By controlling the internal loss of a ring resonator near critical coupling, we demonstrate control of the transmitted power in a fiber that is coupled to the resonator. We also demonstrate wavelength-selective optical amplification and oscillation

Choi, John M.

Lee, Reginald K.

Yariv, Amnon

English

Caltech Authors - Main

1236 OPTICS LETTERS / Vol. 26, No. 16 / August 15, 2001Control of critical coupling in a ring resonator–fiber
configuration: application to wavelength-selective
switching, modulation, amplification, and oscillation
John M. Choi, Reginald K. Lee, and Amnon Yariv
California Institute of Technology, M/S 136-93, 1200 East California Boulevard, Pasadena, California 91125Received March 13, 2001
By controlling the internal loss of a ring resonator near critical coupling, we demonstrate control of the
transmitted power in a fiber that is coupled to the resonator. We also demonstrate wavelength-selective
optical amplification and oscillation. © 2001 Optical Society of America
OCIS codes: 060.2320, 060.4080, 060.1810, 060.2330, 060.4510, 230.5750.The coupling of power between an optical waveguide
and a ring resonator is a subject of continuing inter-
est.1 – 4 This interest intensif ied recently, due, in large
measure, to a recognition of the potential application
of this phenomenon is a variety of tasks important to
optical fiber communication. These include5 – 7 modu-
lation, switching, dispersion compensation, and as we
will show in what follows, wavelength-selective ampli-
fication and oscillation.
The basic experimental conf iguration is shown in
the inset of Fig. 1. A wave of (power-normalized)
amplitude a1 is incident upon the coupling region and
exits as b1. It was shown recently that the
power-transfer characteristics jb1a1j2 of this conf igu-
ration are described by a universal relation5:
Ç
b1
a1
Ç2

a2 1 jtj2 2 2ajtjcos u
1 1 a2jtj2 2 2ajtjcos u
, (1)
where t is the diagonal element of the coupling matrix
relating the input and output f ields at the coupling
element
Ç
b1
b2
Ç

Ç
t k
k 2t
Ç Ç
a1
a2
Ç
, (2)
which in the lossless case obeys jtj2 1 jkj2  1. a rep-
resents the circulation loss factor in the ring, accord-
ing to a2  b2a expiu. In passive resonators a , 1.
In a lossless resonator a  1. The inclusion of an op-
tical amplifier in the ring can allow values of a . 1.
u  bLloop is the circulation phase shift.
At resonance u  m2p (m is an integer), and the
transmission becomes
jb1j2 
a 2 jtj2
1 2 ajtj2
. (3)
A plot of Eq. (3) is shown in Fig. 2. Two features of
this f igure illustrate most of the potential applications
listed above: (1) There will exist a condition, a  jtj,0146-9592/01/161236-03$15.00/0for which the transmitted power is zero. Following the
microwave convention, in which this phenomenon is
well known,8 we previously referred to this condition as
critical coupling.5 At critical coupling the resonator
mode loses the same power to the internal dissipation
mechanisms (proportional to 1 2 a2) as to the coupling
to the outgoing f iber mode (proportional to 1 2 jtj2).
(2) The second important feature is the steepness
of the transmission characteristics at a . jtj. It is
apparent that in reasonably high-Q resonators a  1
small modulation of a, or t, can cause large modula-
tion of the transmitted power. This can be used, for
example, to construct electro-optic modulators with
values of Vp that are 2 orders of magnitude smaller
than those of conventional Mach–Zehnder electro-
optic modulators. It is interesting to note that, in the
undercoupled region, a , t, as the gain is increased,
the power transmission decreases until the critical
coupling point.
To exploit the critical coupling phenomenon prof-
itably we need, according to Eq. (3), to be able to
Fig. 1. Experimental setup used to measure the
fiber-ring–waveguide system. A fused coupler is used
as the coupling mechanism. Erbium-doped fiber (ED)
is used in the ring to allow loss or gain modulation.
A wavelength-division multiplexer (WDM) is used to
add the 980-nm pump, allowing control of the coupling
characteristics. Inset, conventions used in referring
to the resonator–waveguide system. The input port is
a1, the output port is b1, the loss in the resonator is 1 2 a2,
the coupling is t, and the round-trip phase delay from the
resonator is u. From energy conservation, jtj2 1 jkj2  1
and a2  a expiub2.© 2001 Optical Society of America
August 15, 2001 / Vol. 26, No. 16 / OPTICS LETTERS 1237Fig. 2. Theoretical normalized power transmission as a
function of internal cavity loss. The critically coupled
point (zero transmission) occurs at a  jtj. In the under-
coupled region, a , t, increasing the gain in the resonator
up to the critically coupled condition decreases the power
transmission.
Fig. 3. Transmission spectrum of the ring resonator–
waveguide system. The curve with a  0.74 when the
transmission at resonance is 222 dB is a state near critical
coupling. Near-unity transparency a  1.0 is observed
when the 980-nm pump power into the ring is approxi-
mately 6.8 dBm. Frequency-selective amplif ication near
the resonance frequency is observed when a . 1. The
dashed curve shows laser oscillation a  1jtj, which
was observed when the pump power coupled into the ring
was 7.6 dBm.
control, or modulate, the coupling t or the internal
loss a. In this Letter we demonstrate the feasibility
of controlling the internal loss parameter a.
Our experimental arrangement is shown in Fig. 1.
The coupling between the ring resonator and the fiber
waveguide was provided by a fused 3-dB coupler.
Of the 59 cm of the circumference, 43 cm consisted
of an erbium-doped fiber. The erbium-doped fiber
was pumped by a 980-nm pump laser, and control of
this pump power enabled us to control a over a large
region straddling the critical, a  jtj, point. We could
also easily operate with a . 1.
Figure 3 shows experimental transmission plots
as a function of the optical frequency deviation, with
the loss parameter, a, corresponding to a measured
980-nm optical pump power as a parameter. The
loss parameter, a, was calculated from the linewidthFig. 4. Measurement of the transmission coefficient
at resonance as a function of a. Critical coupling (in
this case a 222-dB transmission) as well as net gain is
observed.
and depth of the transmission curve. This fit results
in a very accurate measure of the loss that is due
to the sensitivity of the transmission line shape to
this parameter. We observe the existence of critical
coupling (a 222-dB dip in transmission, ideally a zero
dip) when a is 0.74. The theoretical value of a at
critical coupling is 0.707. Also apparent is a (near)
unity a  1 transmission transparency when the
pump power coupled into the ring is 6.8 dBm and the
net optical gain at higher pump levels a . 1 reaches
a peak gain of 15 dB. Laser oscillation a  1jtj
was observed when a pump power greater than
7.6 dBm was coupled into the ring. The extrema of
the transmission plots of Fig. 3 are plotted in Fig. 4 as
a function of the loss parameter, a. Figure 4 displays
all the basic features of the theoretical plot of Fig. 2
and demonstrates the feasibility of controlling the
transmitted power by electrical means.
The top two curves of Fig. 3 illustrate the possi-
bility of wavelength-selective amplification of light
propagating in the f iber, since only wavelengths
corresponding to resonances of the ring resonator are
amplified (or modulated), while other wavelengths
pass through the ring unaffected. This feature al-
lows the possibility of implementation in wavelength-
division multiplexing systems. The device described
here thus demonstrates some of the main functions
that are important for communication: light genera-
tion and amplification, modulation, and switching. It
can thus play an important role in a future all in the
fiber communication system.
The authors acknowledge the support of the U.S. Air
Force Off ice of Scientif ic Research, the U.S. Off ice of
Naval Research, and the Defense Advanced Research
Projects Agency. J. Choi thanks the Department of
Defense and the American Society for Engineering
Education. J. M. Choi’s e-mail address is johnchoi@
caltech.edu.
References
1. A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass,
S. J. Pearton, and R. A. Logan, “Directional light
coupling from microdisk lasers,” Appl. Phys. Lett. 62,
561–563 (1993).
1238 OPTICS LETTERS / Vol. 26, No. 16 / August 15, 20012. G. Griffel and S. Arnold, “Synthesis of variable opti-
cal filters using meso-optical ring resonator arrays,” in
Proceedings of the IEEE LEOS Annual Meeting, Vol. 2
(Institute of Electrical and Electronics Engineers, Pis-
cataway, N.J., 1997), p. 165.
3. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P.
Laine, “Microring resonator channel dropping f ilters,”
J. Lightwave Technol. 15, 998–1005 (1997).
4. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory
analysis of waveguide-resonator coupling,” Phys. Rev. E
62, 7389–7404 (2000).
5. A. Yariv, “Universal relations for coupling of optical
power between microresonators and dielectric wave-
guides,” Electron. Lett. 36, 321–322 (2000).6. B. E. Little, H. A. Haus, J. S. Foresi, L. C. Kimerling,
E. P. Ippen, and D. J. Ripin, “Wavelength switching and
routing using absorption and resonance,” IEEE Photon.
Technol. Lett. 10, 816–818 (1998).
7. M. Cai and K. Vahala, “Highly efficient optical power
transfer to whispering-gallery modes by use of a sym-
metrical dual-coupling conf iguration,” Opt. Lett. 25,
260–262 (2000).
8. J. C. Slater, Microwave Electronics (Van Nostrand, New
York, 1950).


Control of critical coupling in a ring resonator fiber configuration: application to wavelength-selective switching, modulation, amplification, and oscillation

Directional light coupling from microdisk lasers,”

Highly efficient optical power transfer to whispering-gallery modes by use of a symmetrical dual-coupling conf iguration,”

Microring resonator channel dropping f ilters,”

Scattering-theory analysis of waveguide-resonator coupling,”

Synthesis of variable optical filters using meso-optical ring resonator arrays,”

Universal relations for coupling of optical power between microresonators and dielectric waveguides,”

Wavelength switching and routing using absorption and resonance,”

http://authors.library.caltech.edu/7512/1/CHOol01.pdf

Control of critical coupling in a ring resonator fiber configuration: application to wavelength-selective switching, modulation, amplification, and oscillation

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main