Transmission Characteristics of Tuneable Optical Filters Using Optical Ring Resonator with PCF Resonance Loop

doi:10.4236/opj.2011.14028

Paper Menu >>

Journal Menu >>

Optics and Photonics Journal, 2011, 1, 172-178

doi:10.4236/opj.2011.14028 Published Online December 2011 (http://www.SciRP.org/journal/opj)

Transmission Characteristics of Tuneable Optical Filters

Using Optical Ring Resonator with PCF Resonance Loop

Kazhal Shalmashi1, Faramarz E. Seraji2, Mansur Rezaei Mersagh1

1Physics Group, Islamic Azad University, Tehran Shomal Branch, Tehran, Iran

2Optical Communication Group, Iran Telecom Research Center, Tehran, Iran

E-mail: [email protected]

Received August 30, 2011; revised September 27, 2011; accepted October 11, 2011

Abstract

A theoretical analysis of a tuneable optical filter is presented by proposing an optical ring resonator (ORR)

using photonic crystal fiber (PCF) as the resonance loop. The influences of the characteristic parameters of

the PCF on the filter response have been analyzed under steady-state condition of the ORR. It is shown that

the tuneability of the filter is mainly achieved by changing the modulation frequency of the light signal ap-

plied to the resonator. The analyses have shown that the sharpness and the depth of the filter response are

controlled by parameters such as amplitude modulation index of applied field, the coupling coefficient of the

ORR, and hole-spacing and air-filling ratio of the PCF, respectively. When transmission coefficient of the

loop approaches the coupling coefficient, the filter response enhances sharply with PCF parameters. The

depth and the full-width half-maximum (FWHM) of the response strongly depends on the number of field

circulations in the resonator loop. With the proposed tuneability scheme for optical filter, we achieved an

FWHM of 1.55 nm. The obtained results may be utilized in designing optical add/drop filters used in WDM

communication systems.

Keywords: Optical Ring Resonator, Photonic Crystal Fiber, Tuneable Optical Filter, Optical Fiber

1. Introduction

In last two decades, optical ring resonators (ORR) with

different configurations, based on fiber and wave-guides

[1-4], have been analyzed for different applications such

as polarization sensing [5], bio-sensing [6], optical filters

[7-9], dispersion compensation [10,11], optical triggering

and optical integration/differentiation [2], optical bista-

bility [12,13], add/drop multiplexer [14], optical swit-

ching [15-18], and various other applications [19-21]. In

the early works, steady state [2,22] and dynamic resp-

onses of ORR built on fiber were analyzed [23,24] for

applications in polarization sensing [7], FM deviation

measurement of a laser diode (LD) [24], optical trig-

gering, optical integration/differentiation and fiber disp-

ersion compensation [2], and rotation sensing [22]. Rec-

ently, dynamic resonance characteristic of fiber ring re-

sonator has been analyzed for gyro systems [25].

A basic structure of an ORR consists of a 2 × 2 port

directional coupler and a fiber or waveguide loop con-

necting one of the input ports to one of the output ports,

making a ring resonator with a function similar to a

Fabry-Perot interferometer. To achieve the resonance

effect in an ORR, the loop length could be of the order of

few micrometers [26] to tens of meters [23]. Generally,

the characteristics of ORR based optical filters are

determined by their frequency responses which in turn

depends on the characteristic parameters of the ORR.

The characteristic parameters of an ORR, that influence

filter response, are resonator loop length, coupling coeff-

icient of the coupler, transmission parameters of the loop

fiber, and modulation frequency of the circulating field

intensity in the resonator [23,24].

In accordance with developed theory of the ORR [27],

the objective of this study is to present an analysis of

tuneability of optical filter using an optical ring resonator

when excited by a sinewave-modulated laser diode. Baed

on previous ORR structures [23,24], where singlemode

fiber (SMF) used as the resonator loop, in this paper, we

assume to use a PCF resonance loop built on a PCF

coupler [28,29]. The peculiar properties of PCFs have

interesting effects on transmission function of the ORR.

Two influential parameters of the PCF on transmission are

airhole diameter (d) and the air-hole spacing () [30-32].

173

K. SHALMASHI ET AL.

To quantify the influence of the characteristic para-

meters of the loop PCF on the characteristic response of

the ORR, the ORR loop transmission is analyzed by

using the formulation developed by Pandian et al. [24]

and Seraji et al. [23]. The novelty of the PCF-based ORR

compared with SMF-based ORR is that the tuneability of

response of the former is opened to more characteristic

parameters and can be more compact due to shorter

length of the loop.

2. Analysis of ORR with PCF Resonance Loop

A basic structure of an ORR built in PCF loop with

transmission coefficient α, coupling coefficient κ, cou-

pler insertion loss



0, and loop delay time τ is shown

schematically in Figure 1 with port (1) and (2) as input

Ein(t) and output Eout(t), respectively.

To analyze the field in the loop, the loss is assumed

only to be due to loop bending, and other loss mecha-

nisms such as splice (if any), confinement, and intrinsic

losses of PCF are neglected for simplicity of analysis

[30,32]. The loop transmission coefficient



is de-

fined as α = exp(–2α0L), where

is the loop length of

the resonator (in m), and 0 is the bending loss coef-

ficient in dB/km due to bending radius Rbent, that is given

by [33]:



1.57 12

exp 3

(), bent PCF

eff







 











(1)

where

eff eff

A

is the effective core area and

22 1/2

()

PCFeff coeff

knnV 

is the V-parameter of the PCF,  denotes the air-hole

spacing,β = neffk is the propagation constant, k= 2π/λ is

the wave number, and λ represents the wavelength in

vacuum (For Neper to dB-scale conversion, the above

expression should be multiplied by 8.686). The values of

neff, Aeff and VPCF are determined by improved vectorial

effective index method for different values of Λ and d/Λ,

and the results are tabulated in Table 1 [34].

The transmission coefficient α of the ORR with a loop

length of about 19 mm (Rloop = 3 mm) made with four

PCF structures of similar d/Λ and different Λ(=2.3, 4.0,

6.0, and 8.0 m), is shown in Figure 2. The corresponding

transmission coefficients at 1.55 m wavelength are de-

termined as α = 0.96, 0.36, 0.04, 0.01, respectively. As



increases, the value of α decreases. By doubling the

Λ value, α becomes 36 times higher.

The transmission coefficient is also affected by the

air-filling ratio d/Λ with a constant Λ. By increasing the

ratio d/Λ, the α values will increase. In Figure 3, this

case is depicted for d/Λ = 0.2, 0.3, and 0.4 at Λ = 4 μm.

By comparing Figures 2 and 3, we observe that the

effect of Λ values on the ORR transmission is more than

that of d/Λ variations. In general, with an input of a

sinewave-modulated laser signal Ein(t) with an angular

modulation frequency of ωm, the filtering characteristics

of the ORR in Figure 1, after n number of field circu-

lations in the resonator loop, can be expressed as (see

Equation (2)) [24].

Figure 1. Schematic diagram of an ORR connected to a laser

diode at port 1.

Table 1. Calculated PCF parameters for different structures.



(m)





2.34 6 8 0.2 0.3 0.4

eff

n1.43951.44501.4475 1.4485 1.4550 1.44341.4421

opt

1.2922.4123.672 4.922 2.412 2.516 2.533

eff

V0.9201.2531.397 1.463 1.253 1.672 2.533

eff

371145 204 305 145 151 131





(1)

1sin() exp[cos()]

1sin[()]exp{[cos[()]/2]}

out

mm mFM

mmm FM

EjA ktjt

jBCkt njt nnn



 

 



 





(2)

K. SHALMASHI ET AL.

174

(a) (b)

Figure 2. Transmission coefficient of the ORR in terms of wavelength for (a) d/Λ = 0.2, (b) d/Λ = 0.4, and different values of Λ.

Figure 3. Transmission coefficient of the ORR in terms of

wavelength forΛ = 4μm and different values of d/Λ.

Where β = Imkf /fm is frequency modulation index, kf is

the optical frequency deviation (Hz/mA), fm is modu-

lation frequency, Im is the peak value of ac modulating

current, km is the amplitude modulation index, ΦFM is

angle between optical frequency deviation and amplitude

modulating derive current of the given LD.

(1 )A (1)(1 )B



 

and (1 )C

are constants and all other parameters have the same

definitions as in Figure 1.

With a particular characteristic parameters given in

Table 2, a stop band filter based on ORR is designed

with a characteristic response plotted in Figure 4 at reso-

nance wavelength of 1.55 μm. The full-width at half ma-

ximum of the filter for t = 50τis obtained as 5 nm.

Figure 4. Characteristic response of stop band filter based

on ORR.

3. Effects of Laser Diode Parameters

To tune the filter based on the ORR, we can either change

the parameters of the ORR such as  d/Λ loop length, κ

or/and parameters of input source such as fm and km [24].

For instance, by increasing fm from 95 GHz to 125 GHz,

the resonance filter response shifts from 1.55 µm to

1.615 µm, respectively, as shown in Figure 5. The

FWHM of the response slightly increases by increasing

the modulation frequency of the input source.

The amplitude modulation index km also affects the

filter response. By increasing its value, the effectiveness

of filtration increases at the central wavelength, as shown

in Figure 6(a). Another parameter of laser diode source

influencing on the filter response is the modulation current

Im applied to the laser diode. Similar to effect of km, Im

175

K. SHALMASHI ET AL.

influences the depth of characteristic response, which

increases by increase of Im, as shown in Figure 6(b).

In general, how the filter responds to the variation of Im

is shown in Figure 7. At about Im = 40, 70, and 90 mA,

the filter responses are at maximum values. Extreme low

value occurs at about Im= 65 mA

4. Effects of PCF Parameters

The transmission response of the filter strongly depends

on the hole-spacing Λ of the PCF used in the loop of the

resonator, as shown in Figure 8. For a given



, when

d/Λ goes higher, the filter response goes lower and for a

given d/Λ, higher the value of Λ, lower will be the filter

response.

At a particular values of Λ and d/Λ, when the corre-

sponding α value tends to the value of κ the filter res-

ponse reaches its maximum value.

5. Effects of Characteristic Parameters of

Coupler and Ring

The coupling coefficient of the resonator κ has direct

effects on the filter response. Figure 4 is reproduced here

by changing the value of d/Λ from 0.4 to 0.2, keeping Λ

= 0.4 μm. When d/Λ decreases, the value of κ decreases

for better filter response, as illustrated in Figure 9.

Therefore, for an optimum filter response, the values of

km and κ should be as large as possible, whereas Λ should

be as small as possible. For the best condition, Λ should

(a) (b)

Figure 6. Effect of (a) amplitude modulation index km and (b) modulating current Im on the filter response.

Figure 5. Effect of modulating frequency fm on the filter

response.

Figure 7. Variation of filter response versus modulating

current.

K. SHALMASHI ET AL.

176

(a) (b)

Figure 8. Effects of (a) d/Λ and (b) Λ on the filter response.

(a) (b)

Figure 9. Effect of coupling coefficient κ on the filter response (a) d/Λ = 0.4, 0.99



 and (b) d/Λ = 0.2 and α = 0.11.

be chosen in such a way to operate the resonator at reso-

nance state, i.e., when α = κ [35].

With the elapse of time, trapping of the field in the

resonator loop stabilizes the filter response for narrower

FWHM. In Figure 10, the filter response at λ = 1.55 μm

is illustrated with the same PCF and source parameters

values of Figure 4. The FWHM becomes narrower ex-

ponentially at central wavelength 1.55 m.

Typically, its value becomes 5 nm at circulation time

of t = 50τ ps and reaches to 1.55 nm at t = 150 τ ps. That

is, by tripling the loop delay time of the resonator, we

obtain 70% reduction in value of the FWHM.

6. Filter Tuning Based on Modulating

Frequency

With reference to Figure 5, the response wavelength of

Figure 10. Narrowing of filter response in the resonator

loop by increasing the loop delay time.

177

K. SHALMASHI ET AL.

(a) (b)

Figure 11. (a) Maximum filter response obtained by the applied modulating frequencies and (b) maximum response versus

wavelength for different modulating frequency.

the filter may be shifted up or down by varying modu-

lating frequency fm applied to the laser diode source.

Figure 11(a) illustrates the operating wavelengths in

terms of modulating frequency where the values denoted

by solid circles represent the maximum filter response

obtained by the applied modulating frequencies. At some

modulating frequencies such as 20, 40, 60, 80 GHz, there

are more resonance peaks in the response. To realize the

tuneability of the filter rendered by the modulating fre-

quency, Figure 11(b) is depicted for the maximum re-

sponse as a function of the operating wavelengths. For

fm with values as multiple of 50 GHz, the maximum re-

sponse is almost independent of the wavelength. By us-

ing these curves, one can obtain maximum filter response

at different modulating frequency.

7. Conclusions

In conclusion, we presented a tuneable optical filter

based on an optical ring resonator with a loop made of

photonic crystal fiber. It is shown that the filter response

can be varied by modulation frequency of the input sig-

nal. The transmission amplitude of the filter can be

optimized by parameters such as modulation signal

amplitude, hole-spacing of the PCF, and coupling co-

efficient of the ORR. The filter response enhances

sharply with PCF parameters, when transmission co-

efficient of the loop approaches the coupling coeffi-

cient. It is further illustrated that by signal field circu-

lations in the ORR loop, the filter response stabilizes

to a narrower FWHM.

With the proposed tuneability scheme for optical filter,

we presented maximum filter response with respect to

operating wavelengths and achieved an FWHM of 1.55

nm. The obtained results may be utilized in designing op-

tical add/drop filters used in WDM communication sys-

tems.

8. References

[1] L. F. Stokes, M. Chodorow and H. J. Shaw, “All-Single-

Mode Fiber Resonator,” Optics Letters, Vol. 7, No. 6,

1982, pp. 288-290. doi:10.1364/OL.7.000288

[2] G. S. Pandian and F. E. Seraji, “Optical Pulse Response

of a Fiber Ring Resonator,” IEE Proceedings Journal,

Vol. 138, No. 3, 1991, pp. 235-239.

[3] M. Sumetsky, “Optical Fiber Microcoil Resonator,” Op-

tics Express, Vol. 12, No. 10, 2004, pp. 2303-2316.

doi:10.1364/OPEX.12.002303

[4] H. L. Ma, S. J. Wang, and Z. H. Jin, “Silica WaveGuide

ring Resonators with Multi-Turn Structure,” Optics Com-

munications, Vol. 281, No. 9, 2008, pp. 2509-2512.

[5] G. S. Pandian and F. E. Seraji; “Analysis of a Fibre-Optic

Ring Resonator with Polarization Effects: Application to

Polarization Sensing with Improved Sensitivity,” Journal

of Modern Optics, Vol. 39, No. 5, 1992, pp. 991-1001.

doi:10.1080/09500349214551021

[6] R. W. Boyd and J. H. Heebner, “Sensitive Disk Resonator

Photonic Biosensor,” Applied Optics, Vol. 40, No. 31,

2001, pp. 5742-5747. doi:10.1364/AO.40.005742

[7] Sai T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato and

Yasuo Kokubun, “An Eight-Channel Add/Drop Filter

Using Vertically Coupled Microring Resonator over a

Cross Grid,” IEEE Photoics Technology Letters, Vol. 11,

Issue 6, 1999, pp. 691-693.

[8] S. Mandal, K. Dasgupta, T. K. Basak and S. K. Ghosh, “A

Generalized Approach for Modeling and Analysis of

Ring-Resonator Performance as Optical Filter,” Optics

Communi cations, Vol. 264, No. 1, 2006, pp. 97-104.

doi:10.1016/j.optcom.2006.02.028

K. SHALMASHI ET AL.

178

[9] P. Saeung and P. P. Yupapin, “Generalized Analysis of

Multiple Ring Resonator Filters: Modeling by Using

Graphical Approach,” Optik, Vol. 119, No. 10, 2008, pp.

465-472. doi:10.1016/j.ijleo.2006.12.017

[10] S. Dilwali and G. S. Pandian, “Pulse Response of a Fiber

Dispersion Equalizing Scheme Based on an Optical

Resonator”, IEEE Photonics Technology Letters, Vol. 4,

No. 8, 1992, pp. 942-944. doi:10.1109/68.149917

[11] H. Shen, J.-P. Chen, X.-W. Li and Y.-P. Wang, “Group

Delay and Dispersion Analysis of Compound High Order

Microring Resonator All-Pass Filter,” Optics Communi-

cations, Vol. 262, No. 2, 2006, pp. 200-205.

doi:10.1016/j.optcom.2005.12.060

[12] Y. Dumeige, C. Arnaud and P. Féron, “Combining FDTD

with Coupled Mode Theories for Bistability in Micro-Ring

Resonators,” Optics Communications, Vol. 250, No. 4-6,

2005, pp. 376-383. doi:10.1016/j.optcom.2006.11.065

[13] P. P. Yupapin, “Coupler-Loss and Coupling-Coeffi-Cient-

Dependent Bistability and Instability in a Ring Resona-

tor,” Optik, Vol. 119, No. 10, 2008, pp. 492-494.

doi:10.1016/j.ijleo.2007.01.006

[14] O. Schwelb, “Crosstalk and Bandwidth of Lossy Micro-

ring Add/Drop Multiplexers,” Optics Communications,

Vol. 265, No. 1, 2006, pp. 175-179.

doi:10.1016/j.optcom.2006.02.055

[15] J. Q. Li, L. Li, J. Q. Zhao and C. F. Li, “Ultrafast, Low

Power, and Highly Stable All-Optical Switch in MZI with

Two-Arm-Sharing Nonlinear Ring Resonator,” Optics

Communications, Vol. 256, No. 4-6, 2005, pp. 319-325.

doi:10.1016/j.optcom.2005.06.087

[16] A. Rostami, “Low Threshold and Tuneable All-Optical

Switch Using Two-Photon Absorption in Array of Non-

linear Ring Resonators Coupled to MZI,” Microelectro-

nics Journal, Vol. 37, No. 9, 2006, pp. 976-981.

doi:10.1016/j.mejo.2006.01.021

[17] P. P. Yupapin, P. Chunpang, “An Experimental Investiga-

tion of the Optical Switching Characteristics Using

Optical Sagnac Interferometer Incorporating One and Two

Resonators,” Optics & Laser Technology, Vol. 40, No. 2,

2008, pp. 273-277. doi:10.1016/j.optlastec.2007.04.012

[18] J. L. S. Lima, K. D. A. Sabóia, J.C. Sales, J. W. M. Me-

nezes, W. B. de Fraga, G. F. Guimarães and A. S. B. Som-

bra, “Optical Short Pulse Switching Characteristics of

Ring Resonators,” Optical Fiber Technology, Vol. 14, No.

1, 2008, pp. 79-83. doi:10.1016/j.yofte.2007.07.004

[19] V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Gro-

ver and P. T. Ho, “Optical Signal Processing Using Non-

linear Semiconductor Microring Resonators,” IEEE Jour-

nal of Selected Topics in Quantum Electronics, Vol. 8, No.

3, 2002, pp. 705-713. doi:10.1109/JSTQE.2002.1016376

[20] H. Tazawa and W. H. Steier, “Analysis of Ring Resonator-

Based Traveling-Wave Modulators,” IEEE Photonics Te-

chnology Letters, Vol. 18, No., 2006, pp. 211-213.

[21] B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Micro-

ring Resonator Arrays for VLSI Photonics,” IEEE Photo-

nics Technology Letters, Vol. 12, No. 3, 2000, pp. 320-

325. doi:10.1109/68.826928

[22] F. E. Seraji, “New Methods for Rotation Sensing by Using

a Two-Coupler Fiber-Optic Ring Resonator,” Japanese

Journal of Applied Physics, Vol. 32, No. 4, 1993, pp.

1661-1667. doi:10.1143/JJAP.32.1661

[23] F. E. Seraji and G. S. Pandian, “Dynamic Response of a

Fiber Optic Ring Resonator with Sinusoidal Phase Modu-

lation of the Loop,” Journal of Modern Optics, Vol. 38,

No. 4, 1991, pp. 671-676.

doi:10.1080/09500349114550671

[24] G. S. Pandian and F. E. Seraji, “Dynamic Analysis of a

Fiber-Optic Ring Resonator Excited by a Sinewave-Mo-

dulated Laser Diode,” Japanese. Journal of Applied Phy-

sics, Vol. 29, No. 10, 1990, 1967-1973.

doi:10.1143/JJAP.29.1967

[25] D. Q. Ying, H. L. Ma and Z. H. Jin, “Dynamic Resonance

Characteristic Analysis of Fiber Ring Resonator,” Optical

Fiber Technology, Vol. 15, No. 1, 2009, pp. 15-20.

doi:10.1016/j.yofte.2008.03.005

[26] D. G. Rabus, M. Hamacher and H. Heidrich, “Resonance

Frequency Tuning of a Double Ring Resonator in GaIn-

AsP/InP: Experiment and Simulation,” Japanese Journal

of Applied Physics, Vol. 41, No. 1, 2002, pp. 1186-1189.

doi:10.1143/JJAP.41.1186

[27] J. Heebner, R. Grover and T. Ibrahim, “Optical Microre-

sonators: Theory, Fabrication, and Applications,” Sprin-

ger, Heidelberg, 2007.

[28] H. S. Jang, K. N. Park and K. S. Lee, “Characterization of

Tunable Photonic Crystal Fiber Directional Couplers,”

Applied Optics, Vol. 46, No. 18, 2007, pp. 3688-3693.

doi:10.1364/AO.46.003688

[29] H. Kim, . Kim, U.-C. Paek, B. H. Lee and K. T. Kim,

“Tunable Photonic Crystal Fiber Coupler Based on a

Side-Polishing Technique,” Optics Letters, Vol. 29, No.

11, 2004, pp. 1194-1196.

doi:10.1364/OL.29.001194

[30] F. E. Seraji, M. Rashidi and V. Khasheie, “Parameter

Analysis of a Photonic Crystal Fiber with Raised-Core

Index Profile Based on Effective Index Method,” Chinese

Optics Letters, Vol. 4, No. 8, 2006, pp. 442-445.

[31] M. Koshiba and K. Saitoh, “Structural Dependence of

Effective Area and Mode Field Diameter for Holey

Fibers,” Optics Express, Vol. 11, No. 15, 2003, pp. 1746-

1756. doi:10.1364/OE.11.001746

[32] T. A. Birks, J. C. Knight and P. S. J. Russell, “Endlessly

Single Mode Photonic Crystal Fibre,” Optics Letters, Vol.

22, No. 13, 1997, pp. 961-963.

doi:10.1364/OL.22.000961

[33] M. D. Nielsen, N. A. Mortensen, M. Albertsen, J. R.

Folkenberg, A. Bjarklev and D. Bonacinni, “Predicting

Macrobending Loss for Large-Mode Area Photonic

Crystal Fibers,” Optics Experss, Vol. 12, No. 8, 2004, pp.

1775-1779. doi:10.1364/OPEX.12.001775

[34] Y. F. Li, Y. H. Yao, M. L. Hu, L. Chai and C. Y. Wang,

“Improved Fully Vectorial Effective Index Method for

Photonic Crystal Fibers: Evaluation and Enhancement,”

Applied Optics, Vol. 47, No. 3, 2008, pp. 399-406.

doi:10.1364/AO.47.000399

[35] F. E. Seraji, “Steady-State Performance Analysis of Fiber-

Optic Ring Resonator,” Progress in Quantum Electronics,

Vol. 33, No. 1, 2009, pp. 1-16.

doi:10.1016/j.pquantelec.2008.10.001