All-Fibre Comb Filter with Narrow Bandwidth Based on a Dual-Pass

Mach-Zehnder Interferometer

Li Wei

Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

Keywords: Comb Filter, Mach-Zehnder Interferometer, Fibre Loop Mirror, Tunable, Narrow Bandwidth.

Abstract: A theoretical analysis of an all-fibre comb filter with narrow bandwidth is presented, based on a dual-pass

Mach-Zehnder interferometer (DP-MZI) with two variable ratio couplers. While the DP-MZI has previously

been used to construct a flattop comb filter via the reflection port, in this work it is employed as a narrow

bandwidth comb filter through the transmission port. Two conditions are newly derived to determine how to

choose the coupling ratios to optimize the optical performance of the proposed comb filter. First, to obtain a

lossless narrow-bandwidth filter, the coupling ratios of the two couplers must be equal. Second, to achieve

maximum extinction ratio, these coupling ratios are equal to 0.146 or 0.854. The impact of the coupling ratios

on bandwidth and extinction ratio is investigated. It is shown that the 3-dB bandwidth can be further reduced

by tuning the coupler ratios near the optimal value. This unique property is highly desirable for applications

in fibre lasers, optical sensing technology and reconfigurable optical systems.

1 INTRODUCTION

All-fibre comb filters are essential components for

processing optical signals in wavelength domain.

They have been widely used in dense wavelength-

division multiplexed (DWDM) systems, multi-

wavelength lasers, and fibre sensor systems due to

their low insertion loss, low cost, simple structure,

ease of use and fibre compatibility. Various

techniques have been employed to construct all-fibre

comb filters, including chirped fibre Bragg gratings

(Chen, 2024), an acousto-optic coreless fibre core

mode blocker (Ramírez-Meléndez, 2017), multimode

interference (Zhou, 2018), polarization-diversity loop

configurations (Jung, 2017, 2024), fibre-based Lyot

filter (Zhu, 2020), fibre-based Mach-Zehnder

interferometer (MZI) (Han, 2018), high-birefringent

fibre loop mirror (Wei, 2021), hybrid Fabry-

Perot/Mach-Zehnder interferometer (Han, 2020), and

all-fibre mode selective MZI (Liu, 2021). Much effort

has been focused on developing all-fibre comb filters

with reconfigurable free-spectral-range (FSR), and

tunable wavelength.

On the other hand, the flexibility to control and

adjust the bandwidth of the passband and extinction

ratio of a comb filter is critical for applications in

reconfigurable fibre optical systems (Cheng, 2024),

and fibre lasers (Marrujo-García, 2021). Liu et al.

(Liu, 2024) recently presented a narrow passband

bandwidth-tunable comb filter based on silicon rings.

Jiang et al. demonstrated a wavelength- and

bandwidth-tunable silicon comb filter (Jiang, 2016).

Although research has been predominantly focused

on silicon planar structure, little work has been

reported on manipulating the bandwidth of all-fibre

comb filters.

In this work, we present an all-fibre comb filter

with adjustable bandwidth based on a dual-pass MZI

(DP-MZI) configuration with ratio-variable fused

fibre couplers. The DP-MZI has been previously

employed to construct a multifunctional comb filter

[Luo, 2012], and our group has demonstrated a

continuously tunable flattop comb filter based on this

configuration [Wei, 2019], both of which have used

the reflection port as the output. In this work,

however, the transmission port is employed to

achieve a narrow bandwidth at passband by taking

advantage of the flattop condition at resonance. The

optimum condition for achieving a lossless comb

filter is derived along with the condition for

maximizing the extinction ratio. It is also found that

the bandwidth of the comb filter can be tuned by

adjusting the coupling ratios.

Wei, L.

All-Fibre Comb Filter with Narrow Bandwidth Based on a Dual-Pass Mach-Zehnder Interferometer.

DOI: 10.5220/0013144300003902

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2025), pages 87-91

ISBN: 978-989-758-736-8; ISSN: 2184-4364

2 OPERATION PRINCIPLE

Figure 1: Schematic diagram of the proposed comb filter.

Figure 1 shows the schematic diagram of the

proposed comb filter constructed with two coupling-

ratio variable couplers (OC1 and OC2). Assume that

couplers and fibres are polarization independent. The

path difference between the two arms of the OC1 and

OC2 is

L. The two right ends of the OC2 are spliced

to form a fibre loop mirror (FLM). It is well known

that a FLM with a 3-dB coupler is a 100% reflector.

If OC2 is a 3-dB coupler, the two beams at top- and

bottom-arm will reflect along the same path. As a

result, the comb filter formed by two 3-dB couplers

acts as a regular MZI with the path difference of the

two interference beams being 2

L. When the

coupling ratio of the OC2 is not equal to 50%, both

top- and bottom-beams will be partially reflected via

the same path and partially transmitted to the bottom

and top paths, respectively, creating multiple

interference beams, with path differences being

and 2

L. The output functions at reflective and

transmissive ports can be written as (Luo, 2012):

() ()() ()( )

()()()()

()()

112 2 2 1 2 1 1 2

121212

12 1 2

41 41 1 41 12

8 1 2 1 2 1 1 cos

81 1 cos2,

port

R ccccc ccc c

cccccc

cc c c

=−+−−+−−

+− − − −

−−−

(1)

()()( )( )

()()()()

()( )

212 1 2 1 2

121212

12 1 2

81 1 1212

8 1 2 1 2 1 1 cos

8 1 1 cos 2 ,

port

Tcccc c c

cccccc

cc c c

=−−+−−

−− − − −

+−−

(2)

where c

and c

are the coupling ratios of OC1 and

OC2, and

= nΔL/λ is the phase shift between two

interference beams, n is the refractive index of the

optical fibre, and

is the operation wavelength. The

output includes periodic terms (cos

and cos2

)

with opposite sign, contributed from single- and dual-

pass interference beams. The FSR of the dual-pass

term is half that of the single-pass term. A weak

contribution from dual pass may give rise to a flattop

response at port 1 with twice the FSR of the regular

MZI mentioned above. Note that the proposed filter

is a polarization independent filter.

With properly choosing the coupling ratios of the

two couplers, a flattop spectrum at reflection (output

port1) can be achieved from our previous study (Wei,

2019):

() ()() ()( )

()()()()

()()

12 2 2 1 2 1 1 2

121212

12 1 2

41 41 1 41 12

8 1 2 1 2 1 1

81 1 1,

cc c c c c c c c

cccccc

cc c c

−+ − −+ − −

+− − − −

−−−=

(3)

where Eq. (3) is obtained by setting the reflectance (at

port 1) to be unit, i.e., R =1 at the resonance condition.

The equation above is equivalent to the condition

by setting the transmission (at port 2) to be zero at

resonance, i.e., T = 0 as follows:

()()( )( )

()()()()

()()

12 1 2 1 2

121212

12 1 2

81 1 1212

81 2 1 2 1 1

81 1 0.

cc c c c c

cccccc

cc c c

−−+− −

−− − − −

+−−=

(4)

The flattop condition in Eq. (4) can be further

simplified:

() ( )

11 2 2

14 1 4 1 0.ccc c−−−−=

(5)

Eq. (5) will be used to find the optimal value of the

coupling ratio for maximizing the extinction ratio.

Additionally, Eq. (5) can be solved as:

()

211

12 1 .

ccc=± −

(6)

Eq. (6) agrees with the simulated results from our

previous study (Wei, 2019).

While the passband spectrum of the comb filter at

port 1 for reflection can be flattened with increased

bandwidth at resonance, the bandwidth of the comb

filter at port 2 for transmission can be significantly

narrowed at anti-resonance. This unique property can

be utilized in designing narrow-bandwidth comb

filter by using port 2 as output.

To obtain a lossless narrow-bandwidth spectral

response, the transmission of the comb filter at port 2

must have a unit magnitude at anti-resonance (i.e.,

pπ, where p is an odd integer), which gives the

following condition:

()()( )( )

()()()()

()()

12 1 2 1 2

121212

12 1 2

81 1 1212

81 2 1 2 1 1

8 1 1 1.

cc c c c c

cccccc

cc c c

−−+− −

+− − − −

+−−=

(7)

By solving Eq. (7), the solution is found to be:

.cc=

(8)

PHOTOPTICS 2025 - 13th International Conference on Photonics, Optics and Laser Technology

Therefore, the optimum condition for a lossless

narrow-bandwidth comb filter is that the two couplers

must have identical coupling ratios.

Note that Eq. (8) represents the lossless condition,

i.e., the zero insertion condition. On the other hand,

high extinction is desirable to effectively isolate noise

in the stopband. To achieve maximum extinction

ratio, the transmission at the stopband must be zero,

which corresponds to the flattop condition in Eq. (5)

at resonance for a flattop comb filter. By solving Eq.

(5) and Eq. (8), we can find the solution to achieve

maximum extinction ratio for a narrow bandwidth is:

(9)

This indicates that the coupling ratios of the two

couplers are equal and can be either 0.146, or 0.854.

In Section 3, we will present simulated results of

the proposed narrow bandwidth comb filter, and

characterize the impact of the coupling ratios to the

bandwidth and extinction ratio of the transmissive

comb filter.

3 NUMERICAL RESULTS

Figure 2 shows the narrow bandwidth spectra of the

proposed comb filter for three different coupling

ratios where c

= c

. It is evident that the peaks of the

three curves overlap at unit for different coupling

ratios, indicating that the comb filter remains lossless

as long as the two couplers have the equal coupling

ratios. The red curve with c

= c

= 0.146, represents

the optimized solution in Eq. (9), demonstrating that

zero transmission at stopband with a flattop shape,

indicating the extinction ratio reaches its maximum.

When the coupling ratio deviates from the optimal

value, the transmission at stopband increases,

suggesting a degradation in the extinction ratio. For

the coupling ratios smaller or larger than the optimal

value (as shown in the green and blue curves), the

bandwidth increases or decreases, respectively.

To clearly illustrate the impact of varying the

coupling ratio with c

= c

, Fig. 3 plots the 3-dB

bandwidth and the extinction ratio as the coupling

ratio varies from 0.106 to 0.186. The FSR of the comb

filter is 0.82 nm. At the optimal coupling ratio

(0.146), the extinction ratio reaches its maximum and

the 3-dB bandwidth is 0.298 nm. For comparison, the

3-dB bandwidth of a standard MZI is half of the FSR,

i.e., 0.41 nm. The means the 3-dB bandwidth of the

proposed comb filter is 27.3% narrower than that of

the standard MZI.

Furthermore, as the coupling ratio increases the 3-

dB linewidth decreases, suggesting that the

bandwidth of the comb filter can be further narrowed

by increasing the coupling ratio, though at the

expense of the extinction ratio.

Figure 2: The spectra of the proposed comb filter for

different coupling ratios with c

= c

Note that in Fig. 3, the same coupling ratio is used

for both couplers. It would be very insightful to

explore how the key specifications change when the

coupling ratios c

and c

are different.

Figure 3: The 3-dB bandwidth and extinction ratio as a

function of the coupling ratio with c

= c

Fig. 4(a) show the performance of the 3-dB

bandwidth for three fixed values of c

, while c

varies.

For a fixed coupling ratio c

, the 3-dB bandwidth

decreases as c

increases. Additionally, increasing the

fixed coupling ratio c

results in a narrower 3-dB

bandwidth.

Fig. 4(b) displays the extinction ratio as a function

of c

for three fixed values of c

. When c

is set to be

the optimal value (see the red line), the curve shows

All-Fibre Comb Filter with Narrow Bandwidth Based on a Dual-Pass Mach-Zehnder Interferometer

near symmetry at c

= c

; however, when c

deviates

from the optimal value

the extinction ratio degrades.

When c

is smaller than the optimal value (as shown

by the grey line), the extinction ratio increases with

. Conversely, when c

is larger than the optimal

value, the extinction ratio (as shown in blue line)

decreases as c

increases.

Fig.4: (a) The 3-dB bandwidth and (b) extinction ratio as a

function of c

with different fixed c

Thus, both the 3-dB bandwidth and extinction

ratio can be dynamically tuned with adjusting the two

coupling ratios. As shown in Fig. 4, desirable optical

performance can also be achieved by suitable

choosing the combination of c

and c

. To obtain a

narrow bandwidth with a high extinction ratio, if c

smaller than the optimal value, then c

must be greater

than the optimal value, and similarly, if c

is larger

than the optimal value, then c

must be smaller than

the optimal value.

Furthermore, the analysis above is based on the

optimal solution at c

= 0.146. It is worth noting that

for the other optimal solution at c

= 0.854, same

behaviour regarding the impact of the coupling ratios

on the 3-dB bandwidth and extinction ratio is

expected.

4 CONCLUSIONS

A theoretical study of all-fibre comb filter with

narrow bandwidth based on a dual-pass Mach-

Zehnder interferometer is presented. The condition

for a lossless comb filter with narrow bandwidth is

newly derived. The coupling ratios of the two

couplers must be equal for achieving a lossless comb

filter. Additionally, the condition for achieving a

maximum extinction ratio is found to be c

= c

0.146, or 0.854. The proposed comb filter has a 3-dB

bandwidth that is 27.3% smaller than that of the

standard MZI. The bandwidth and the extinction ratio

can be also tailored by using variable coupling ratio

couplers. Narrow bandwidth with high extinction

ratio could be achieved by appropriately selecting the

values of the coupling ratios. This property is

extremely useful for applications in reconfigurable

photonic filtering, photonic signal processing, and

multiwavelength fibre lasers.

ACKNOWLEDGEMENTS

This research was funded in part by the Natural

Science and Engineering Research Council of Canada

(NSERC) and Wilfrid Laurier University.

REFERENCES

Chen, P., Liang, X., Ma, J., Zhang, X. (2024), “Research

and fabrication of the chirped Moiré fiber Bragg grating

with tunable channels based on temperature control,” J.

Lightw. Technol. 42(10), 3852-3861.

Ramírez-Meléndez, G., Bello-Jiménez, M., Pottiez, O.,

Andrés, M.V. (2017), “Improved all-fiber acousto-optic

tunable bandpass filter,” IEEE Photon. Technol. Lett.,

29(12), 1015-1018.

Zhou, G., Kumar, R., et al. (2018), “A simple all-fiber comb

filter based on the combined effect of multimode

interference and Mach-Zehnder interferometer,” Sci.

Rep. 8(1), 11803.

Jung, J., Lee, Y.W. (2017), “Continuously tunable

polarization-independent zeroth-order fiber comb filter

based on polarization-diversity loop structure,” Appl.

Phys. B., 123(4), 106.

Jung, J., Lee, Y.W. (2024), “Wavelength-tunable first-order

narrowband fiber comb filter incorporating all-quarter-

wave polarization transformation,” IEEE Photon. J.,

16(3), 7101007.

Zhu, Y., Cui., Z., Sun, X., Shirahata, T., Jin, L., Yamashita,

S., Set, S.Y. (2020), “Fiber-based dynamically tunable

Lyot filter for dual-wavelength and tunable single-

wavelength mode-locking of fiber lasers,” Opt.

Express, 28(19), 27250-27257.

Han, M., Li, X., Zhuang, S., Han, H., Liu, J., Yang, Z.

(2018), “Tunable and channel spacing precisely

controlled comb filters based on the fused taper

technology,” Opt. Express, 26(1), 265-272.

Wei., L., Xu, X., Khattak, A., Henley, B. (2021),

“Continuously tunable comb filter based on a high-

PHOTOPTICS 2025 - 13th International Conference on Photonics, Optics and Laser Technology

birefringence fiber loop mirror with a polarization

controller,” J. Lightw. Technol. 39(14), 4800-4808.

Han, Y., Liu, B., Wu, Y., Mao, Y., Zhao, L., Sun, T., Nan,

T., Wang, J., Tang, R (2020), “Fiber sensor based on

Fabry Perot/Mach-Zehnder hybrid interferometer for

transverse load and temperature,” Microw. Opt.

Technol. Lett. 63, 679-684.

Liu, M., Tang, M., Cao, M., Mi, Y., Guan, P., Ren, W., Ren,

G. (2021), “All-fiber mode selective comb filter based

on Mach–Zehnder interferometer,” Opt. Commun.,

492, 126964.

Cheng, W., Guo, C., Wang, J., Shi, S., Chen, Y., Wang, P.,

Niu, H., Hu, G., Cui, Y., Yun, B. (2024), “Flexible and

reconfigurable integrated optical filter based on tunable

optical coupler cascaded with coupled resonator optical

waveguide,” Opt. Express, 32(14), 24058-24071.

Marrujo-García, S., Herrera-Piad, L.A., Hernandez-

Romano, I., MayArrioja, D.A., Minkovich, V.P.,

Torres-Cisneros, M. (2021), “Narrow spectral

linewidth and tunable erbium-doped fiber ring laser

using a MZI based on CHCF,” Opt. Fiber Technol., 67,

102739.

Liu, L., Chen, C., Hu, C., Zhao, P. (2024), “Narrow

passband tunable optical filter based on silicon high-Q

rings assisted MZI structure,” J. Lightw. Technol.

42(6), 2049-2056.

Jiang, X., Wu, J., Yang, Y., et al. (2016), “Wavelength and

bandwidth-tunable silicon comb filter based on Sagnac

loop mirrors with Mach-Zehnder interferometer

couplers,” Opt. Express 24(3), 2183-2188.

Luo, Z., Cao, W., Luo, A., Xu, W. (2012), “Polarization-

independent, multifunctional all-Fiber comb filter using

variable ratio coupler-based Mach–Zehnder

Interferometer,” J. Lightw. Technol. 30(12), 1857-

1862.

Wei., L., Tatel, G. (2019), “Wavelength continuously

tunable all-fiber flat-top comb filter based on a dual-

pass Mach–Zehnder interferometer,” J. Lightw.

Technol. 37(15), 3740-3749.

All-Fibre Comb Filter with Narrow Bandwidth Based on a Dual-Pass Mach-Zehnder Interferometer