Waveguiding and Waveguide Applications of Nonlinear Organic

Chapter 7

Waveguiding and Waveguide Applications of Nonlinear Organic Materials 1

Downloaded by PENNSYLVANIA STATE UNIV on September 3, 2013 | http://pubs.acs.org Publication Date: March 11, 1991 | doi: 10.1021/bk-1991-0455.ch007

George I. Stegeman

Optical Sciences Center, University of Arizona, Tucson, AZ 85721

Optical waveguides offer optimum conditions for nonlinear optical interactions involving, for example, nonlinear organic materials. In this tutorial we review the basic concepts of waveguiding, techniques for fabricating waveguides, and methods for exciting waveguide modes, concentrating on polymeric materials. In addition, we will discuss the operating principles of second harmonic generators and all-optical devices based on an intensity-dependent refractive index. The material requirements and figures of merit necessary for waveguide devices will be described.

The field of nonlinear optics has been active for more than 25 years. Frequency doublers for high-power lasers, usually used in research (but with a sizeable market, nonetheless) have represented the prime commercial application of nonlinear optics. In the last decade, however, data storage and duplicating applications have emerged for efficient doubling of GaAs lasers operating with 100-mW input powers. The pertinent nonlinearity is given by the third-rank tensor, x((2))ijk(2co;a),co). In response, there have been two developments in the area of nonlinear organics. New single-crystal organic materials have been developed. In addition, highly nonlinear molecules have been preferentially orientated (poled) in glassy polymer films, allowing the production of films with a second-order nonlinearity. Such poled polymers are ideal for electrooptic devices, which will be discussed in another chapter here. The most efficient application of both approaches is in waveguides, which will be discussed in this tutorial. Recently, new device possibilities for materials with xijw nonlinearities have been projected for applications in optical computing, signal processing, and other areas. The key to these applications is that the local refractive index can be changed by the local optical intensity I, that is. An = n + n I. A well-developed field already exists that utilizes the electrooptic effect in integrated optics waveguides to perform switching. That is, the output channel can be changed by applying a voltage to a pair of electrodes. These devices can be made all-optical using media with n 0. The switching function is achieved by changing the intensity of the 0

2

2

Current address: CREOL, University of Central Florida, 12424 Research Parkway, Orlando, FL 32826

0097-6156/91/0455-0113$06.00/0 © 1991 American Chemical Society In Materials for Nonlinear Optics; Marder, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

114

MATERIALS FOR NONLINEAR OPTICS: CHEMICAL PERSPECTIVES

incident field. To date, a number of these switches have been demonstrated, including one using a nonlinear polymeric material. The purpose of this tutorial is to introduce the material scientist to nonlinear optics in waveguides. We begin by discussing the principles of waveguiding, waveguide fabrication techniques, and ways in which waveguide modes are excited. We then introduce nonlinear optics, make the argument that waveguide media are ideal geometries for efficient nonlinear interactions, and identify the key features of nonlinear optics in waveguides. Finally, we summarize existing progress, and identify materials requirements.


Waveguiding There are three basic types of waveguides, summarized schematically in Figure 1 (1). The simplest waveguide consists of a film whose thickness is comparable to the wavelength of light. Beam confinement is achieved in one transverse dimension only, and the beam diffracts in the usual way in the plane of the film. Essentially, a film of refractive index larger than the surrounding media (the cladding and substrate) is required. If the surrounding media do not have the same index, the film must have a certain minimum thickness for waveguiding to occur. Because it is the simplest, we will use this system to illustrate the basic concepts of waveguiding. Planar waveguides can be fabricated by vacuum coating or spinning a film onto a substrate by material deposition, by transfer of a film onto a surface by dipping, or by the in- or out-diffusion of atomic or molecular species through the substrate surface (2-8). Vacuum deposition includes electron or thermal evaporation (including MBE), RF sputtering, and MOCVD. Current dipping techniques include LB monolayer deposition, and pulling substrates from molten liquids of plastics (4,5K The difference in chemical potentials can be used to make species near the surface of a substrate diffuse out of the substrate, and/or to make another species in solution adjacent to the surface diffuse into the substrate (6). In the latter case, the index distribution is not step-wise, and usually decays with distance into the substrate. Channel waveguides provide beam confinement in two transverse dimensions, so the light propagates totally in a diffraction-free manner. That is, the beam crosssection remains the same for distances limited either by absorption or by scattering by waveguide inhomogeneities. The characteristic 1/e attenuations vary from 0.1 to 10 cm" , depending on waveguide quality. Channel waveguides are usually fabricated through thin-film techniques, but with a mask first deposited onto the substrate surface so that the film deposition or species exchange occurs only through the openings in the mask (2,3,7,8). Alternatively, ion-milling or plasma etching can be used to produce ridges in thin films or substrates (2,3,7,8). Another approach recently developed for channel waveguides in polydiacetylenes is to produce channel ion-exchanged regions in a glass, and to overcoat the waveguide with a poly-4BCMU film to obtain channel guiding in the polymer. The appropriate design can result in up to 80% of the power guided in the polymer (9). Most efficient guided wave devices will be made in channel waveguides. There has been limited progress in the fabrication of fiber waveguides from nonlinear organic materials. Although plastic fibers (highly multimode) have been made, to date such waveguides have not been made in single-mode form with interesting nonlinear dopants. Some single-crystal fibers have been drawn with second-order active materials (10-12). In general, short fibers of organic materials have been used, and their features are similar to those found in channel waveguides. We will not, therefore, discuss the fiber case further. The optical fields in the vicinity of a waveguide consist of guided modes and radiation fields that transport power away from the immediate vicinity of the 1

In Materials for Nonlinear Optics; Marder, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

7.

STEGEMAN

115

Waveguiding and Waveguide Applications

waveguide. For optically isotropic media, the modes for a planar waveguide can be separated into a pure T E mode (E-field polarized along the y-axis, orthogonal to both the surface normal and propagation wavevector) and a pure T M mode (H-field polarized along the y-axis, and E-field components along the x- and z-axes). A finite number of discrete modes exist for a given film thickness, and the field distributions associated with the first few T E and T M waves, shown in Figure 2, exhibit oscillatory behavior in the film, decaying exponentially with distance into the cladding and substrate. Nonlinear interactions, therefore, can take place in any one of the three media. One of the unique features of thin-film guided waves (as compared to plane waves) is that the the guided wave wavevectors j3( ), for each mode depend on film thickness. See, for example, solutions to the dispersion relations in Figure 3. The T M waves have similar characteristics, but the dispersion relations are different leading to different variation with film thickness. The guided-wave field of a planar waveguide is written as (1) m

m


m

E(r.t) = iE(^)(x,y)aM(z)e

iM

"^

+ c.c. ,

(1)

where "m" defines the mode number and is the guided-wave wavevector. a(z) is the amplitude coefficient, with the detailed cross-sectional dependence of the guided wave given by E(x,y), normalized so that |a(z)| is the guided-wave power in watts. This requires that 2

r°°

-

r oo dy EH(x.y)-E*M( ,y) - 8 , .

*

x

m

(2)

Note that it is primarily this normalization which makes the subsequent formulae appear different from the well-known plane wave cases. For a planar waveguide, it is useful to assume that the guided-wave beam is very wide (D » X) and uniform along the y-axis, so that the field distribution is independent of y, and the integral over y just produces D, the beam width. The term /# tyk plays the role of a refractive index for propagation along the z-axis, and is called "the effective index," n . Its value is obtained from an eigenvalue equation or dispersion relation by satisfying the boundary conditions across each interface. Typical variations in n with normalized waveguide thickness are shown in Figure 3 for a thin film bounded by a substrate (s) and air (c = cladding). Near the minimum film thickness for a given mode, called cut-off, eff - s * fi ld penetrates deeply into the substrate, resulting in low intensities for a given power. For thick films, n •* n and, although the field is localized within the film, the intensity again drops with increasing film thickness. There is, in fact, a film thickness which optimizes the intensity for a given power. The situation is more complex for channel waveguides. Here D £ X, and resonances across the y-dimension occur also. Typical fields are shown in Figure 2. Two sets of orthogonal normal modes remain in the sense of Equation 2. Both modes however, contain all three electric-field components [E^, Ey, and (usually small)]. The mode with Ey as the dominant field component is designated T E , and the mode for which is dominant is called T M . Note that the modes are now designated by two integers because the field is confined and resonances occur in 2 dimensions. This is in contrast to the planar one-dimensionally confined modes described by a single integer. The dispersion relations are very complicated, and cannot be expressed in analytical form, requiring numerical techniques for evaluation. Here n varies with two normalized thickness dimensions. m

0

eff

eff

n

n

a n c

t n e

e

eff

f

m n

m n

eff



116


Figure 1. Three common types of waveguides: (a) fiber, (b) thin film, and (c) channel. In each case the guiding medium, fiber core, thin film, and channel region has a higher refractive index than the surrounding media.

t Figure 2. Typical field distributions for waveguides. For the channel case, the transverse distribution f(x,y) is approximated by f(x)f(y). The arrows indicate the dominant field component, (a) T E channel modes, (b) T M channel modes, (c) T E slab field distributions and, (d) T M slab waveguide fields. m n

m

m n

m


7.

STEGEMAN


^

n(2co) n(co) n(2co) n(co) 0

111

•

0

e

e

TM (2co)

0)

/

0

X

X.' / V T M ( c o ) / V TE (co)

TE (2a»

0

0


0

1 1 1 2

3 1 6

2 | I 4

5 knh [CO] 1 10 (2ko)h [2co]

4 1 8

Figure 3. The guided mode dispersion curves used to determine phasematching possibilities (intersection of the fundamental and harmonic dispersion curves) for isotropic media. Because p > nk , where n is the largest index of the surrounding media, waveguide modes cannot be excited simply by illuminating the waveguide surfaces. One of the three commonly used excitation methods shown in Figure 4 must be employed. Both prism (n > j8( - ); /3( . ) = n kosin0) and grating coupling ($ < ) = k sin0 + 2ir/l) require wavevector conservation parallel to the surface for efficient coupling. In the prism case, the light is incident on the base of the prism at angles 6 larger than the critical angle for the prism-air interface, and the mode is excited by the evanescent field in the air gap that penetrates the film. For channel waveguides (and for fibers), light is focused onto the end face of the channel, with the best efficiency obtained when the transverse spatial profile of the incident field matches that of the launched guided wave. Care must be taken to use single-mode waveguides, as all of the modes are excited to some degree in end-fire coupling. It is difficult to judge the optical quality of a waveguide film by any simple technique, such as visual inspection. Waveguides typically are only a few wavelengths thick, and propagation of thousands of wavelengths down the film is required for useful waveguiding. It is necessary to excite waveguide modes and measure the lengths of their propagation "streaks." 0

m n

m n

m

p

n

p

o

Nonlinear Optics Nonlinear optics entails the mixing of one (with itself in some cases) or more fields to produce a nonlinear polarization source term, which in turn can radiate a new electromagnetic wave (13,14). This term is usually written as pNL , ) . ( r

t

' p N L ^ e i e V - V r ) + ex.

(3a)

Restricting ourselves to three input guided waves of frequency co , oo and co (of which two may be equal), a

b

c

P (r,w ) = e x (-co ;co ,±a> ):E( ' )(x,y)E( ' )(x,y) a( ' )(z)a< ' )(z) NL

(2)

m

0

s

s

a

a

m

b

m a

m b

b

(3b) + e x( H-w ;co ,±co ,±co ):- E( - )(x,y)E( ' )(x,y)E( )(x,y) 3

0

m a

s

a

b

m b

m

c

m a

m

b

m

c

x a( ' )(z)a( '- )(z)a( "- )(z) ,


118


where x^ ^d are the second- and third-order susceptibilities (material parameters), and a minus sign for a frequency corresponds to taking the complex conjugate of the appropriate field. Note that /3 - /S( - ) ±ft '- )± 0^ ,c) the wavevector associated with the nonlinear polarization source field, and is not necessarily equal to fl ' \ which is the value appropriate to a propagating field of that frequency (oo). The case p = /# ') corresponds to phase-matching, as will be discussed later. For the second-order processes, two possible input waves exist, with frequencies co and which produce polarization and signal fields at co = ^ ± 0 ^ . For third-order processes, the nonlinear polarizations can occur at the frequencies co = (o ±a> ±a) . Many of these interactions have been demonstrated in nonlinear guided-wave experiments (15-17). The processes and their nomenclature are listed in Table 1. Henceforth, we will discuss only second harmonic generation and intensity-dependent refractive index phenomena. a

m a

m

b

n

p

n

l s

s

n s

s

p

a

s

s


a

b

c

i

Figure 4. Techniques for coupling an external radiation field into optical waveguides: (a) prism coupling, (b) grating coupling, and (c) end-fire coupling.


7.

STEGEMAN

Table 1.


Glossary of nonlinear interactions and their common nomenclature

Input Beams

Process


119

Frequencies

Second Harmonic Generation

1

co + co -* 2co

Sum and Difference Frequency Generation

2

"

Optical Parametric Oscillator

1

co - co + oo

Third Harmonic Generation

1

co + CO + CO

Intensity-Dependent Refractive Index

1

CO + CO - CO •+ CO

Degenerate Four-Wave Mixing

3

CO + CO - CO •+ CO

Coherent Anti-Stokes Raman Scattering

2

co + co - co - 2co - COb

w

* b •* c

a

a

b

a

c

a

3co

b

a

The existence of the nonlinear polarization field does not ensure the generation of significant signal fields. With the exception of phenomena based on an intensitydependent refractive index, the generation of the nonlinearly produced signal waves at frequency co can be treated in the slowly varying amplitude approximation with well-known guided wave coupled mode theory (1). As already explicitly assumed in Equation 1, the amplitudes of the waves are allowed to vary slowly with s

n s

n s

propagation distance z, that is, -^afa^Hz) « /# ' ) -^-a( -)(z), which leads to

A (n. a

s)(z)

i(P

. j^L

d

x

d

y

P

))z

NL , ).E*("^)(x,y) e P

" ) - /# « )), and K is called the overlap integral.

2

The sin 0/0

term describes the effect of phase mismatch, that is, A/3L # 0. Efficient conversion can be accomplished only when the phase mismatch A/SL < 7r/4. Optimum occurs conversion for A/3 = 0, the phase-matched case. From Equations 6, it is clear that there are a number of key factors governing efficient conversion. These factors are 1) phase-matching; 2) optimization of the overlap integral; 3) large nonlinear coefficients consistent with phase-matching; and 4) low waveguide losses (large L). Phase matching requires a geometry for whichft > ">)= fiw). Figure 3 illustrated the problems associated with phase matching for a slab waveguide. Plotted is the effective index n = /3/k for both fundamental and harmonic waves of both polarizations. The goal is to find an intersection between the dispersion curves for a fundamental and harmonic guided wave. In the absence of material birefringence, such crossings effectively occur only forfl '">)= 0(n.2w) e n n > m. That is, the mode numbers are different for the fundamental and harmonic waves, indicating that the respective field distributions have a different number of zeros inside the film. However, given thick enough films (and enough modes), phasematching conditions can always be found, which is an advantage in using waveguides. Tolerances on waveguide dimensions can also be understood from Figure 3. The propagation wavevector varies with the waveguide dimensions through the dispersion relations. The ideal situation, in terms of thickness tolerances and fluctuations, is for the relative angle between the crossing dispersion relations to be small, and for the curves to be parallel to the thickness axis. In terms of index uniformity, again a small crossing angle is advantageous, with the curves approximately parallel to the index axis at the phase-matching condition. The key point is the small crossing angle, which implies that little dispersion in the effective index with wavelength is desirable. Typically, tolerances on the order of 5 nm in waveguide dimensions are sufficient. Uniformity of refractive index and waveguide dimensions both pose problems in technology, and are not easily solved. The overlap integral (K) can dramatically reduce the efficiency of a doubling phase-matching configuration, if the mode numbers of the interacting fields differ (15-17). This is clear from Figure 5 if both films constituting the waveguide are of the same material and are nonlinear. K is proportional to the integral over the two field distributions involved in the mixing interaction. For example, interference effects occur when m # n, thereby reducing K. This property negates an apparent advantage in using guided waves, namely the availability of a range of /2s at a given frequency for phase matching. Figure 5 also shows a solution to this problem. By making the guiding film a layered combination of linear and nonlinear films, the interference effects can be eliminated with a reduction (in Figure 5) in K of only a factor of 2 to 4 (]8). m

eff

2

0

m

t w n


2

7.

STEGEMAN


121

Material birefringence, or the natural birefringence arising from the dissimilar dispersion relations of the T E and T M modes can also be used to obtain phase matching with orthogonally polarized modal fields of the same mode number (15-17). An example is shown in Figure 6, where phase matching between the TEQ and TMQ modes is illustrated. (Here material dispersion in the film only was assumed for simplicity.) Small birefringence, on the order of the material dispersion with wavelength, is desirable. The problem with this aproach is that it requires offdiagonal tensor elements which, unfortunately, tend to be smaller than the diagonal elements. The advantages of using waveguides for SHG are numerous. Waveguides maintain high intensities (and therefore intense fields) for centimeter distances. As a result, the SHG conversion efficiency is proportional to L , rather than to L, as for focused plane-wave beams. The existence of discrete modes, each with its associated wavevector, allows greater flexibility in achieving phase matching. Although the use of modes with different mode numbers can lead to a large reduction in the overlap integral, this loss in efficiency can be reduced by using carefuly engineered multilayer waveguides. Although a large variety of nonlinear materials have been used in prototype harmonic doublers (15-17), only waveguide doublers in LiNb0 have been of usable quality. A list of previous waveguide doublers can be found in references 15-17. The key figure of merit is


2

3

This figure quantifies the intrinsic conversion efficiency of a material-waveguide combination, independent of the device length. Taniuchi and co-workers allowed the second harmonic to leave the waveguide region in the form of Cerenkov radiation (19). Here wavevector conservation parallel to the surface is achieved by the radiation field. When channel waveguides are used, the harmonic light appears in an arc, not all of which can be focused down to the diffraction limit. The best results correspond to T? £ 40 W^cnr . This finding implies that, for typical 40-mW semiconductor laser powers, 1.6 mW of blue light can be generated. Another approach is to use gratings with periodic reversals in to implement phase matching, called quasi-phasematching (20,21). The periodicity provides the wavevector component required for phase matching. The theoretical value for TJ is > 300 W cm" , making this approach very promising. The flexibility associated with both the Cerenkov and quasi-phase-matching techniques allows any wavelength to be doubled, as long as both the fundamental and harmonic fall within the material's transparency band. A number of nonlinear organic materials have been used in prototype waveguide doublers (15-17). In every case to date, the waveguides have exhibited too much loss and/or nonuniformity to achieve efficient doubling, especially in those cases where the organic material was vacuum deposited. The most promising result so far has been obtained in poled polymer films, the fabrication of which is discussed in detail elsewhere in this volume (22). In brief, a polymer host, charged with molecules exhibiting both large dipole moments and molecular hyperpolarizabilities, is heated above its glass transition temperature and a field is applied to orient the molecules via their dipole moment. The field is maintained through the cooling phase, locking in the molecular orientation. Phase matching is achieved by alternating the voltages applied to periodic electrodes—this results in an alternating x®. with the period chosen specifically for phase matching (23). The potential of organic materials for efficient doublers is clearly seen in Table 2, from a very simple figure of merit (15-17). The challenge is to produce 2

_1

2



122


Figure 5. Optimization of the cross-section for guided wave second harmonic generation. Phase-matching occurs between two dissimilar modes and the overlap integral is optimized by causing the interference effects to occur in linear regions of the waveguide only. For the case of a single nonlinear film, interference effects occur as the field product is integrated over the thickness dimension.

2TE M 0

- ^ T E ^ c u )

n (2w) f

n (cj) f

n (2cu) s

k h 0

^

Figure 6. The guided mode dispersion curves for a birefringent film and an optically isotropic substrate. Both the fundamental and harmonic curves are shown. The T E mode utilizes the ordinary refractive index and T M primarily the extraordinary index. Note the change in horizontal axis needed to plot both the fundamental and harmonic dispersion curves. Phase-matching of the TEQ(CO) to the TMo(2co) is obtained at the intersection of the appropriate fundamental and harmonic curves.


7.

STEGEMAN

123


single-crystal channels of appropriate orientation and uniformity, and poled films with larger net nonlinearities. In fact, it is not clear whether or not larger molecular nonlinearities are required. Material processing, instead, seems to be a more important issue.


Table 2.

Second harmonic generation figures of merit relative to LiNb0 coefficient) for materials with potential for waveguide applications

Material

d

LiNb0 LiNb0 (d ) KTP MNA NPP (PS)O-NPP DCV/PMMA HCC01232

1.2xl08.5x10"* * IO7x10-* 2xl02X107xl02.5xl0"

(esu)

2

d /n

33

(d

13

3

1 50 1.5 75 600

8

3

3

eff

3

8

7

8

85

8

7

MNA - metanitroaniline NPP - N-(4-nitrophenyl)-L-prolinol (PS)O-NPP - chromophore functionalized polymer (29) DCV/PMMA - dicyanovinyl azo dye in PMMA HCC/ 232 - (CH^-amino-nitrostilbene 1

Third-Order Nonlinear Integrated Optics One of the fastest growing areas in nonlinear integrated optics involves phenomena based on an intensity-dependent refractive index. We restrict our discussion of third-order phenomena to this case (15-17,24). The refractive index experienced by a wave of frequency co can be changed by a second beam at a different frequency (cross phase modulation), by a wave of the same frequency (co) but of orthogonal polarization (cross phase modulation), or by the original beam itself (self phase modulation). Thus there are many ways of ail-optically inducing a change in refractive index. Restricting our discussion to self phase modulation and the pure cubic nonlinearity associated with an ideal Kerr-law medium, the total polarization can be written as Pi(r,co) = e [x ii(";a>) + iiii(co;co,-co,co)| Ej(co)| ] Eg(w) , (1)

(3)

0

2

X

(8)

where the quantity in the square brackets can be interpreted as an intensitydependent dielectric constant, that is, n . This leads to n - n + n I, with 2

0

2

(3)

0 112

=

3

X ini(^;^-^^) n ^ *

,v Q

2

W

There are two limits in which such an optically induced refractive index change can be utilized in waveguide geometries (15-17,24). The waveguide is defined in the first place by refractive index differences between the central guiding region and the bounding media, the largest being An . For An/An « 1, where An 0

0


124


is the optically induced change, the guided-wave field distribution corresponds to that of the normal mode, and only a small change in the propagation wavevector is induced. But for An ^ An , the field distributions depend on power, and it is necessary to solve the nonlinear wave equation with the boundary conditions, this time with a field dependent refractive index. We limit our discussion to the more common, small index change, case. The power-dependent refractive index change is obtained by taking a suitable average of the nonlinearity over the intensity distribution associated with the guided wave. The propagation wavevector can be written as 0

0 = 0 + Aft|a(z)| , 2

(10a)


O

Aft = 3a*

0

2

dx dy mP J -oo J -oo

A

2

I E;(x,y)| | EgX,y)| ,

X

(10b)

( 1 0 c )

0 ° - ^ x ^ < c

A

eff

where A is the effective cross-sectional area over which the nonlinear interaction occurs. A number of all-optical integrated optics devices are summarized in Figure 7 (24). The output can be tuned by changing the input power. Although all of these devices require a power-dependent 0, they can further be subdivided into two interaction geometries: 1) in which two guided wave modes interact with propagation distance, and for which the nonlinearity affects this interaction; and 2) in which a guided mode independently undergoes a nonlinear phase shift, which changes its interference condition with another optical field. The first category includes the nonlinear directional coupler (NLDC) and its variants, nonlinear distributed feedback gratings (NLDFB), and the nonlinear X - and Y-junctions. Belonging to the second category are the nonlinear Mach-Zehnder interferometer and the nonlinear distributed (prism or grating) coupler. It is noteworthy that the nonlinear coupled-mode devices exhibit the sharpest switching charactertistics. The simplest device is a nonlinear Mach-Zehnder interferometer, as depicted in Figure 7d. Consider the two channels to be of equal length, with a nonlinearity in channel 1 only (difficult to implement). They are sufficiently well separated so that there is essentially zero field overlap. Thus the differential phase shift between the two channels of length L is A 0 = Aj3 LP /2, where L is the length of the nonlinear region and P: is the input power (half of which propagates in each channel). Whenever A0™L changes by 7T, the output changes from a maximum to a minimum, producing the response sketched in Figure 7d. The nonlinear directional coupler is potentially a useful device because it has four ports, two input and two output, and because the outputs can be manipulated with either one or two inputs. Optimally the two channels are identical, and the coupling occurs through field overlap between the two channels. As a result, when only one of the channels is excited with low powers at the input, the power oscillates between the two channels with a beat length L , just like what occurs in a pair of weakly coupled identical pendulii. As the input power is increased, a mismatch is induced in the wavevectors of the two channels, which decreases the rate of the power transfer with propagation distance. This leads to an increase in the effective beat length. There is a critical power associated with this device, for which an infinitely long, lossless NLDC acts as a 50:50 splitter, that is, L -* oo. For higher input powers, the initial wavevector mismatch is too large to overcome, and the power effectively stays in the input channel. Therefore, if the device e f f

N L

0

in

b

5


7.

STEGEMAN


n

2

-

0

Nonlinear Directional Coupler


^ /

#

1/2 Beat Length

\

(b) Nonlinear Bragg Reflector Pi

(c)

" Po

Mach-Zehnder (d) Mode-Sorter (e) 91 X-Junction (f)

X

1 Pi

Figure 7. A number of all-optical guided wave devices and their responses to increasing power. (a) Half beat length directional coupler. (b) One beat length directional coupler. (c) Distributed feedback grating relector. (d) Nonlinear Mach-Zehnder interferometer. (e) Nonlinear mode mixer. (f) Nonlinear X-switch. For nonlinear media (n ^0), the input power determines the output state. 2


125

126


length is terminated at 1^/2, at low powers the signal comes out of channel 2 and at high powers out of channel 1. This is essentially an all-optical switch. The net result is the response sketched in Figure 7a. The operating characteristics of these devices are governed by a number of material parameters (24-26). The larger n ( 10" m /W. The device lengths required are about 1 centimeter, implying that a < 0.5 cm", and preferably 0.1 cm", to obtain good device throughput, and a nonlinearity recovery time < 1 ps. In many cases, the index change saturates (An ) with increasing power, which leads to the figure of merit W = An^/aX. W must be larger than 0.5 •* 3.7, depending on the device (see Figure 7). In fact, it is the potentially large values for this figure of merit in nonlinear organics off resonance which has spurred interest in this material system for these switching applications. Finally, two-photon absorption can limit the effective length of a device through an absorption a = 7I, where 7 is the two photon-coefficient (25,26). This yields a figure of merit T = yfKn > which must be less than unity for switching to occur. At this time, many of the parameters listed above have not been measured for nonlinear organic materials. Measurement will be necessary for an assessment of the full potential of such materials. To date, only a nonlinear directional coupler has been implemented in a nonlinear polymer, (poly-4BCMU). For this device at 1060 nm, the nonlinear response was dominated by two-photon absorption, and some limited switching attributable to absorption changes was observed (27). More recent work at 1030 nm appeared to show switching attributable to refractive nonlinearities (28). Clearly there is much progress to be made. 2

15

2

1

1


sal

2

Summary We have presented a review of the salient features of nonlinear integrated optics. It appears that nonlinear organic materials can play an important role in second- and third-order guided-wave devices. This field requires a great deal of material characterization and processing, however, before significant advances are realized. Literature Cited 1. Marcuse, D. Theory of Dielectric Optical Waveguides; Academic Press: New York, 1974. 2. Numerous articles in Integrated Optics; Tamir, T., Ed.; Topics in Applied Physics Vol. 7; Springer-Verlag: Berlin, 1975. 3. Lalama, S. J.; Sohn, J. E.; Singer, K. D. Proc. SPIE 1985, 578, 168. 4. Grunfield, F.; Pitt, C.W. Thin Solid Films 1983, 99, 249, 5. Carter, G. M.; Chen, Y. J.; Tripathy, S. K. Appl. Phys. Lett. 1983, 43, 891. 6. Goodwin, M. J.; Glenn, R.; Bennion, I. Electron. Lett. 1987, 22, 789. 7. Ulrich, R.; Weber, H.P. Appl. Opt. 1972, 11, 428. 8. Lipscomb, G. F.; Thackara, J.; Lytel, R.; Altman, J.; Elizondo, P.; Okazaki, E. Proc. SPIE 1986, 682, 125. 9. Schlotter, N. E.; Jackel, J. L.; Townsend, P. D.; Baker, G. L. Appl. Phys. Lett. 1990, 56, 13. 10. Nayar, B. K. In Nonlinear Optics: Materials and Devices; Flytzanis, C.; Oudar, J.L. Eds.; Springer-Verlag: Berlin, 1986, p 142. 11. White, K.I.; Nayer, B.K. Proc. SPIE 1987, 864, 162. 12. Kashyap, R. Proc. SPIE 1986, 682, 170. 13. Hopf, F.; Stegeman, G.I. Advanced Classical Electrodynamics Vol. II: Nonlinear Optics; John Wiley and Sons: 1986



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14. Shen, Y.R. The Principles of Nonlinear Optics; John Wiley and Sons: New York, 1984. 15. Stegeman, G.I.; Seaton, C.T. Applied Physics Reviews (J. Appl. Physics) 1985, 58, R57-78. 16. Stegeman, G. I.; Zanoni, R.; Finlayson, N.; Wright, E. M.; Seaton, C. T. J. of Lightwave Technology 1988, 6, 953. 17. Stegeman, G.I. In Proceedings of Erice Summer School on Nonlinear Waves in Solid State Physics; Boardman, A,D.; Twardowski, T., Eds.; in press 18. Ito, H.; Inaba, H. Opt. Lett. 1978, 2, 139. 19. Taniuchi, T.; Yamamoto, K. Digest of CLEO'86; Optical Society of America: Washington, 1986; paper WR3. 20. Lim, E. J.; Fejer, M. M.; Byer, R. L. Electron. Lett. 1989, 25, 174. 21. Lim, E.J.; Fejer, M.M.; Byer, R.L.; Kozlovsky, W.J. Electron Lett. 1989, 25, 731. 22. Lytel, R.; Lipscomb, F. Electro-Optic Polymer Waveguide Devices: Status and Applications, this volume 23. Khanarian, G.; Norwood, R.; Landi, P. Proc. SPIE 1989, 1147, 129. 24. Stegeman, G. I.; Wright, E. M.; J. Optical and Quant. Electron. 1990, 22, 95-122. 25. Mizrahi, V.; DeLong, K. W.; Stegeman, G. I.; Saifi, M. A.; Andrejco, M. J. Opt. Lett. 1989, 14, 1140. 26. DeLong, K.; Rochfort, K.; Stegeman, G. I. Appl. Phys. Lett. 1989, 55, 1823. 27. Townsend, P. D.; Jackel, J. L.; Baker, G. L.; Shelbourne III, J. A.; Etemad, S. Appl. Phys. Lett. 1989, 55, 1829. 28. Townsend, P.D.; Baker, G.L.; Jackel, J.L.; Shelburne III, J.A.; Etemad, S. Proc. SPIE 1989, 1147, 256. 29. Ye, C.; Minami, N.; Marks, T. J.; Yang, J.; Wong, G. In Nonlinear Optical Effects in Organic Polymers; Messier, J.; Kajzar, F.; Prasad P.; Ulrich, D.; Eds.; NATO ASI Series; Kluwer Academic Publishers: Dordecht The Netherlands; Vol 162, p 173. RECEIVED July 18, 1990


Waveguiding and Waveguide Applications of Nonlinear Organic

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