**2. Fiber-chip coupling**

The behavior of the optical beam can normally be described by classical ray optical func‐ tions for lenses with focus length and focus point. If the dimensions of the optical beam come close to 1.5μm, which is the wavelength used in optical networks, the behavior of the beam must be described by wave optical functions.

$$p(\mathbf{r}) = p(\mathbf{0}) \times \exp\left\{-2\left[\frac{\mathbf{r}}{\omega\_0}\right]^2\right\} \tag{1}$$

$$\mathcal{DW}\_0 \text{ =Mode field diameter(MFD)}$$

$$\mathbf{w}\_{0}(z) = \sqrt{\left[\mathbf{w}\_{0}^{2} + \left(\frac{z\mathcal{A}}{2n\pi\omega\_{0}}\right)^{2}\right]}\tag{2}$$

Here, the optical field within a wave-guide can be described nearly perfectly by a Gaussi‐ an intensity distribution, called p(r), which can be expressed with equation (1). If the wave travels within the waveguide, the mode field diameter is constant due to the com‐ bining function of the waveguide itself. At the end of the waveguide, the optical field is not guided and the field expands with increasing distance to the output facet. The expan‐ sion of the field can be calculated by equation (2). The point at which the intensity has fallen down to 1/e2 or 13.5% of the maximum intensity in radial direction, which is shown in figure 2, defines the mode field diameter.

**Figure 2.** Intensity distribution of the optical mode field.

different kinds of start of the art optical modules will be depicted followed by a short over‐

*"Opto-electronic packaging means working on the connection of opto-electronic integrated circuits to optical and electrical transmission lines and bias supply combined in a environmental stable housing."*

In the following several different technologies are listed which are essential to develop a

The behavior of the optical beam can normally be described by classical ray optical func‐ tions for lenses with focus length and focus point. If the dimensions of the optical beam come close to 1.5μm, which is the wavelength used in optical networks, the behavior of the

At this point I would like to define the opto-electronic packaging which was given by [8]:

view of long-term stability tests.

420 Optoelectronics - Advanced Materials and Devices

**Figure 1.** Basic package design for opto-electronic modules.

**2.** Classical ray tracing optics & wave optics

**3.** Mechanical construction / CAD-design

**5.** Heat dissipating management / cooling

beam must be described by wave optical functions.

**6.** Communications engineering

new package:

**1.** RF-technique

**4.** Wire bond technique

**7.** Solid state physics

**9.** Thick film circuits

**8.** Micro systems design

**10.** Gluing, welding, soldering

**2. Fiber-chip coupling**

After leaving the waveguide, the optical mode field radius, which is half of the spot-size, expands with increasing distance to the facet. For distances of less than 200 μm the field dis‐ tribution is called "near-field" and for larger distances "far-field". The angle where the in‐ tensity is fallen to 1/e2 or 13.5% of the maximum intensity is called "far-field angle" which corresponds to the near-field radius. These parameters are normally shown in the data sheets of laser diodes or LEDs.

For an efficient transfer of optical energy from the SMF and a laser diode wave guide, the mode profiles should "overlap" as much as possible which is described by [9]and is depict‐ ed in equation (3). The coupling efficiency between two Gaussian beams can be expressed by means of the mode fields of laser diode *w* ld, and fiber *w* SMF and also as a function of later‐ al, angular and longitudinal misalignment between the two wave guides:

$$\eta = \kappa \cdot \exp\left[-\kappa \left\{\frac{\mathbf{x}^2}{2} (1/\,\mathrm{w}\_{\mathrm{ID}}^2 + 1/\,\mathrm{w}\_{\mathrm{SMF}}^2) + \pi^2 \theta^2 \left[\,\mathrm{w}\_{\mathrm{ID}}^2(\boldsymbol{\varpi}) + \,\mathrm{w}\_{\mathrm{SMF}}^2\right] / 2\,\mathrm{\mathcal{X}}^2 - \mathrm{x}\_0 \theta \boldsymbol{\varpi} / \,\mathrm{w}\_{\mathrm{AWG}}^2\right\}\right] \tag{3}$$

Where

$$\mathbf{K} = \mathbf{4} \,\mathrm{w}\_{\mathrm{LD}}^2 \,\mathrm{w}\_{\mathrm{SMF}}^2 \left/ \left[ \left( \mathrm{w}\_{\mathrm{LD}}^2 + \mathrm{w}\_{\mathrm{SMF}}^2 \right)^2 + \mathrm{\mathcal{A}}^2 \boldsymbol{\varpi}^2 \, / \,\pi^2 \,\mathrm{n}\_{\mathrm{gap}}^2 \right] \tag{4}$$

The far field angle of the fiber is defined to a small value of 11.5°. A typical laser diode shows different values for lateral and vertical axis of 20° to 30° and 30° to 40°, respectively.

If one compares the field parameters of fiber and laser diode a great mismatch can be found. Consequently, the optical coupling efficiency between these two devices is very low. The coupling loss between the two fields without additional mechanical misalign‐ ments can be calculated in decibel with Saruwatari's formula from equ. (3), which can be

{ }

With this formula the mode field mismatches between the single mode components and the corresponding mismatch loss can be calculated to equ. (6), all lateral and angular misalign‐ ments of the fiber axis relative to the incident beam of the laser waveguide are set to zero.

Different mode fields can be adapted by so called "mode field transformers". These devices are, for example, lenses or lens systems, which are shown in figure 4. With these devices, a

1 2 2 1

<sup>4</sup> *<sup>R</sup> w w w w*

=

**Figure 4.** Mode field adaptation by an optical lens or lens system.

2

*Loss R R dB* ( ) 10log( ) » - [ ] (6)

<sup>+</sup> (7)

Opto-Electronic Packaging http://dx.doi.org/10.5772/51626 423

**Figure 3.** Far field of an optical fiber in comparison to the field of a laser diode.

simplified into the formula (7):

With

*λ*- wavelength

Ngap – referactive index of medium between the waveguide and fiber

X0 – lateral misalignment

θ- angular misalignment

Z – longitudinal misalignment

To measure the loss in decibel, the efficiency must be multiplied 10 times by the loga‐ rithm10 which is designated here as L:

$$L(\eta) = 10 \log(\eta) \quad \text{[dB]} \tag{5}$$

#### **3. Basic coupling concepts**

A comparison of the optical mode fields of the optical standard monomode fiber called SMF with a typical laser diode is shown in figure 3, where also the mode field diameter of a standard single mode fiber is depicted, respectively The properties of the SMF are standar‐ dized through the International Telecommunication Union [10].

The far field angle of the fiber is defined to a small value of 11.5°. A typical laser diode shows different values for lateral and vertical axis of 20° to 30° and 30° to 40°, respectively.

**Figure 3.** Far field of an optical fiber in comparison to the field of a laser diode.

tribution is called "near-field" and for larger distances "far-field". The angle where the in‐

corresponds to the near-field radius. These parameters are normally shown in the data

For an efficient transfer of optical energy from the SMF and a laser diode wave guide, the mode profiles should "overlap" as much as possible which is described by [9]and is depict‐ ed in equation (3). The coupling efficiency between two Gaussian beams can be expressed by means of the mode fields of laser diode *w* ld, and fiber *w* SMF and also as a function of later‐

> *w w w z w x zw LD SMF* p q

ë û ë û ï ï î þ

é ù ì ü ï ï =× + + + - ê ú í ý é ù

2 2 2 2 2 22 22 4 /( ) /

*gap* = ++ é ù

To measure the loss in decibel, the efficiency must be multiplied 10 times by the loga‐

*L*( ) 10log( ) dB

 h

A comparison of the optical mode fields of the optical standard monomode fiber called SMF with a typical laser diode is shown in figure 3, where also the mode field diameter of a standard single mode fiber is depicted, respectively The properties of the SMF are standar‐

*ww w w z n LD SMF LD SMF*

Ngap – referactive index of medium between the waveguide and fiber

h

dized through the International Telecommunication Union [10].

2 2 22 2 2 2 2

l

 p

*LD SMF*

0

 q*AWG* (3)

l

ë û (4)

= [ ] (5)

al, angular and longitudinal misalignment between the two wave guides:

exp - (1/ 1/ ) ( ) / 2 / <sup>2</sup>

or 13.5% of the maximum intensity is called "far-field angle" which

tensity is fallen to 1/e2

hk

Where

With

*λ*- wavelength

X0 – lateral misalignment

θ- angular misalignment

Z – longitudinal misalignment

rithm10 which is designated here as L:

**3. Basic coupling concepts**

sheets of laser diodes or LEDs.

422 Optoelectronics - Advanced Materials and Devices

0 2

k

x

 k

> If one compares the field parameters of fiber and laser diode a great mismatch can be found. Consequently, the optical coupling efficiency between these two devices is very low. The coupling loss between the two fields without additional mechanical misalign‐ ments can be calculated in decibel with Saruwatari's formula from equ. (3), which can be simplified into the formula (7):

$$Loss(R) \approx -10\log(R) \text{[dB]} \tag{6}$$

$$R = \frac{4}{\left(\bigvee\_{\mathbf{w}\_2} + \bigvee\_{\mathbf{w}\_1} \right)^2} \tag{7}$$

With this formula the mode field mismatches between the single mode components and the corresponding mismatch loss can be calculated to equ. (6), all lateral and angular misalign‐ ments of the fiber axis relative to the incident beam of the laser waveguide are set to zero.

**Figure 4.** Mode field adaptation by an optical lens or lens system.

Different mode fields can be adapted by so called "mode field transformers". These devices are, for example, lenses or lens systems, which are shown in figure 4. With these devices, a nearly perfect coupling between the two wave-guides is possible. Due to limitations in costs, several lens configurations have been proposed for the optical coupling of laser diodes to single mode fibers. As shown in figure 5, simple ball lenses can be used to adapt the two mode fields. Coupling efficiencies of up to 30% are possible. A better approach is the use of graded index lenses or Selfoc-lenses. For a focusing lens, so-called half-pitch devices are used. Whereas quarter-pitch lenses are used to form parallel beams. These can reach effi‐ ciencies of 70%. Another approach is to form a lens at the end of the fiber, which is called fiber taper. With this device, efficiencies up to 90% have been achieved.

handling of the parts because there are several parts including one ore two lenses, the fiber and the chip, which must be handled for optical alignment. The consequence is a rather cost‐

Opto-Electronic Packaging http://dx.doi.org/10.5772/51626 425

**Figure 6.** left side: Sketch of a melted fiber taper in front of an OEIC, right side: photograph.

**Figure 7.** X and Y-axis: 2µm tolerance for 0.5 dB additional coupling loss.

As an example for integrated lens design, lenses can be made at the end of the fiber by melting the glass fiber and pulling it. This kind of fiber end is called fiber taper and works like a lens with typical diameters from 20 μm to 50 μm. In figure 6 you can see at the left side the chip facet and its wave guide and at the right side the melted fiber taper in front of the wave-guide. The fiber is additionally fixed into a metal cannula. With these tapered fibers a coupling efficiency of more than 50% can be realized. Unfortunately, a high precision fixation of better than 0.5 μm is necessary to mount the tapered fiber in front of the OEIC without additional losses. Therefore, the mechanical resolution of the coupling mechanism must be better than this value. The fixing procedure after coupling should not introduce additional displacements and must be stable enough to fix the cou‐ pling mechanism, which is important for a good long-term stability. The short working distance of 10 μm between fiber taper and laser which can be seen in the photograph is

ly of opto-electronic packaging.

**Figure 5.** Mode field adaptation by several micro-optic solutions.
