is transmitted to a phase modulator (PM). An electrical signal, produced by an EVNA through frequency scanning, is introduced into the PM. Subsequently, the phase modulated signal output from the PM is then directed to an ODUT with a bandpass filter response. The optical carrier power and the upper sideband power are significantly attenuated outside the passband of the ODUT. The sideband situated at a lower frequency will remain unaffected, as it resides within the frequency range designated for passage. Subsequently, the lower sideband linked to the diminished optical carrier is directed to the DFB-SOA. The DFB-SOA functions as an active optical filter characterized by a tightly confined passband, thereby selectively amplifying a specific wavelength. The optical carrier, aligned with the gain peak of the DFB-SOA, undergoes amplification solely for its power, while the lower sideband remains unaltered. Following the modulation of the optical carrier and the associated sidebands within the photodetector during the photoelectric conversion process, a microwave signal is generated and subsequently routed back to the EVNA for comprehensive transmission spectrum evaluation. In the experimental setup, the microwave signal output is contingent on the lower sideband’s traversal across the ODUT’s passband. Consequently, the ODUT’s transmission spectrum, featuring a bandpass response, is measured via electrical domain analysis. It is worth noting that, the passband of the ODUT should be outside of the gain peak of the DFB-SOA and the wavelength difference between the passband of the ODUT and the gain peak of DFB-SOA should be within the bandwidth of the employed optoelectronic devices and the EVNA.

The key device of the OVNA we have proposed is the DFB-SOA. Refer to Figure 3 for the diagram of the DFB-SOA, observing it reveals the placement of two identical fiber Bragg gratings (FBGs) side by side, each with a π-phase-shift in the center, encircling the DFB-SOA’s active layer. Both ends of this phase-shifted structure feature anti-reflection (AR) coatings, allowing the input light signal to traverse the component unimpeded. An additional current is directed through this phase-shifted DFB-SOA, enabling the manipulation of the active layer’s gain.

The π-phase-shifted fiber Bragg grating is segmented into three grating segments, which may be viewed as a cascade of two equivalent cavities with coupling effects among them. By employing the coupled-mode equations and the transfer-matrix approach [21], the amplitude response of the π-phase-shifted FBG may be represented as

$$\left[\begin{array}{l}{A}_f\left(0\right)\\ A_b\left(0\right)\end{array}\right]=\left[\begin{array}{l}{F}_{11}^1\hspace{1em}{F}_{12}^1\\ F_{21}^1\hspace{1em}{F}_{22}^1\end{array}\right]\cdot \left[\begin{array}{cc}\exp \left(j\pi /2\right)& 0\\ 0& \exp \left(-j\pi /2\right)\end{array}\right]\cdot \left[\begin{array}{l}{F}_{12}^2\hspace{1em}{F}_{12}^2\\ F_{21}^2\hspace{1em}{F}_{22}^2\end{array}\right]\cdot \left[\begin{array}{l}{A}_f\left(L\right)\\ A_b\left(L\right)\end{array}\right]$$

(1)

where $A_f\left(z\right)$ and $A_b\left(z\right)$ are the amplitude of the optical signal propagating forward and backward along the grating fiber, $L$ is the length of the π-phase-shifted FBG. The $2 \times 2$ matrix $F^i$ represents the amplitude response related to the $i$th grating section. Its elements are given by

$$F_{11}^i={\left(F_{22}^i\right)}^{\ast }=\cosh \left(\gamma L_i\right)-j\left(\sigma /\gamma \right)\sinh \left(\gamma L_i\right)$$

(2)

$$F_{12}^i={\left(F_{21}^i\right)}^{\ast }=-j\left(\kappa /\gamma \right)\sinh \left(\gamma L_i\right)$$

(3)

where $\ast$ denotes complex conjugation, $L_i$ is the length of $i$th grating section, $\gamma =\sqrt{k^2-{\sigma }^2}$, $\kappa$ represents the “ac” coupling coefficient and $\sigma$ represents the general “dc” self-coupling coefficient which is defined by

$$\sigma =n_{eff}\frac{\omega }{c}-\frac{\pi }{\Lambda }-\frac{g}{2}\alpha -j\frac{g-{\alpha }_{\mathrm{int}}}{2}$$

(4)

where $n_{eff}$ is the effective mode refractive index, $c$ is the speed of light in a vacuum, $\Lambda$ is the grating period, $\alpha$ symbolizes the linewidth enhancement factor of active layer. The coefficient of power gain under unsaturated conditions is denoted as $g=\Gamma a{N}_0(I/I_0-1)$. $\Gamma$ denotes the confinement factor, $a$ represents the differential gain, $N_0$ is the carrier density at transmission, $I_0$ signifies the current required to reach transparency, and ${\alpha }_{\mathrm{int}}$ corresponds to the internal loss coefficient.

The gain spectrum of the DFB-SOA can be expressed as

$$G(\omega )=1{\displaystyle /}\left\{j\frac{k^2}{{\gamma }^2}{\sinh }^2(\gamma l)-j{\left[\cosh (\gamma l)-j{\displaystyle \frac{\sigma }{\gamma }}\sinh (\gamma l)\right]}^2\right\}$$

(5)

Certainly, Equations (4) and (5) shows that the gain spectrum of the DFB-SOA is determined by the injected current. The manipulation of the resonant wavelength and power gain can be achieved through the precise regulation of the injected current.

Mathematically, the optical field of the optical signal output from the PM can be described as

$$E_{PM}(t)=A\exp [j{\omega }_{c}t+j\beta \sin ({\omega }_{m}t)]$$

(6)

The amplitude of the optical carrier from the TLS is denoted as $A$. Let angular frequency ${\omega }_c$ represents the optical carrier, and assign ${\omega }_m$ for the microwave signal’s angular frequency. The first kind Bessel functions of the $n$th order are represented by $J_n(\cdot )$ while the phase modulation index of the PM is denoted by $\beta$.

The Fourier transform is utilized to manipulate Equation (6). The optical signal output from the phase modulator in the frequency domain can be expressed as

$$E_{PM}(\omega )=2\pi A{\displaystyle \sum _{n=-\infty }^{\infty }{J}_n(\beta )\delta [\omega -({\omega }_c+n{\omega }_m)]}$$

(7)

Subsequently, the phase-modulated signal is transmitted to the ODUT. It is postulated that the ODUT transmission response is characterized by $H(\omega )$ with a unitary passband centered at ${\omega }_c-{\omega }_m$, effectively attenuating the optical carrier and any unwanted sidebands. The phase-modulated signal is transmitted to the ODUT. Consequently, the lower sideband at ${\omega }_c-{\omega }_m$ is able to transmit through the ODUT with minimal obstruction. Disregarding the negligible undesired sidebands of minimal intensity, the optical carrier-suppressed single-sideband (CS-SSB) signal emanating from the ODUT can be represented as

$$E_{ODUT}(\omega )=2\pi A{J}_0(\beta )H({\omega }_c)\delta (\omega -{\omega }_c)+2\pi A{J}_{-1}(\beta )H({\omega }_c-{\omega }_m)\delta \left[\omega -({\omega }_c-{\omega }_m)\right]$$

(8)

The CS-SSB signal is subsequently injected into the DFB-SOA. Given that the gain peak is located at ${\omega }_c$, The emitted optical signal from the DFB-SOA solely comprises the regenerated optical carrier and the scanning lower sideband. Thus, the equation presented in Equation (8) can be rewritten as

$$E_{out}(\omega )=2\pi A{J}_0(\beta )G({\omega }_c)H({\omega }_c)\delta (\omega -{\omega }_c)+2\pi A{J}_{-1}(\beta )H({\omega }_c-{\omega }_m)\delta \left[\omega -({\omega }_c-{\omega }_m)\right]$$

(9)

where $G(\omega )$ is the gain spectrum of the DFB-SOA which can be tuned by the injected current. Following square-law detection at the photodiode, the resulting microwave photocurrent corresponding to the specific component can be extracted as

$$i({\omega }_m)\propto C\cdot H({\omega }_c-{\omega }_m)$$

(10)

where $C=4{\pi }^2{A}^2{J}_0(\beta )J_{-1}(\beta )G({\omega }_c)H({\omega }_c)$ represents a constant, derived from the multiplication of the magnitude response of the optical filter and the DFB-SOA at a specified frequency. As can be seen from Equation (10), to obtain the transfer function of the ODUT, it is possible to extract it from the detected microwave photocurrent, which is determined by

$$H({\omega }_c-{\omega }_m)\propto i({\omega }_m)/C$$

(11)

It can be clearly seen from Equation (11) that optical-to-electrical domain conversion response of the ODUT is characterized through frequency scanning utilizing an EVNA. The primary advantage of our novel OVNA lies in its capability to measure optical devices featuring a bandpass response, distinct from the traditional OSSB-based OVNA. Additionally, by mitigating the effects of adjacent high-order sideband beating, our novel OVNA system is capable of attaining measurements with enhanced precision.

3. Experimental Demonstration

The configuration of the packaged DFB-SOA is illustrated in Figure 4. For maintaining the stability of the device, a temperature regulation module is integrated within the π-phase-shifted DFB-SOA. The relationship between the self-emission power and the injected current is depicted in Figure 5. Observably, the π-phase-shifted DFB-SOA necessitates a threshold current of approximately 23.1 mA. The π-phase-shifted DFB-SOA is responsible for both spectrum selection and amplification of the input optical signal.

An experimental study is conducted in accordance with the schematic diagram depicted in Figure 1. Figure 6 illustrates the experimental transmission spectrum of the DFB-SOA biased at 23 mA, with the peak gain located at 1546.39 nm. An optical carrier with a constant power level of 10 dBm is produced using a TLS (Agilent 8164B model, characterized by a linewidth of less than 100 KHz).The central wavelength of the optical carrier is adjusted to 1546.39 nm. An electrical signal with a fixed power of −5 dBm, produced by the EVNA (model Agilent 8722ET), is directed towards a 40-GHz phase modulator. A 40-GHz photodiode with optical-to-electrical conversion efficiency of 0.65 W/A is utilized. All optical spectra are characterized using an optical spectrum analyzer (OSA) possessing a minimum tuning step of 0.01 nm.

Firstly, we assess the optical carrier recovery performance achieved through the DFB-SOA. An optical signal, which is modulated utilizing a single-sideband technique with the intentional suppression of the carrier, is injected into the DFB-SOA. The optical carrier amplitude, represented by the blue line in Figure 7, is approximately −55 dBm, which is significantly reduced by a minimum of 30 dB when compared to the lower sideband signal. The output from the DFB-SOA within the optical spectrum is also presented in Figure 7 (indicated by the red line). One can see that there is a notable amplification of the optical carrier, which reaches approximately 24.3 dB gain increase as result of the amplification mechanism within the DFB-SOA. The amplitude of the lower sideband is diminished by approximately 15 decibels due to the presence of propagation loss within the DFB-SOA. Additionally, an increase in the noise floor by approximately 10 dB is observed, which could potentially degrade the noise figure of the system.

Subsequently, an OVNA incorporating a DFB-SOA is constructed to quantify the transmission characteristics of an ODUT. The ODUT is interposed within the interconnection segment between the PM and the DFB-SOA. Subsequently, the magnitude response is quantified, as depicted in Figure 8 (green line). The experimental results indicate the achievement of a passband with a bandwidth of 9 GHz and a suppression ratio of 35 dB. Given that the scanning frequency interval of the EVNA is predetermined at 25 MHz, the measurement resolution of the proposed OVNA is accordingly configured at 25 MHz. The scanning step for commercially available EVNAs can be adjusted to the Hz scale, which enhances the measurement resolution of the proposed OVNA to several kHz or even lower. The ODUT’s magnitude response is also characterized using a broadband light source and an OSA, as illustrated in Figure 8 (blue line). The concordance between the two measurement outcomes is distinct and evident. Nevertheless, constraints imposed by the resolution of the OSA necessitate a reduction in the measurement resolution when employing a broadband light source in conjunction with the OSA, limiting the precision to merely 0.01 nm (i.e., 125 MHz) which is significantly inferior to that of the proposed OVNA. Utilization of a high-Q micro-ring resonator as the ODUT would significantly enhance the performance of the proposed OVNA. Additionally, the measurement range is primarily determined by the bandwidth of the employed optoelectronic devices and the EVNA, limiting our proposed OVNA to the capability of measuring transmission spectra encompassing up to 40 GHz. Utilizing broad bandwidth optoelectronic devices and EVNA within our system may potentially expand the measurement range of the proposed OVNA. The phase response of the ODUT, which is measured by our proposed OVNA, is illustrated in the inset with a red line. It is essential to highlight that the observed ripple characteristics in the measured magnitude and phase response in our experiment are mainly resulted from the spontaneous emitting noise of the DFB-SOA. However, the application of a meticulously packaged and precisely controlled DFB-SOA within our OVNA could markedly mitigate the noise impacts effectively. Although the absence of a commercially available OVNA, such as the LUNA, in our laboratory precludes the comparison of phase responses with our proposed OVNA. However, from the phase response we measured, it is clear that it conforms to the phase response law of a bandpass filter, thus indicating the correctness of our measurement. Furthermore, as optoelectronic technology advances, our proposed OVNA exhibits considerable potential for integration into a chip utilizing the InP/InGaAsP platform. Consequently, this is expected to result in a reduction in costs, concomitant with enhanced performance outcomes in the future [22]. It is worth noting that, our proposed OVNA is focus on achieving spectrum characterization for ODUT with bandpass response. However, if another direct branch is added between the TLS and the PD, and the DFB-SOA is exchanged position with the ODUT, those slight modifications would make it possible for measuring bandstop optical filters [16].

4. Discussion

It is known that the dynamic rang is a key performance parameter of the OVNA, which is the difference between the maximum input power and the minimum measurable power into the receiver of the OVNA. To make sure the measurement effective, the dynamic range of the OVNA should be greater than the dynamic response exhibited by the ODUT. Particularly, if it is necessary to measure significant changes in signal amplitude, such as high-Q optical bandpass filter, increasing the dynamic range is important. One effective method to expand the dynamic range of OVNA for measuring high-Q optical bandpass filter is to increase the signal power into the receiver. As can be seen from Equations (4) and (5), the gain spectrum of the DFB-SOA could be tuned by the driven current. When an optical bandpass filter with different out of band rejection is measured in our proposed OVNA, we can tune the driven current to adjust the magnitude of the recovered optical carrier and thus ensure the power into the receiver is within the measurement range of the OVNA. In order to verify the idea, a theoretical model is established and the gain spectrum of the DFB-SOA driven by different current is investigated. Figure 9 illustrates the computed magnitude response of the DFB-SOA as influenced by varying gain coefficients, which are determined by the applied drive current. It is evident that the peak gain is positively correlated with the gain coefficient. Additionally, the 3-dB bandwidth of the gain peak contracts as the gain coefficient augments, leading to a modification in the Q factor. It is important to observe that the peak gain shifts towards the shorter wavelength spectrum as a result of the refractive index alteration in the active region caused by carrier injection. Consequently, it is necessary to modulate the central wavelength of the optical carrier to align with the new position of the gain peak. Figure 10 illustrates the experimental gain spectrum of the DFB-SOA under varying bias currents. Upon examination, it is noted that an adjustment of the driven current from 20 to 23 mA results in a peak gain enhancement of 7 dB. The result indicates that the dynamic range of our proposed OVNA can be expanded by adjust the driven current under the DFB-SOA for measuring optical bandpass filter with different out of band suppression ratio. It is worth noting that, the gain of the DFB-SOA is sensitive to the polarization state of the input light due to the nature of the polarization dependence of the DFB-SOA [23,24]. If the polarization of the input OSSB-modulated signal is inconsistent with that of the DFB-SOA, the recovery of the optical carrier could be deeply affected since the polarization-dependent gain loss. As the result, the generated microwave signal in the photodetector many be extremely weak, resulting in large measurement errors and reduced dynamic range.

5. Conclusions

A DFB-SOA-based OVNA was introduced and validated experimentally. The proposed OVNA has the capability to conduct transmission response measurements in the electrical domain, thereby obviating the need for optical domain analysis. Compared with the OSSB modulation based OVNAs, the DFB-SOA-associated optical carrier recovery enables the measurement of the ODUT with bandpass response using our proposed OVNA. The experimental findings indicate the successful measurement of an optical filter possessing a 9-GHz passband, achieving a high level of resolution at 25 MHz. The dynamic range of our proposed OVNA can be broadened by adjusting the driven current within the DFB-SOA. Furthermore, the integration of broadband optoelectronic devices into our system allows for an expanded measurement range. Furthermore, the OVNA we have proposed exhibits high potential for integration into a microchip.