Pulse Compression

Pulse compression techniques are an important application of nonlinear and dispersive effects in optical fibres. They have enabled pulses as short as 6 fs to be generated^* - the shortest optical pulses ever reported which were only six optical cycles in length. There are two possible schemes for pulse compression depending on the wavelength region of interest - fibre-grating/prism pulse compressors which use fibres in the normal dispersion region followed by a grating or prism sequence providing negative GVD and soliton effect compressors which use higher order solitons supported in the anomalous dispersion region of optical fibres.

The basic idea for pulse compression was borrowed from chirp radar where microwave pulses having an initial frequency chirp were passed through a dispersive delay line. As outlined above, a linear dispersive medium will impose a linear frequency chirp on pulses propagating through it. If the product of the chirp parameter and the GVD parameter, P2C < 0, then the dispersion induced chirp will tend to cancel the initial chirp and a shorter pulse can be obtained at the output of the delay line. For maximum effect the input pulse

Figure 1.10. Schematic diagram of the diffraction-grating pair used for extracavity pulse compression.

should be linearly chirped so that the GVD (which also produces a linear chirp) can provide complete cancellation. The delay line must be constructed so that this cancellation occurs at its output.

The first experiments, which involved compression of inherently chirped pulses, used the dispersion provided by liquids or solids or by a grating pairi*9,S0 i% 9 it was suggested that the nonlinear process of SPM could be used for pulse compression^!, but the idea was not d e m o n s t r a t e d ^ ^ until single mode optical fibres became available in the 1980’s. In the fibre grating compressor the combined action of SPM and GVD in the fibre provides a nearly linear positive frequency chirp on the pulse and a grating pair then provides the required negative GVD. In soliton compression schemes only a single length of fibre is used. The pulse propagates in the anomalous dispersion regime and is compressed through the interplay of SPM and GVD which leads to soliton formation and pulse compression under the proper conditions. The compression results from the initial narrowing phase through which all higher order solitons go before the initial shape is restored after one soliton period. It is the peak power that determines the soliton order and hence the final compression factor.

Soliton effect compressors are only effective in the anomalous dispersion region where solitons can be propagated. Fibre grating compressors can be used in the normal dispersion region and will now be considered in more detail. The different spectral components of a

Chapter 1: Introduction and Basic Theory 40

pulse incident on a diffraction grating will be diffracted at slightly different angles and as a result will experience different time delays during their passage through a grating pair. The blue shifted components arrive before the red ones and so the trailing edge of a positively chirped pulse can catch up with the leading edge as it travels through the grating pair.

Referring to figure 1.10, it can be shown that for first order diffraction, the angle of diffraction from the normal to the grating is given by

sinQr = ^ - sinOi (1.34)

where A is the grating period, ie. the line spacing and 6| is the angle of incidence. The time delay for propagation through the gratings is

l(co) _ ^ dco

tdW = ^ (1.35)

where l(co) is the optical path length and (j)(co) is the phase shift acquired by light of frequency CO. This phase shift can be expanded as a Taylor series about cOg. The second order coefficient in this expansion is given by'*!

_ 47ç2cbg CO^A^cosOig

where 6j-g is given by equation (1.34) with co = cog and where bg - dg secG^g is the centre- to-centre grating spacing. The grating pair produces a negative phase shift which corresponds to an anomalous dispersion with an effective GVD parameter given by

P f = - ^ (1.37)

Grating pairs have a few disadvantages associated with them. The output pulses are spatially dispersed so that the output beam is elliptical in shape, however, a double pass configuration can be used to remedy this problem and double the available GVD. Also, because most gratings are only 60 - 80% reflective in the first order there is a factor of two reduction in the energy throughput of a grating pair and a factor of four for a double pass

configuration. Alternatively, a Gires-Toumois interferometer or a prism sequence can be used which generally have much smaller losses. The GVD provided by a prism sequences is, however, much smaller so that larger separations are required - often by two orders of magnitude. High dispersion materials such as Te02^^ or ZnSe^^ and high dispersion configurations may be used to make the separation more convenient, but these have correspondingly higher third order dispersion.

To get the best performance fi-om a compressor it is important to be able to estimate the optimum fibre length and grating separation required to produce high quality output pulses with maximum compression for a given set of input pulse parameters. The fibre grating compressor can be modelled by numerically solving the wave equation governing pulse propagation in the fibre in the presence of GVD and SPM. The output pulse obtained from this analysis is then used as the input to the grating pair. The parameter a^ given by equation (1.36) can be adjusted to obtain the optimum pulse compression, ie. the peak power at the output is maximised.

The results show that the SPM induced frequency chirp in the absence of GVD, is linear only over the central portion of the pulse so that only this part can be properly compressed. A significant amount of energy remains in the wings so that the resulting pulses are not of a high quality. Fortunately SPM in the presence of GVD, broadens and reshapes the pulse to become nearly rectangular with a nearly linear frequency sweep across its entire width. The gratings or prisms can therefore compress most of the energy into a short pulse, but the benefits of improved quality are only achieved at the expense of reduced compression at a given value of input peak power.

The results of the simulations suggest some simple design rules for optimising the performance of the pulse compressors^. These can be expressed mathematically as follows

^ = W (138)

Chapter 1: Introduction and Basic Theory 42

(•■«)

where Zqp^ is the optimum fibre length to just linearise the SPM induced chirp, Xj and x^ are the full widths at half maximum intensity of the input and compressed pulses respectively and Fg is the compression factor. The parameters, zg and N, are those already identified for soliton propagation. The soliton period, zg, also has an useful interpretation in the normal dispersion region - it is the length at which the initial pulse width has nearly doubled in the absence of SPM55.

The factor of 1.6 is dependent on the input pulse shape being sech^ and is slightly different for other pulse shapes, however if N > 10 this slight difference can be ignored. These equations also assume unchirped input pulses, but again provided N > 10, the effects of chirp are typically less than 10% on the final pulse shapes. The effects of higher-order nonlinearity and dispersion have also been neglected, which provides an accurate approximation provided Aco « cog. The results have been shown to be fairly accurate for Xp > 200 fs. Further, if Xp < 100 fs, the gratings no longer act as quadratic compressors and the cubic phase terms become important^. It is also worth noting that the pulse energies in the fibre should be kept below the Raman t h r e s h o l d ^ ^