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Flat-top and low-dispersion interleavers using Gires–Tournois etalons as phase dispersive mirrors in a Michelson interferometer
Optics Communications 237 (2004) 285–293 www.elsevier.com/locate/optcom
Flat-top and low-dispersion interleavers using Gires–Tournois etalons as phase dispersive mirrors in a Michelson interferometer C.H. Hsieh a, C.W. Lee a, S.Y. Huang a, R. Wang b, P. Yeh c, W.H. Cheng a
a,*
Institute of Electro-Optical Engineering, National Sun Yat-sen University, No.70 Lien Hai Rd., Kaohsoung 80424, Taiwan b Accumux Technologies, 834 Calle Plano, Camarillo, CA 93012, USA c Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA Received 18 December 2003; received in revised form 27 March 2004; accepted 31 March 2004
Abstract We demonstrate a flat-top and low-dispersion optical interleavers using Gires–Tournois etalons (GTEs) as phase dispersive mirrors in a Michelson interferometer. The spectral characteristics of the 50- and 25-GHz interleavers using one GTE and two GTEs are compared. The interleavers with two GTEs in a 50-GHz channel spacing application exhibit a 0.5-dB passband larger than 43.8 GHz, a 25-dB stopband greater than 40 GHz, and a channel isolation higher than 30 dB. The chromatic dispersion of the interleaver can be compensated within a 10 ps/nm. The results clearly show that the interleaver interferometer using phase dispersive nature of the GTE technique can simultaneously produce low dispersion, low insertion loss, and both a 0.5-dB passband and a 25-dB stopband wider than other interferometer techniques. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Dense wavelength division multiplexing; Interleaver; Gires–Tournois etalon
1. Introduction As the network traffic continues to increase, more bandwidths are needed to accommodate the transmission of the information. The most economical way of increasing the information transmission capacity is to simply increase the number *
Corresponding author. Tel.: +886752520004453; fax: +88675254499. E-mail address: [email protected] (W.H. Cheng).
of channels in dense wavelength division multiplexing (DWDM) networks [1]. Several techniques, including dielectric thin-film filters, array waveguide gratings (AWG), Fabry–Perot filters, diffraction gratings, and unbalanced Mach–Zehnder interferometers, can be employed in DWDM systems for packing as many channels as possible into fiber-optic networks. In WDM system each high-speed data channel transmits its information at a pre-defined wavelength on a single optical channel. At a receiver
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.03.085
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end, channels of different wavelengths are generally separated by narrow band filters and then detected. In practice, the number of channels that can be carried by a single optical channel in a WDM system is limited by crosstalk, narrow operating bandwidth of optical amplifiers, and/or optical fiber nonlinearities. Furthermore, such systems require an accurate band selection, stable tunable lasers or filters, and spectral purity that increase the cost of WDM systems and add to their complexity. Currently, most of the commercial systems employ the standard carrier frequencies with channel spacing of 100 GHz (equivalent to 0.8 nm) specified by the International Telecommunication Union (ITU). When the channel separation decreases, the requirement for more precise demultiplexing circuitry capable of ultranarrow-band filtering, minimum crosstalk, increases. Using conventional thin-film filters to separate channels spaced by 0.4 nm or less without crosstalk is impracticable and such filters are difficult to fabricate. In this study, we present a novel interleaver for filtering or separating closely spaced channels that would otherwise not suitably be filtered by conventional optical filters. An interleaver can provide a cost-effective method to increase the transmission capacity, it can double the capacity of an existing network, and enable new designs for a very high channel count systems leading to Terabit capacities. Basically, two separate mux or demux devices with twice the channel target spacing are combined to cover the entire operating window by interleaving the channels. One mux or demux covers the odd channels and the other covers the even ones, as shown in Fig. 1. For example, a 50GHz interleaver can be used to separate one set of 50 GHz spaced signals into two sets of 100 GHz spaced signals, or to combine the two sets of 100 GHz spaced signals into one set of 50 GHz spaced signals. This approach allows a technology that performs better at a wider channel spacing to address a narrower one. Most optical interleaver designs are based on Michelson–Gires–Tournois interferometer [2,3], ring resonator type filters [4,5], hybrid coupler and delay line on planar lightwave circuits [3,6], hybrid filters and array waveguides [7], and birefringent
1 3 5 123456
Interleaver
2 4 6
Input
Output
Fig. 1. An interleaver.
crystals [8]. When we compare Michelson type interleavers with birefringent GTI interleaver, the temperature change may induce an isolation decrease due to the phase difference change in the two arms in Michelson type interleavers. In the birefringent GTI interleaver the isolation may be stable. However, PMD will change with temperature, especially, at the GTI’s resonant frequencies. Unless the two etalons have the same resonant frequency which is difficult to achieve over a wide temperature range, the resonant frequency difference will translate the chromatic dispersion into PMD. Recently, flat-top interleavers using two Gires– Tournois etalons (GTEs) as phase dispersive mirrors in a Michelson interferometer have been reported [9]. For the work reported in this paper, we extended the previous work to both the 50- and 25-GHz interleavers with one GTE and two GTEs. We also measured their chromatic dispersion characteristics. Then we included a dispersioncompensation element in order to obtain both the low-dispersion and flat-top interleavers. The phase dispersive nature of the etalon-based GTE exhibits a periodic dependence on the frequency of light, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off. The benefits of proposed interleaver interferometer with novel GTE technique can simultaneously produce low residual dispersion, both a 0.5-dB passband and a 25-dB stopband wider than other interferometer techniques. This interleaver is suitable for capacity upgrade in highspeed DWDM applications.
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This paper is organized as follows. Section 2 describes the optimum design of flat-top and lowdispersion interleavers. The results of numerical simulations of interleavers are presented in Section 3. The measurement results of interleavers are presented in Section 4. A discussion and brief summary are given in Section 5. 2. Optimum design of flat-top and low-dispersion interleavers Generally speaking, interleavers are made of optical interferometers. The interference creates an optical output which is a periodic function of frequency. The period is determined by the path length difference in the two arms of the interferometer. Fig. 2 shows the experimental setup of an interleaver. In this case, the interleaver consists of a 50:50 beam splitter for splitting and recombining the beams, and two GTEs. The GTE, acting as phase dispersive mirrors, consists of a front mirror of finite reflectivity and a rear mirror of near 100% reflectivity. Both two GTEs are aligned perpendicular with the light beams. The phase dispersion of the etalon exhibits a periodic dependence on the frequency of light. The output intensity of the interleaver depends on the path length difference as well as the cavity spacing of the etalon. For optimum interleaver performance, the path difference DL ¼ L1 L2 is chosen to be one-half of the air space inside the GTE, as shown in Fig. 2. Such interferometers can be employed as spectral interleavers for DWDM applications. A desirable interleaver should provide a flat-top spectral R=1
Gires – Tournois Etalon
d R1<1 L1
Input beam
Beam Splitter d
Output port 2
Output port 1
L2 R2<1 R=1 Gires – Tournois Etalon
Fig. 2. Schematic drawing of the Gires–Tournois etalon interleaver.
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transmission passband for each of the ITU frequency channels. 2.1. Michelson interferometer Conventional optical interferometer, such as Michelson or Mach–Zehnder, is made of optical interferometers that employ a beam splitter to split the input beam into two. These two beams are then recombined at the beam splitter by using two mirrors to provide the redirection. Fig. 2 can also show a Michelson interferometer by replacing the GTE as a regular mirror. The intensity of one of the output ports is sinusoidal function of frequency and can be written as I0 2p I1 ¼ m2DL ; ð1Þ 1 þ cos c 2 where I0 is the intensity of the input beam, DL is the one-way path length difference of the two arms, c is the speed of light in vacuum, and m is the optical frequency. The factor 2 in front of DL accounts for the round-trip propagation. The transmittance in dB, T1 , can be expressed as T1 ¼ 10 logðI1 =I0 Þ:
ð2Þ
2.2. Interleaver interferometer If mirrors of different dispersive properties are employed, such as interleaver as shown in Fig. 2, the intensity from Eq. (1) becomes I0 2p I2 ¼ m2DL þ ðu2 u1 Þ ; 1 þ cos ð3Þ c 2 where u2 and u1 are the phase shifts of the second and first GTE mirrors, respectively. The transmittance in dB, T2 , can be expressed as T2 ¼ 10 logðI2 =I0 Þ:
ð4Þ
From Eq. (3), we need at least one dispersive mirror to obtain an intensity transmission function that is different from the sinusoidal function. Furthermore, the frequency dependence of the phase shift must exhibit a periodic variation, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off.
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The reflection coefficient of the GTE can be written as [10] r¼
r1 þ r2 e2i/ ; 1 þ r1 r2 e2i/
ð5Þ
where / ¼ 2pd=k and is the phase shift due to the one-way propagation through the air space of d inside the GTEs for an optical beam with a wavelength pofffiffiffi k. For an ideal GTE, we can choice r1 ¼ R and r2 ¼ 1, where R is the power reflectance of the GTE. In the Michelson interferometer, the GTEs serve as spectrally dispersive mirrors. The phase shift difference u2 u1 between the two GTEs can be written as [10, Chapter 3;12] pffiffiffiffiffi 1 þ R2 p ffiffiffiffiffi u2 u1 ¼ 2 tan tanð/Þ 1 R2 pffiffiffiffiffi R1 1 1 þ pffiffiffiffiffi tanð/Þ ; þ 2 tan 1 R1 1
ð6Þ
where R1 and R2 are the reflectivity of the front mirror for the first and second GTE, respectively. In this study, the optimum reflectivities of the flattop bandwidth intervleaver are around R1 ¼ 50:5% and R2 ¼ 5:5%. The phase dispersion of the etalon exhibits a periodic dependence on the frequency of light, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off. The phase shift of the GTE satisfies such requirements [10, Chapter 3;11–13]. The phase shift varies from zero to 2p and is a periodic function of frequency with a period of c=2d, where d is the air space of the GTE. A proper relationship between the air space of the GTE and the path difference is needed to ensure a desirable transmission function. In general, the path difference DL is chosen to be one-half of the air space inside the GTE. In addition, a proper constant phase bias of p=2 is often needed to ensure the desirable flat-top transmission function. 2.3. Chromatic dispersion The chromatic dispersion in fiber becomes important when the transmission speed is higher than 10 Gb/s. The group delay si ðxÞ is defined by
duı ðxÞ=dx [14] where i ¼ 1 or 2. The output group delay from the Michelson Interferometer can be viewed as the average group delay from two arms, sðxÞ ¼ ðs1 ðxÞ þ s2 ðxÞÞ=2, and can be derived from Eq. (6) as 1 R2 pffiffiffiffiffi 1 þ R2 2 R2 cos 4p d k ! 1 R1 ; pffiffiffiffiffi þ 1 þ R1 2 R1 cos 4p d k
sðxÞ ¼
T 2
ð7Þ
where x ¼ 2pc=k and is the optical angular frequency, T ¼ 2d=c and is the round-trip time in the GTE, R1 and R2 are the reflectivity of the front mirror for the first and second GTE, respectively, and k ¼ c=t. Then the chromatic dispersion is given by DðkÞ ¼ ds=dk (ps/nm) [14] and can be derived from Eq. (7) as ( pffiffiffiffiffi T 4pd sin 4p d R2 ð1 R2 Þ k DðkÞ ¼ 2 pffiffiffiffiffi k2 1 þ R2 2 R2 cos 4p d k ) pffiffiffiffiffi R1 ð1 R1 Þ þ ð8Þ 2 : pffiffiffiffiffi 1 þ R1 2 R1 cos 4p d k 2.4. Chromatic dispersion compensation The CD of the interleaver can be compensated by placing an etalon at the output of the interleaver. The key for compensating the CD is to match the opposite amount of the CD in the passband. Here we chose an etalon with multi-cavity as our dispersion-compensation element. A multi-cavity etalon provides the advantage of replacing multiple single cavity etalons, simplifying tuning control, designing flexible and reducing insertion loss. Increasing the number of cavities per etalon typically achieves the available desire dispersion slope [15]. We used two cavities per etalon. The gap distance dc between the 1st and 2nd surfaces is equal to that between the 2nd and 3rd surfaces. The reflectivities for each surface are R1c , R2c , and 1, respectively. The phase shift uc of the etalon can be expressed as ( ) pffiffiffiffiffiffiffi 1 þ R ð Þ sin 2/ 1c c pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi ; uc ¼ 2 tan1 1 R1c cos ð2/c Þ R2c ð9Þ
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where /c ¼ 2pdc =k and is the phase shift due to the one-way propagation through the air gap. The group delay sðxÞ is defined by duðxÞ=dx [14] and can be derived from Eq. (9) as
sðxÞ ¼
GHz) of 50-GHz channel spacing. In the case of one GTE, the 0.5-dB passband is only 85% (43 GHz). This clearly indicates that interleavers with two GTEs provide a wider 0.5-dB passband.
pffiffiffiffiffiffiffi 2 T 1 R1c pffiffiffiffiffiffiffi 2 ; pffiffiffiffiffiffiffi2 pffiffiffiffiffiffiffi2 2 4p d þ 1 þ R sin d 1 R1c cos 4p R c 2c 1c c k k
where x ¼ 2pc=k and is the optical angular frequency, T ¼ 2d=c and is the round-trip time in the GTE, the gap distance dc between the 1st and 2nd surfaces is equal to that between the 2nd and 3rd surfaces. The reflectivities for each surface are R1c , R2c , and 1, respectively, and k ¼ c=t. Then the dispersion of the compensating etalon can be derived from the relation, Dc ðkÞ ¼ ds=dk. Therefore, the total dispersion of the interleaver is Dt ðkÞ ¼ DðkÞ þ Dc ðkÞ. In this study, the optimum reflectivities of the dispersion compensated etalon are about R1c ¼ 0:01% and R2c ¼ 33%.
289
ð10Þ
Fig. 4 shows the simulation results of the stopband and channel isolation for one GTE, two GTEs, and a simple Michelson interferometers (without GTE) in 50-GHz channel spacing application. The 25-dB stopbands were found to be 0.27, 0.33, and 0.03 nm for one GTE, two GTEs, and Michelson interferometers, respectively. Fig. 4 shows that the 25-dB stopband of interleaver
3. Simulation results 3.1. Flat-top interleaver GTE mirrors are desirable in many applications. These include high finesse Fabry–Perot interferometers and low loss laser resonators. Eq. (6) indicates that the phase shift of the GTEs depends on the reflectivity of the front mirror for the first and second GTE. Hence, only the right reflectivity can meet the flat-top bandwidth. Based on Eqs. (1)–(4) and (6), the simulation results of the 0.5-dB passband, where we define 0.5-dB passband as full width of 0.5 dB down from the top, for one GTE, two GTEs, and a simple Michelson interferometers (without GTE) in 50-GHz channel spacing application are shown in Fig. 3. From Fig. 3(a) it is seen that the flat-top ripple decreases from 0.01 to 0.001dB as the GTE increases from one to two. Fig. 3(b) shows that the 0.5-dB passbands of one GTE, two GTEs, and Michelson interferometers (without GTE) are 0.34, 0.37, and 0.18 nm, respectively. Fig. 3(b) shows that the 0.5-dB passband of interleaver with two GTEs is near 93% (46
Fig. 3. The simulation results of (a) the ripple and (b) the 0.5dB passband for Michelson (without GTE), one GTE, and two GTEs interferometers in a 50-GHz channel spacing.
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Fig. 4. The simulation results of the 25-dB stopband and channel isolation for Michelson (without GTE), one GTE, and two GTEs interferometers in a 50-GHz channel spacing.
Fig. 5. The dispersion simulations of the 25-GHz passband for one GTE and two GTEs in a 50-GHz interleaver channel spacing.
interferometer with two GTEs is near 82% (41 GHz) of 50-GHz channel spacing compared to one GTE 67% (34 GHz). This clearly indicates that interleavers with two GTEs provide a wider 25-dB stopband. Fig. 4 also shows that the channel isolation increases from 26 to 36 dB as the GTE increases from one to two. 3.2. Dispersion in interleavers Using Eqs. (7) and (8), the dispersion simulations of the 25-GHz passband for one GTE and two GTEs in a 50-GHz interleaver channel spacing are shown in Fig. 5. From Fig. 5 it is seen that the dispersion of the 25-GHz passband increases from )5865 to )100120 ps/nm range as the GTE increases from one to two. Similar results of the 12.5-GHz passband for one GTE and two GTEs in a 25-GHz interleaver channel spacing are shown in Fig. 6. The dispersion of the 12.5-GHz passband increases from )275245 to )450450 ps/nm range as the GTE increases from one to two. 3.3. Chromatic dispersion compensation In lightwave communication applications, interleaver with low chromatic dispersion is required. To reduce chromatic dispersion in the proposed interleaver, an additional GTE with two cavities may be introduced to compensate the
Fig. 6. The dispersion simulations of the 12.5-GHz passband for one GTE and two GTEs in a 25-GHz interleaver channel spacing.
chromatic dispersion caused by the original GTE configuration, as shown in Fig. 7. Based on Eqs. (7)–(10), the simulation of chromatic dispersion of the 50-GHz interleaver before, with additional etalons, and after dispersion compensation are shown in Fig. 8. Fig. 8 shows that the simulation of chromatic dispersion of the 50-GHz interleaver can be compensated within a 10 ps/nm. This residual dispersion will not cause a noticeable penalty for the high-speed optical fiber communication systems. Clearly, the detailed understanding of the dispersion and its compensation in the real device is necessary and will be pursued in a separate study.
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stopband, and channel isolation are measured from the waveform monitor. 4.1. Spectral characteristics of interleavers
Fig. 7. Schematic drawing of the Gires–Tournois etalon with dispersion-compensation element interleaver.
The channel isolation of the 50-GHz interleaver with two GTEs for output port 1 and port 2 is shown in Fig. 9(a). Fig. 9(a) shows that the interleaver in a 50-GHz channel spacing exhibits a channel isolation better than 30 dB between adjacent channels. Fig. 9(b) shows the 0.5-dB passband and 25-dB stopband of our interleaver with 50-GHz channel spacing for output port 2. This spectral characteristic exhibits a 0.5-dB passband of 0.35 nm (43.8 GHz), a 25-dB stopband of 0.32 nm (40 GHz), and a insertion loss of 1.3 dB. The measured results of 0.5-dB passband and 25-dB
Fig. 8. The simulated chromatic dispersion of the 50-GHz interleaver before, with additional etalons, and after dispersion compensation.
4. Measurement results For the purpose of our measurement, a circulator for output port 2 and a collimator for output port 1 are used. The optical path difference of two arms is adjusted to equal to one-half of the air spacing in the GTE to ensure a period of 50 GHz. The substrate of the regular mirror is chosen to be the same as that of the partial reflecting dielectric mirror. This is to ensure a complete cancellation of the phase between the paths due to the glass substrates. A C-band tunable laser as light source and an optical spectral analyzer as waveform monitor are used for the interference measurements. The periodic channel spacing, 0.5-dB passband, 25-dB
Fig. 9. The measured (a) the channel isolation for output port 1 and port 2, and (b) the 0.5-dB passband and 25-dB stopband for output port 2 in a 50-GHz interleaver channel spacing.
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stopband in Fig. 9 are in good agreement with the simulation results in Figs. 3 and 4. Similar result of the channel isolation of the 25GHz interleaver with two GTEs for output port 1 and port 2 is shown in Fig. 10. Fig. 10 shows that the interleaver in a 25-GHz channel spacing exhibits a channel isolation better than 32 dB between adjacent channels. This spectral characteristic also exhibits a 0.5-dB passband of 0.17 nm (21.3 GHz) and a 25-dB stopband of 0.16 nm (20 GHz). 4.2. Dispersion in interleavers Fig. 11 shows the measured chromatic dispersion of the interleaver with two GTEs in a 50-GHz channel spacing. The chromatic dispersion of the 25-GHz passband was measured between )95 and 113 ps/nm ranges. The measured result of the chromatic dispersion of 25-GHz passband for a 50-GHz interleaver with two GTEs is in good agreement with the simulation results in Fig. 5. Fig. 10 also shows the chromatic dispersion of the interleaver with two GTEs in a 25-GHz channel spacing. The chromatic dispersion of the 12.5-GHz passband was measured approximately between )440 and 430 ps/nm ranges. The measured result of the chromatic dispersion of 12.5GHz passband for a 25-GHz interleaver with two GTEs is also in good agreement with the simulation results in Fig. 6.
Fig. 11. The measured chromatic dispersion of the interleaver with two GTEs in a 50-GHz channel spacing.
In this study, the chromatic dispersions were measured about 100 and 440 ps/nm for 50- and 25-GHz interleavers, respectively. 4.3. Bandwidth compared to the other-type interleavers Fig. 9(b) shows that the 0.5-dB passband is near 88% (43.8 GHz) of the 50-GHz channel spacing with two GTEs configuration. Fig. 10 also shows that the 0.5-dB passband is near 85% (21.3GHz) of the 25-GHz channel spacing with two GTEs. These results are much better as compared with hybrid coupler and delay line on planar lightwave circuits (70% of the spacing) [3,6], hybrid filter and array waveguides (60% of the spacing) [7], and birefringent crystals (77% of the spacing) [8]. Furthermore, the results indicate that the interleaver interferometer with novel GTE technique exhibits a wider 0.5-dB passband and 25-dB stopband when compared to current fabrication interleaver interferometer technologies.
5. Discussion and conclusion
Fig. 10. The measured the channel isolation for output port 1 and port 2, the 0.5-dB passband and 25-dB stopband for output port 2, and the chromatic dispersion in a 25-GHz interleaver channel spacing.
In summary, we have developed and fabricated the flat-top and low-dispersion 50- and 25GHz optical interleavers for DWDM optical networks. The spectral characteristics of the interleaver with two GTEs in a 50-GHz channel
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spacing application exhibited a 0.5-dB passband larger than 43.8 GHz (88% of the spacing), a 25dB stopband greater than 40 GHz (80% of the spacing), and a channel isolation higher than 30 dB. The interleaver with two GTEs in a 25-GHz channel spacing application also exhibited a 0.5dB passband larger than 21.3 GHz (85% of the spacing), a 25-dB stopband greater than 20 GHz (80% of the spacing), and a channel isolation higher than 32 dB. The benefit of this novel interleaver utilizes the phase dispersive nature of the GTE mirrors to ensure flat-top transmission passbands, as well as superior channel isolation. The phase dispersion of the etalon-based GTE exhibits a periodic dependence on the frequency of light, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off. The results clearly indicate that the interleaver interferometer with novel GTE technique can simultaneously produce a 0.5-dB passband and a 25-dB stopband wider than other interferometer techniques. We also showed that the chromatic dispersion of the proposed interleaver could be compensated within a 10 ps/nm. A similar flat-top and low-dispersion interleavers using GTE technique in smaller channel spacing may also be fabricated. The flexibility in design and the excellent performance of interleaver make the GTE-based interleaver extremely attractive for using in very
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high channel count systems leading to Terabit capacities.
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Flat-top and low-dispersion interleavers using Gires–Tournois etalons as phase dispersive mirrors in a Michelson interferometer C.H. Hsieh a, C.W. Lee a, S.Y. Huang a, R. Wang b, P. Yeh c, W.H. Cheng a
a,*
Institute of Electro-Optical Engineering, National Sun Yat-sen University, No.70 Lien Hai Rd., Kaohsoung 80424, Taiwan b Accumux Technologies, 834 Calle Plano, Camarillo, CA 93012, USA c Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA Received 18 December 2003; received in revised form 27 March 2004; accepted 31 March 2004
Abstract We demonstrate a flat-top and low-dispersion optical interleavers using Gires–Tournois etalons (GTEs) as phase dispersive mirrors in a Michelson interferometer. The spectral characteristics of the 50- and 25-GHz interleavers using one GTE and two GTEs are compared. The interleavers with two GTEs in a 50-GHz channel spacing application exhibit a 0.5-dB passband larger than 43.8 GHz, a 25-dB stopband greater than 40 GHz, and a channel isolation higher than 30 dB. The chromatic dispersion of the interleaver can be compensated within a 10 ps/nm. The results clearly show that the interleaver interferometer using phase dispersive nature of the GTE technique can simultaneously produce low dispersion, low insertion loss, and both a 0.5-dB passband and a 25-dB stopband wider than other interferometer techniques. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Dense wavelength division multiplexing; Interleaver; Gires–Tournois etalon
1. Introduction As the network traffic continues to increase, more bandwidths are needed to accommodate the transmission of the information. The most economical way of increasing the information transmission capacity is to simply increase the number *
Corresponding author. Tel.: +886752520004453; fax: +88675254499. E-mail address: [email protected] (W.H. Cheng).
of channels in dense wavelength division multiplexing (DWDM) networks [1]. Several techniques, including dielectric thin-film filters, array waveguide gratings (AWG), Fabry–Perot filters, diffraction gratings, and unbalanced Mach–Zehnder interferometers, can be employed in DWDM systems for packing as many channels as possible into fiber-optic networks. In WDM system each high-speed data channel transmits its information at a pre-defined wavelength on a single optical channel. At a receiver
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.03.085
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end, channels of different wavelengths are generally separated by narrow band filters and then detected. In practice, the number of channels that can be carried by a single optical channel in a WDM system is limited by crosstalk, narrow operating bandwidth of optical amplifiers, and/or optical fiber nonlinearities. Furthermore, such systems require an accurate band selection, stable tunable lasers or filters, and spectral purity that increase the cost of WDM systems and add to their complexity. Currently, most of the commercial systems employ the standard carrier frequencies with channel spacing of 100 GHz (equivalent to 0.8 nm) specified by the International Telecommunication Union (ITU). When the channel separation decreases, the requirement for more precise demultiplexing circuitry capable of ultranarrow-band filtering, minimum crosstalk, increases. Using conventional thin-film filters to separate channels spaced by 0.4 nm or less without crosstalk is impracticable and such filters are difficult to fabricate. In this study, we present a novel interleaver for filtering or separating closely spaced channels that would otherwise not suitably be filtered by conventional optical filters. An interleaver can provide a cost-effective method to increase the transmission capacity, it can double the capacity of an existing network, and enable new designs for a very high channel count systems leading to Terabit capacities. Basically, two separate mux or demux devices with twice the channel target spacing are combined to cover the entire operating window by interleaving the channels. One mux or demux covers the odd channels and the other covers the even ones, as shown in Fig. 1. For example, a 50GHz interleaver can be used to separate one set of 50 GHz spaced signals into two sets of 100 GHz spaced signals, or to combine the two sets of 100 GHz spaced signals into one set of 50 GHz spaced signals. This approach allows a technology that performs better at a wider channel spacing to address a narrower one. Most optical interleaver designs are based on Michelson–Gires–Tournois interferometer [2,3], ring resonator type filters [4,5], hybrid coupler and delay line on planar lightwave circuits [3,6], hybrid filters and array waveguides [7], and birefringent
1 3 5 123456
Interleaver
2 4 6
Input
Output
Fig. 1. An interleaver.
crystals [8]. When we compare Michelson type interleavers with birefringent GTI interleaver, the temperature change may induce an isolation decrease due to the phase difference change in the two arms in Michelson type interleavers. In the birefringent GTI interleaver the isolation may be stable. However, PMD will change with temperature, especially, at the GTI’s resonant frequencies. Unless the two etalons have the same resonant frequency which is difficult to achieve over a wide temperature range, the resonant frequency difference will translate the chromatic dispersion into PMD. Recently, flat-top interleavers using two Gires– Tournois etalons (GTEs) as phase dispersive mirrors in a Michelson interferometer have been reported [9]. For the work reported in this paper, we extended the previous work to both the 50- and 25-GHz interleavers with one GTE and two GTEs. We also measured their chromatic dispersion characteristics. Then we included a dispersioncompensation element in order to obtain both the low-dispersion and flat-top interleavers. The phase dispersive nature of the etalon-based GTE exhibits a periodic dependence on the frequency of light, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off. The benefits of proposed interleaver interferometer with novel GTE technique can simultaneously produce low residual dispersion, both a 0.5-dB passband and a 25-dB stopband wider than other interferometer techniques. This interleaver is suitable for capacity upgrade in highspeed DWDM applications.
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This paper is organized as follows. Section 2 describes the optimum design of flat-top and lowdispersion interleavers. The results of numerical simulations of interleavers are presented in Section 3. The measurement results of interleavers are presented in Section 4. A discussion and brief summary are given in Section 5. 2. Optimum design of flat-top and low-dispersion interleavers Generally speaking, interleavers are made of optical interferometers. The interference creates an optical output which is a periodic function of frequency. The period is determined by the path length difference in the two arms of the interferometer. Fig. 2 shows the experimental setup of an interleaver. In this case, the interleaver consists of a 50:50 beam splitter for splitting and recombining the beams, and two GTEs. The GTE, acting as phase dispersive mirrors, consists of a front mirror of finite reflectivity and a rear mirror of near 100% reflectivity. Both two GTEs are aligned perpendicular with the light beams. The phase dispersion of the etalon exhibits a periodic dependence on the frequency of light. The output intensity of the interleaver depends on the path length difference as well as the cavity spacing of the etalon. For optimum interleaver performance, the path difference DL ¼ L1 L2 is chosen to be one-half of the air space inside the GTE, as shown in Fig. 2. Such interferometers can be employed as spectral interleavers for DWDM applications. A desirable interleaver should provide a flat-top spectral R=1
Gires – Tournois Etalon
d R1<1 L1
Input beam
Beam Splitter d
Output port 2
Output port 1
L2 R2<1 R=1 Gires – Tournois Etalon
Fig. 2. Schematic drawing of the Gires–Tournois etalon interleaver.
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transmission passband for each of the ITU frequency channels. 2.1. Michelson interferometer Conventional optical interferometer, such as Michelson or Mach–Zehnder, is made of optical interferometers that employ a beam splitter to split the input beam into two. These two beams are then recombined at the beam splitter by using two mirrors to provide the redirection. Fig. 2 can also show a Michelson interferometer by replacing the GTE as a regular mirror. The intensity of one of the output ports is sinusoidal function of frequency and can be written as I0 2p I1 ¼ m2DL ; ð1Þ 1 þ cos c 2 where I0 is the intensity of the input beam, DL is the one-way path length difference of the two arms, c is the speed of light in vacuum, and m is the optical frequency. The factor 2 in front of DL accounts for the round-trip propagation. The transmittance in dB, T1 , can be expressed as T1 ¼ 10 logðI1 =I0 Þ:
ð2Þ
2.2. Interleaver interferometer If mirrors of different dispersive properties are employed, such as interleaver as shown in Fig. 2, the intensity from Eq. (1) becomes I0 2p I2 ¼ m2DL þ ðu2 u1 Þ ; 1 þ cos ð3Þ c 2 where u2 and u1 are the phase shifts of the second and first GTE mirrors, respectively. The transmittance in dB, T2 , can be expressed as T2 ¼ 10 logðI2 =I0 Þ:
ð4Þ
From Eq. (3), we need at least one dispersive mirror to obtain an intensity transmission function that is different from the sinusoidal function. Furthermore, the frequency dependence of the phase shift must exhibit a periodic variation, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off.
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The reflection coefficient of the GTE can be written as [10] r¼
r1 þ r2 e2i/ ; 1 þ r1 r2 e2i/
ð5Þ
where / ¼ 2pd=k and is the phase shift due to the one-way propagation through the air space of d inside the GTEs for an optical beam with a wavelength pofffiffiffi k. For an ideal GTE, we can choice r1 ¼ R and r2 ¼ 1, where R is the power reflectance of the GTE. In the Michelson interferometer, the GTEs serve as spectrally dispersive mirrors. The phase shift difference u2 u1 between the two GTEs can be written as [10, Chapter 3;12] pffiffiffiffiffi 1 þ R2 p ffiffiffiffiffi u2 u1 ¼ 2 tan tanð/Þ 1 R2 pffiffiffiffiffi R1 1 1 þ pffiffiffiffiffi tanð/Þ ; þ 2 tan 1 R1 1
ð6Þ
where R1 and R2 are the reflectivity of the front mirror for the first and second GTE, respectively. In this study, the optimum reflectivities of the flattop bandwidth intervleaver are around R1 ¼ 50:5% and R2 ¼ 5:5%. The phase dispersion of the etalon exhibits a periodic dependence on the frequency of light, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off. The phase shift of the GTE satisfies such requirements [10, Chapter 3;11–13]. The phase shift varies from zero to 2p and is a periodic function of frequency with a period of c=2d, where d is the air space of the GTE. A proper relationship between the air space of the GTE and the path difference is needed to ensure a desirable transmission function. In general, the path difference DL is chosen to be one-half of the air space inside the GTE. In addition, a proper constant phase bias of p=2 is often needed to ensure the desirable flat-top transmission function. 2.3. Chromatic dispersion The chromatic dispersion in fiber becomes important when the transmission speed is higher than 10 Gb/s. The group delay si ðxÞ is defined by
duı ðxÞ=dx [14] where i ¼ 1 or 2. The output group delay from the Michelson Interferometer can be viewed as the average group delay from two arms, sðxÞ ¼ ðs1 ðxÞ þ s2 ðxÞÞ=2, and can be derived from Eq. (6) as 1 R2 pffiffiffiffiffi 1 þ R2 2 R2 cos 4p d k ! 1 R1 ; pffiffiffiffiffi þ 1 þ R1 2 R1 cos 4p d k
sðxÞ ¼
T 2
ð7Þ
where x ¼ 2pc=k and is the optical angular frequency, T ¼ 2d=c and is the round-trip time in the GTE, R1 and R2 are the reflectivity of the front mirror for the first and second GTE, respectively, and k ¼ c=t. Then the chromatic dispersion is given by DðkÞ ¼ ds=dk (ps/nm) [14] and can be derived from Eq. (7) as ( pffiffiffiffiffi T 4pd sin 4p d R2 ð1 R2 Þ k DðkÞ ¼ 2 pffiffiffiffiffi k2 1 þ R2 2 R2 cos 4p d k ) pffiffiffiffiffi R1 ð1 R1 Þ þ ð8Þ 2 : pffiffiffiffiffi 1 þ R1 2 R1 cos 4p d k 2.4. Chromatic dispersion compensation The CD of the interleaver can be compensated by placing an etalon at the output of the interleaver. The key for compensating the CD is to match the opposite amount of the CD in the passband. Here we chose an etalon with multi-cavity as our dispersion-compensation element. A multi-cavity etalon provides the advantage of replacing multiple single cavity etalons, simplifying tuning control, designing flexible and reducing insertion loss. Increasing the number of cavities per etalon typically achieves the available desire dispersion slope [15]. We used two cavities per etalon. The gap distance dc between the 1st and 2nd surfaces is equal to that between the 2nd and 3rd surfaces. The reflectivities for each surface are R1c , R2c , and 1, respectively. The phase shift uc of the etalon can be expressed as ( ) pffiffiffiffiffiffiffi 1 þ R ð Þ sin 2/ 1c c pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi ; uc ¼ 2 tan1 1 R1c cos ð2/c Þ R2c ð9Þ
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where /c ¼ 2pdc =k and is the phase shift due to the one-way propagation through the air gap. The group delay sðxÞ is defined by duðxÞ=dx [14] and can be derived from Eq. (9) as
sðxÞ ¼
GHz) of 50-GHz channel spacing. In the case of one GTE, the 0.5-dB passband is only 85% (43 GHz). This clearly indicates that interleavers with two GTEs provide a wider 0.5-dB passband.
pffiffiffiffiffiffiffi 2 T 1 R1c pffiffiffiffiffiffiffi 2 ; pffiffiffiffiffiffiffi2 pffiffiffiffiffiffiffi2 2 4p d þ 1 þ R sin d 1 R1c cos 4p R c 2c 1c c k k
where x ¼ 2pc=k and is the optical angular frequency, T ¼ 2d=c and is the round-trip time in the GTE, the gap distance dc between the 1st and 2nd surfaces is equal to that between the 2nd and 3rd surfaces. The reflectivities for each surface are R1c , R2c , and 1, respectively, and k ¼ c=t. Then the dispersion of the compensating etalon can be derived from the relation, Dc ðkÞ ¼ ds=dk. Therefore, the total dispersion of the interleaver is Dt ðkÞ ¼ DðkÞ þ Dc ðkÞ. In this study, the optimum reflectivities of the dispersion compensated etalon are about R1c ¼ 0:01% and R2c ¼ 33%.
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ð10Þ
Fig. 4 shows the simulation results of the stopband and channel isolation for one GTE, two GTEs, and a simple Michelson interferometers (without GTE) in 50-GHz channel spacing application. The 25-dB stopbands were found to be 0.27, 0.33, and 0.03 nm for one GTE, two GTEs, and Michelson interferometers, respectively. Fig. 4 shows that the 25-dB stopband of interleaver
3. Simulation results 3.1. Flat-top interleaver GTE mirrors are desirable in many applications. These include high finesse Fabry–Perot interferometers and low loss laser resonators. Eq. (6) indicates that the phase shift of the GTEs depends on the reflectivity of the front mirror for the first and second GTE. Hence, only the right reflectivity can meet the flat-top bandwidth. Based on Eqs. (1)–(4) and (6), the simulation results of the 0.5-dB passband, where we define 0.5-dB passband as full width of 0.5 dB down from the top, for one GTE, two GTEs, and a simple Michelson interferometers (without GTE) in 50-GHz channel spacing application are shown in Fig. 3. From Fig. 3(a) it is seen that the flat-top ripple decreases from 0.01 to 0.001dB as the GTE increases from one to two. Fig. 3(b) shows that the 0.5-dB passbands of one GTE, two GTEs, and Michelson interferometers (without GTE) are 0.34, 0.37, and 0.18 nm, respectively. Fig. 3(b) shows that the 0.5-dB passband of interleaver with two GTEs is near 93% (46
Fig. 3. The simulation results of (a) the ripple and (b) the 0.5dB passband for Michelson (without GTE), one GTE, and two GTEs interferometers in a 50-GHz channel spacing.
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Fig. 4. The simulation results of the 25-dB stopband and channel isolation for Michelson (without GTE), one GTE, and two GTEs interferometers in a 50-GHz channel spacing.
Fig. 5. The dispersion simulations of the 25-GHz passband for one GTE and two GTEs in a 50-GHz interleaver channel spacing.
interferometer with two GTEs is near 82% (41 GHz) of 50-GHz channel spacing compared to one GTE 67% (34 GHz). This clearly indicates that interleavers with two GTEs provide a wider 25-dB stopband. Fig. 4 also shows that the channel isolation increases from 26 to 36 dB as the GTE increases from one to two. 3.2. Dispersion in interleavers Using Eqs. (7) and (8), the dispersion simulations of the 25-GHz passband for one GTE and two GTEs in a 50-GHz interleaver channel spacing are shown in Fig. 5. From Fig. 5 it is seen that the dispersion of the 25-GHz passband increases from )5865 to )100120 ps/nm range as the GTE increases from one to two. Similar results of the 12.5-GHz passband for one GTE and two GTEs in a 25-GHz interleaver channel spacing are shown in Fig. 6. The dispersion of the 12.5-GHz passband increases from )275245 to )450450 ps/nm range as the GTE increases from one to two. 3.3. Chromatic dispersion compensation In lightwave communication applications, interleaver with low chromatic dispersion is required. To reduce chromatic dispersion in the proposed interleaver, an additional GTE with two cavities may be introduced to compensate the
Fig. 6. The dispersion simulations of the 12.5-GHz passband for one GTE and two GTEs in a 25-GHz interleaver channel spacing.
chromatic dispersion caused by the original GTE configuration, as shown in Fig. 7. Based on Eqs. (7)–(10), the simulation of chromatic dispersion of the 50-GHz interleaver before, with additional etalons, and after dispersion compensation are shown in Fig. 8. Fig. 8 shows that the simulation of chromatic dispersion of the 50-GHz interleaver can be compensated within a 10 ps/nm. This residual dispersion will not cause a noticeable penalty for the high-speed optical fiber communication systems. Clearly, the detailed understanding of the dispersion and its compensation in the real device is necessary and will be pursued in a separate study.
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stopband, and channel isolation are measured from the waveform monitor. 4.1. Spectral characteristics of interleavers
Fig. 7. Schematic drawing of the Gires–Tournois etalon with dispersion-compensation element interleaver.
The channel isolation of the 50-GHz interleaver with two GTEs for output port 1 and port 2 is shown in Fig. 9(a). Fig. 9(a) shows that the interleaver in a 50-GHz channel spacing exhibits a channel isolation better than 30 dB between adjacent channels. Fig. 9(b) shows the 0.5-dB passband and 25-dB stopband of our interleaver with 50-GHz channel spacing for output port 2. This spectral characteristic exhibits a 0.5-dB passband of 0.35 nm (43.8 GHz), a 25-dB stopband of 0.32 nm (40 GHz), and a insertion loss of 1.3 dB. The measured results of 0.5-dB passband and 25-dB
Fig. 8. The simulated chromatic dispersion of the 50-GHz interleaver before, with additional etalons, and after dispersion compensation.
4. Measurement results For the purpose of our measurement, a circulator for output port 2 and a collimator for output port 1 are used. The optical path difference of two arms is adjusted to equal to one-half of the air spacing in the GTE to ensure a period of 50 GHz. The substrate of the regular mirror is chosen to be the same as that of the partial reflecting dielectric mirror. This is to ensure a complete cancellation of the phase between the paths due to the glass substrates. A C-band tunable laser as light source and an optical spectral analyzer as waveform monitor are used for the interference measurements. The periodic channel spacing, 0.5-dB passband, 25-dB
Fig. 9. The measured (a) the channel isolation for output port 1 and port 2, and (b) the 0.5-dB passband and 25-dB stopband for output port 2 in a 50-GHz interleaver channel spacing.
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stopband in Fig. 9 are in good agreement with the simulation results in Figs. 3 and 4. Similar result of the channel isolation of the 25GHz interleaver with two GTEs for output port 1 and port 2 is shown in Fig. 10. Fig. 10 shows that the interleaver in a 25-GHz channel spacing exhibits a channel isolation better than 32 dB between adjacent channels. This spectral characteristic also exhibits a 0.5-dB passband of 0.17 nm (21.3 GHz) and a 25-dB stopband of 0.16 nm (20 GHz). 4.2. Dispersion in interleavers Fig. 11 shows the measured chromatic dispersion of the interleaver with two GTEs in a 50-GHz channel spacing. The chromatic dispersion of the 25-GHz passband was measured between )95 and 113 ps/nm ranges. The measured result of the chromatic dispersion of 25-GHz passband for a 50-GHz interleaver with two GTEs is in good agreement with the simulation results in Fig. 5. Fig. 10 also shows the chromatic dispersion of the interleaver with two GTEs in a 25-GHz channel spacing. The chromatic dispersion of the 12.5-GHz passband was measured approximately between )440 and 430 ps/nm ranges. The measured result of the chromatic dispersion of 12.5GHz passband for a 25-GHz interleaver with two GTEs is also in good agreement with the simulation results in Fig. 6.
Fig. 11. The measured chromatic dispersion of the interleaver with two GTEs in a 50-GHz channel spacing.
In this study, the chromatic dispersions were measured about 100 and 440 ps/nm for 50- and 25-GHz interleavers, respectively. 4.3. Bandwidth compared to the other-type interleavers Fig. 9(b) shows that the 0.5-dB passband is near 88% (43.8 GHz) of the 50-GHz channel spacing with two GTEs configuration. Fig. 10 also shows that the 0.5-dB passband is near 85% (21.3GHz) of the 25-GHz channel spacing with two GTEs. These results are much better as compared with hybrid coupler and delay line on planar lightwave circuits (70% of the spacing) [3,6], hybrid filter and array waveguides (60% of the spacing) [7], and birefringent crystals (77% of the spacing) [8]. Furthermore, the results indicate that the interleaver interferometer with novel GTE technique exhibits a wider 0.5-dB passband and 25-dB stopband when compared to current fabrication interleaver interferometer technologies.
5. Discussion and conclusion
Fig. 10. The measured the channel isolation for output port 1 and port 2, the 0.5-dB passband and 25-dB stopband for output port 2, and the chromatic dispersion in a 25-GHz interleaver channel spacing.
In summary, we have developed and fabricated the flat-top and low-dispersion 50- and 25GHz optical interleavers for DWDM optical networks. The spectral characteristics of the interleaver with two GTEs in a 50-GHz channel
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spacing application exhibited a 0.5-dB passband larger than 43.8 GHz (88% of the spacing), a 25dB stopband greater than 40 GHz (80% of the spacing), and a channel isolation higher than 30 dB. The interleaver with two GTEs in a 25-GHz channel spacing application also exhibited a 0.5dB passband larger than 21.3 GHz (85% of the spacing), a 25-dB stopband greater than 20 GHz (80% of the spacing), and a channel isolation higher than 32 dB. The benefit of this novel interleaver utilizes the phase dispersive nature of the GTE mirrors to ensure flat-top transmission passbands, as well as superior channel isolation. The phase dispersion of the etalon-based GTE exhibits a periodic dependence on the frequency of light, a strong dispersion in some spectral regions, and a weak dispersion in other spectral regions. This is to ensure flat-top transmission maximum with a sharp cut-off. The results clearly indicate that the interleaver interferometer with novel GTE technique can simultaneously produce a 0.5-dB passband and a 25-dB stopband wider than other interferometer techniques. We also showed that the chromatic dispersion of the proposed interleaver could be compensated within a 10 ps/nm. A similar flat-top and low-dispersion interleavers using GTE technique in smaller channel spacing may also be fabricated. The flexibility in design and the excellent performance of interleaver make the GTE-based interleaver extremely attractive for using in very
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high channel count systems leading to Terabit capacities.
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