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Study of transmission response of edge filters

employed in wavelength measurements

Qian Wang, Gerald Farrell, and Thomas Freir

The ratiometric wavelength-measurement system is modeled and an optimal design of transmission

response of the employed edge filter is demonstrated in the context of a limited signal-to-noise ratio of the

signal source. The corresponding experimental investigation is presented. The impact of the limited

signal-to-noise ratio of the signal source on determining the optimal transmission response of edge filters

for a wavelength-measurement application is shown theoretically and experimentally.

Society of America

OCIS codes:

120.2440, 120.4570, 060.2380.

© 2005 Optical

1.

Wavelength measurements are required for many op-

tical systems. Examples include wavelength measure-

ment in a multichannel dense wavelength-division-

multiplexing optical communication system and fiber-

Bragg-grating-based optical sensing systems.1–5There

are different wavelength-measurement schemes, and

among them the ratiometric detection scheme,2–5

which converts the wavelength measurement into a

signal-intensity measurement, has a simple configura-

tion and offers a high-speed measurement as com-

pared with, e.g., wavelength-scanning-based active

measurement schemes. The ratiometric detection

scheme employs an edge filter and utilizes the transi-

tion region of its transmission response. The employed

edge filters could be bulk thin-film filters,2biconical

fiber filters,4fiber gratings,5multimode interference

couplers,6directional couplers,7and so on.

Previous publications about the ratiometric detec-

tion scheme have mainly focused on different types of

edge filters, and there have been few investigations

concerning the transmission response of the edge fil-

ter. Defining the transmission response, specifically

the wavelength range and slope of the transition re-

gion, is the preliminary work in optimal design of

these edge filters. A straightforward approach is to

Introduction

make the slope of the transmission response for the

edge filters as large as possible to ensure a high res-

olution of the measurement system, given the limited

precision of power detectors. This paper studies the

optimal transmission response of the edge filter for

wavelength measurement in the context of the ef-

fect of a limited signal-to-noise ratio (SNR) of the

signal source, e.g., signal to spontaneous-emission

ratio for the lasers, which has not been addressed in

related literature. In Section 2, the wavelength-

measurement system involving the source, the edge

filter, and the photodiodes is modeled and design of

the transmission response of edge filters is subse-

quently demonstrated. Corresponding experimen-

tal investigations are presented in Section 3.

Theoretical and experimental results indicate that

the limited SNR of a signal source has a significant

impact in the optimal design of the transmission

response for the edge filters applied in wavelength

measurements.

2.

Systems and Optimal Design of Edge Filter’s

Transmission Response

Figure 1 gives the schematic configuration of a ratio-

metric wavelength-measurement system employing

an edge filter. The input signal is split into two equal

signals. One passes through a reference arm (arm B)

and the other passes through the edge filter (arm A).

Two photodiodes are placed at the ends of both arms.

By measuring the ratio of the electrical outputs of the

two photodiodes, we can determine the wavelength of

the input signal assuming a suitable calibration has

taken place.

In a ratiometric wavelength-measurement system,

Theoretical Modeling of Wavelength-Measurement

The authors are with the Applied Optoelectronics Centre, School

of Electronics and Communications Engineering, Dublin Institute

of Technology, Kevin Street, Dublin 8, Ireland.

Received 8 July 2005; revised 18 August 2005; accepted 19 Au-

gust 2005.

0003-6935/05/367789-04$15.00/0

© 2005 Optical Society of America

20 December 2005 ? Vol. 44, No. 36 ? APPLIED OPTICS7789

Page 2

the narrowband input signal with a center wave-

length ?0could be from a tunable laser or the reflec-

tion of a Bragg grating sensor. Such an input signal

can be approximated by a Gaussian function with a

spectral width ?? and center wavelength ?0. In prac-

tice, the input signal generally has a limited SNR,

which means that there is measurable power even far

from the center wavelength in the spectrum. Figure 2

presents typical spectral distributions of the output

intensity from a tunable laser at different central

wavelengths, which are measured by an optical spec-

tral analyzer in a wavelength range from 1500 to

1600 nm. From these measured spectral distribu-

tions one can see that, for this tunable laser, the

spontaneous-emission ratio is ?40 dB and it has dif-

ferent values for different output center wavelengths.

Therefore, considering the SNR the output spectral

response of source can be simply described as2,8,9

(suppose the power at the peak wavelength is 0 dBm)

?

?S?r(?0),

10 log10[I?0(?)]?

10 log10?exp??4 ln 2

(???0)2

??0

2 ??,

|???0|??

|???0|??

,

(1)

where S is the SNR for the source, r??0? is a small

random number (typical range is from 0 to 1 dB), and

? is determined by the source with a given SNR,

i.e., 10 log10?exp??4 ln 2??2???0

the transmission response of the edge filter in arm A

is Tf??? {denote T?f?f? ? ?10 log10?Tf???? in decibels}. It

is known that photodiodes give the integral power

over a wavelength range. Therefore the ratio of the

outputs from the two photodiodes at a wavelength ?0

is

2??? ? ?S. Assume

R??0???10 log10?

?I?0(?)Tf(?)d?

? I?0(?)d? ?

.(2)

From this equation one knows that, for an ideal

source, i.e., the SNR is infinite, the ratio R??0? is

extremely close to the transmission response T?f??0?.

A simple case for the transmission response T?f??? of

an edge filter in wavelength range (?1, ?2) is a linear

function, i.e.,

T?f(?)?T?f(?1)?[T?f(?2)?T?f(?1)]

(?2??1)

(???1).(3)

With this linear transmission response, numerical

examples are given below that model performances of

the ratiometric wavelength-measurement system.

Assume the input signal has a 55-dB SNR in a wave-

length range from 1500 to 1600 nm with a maximum

r ? 1 dB. Six edge filters are considered, of which

T?f??1? ? 0 dB and T?f??2? is chosen to be from 10 to

60 dB with an increment of 10 dB. Corresponding

numerical results of the output ratio R are shown in

Fig. 3. Transmission responses of these six edge fil-

ters are also presented in Fig. 3. From these numer-

ical results one can see that, with the increase in

slope of the transmission response of the edge filters

for a given measurable wavelength range, the calcu-

Fig. 1.

wavelength-measurement system.

Schematic configuration of edge-filter-based ratiometric

Fig. 2.

wavelength range from 1500 to 1600 nm.

Measured intensity distributions for a tunable laser in the

Fig. 3.

ratios R of systems.

Transmission responses of edge filters and corresponding

7790APPLIED OPTICS ? Vol. 44, No. 36 ? 20 December 2005

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lated ratios R start to diverge from the transmission

response of the edge filters at the end region of the

wavelength range as a result of the limited SNR of

the source. This indicates that the straightforward

design approach mentioned in the introduction could

be wrong and there exists a maximal slope for the

transmission response of the edge filter beyond which

significant measurement error will occur because of

the finite SNR of the signal source.

To find the maximal transmission response slope

for a given wavelength range one can use the differ-

ence between transmission response and the output

ratio R of the system at wavelength ?2, i.e., ?T

? T???2? ? R??2?. Figures 4(a) and 4(b) give the calcu-

lated ?T against transmission T???2? for two source

signals with SNRs of 55 and 70 dB, respectively. The

considered wavelength range in Figs. 4(a) and 4(b) is

(in nanometers) (1500, 1600) and (1500, 1550), re-

spectively. Assume that the difference is required to

be within 0.01 dB (comparable with the precision of

the power detectors). From these calculation results,

one can see that for the signal with a SNR of 55 dB

and measurement range of (1500 nm, 1600 nm), the

transmission at 1600 nm should be no larger than

13 dB (i.e., slope 0.13 dB?nm). When the required

measurable wavelength

1550 nm), the transmission at 1550 nm should be no

larger than 17 dB (i.e., slope 0.34 dB?nm). When the

SNR of the input signal is higher at ?70 dB, the

transmission at 1600 nm should be no larger than

32 dB (i.e., slope 0.32 dB?nm) and the transmission

at 1550 nm should be no larger than 34 dB (i.e., slope

0.68 dB?nm).Inthecontextofthelimitedprecisionof

the power detectors, one can see that the SNR of the

signal source has a significant impact on the trans-

mission spectrum of edge filters and, as a conse-

quence, affects the measurement system’s resolution.

rangeis (1500 nm,

3.

Signal-to-Noise Ratio

To verify the above theoretical modeling, a ratiomet-

ric wavelength-measurement system was built and

corresponding experimental measurements were car-

ried out. A tunable laser is chosen as the signal

source, and its corresponding SNR is ?40 dB. Eight

edge filters operatingat

(1500 nm,1600 nm)withdifferentspectralresponses

were used, which utilize the wavelength sensitivity of

bend loss for a single-mode fiber.10It should be noted

that the transmission responses of the edge filters are

not strictly linear functions of the wavelength as used

in the theoretical modeling. Figure 5(a) gives the

measured transmission responses of the edge filters

by an optical spectral analyzer (circles). Simulated

output ratios R of the system with the above model

are also presented as dotted curves. Figure 5(b) gives

corresponding measured ratios R of the system with

a dual-channel power meter. Comparing Figs. 5(a)

and 5(b), one can see that the simulated results have

a good agreement with the measured results. Again

the experimental results show that, because of the

limited SNR of the source, with the increase in the

slope of the transmission response of the edge filter,

the output ratios R diverge from the actual transmis-

sion response of the edge filters within the end region

of the wavelength range, and furthermore these dif-

ferences vary from each measurement, which means

that it is not suitable for a wavelength-measurement

application. Therefore the slope of the transmission

response of edge filters is strictly limited. To find the

optimal transmission response for a required wave-

length range or find the measurable wavelength

range for a given transmission response of edge filter,

one can apply the theoretical model and design

method demonstrated in Section 2. For the SNR of

the source used in the experiment, both the theo-

retical model and the experiment show that the

measurable wavelength range for the uppermost

transmission response is approximately (1500 nm,

1550 nm)andthecorrespondingslopeis?0.3 dB?nm.

Experimental Investigation of Impact of the

awavelengthrange

Fig. 4.

ratio of the system at (a) ?2? 1600 nm and (b) ?2? 1550 nm.

Differences between transmission response and output

20 December 2005 ? Vol. 44, No. 36 ? APPLIED OPTICS7791

Page 4

4.

The spectral responses of edge filters employed in

wavelength-measurementsystemshavebeenstudied

theoretically and experimentally. A simple model

Conclusion

has been presented that describes a ratiometric

wavelength-measurement system. The design of the

transmission response of an edge filter has been dem-

onstrated. The simulation results and experimental

results have shown that the limited SNR of the signal

source affects not only the maximum slope of the edge

filter’s spectral response over a given wavelength

range, but also affects the wavelength range. Accord-

ing to the theoretical and experimental results pre-

sented in this paper, for a SNR of 40 dB, the widest

wavelength range is ?50 nm with an edge filter’s

slope of 0.3 dB?nm. The widest wavelength range

increases as the SNR of the source improves for a

given slope of the edge filter or as the slope decreases

for a given SNR of the source.

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Fig. 5.

and calculated ratios of the system, (b) measured transmission

responses of the edge filters and measured ratios of the system.

(a) Measured transmission responses of the edge filters

7792 APPLIED OPTICS ? Vol. 44, No. 36 ? 20 December 2005