Dual-slope linear optical frequency discriminator for

Dual-slope linear optical frequency discriminator for flexible, high performance frequency modulated direct detection (FM-DD) microwave photonics links Benjamin Dingel Nasfine Photonics Inc. Painted Post, New York, NY, USA E-mail:[email protected] Abstract—We present a linear optical frequency discriminator (FD) filter with (i) selectable dual-slope functionality and (ii) switchable slope (positive or negative) signs for flexible frequency-modulated / phase-modulated direct-detection (FM/PM-DD) microwave photonics links (MPLs). The FD uses only two Mach–Zehnder interferometers (MZIs) and one Ybranch combiner. When the optical path-length differences (OPLDs, ∆L2 = - ∆L1) of the two MZIs have equal magnitude but opposite sign, the FD filter (refer to as FD-1) has a linear slope value of -0.63 and a corresponding full bandwidth utilization (BWU). On the other hand, when the two OPLDs (∆L2 = ∆L1), have equal magnitude and same sign, the FD filter (refer to as FD2) has a linear slope value of -1.23 but its BWU is reduced to ~ 0.4 BWU. The second dynamic feature, switchable slope (positive or negative) sign is achieved if the both OPLDs, ∆L2 and ∆L1 are made tunable. Both slopes have excellent linearity performance when the power split ratio r of the Y-branch combiners is set to 0.113. The link gain is enhanced by the increase in the slope value. The dual-slope FD filter opens up the possibility of a flexible and dynamic MPLs and systems. Keywords—optical frequency discriminator, frequency modulated–direct detection (FM-DD); phase-modulated–direct detection (PM-DD); microwave photonics links

I. INTRODUCTION As microwave photonic links (MPLs) and systems become increasingly more sophisticated, it is important to develop new components that would provide not only high performance in miniaturized and integrated forms [1, 2] but also configurability or programmability features for flexible and advanced MPLs systems. In the last decade, high performance MPLs using frequency-modulated direct-detection (FM-DD) or phase-modulated direct-detection (PM-DD) techniques [3, 4] have been gaining lots of interest compared with the traditional intensity-modulated direct-detection (IM-DD) scheme. Fig. 1(a) shows generic FM-DD / PM-DD links for the case of externally modulated laser. It consists of a laser source, a frequency (or phase) modulator, optical fiber, power splitter, two complementary frequency discriminators, and balanced detectors. The laser source and modulator can also be replaced by directly modulated laser as shown in Fig. 1(b).

978-1-5090-4909-7/17/$31.00 ©2017 IEEE

(a) FM (or PM) Modulator Laser

Fiber

Frequency Balanced Discriminator Detector PD H1(f) Output Signal

Splitter Input Signal

H2(f)

PD

(b) Directly Modulated Laser

Fiber

Frequency Balanced Discriminator Detector PD H1(f) Output Signal

Splitter

H2(f)

PD

Input Signal Fig. 1. Generic FM-DD scheme for (a) externally modulated laser source, and (b) directly modulated laser.

The significant components in these links are the (i) two complementary optical frequency discriminator (FD) filters, and (ii) two balanced detectors. The FD filters convert the FM signal into intensity modulated (IM) signal before they are detected by the balanced photodetectors. FD filters with linear amplitude and phase responses produce no third-order or higher-order distortions that to leads higher spurious free dynamic range (SFDR) and better noise figure (NF) [5]. On the other hand, the balanced detectors suppress the remaining second-order distortion to increase its dynamic range [6]. Various linear optical FD filters have been proposed and implemented using (i) interferometric-based approaches via birefringent crystals [7], Mach-Zenhder interferometer (MZI) [8-9], Sagnac interferometer (SI) [10], or (ii) resonator-based approaches via Fabry-Perot filters [11], Fiber-Bragg Gratings [12], and ring resonator [13-14], and different variations of ring resonator-assisted MZI [15-16]. Oftentimes, when these FD filters are fabricated, their slope value are fixed. In this paper, we report for the first time to our knowledge, an ultra-linear FD filter with (i) selectable slope values (or dual-slope functionality) and (ii) switchable positive/negative slope signs based on our previous FD filter design [17]. These

are achieved by operating the FD filter under new condition. These new functionalities and their consequences in MPLs have not been recognized before, and have never been reported till now. The dual-slope functionality is very significant because FD filter’s slope directly affects link gain (G). Furthermore, note that these new functionalities do not require any additional components to the original filter. These support operational flexibility and open up for future dynamic MPLs and systems. However, an important consequence of the dual-slope function is the existence of a trade-off between (i) increased slope value, and (ii) reduction in its linear BWU. This paper is organized as follows. In section II, we briefly review our linear FD filter, and discuss its first-slope functionality and BWU characteristics. In section III, we report our second-slope functionality and the associated parameter adjustment. Then, we compare their respective slope linearity and BWU values with standard MZI. In section IV, we discuss the switchable slope sign function before giving our conclusion in section V. II. FIRST SLOPE OF THE LINEAR FREQUENCY DISCRIMINATOR Previously, we reported a compact optical FD filter [17] with linear amplitude and phase responses using only two MZIs and one Y-branch combiner, as shown in Fig. 2. Compared with standard MZI, it has excellent slope linearity, and wider linear bandwidth utilization (BWU) that lead to higher SFDR. Structurally speaking, it consists of (i) two MZIs (MZI-1 and MZI-2) having 50:50 directional couplers, and (ii) an asymmetric Y-branch combiner (Y1) having a power split ratio of (1−r: r). We assumed that the input and output couplers for both MZIs have ideal 50/50 couplers. The two MZIs are arranged in series. An important parameter setting is that the optical path length difference, [OPLD, ∆L1= (d1-d2-π)/2] of MZI-1 has positive number while the OPLD (∆L2) of MZI-2 has equal magnitude but negative sign. The initial bias settings

MZI-2

=

3

Eo

1

= 4

r 2

MZI-1

5

1−r

Fig. 2. Optical FD filter with linear electric-field amplitude and phase responses.

for the two MZIs are assumed zero (for simplicity) so that MZI-1 generates E6=-Sin[ ߂ߔଵ ]ejΦ1 and E5=Cos[ ߂ߔଵ ]ejΦ1 signals exiting from its two output ports while MZI-2 produces

the corresponding E9 = E5 Cos[ ߂ߔଶ ]ejΦ2 and E11 = - E5 Sin[߂ߔଶ ]ejΦ2 signals. Finally, the E11 signal (delayed version of E10) is combined with E12 signal (delayed version of E6, where the phase term ϕ5 accounts for the waveguide delay line, WDL) by the Ycombiner to give the resultant complex electric field output signal, E13 [17] as,

 j 2Ψ E13  − 1 − r Sin[ ∆Φ 1 ] e = E 0  − r Cos[ ∆Φ 1 ] Sin[ ∆Φ 2 ] 

(1)

where, the following terms are defined as Φ1= (ϕ1+ ϕ2 +π)/2, ∆Φ1= (ϕ1− ϕ2 −π)/2 = kη∆L1=kη(d1-d2 −π)/2 , Φ2= (ϕ3 + ϕ4 + π)/2, ∆Φ2= (ϕ3 − ϕ4 − π)/2 = kη∆L2= kη(d3-d4-π)/2. The parameters d1, d2, d3, d4 and d5 are the arm lengths of the two MZIs, and WDL. The overall phase response, is given as Ψ. We have equated Ψ= Φ1 + ϕ5 = Φ1 + Φ2 by adjusting the phase term ϕ5. Clearly, the phase response is a linear function which implies constant group delay. Physically, the role of the second term, the scaled down version of Cos[∆Φ1]Sin[∆Φ2] signal is to compensate for the nonlinearity in the first term and main signal, Sin[∆Φ1]. By properly choosing the value of power split ratio, r to be around r=0.11 ~ 0.15 and noting that ΔL2 = - ΔL1, or ∆Φ2 = ∆Φ1 we can get the final complex electric field, E13 as

E13  − 1 − r Sin[∆Φ 1 ] = E 0  + r Sin[ 2∆Φ 1 ]

 j 2Ψ e  

(2).

Under this condition, we refer to this filter as FD-1. This represents its first slope value in this dual-slope FD filter. To appreciate this linear function, we compare it with standard MZI. Fig. 3(a) shows the typical electric field amplitude response of a standard MZI as a function of the normalized frequency offset (∆Ω) together with its best fit line to produce a slope value of -1. The corresponding deviation between the MZI curve (red color) and its associated best fit line (green color) is depicted by the blue curve. We defined the linear BWU to be the frequency range where the deviation is less than 2.5%. The linear amplitude response of FD-1 as a function of the normalized frequency offset (∆Ω) is shown in Fig. 3(b). We observed that the straight line representing the best fit line (green color) matches very well with the FD-1 curve (red color). It has an excellent slope linearity. This is also reflected by the deviation curve (blue line) producing a wider BWU range, which is 1.75 times twice as the BWU of MZI. However, the calculated slope value of FD-1 is smaller (value= -0.63) compared with the standard MZI having a slope value of -1. Again, this represents its first slope value in this dual-slope FD filter.

Difference

MZI

0.0

BWU

- 0.5

- 1.0 -2

-1

0

1

1.0

MZI 0.0

BWU

- 0.5

- 1.0 -2

2

-1

Sin-Sin2 FD

0.0

Difference - 0.5

BWU

Electric Field Amplitude

Best fit line Slope = -0.63

- 1.0 -1

0

1

2

Normalized Frequency Offset (∆Ω)

III. SECOND SLOPE OF THE LINEAR FREQUENCY DISCRIMINATOR The second slope value of our FD filter is obtained when the two OPLDs are equal in magnitude and the same in sign (∆L2=∆L1). Under this condition, the resultant output signal is,

 j 2Ψ e  

2

Difference

0.5

0.0

Best fit line Slope = -1.23

Sin-Sin2 FD BWU

- 0.5

- 1.0 -1

0

1

2


Fig. 3. The electric-field amplitude response of (a) standard MZI, and (b) FD-1 filter with their best fit lines, slopes, and linear bandwidth utilizations (BWUs).

E13  − 1 − r Sin[∆Φ 1 ] = E 0  − r Sin[ 2∆Φ1 ]

1

1.0

-2

-2

0


Deviation (scale: x 10)


0.5

Difference

0.5

Normalized Frequency Offset (∆Ω) 1.0

Best fit line Slope = -1


0.5


Best fit line Slope = -1



1.0


FSRMZI

FSRMZI

Fig. 4. . The electric-field amplitude response of (a) standard MZI, and (b) FD-2 filter with their best fit lines, slopes, and linear bandwidth utilizations (BWUs).

The fourth observation is related to the ease in selecting between the functional performance of FD-1 and FD-2. It requires only one parameter to switch from FD-1 to FD-2 by adjusting the OPLD of MZI-2. This is a big operational advantage compared with previous FD filters. There is no need for any additional components since MZIs have already thermal-optics elements installed for parameter tuning. Also note that the parameter setting of the power split ratio, (r=0.113) for FD-1 and FD-2 are unchanged.

(3)

Note the change in sign before the second term compared with Eq.(2). Under this condition, we refer to this filter as FD-2. Fig. 4(a) shows the typical response of MZI while Fig. 4(b) depicts the corresponding linearized electric-field amplitude response of FD-2 and its associated best fit line-2. The linear FD-2 has a steeper slope (value=-1.23) compared with MZI slope (value=-1), and FD-1 slope (value=-0.63). FD-2 shows excellent linearity, but at high frequencies near the band edges, there is a clear deviation from the ideal best fit line-2. We note four important observations. First, the link gain G of FD-2 would be higher compared to MZI and FD-1 since its slope is steeper. Second, the linearity of its phase response is unchanged. Third, the corresponding BWU of FD-2 is smaller compared with both the BWUs of FD-1 and MZI. Its BWU reduces to ~ 0.4 BWU compared with FD-1. This represents a performance trade-off.

IV. SWITCHABLE POSITVE / NEGATIVE SLOPE Note the dual-slope feature of Sin-Sin2 FD filter discussed in sections II and III assumed that only the optical length difference (OPLD, ∆L2) of MZI-2 is made tunable while the OPLD (∆L1) of MZI-1 is fixed with positive value. The sign of the ∆L1 determines the sign of the slope of FD filter. If we allow both MZIs (MZI-1 and MZI-2) to have tunable OPLDs, then we can have the second dynamic feature (switchable positive / negative slope sign) that depends on the sign of ∆L1. The resultant performances will be similar to Fig. 3 and Fig. 4 except that their slope signs are now reversed as depicted in Fig. 5. As a summary, the above new functionalities (dual-slope and switchable positive/negative slope) and its associated advantages open up the possibility for future dynamic MPLsbased systems where performance merits link chain, (G), SFDR, and linear BWU can actively be traded per link on-a-fly.

Best fit line Slope=0.63

(a)

FD-1

0.5


0.0

Parameter: - 0.5

BWU

r=0.113

Difference

- 1.0 -2

1.0

0.5

-1

0

1

2

(b) Best fit line Slope=1.23

FD-2

Deviation ( scale: X 10 )

1.0

0.0

Parameter:

r=0.113 - 0.5

BWU

Difference

- 1.0 -2

-1

0

1

2

Normalized Frequency Offset (∆Ω) Fig. 5. The electric-field amplitude responses of (a) FD-1, and (b) FD-2 filter when the OPLD of MZI-1 has negative sign so that the overall slope sign of the filter is reversed compared with Fig. 3 and Fig. 4.

V. CONCLUSION We report two new functionalities (selectable dual-slope capability, and switchable positive/negative slope) to our FD filter which has linear amplitude and phase responses. The dual slope function is achieved when the two OPLDs is either (∆L2=∆L1) or (∆L2= -∆L1). Unfortunately, the higher slope comes with a corresponding reduction in its BWU. The second functionality is achieved when both OPLDs of MZI-1 and MZI2 are made tunable. These functionalities require no new components to the original simple structure filter. They open up for future dynamic MPL-based systems where variable merit performance can be traded on-a-fly. REFERENCES [1] A. J. Seeds and K. J. Williams, “Microwave Photonics,” J. Lightwave Technol. 24(12), 4628–4641 (2006). [2] J. Capmany and D. Novak, B,”Microwave Photonics combines two Worlds, Nat. Photon., vol. 1, no. 6, pp. 319–330, Jun. 20072008. [3] Capmany Francoy, José, and Ivana Gasulla Mestre. "Analytical model and figures of merit for filtered Microwave photonic links." Optics Express 19.20 (2011): 19758-19774. [4] P. Driessen, T. Darcie, and J. Zhang, “Analysis of a class-B microwavephotonic link using optical frequency modulation,” J. Lightw. Technol., vol. 26, no. 15, pp. 2740–2747, 2008. [5] J. M. Wyrwas, et.al., “Linear phase-and-frequency-modulated photonic links using optical discriminators,” Opt. Express, vol. 20, pp. 2629226298, 2012. [6] J. M. Wyrwas and M. C. Wu, “Dynamic range of frequency modulated direct-detection analog fiber optic links,” J. Lightw. Technol., vol. 27, no. 24, pp. 5552–5561. 2009. [7] S. E. Harris, Demodulation of phase-modulated light using birefringent crystals," Proceedings of the IEEE, vol. 52, no. 7, pp. 823- 831, Jul 1964.

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