I was in New York for Prime Minister Narendra Modi's visit, and returned to India before he turned his attention to Washington. Here are some quick impressions of the New York leg of his visit, jotted down on the plane. (More to follow on Washington, and Indo-US relations, when he concludes that visit.)

Mr Modi is undoubtedly already a considerable presence on the world stage. We should take with a fistful of salt the over-the-top pronouncements of his being a "rock star of diplomacy", but it is undeniable that with his style, commanding presence and overwhelming confidence, our Prime Minister has made an impact wherever he goes. (I was in Nepal the previous week and heard similar enthusiasm for his words and deeds there.)

This does not necessarily deliver results for India, but it does mean that the Indian leader's presence is noticed, in a very different manner from his understated predecessor. Dr Manmohan Singh was greatly respected for his intellect and his unrivalled expertise and wisdom on global economic issues; no one would seek Mr Modi's views on fiscal markets or quantitative easing. But as Mr Modi arrived at the UN with a thousand supporters cheering him on, or as he alighted from his vehicle to glad-hand curious onlookers, it was evident that India's leadership had emerged from the conference chambers and meeting rooms of international diplomacy to make a mark on the imaginations of people who have no place behind those closed doors.

The Prime Minister's speech to the UN General Assembly was a strong one. It was marked by a soaring internationalism that one could unembarrassedly call Nehruvian, effective messaging on environmentalism and terrorism, and a good response to Pakistan's needling on Kashmir. I did not hesitate, when asked by Barkha Dutt on NDTV, to award Mr Modi's performance at the podium an "A", a high rating indeed in the long and largely uninspiring annals of Prime Ministerial speeches at the UN.

By speaking in Hindi at the UN, Mr Modi reasserted his now-familiar brand of nativism and reached out to his principal audience back home. There was nothing intrinsically wrong with doing so; though Hindi is not one of the six official languages of the United Nations, leaders may speak in another one, provided they bear the costs of interpretation. Mr Modi is very much more comfortable in Hindi than in his somewhat wooden and stilted English, so he was right to play to his own strengths. The price he paid for that was that everyone in attendance at the General Assembly hall heard him through the filter of a translation, and his audience was not as attentive as he deserved.

The dangers of extempore speaking in international affairs also became apparent when the PM referred carelessly to Pakistan-Occupied Kashmir as "Pakistan" - unwise for an Indian Prime Minister, given that New Delhi still claims the territory to be ours. The official written transcript put out by the Indian delegation hastily corrected the error, but there must have been some gleeful chortling in Islamabad over the apparent relinquishing of a perennial Indian claim.

The visit to Ground Zero, site of the 9/11 terrorist attacks, was an excellent idea and situated India firmly on the right side on the issue of international terrorism. Pushing at the UN for a Comprehensive Convention on Terrorism was also well taken, though we still have a lot of work to do to overcome the reservations of many Islamic countries about the idea of such a convention and the specifics of the draft text we have been promoting.

Dropping in at a rock concert for charity at Central Park and saying a few words to the crowd there was a neat trick. One cannot imagine any other Indian Prime Minister doing it. Mr Modi is well on his way to creating a distinctively different Prime Ministry that is singularly his. Whether that can be leveraged to India's benefit, and not just for the PM's PR, remains to be seen.

The Madison Square Garden extravaganza went exactly as planned, even if it left some observers bemused. Mr Modi wanted to doff his cap to his enthusiastic supporters in the US, who had stood by him during the dark days of the visa denial and contributed heavily to his electioneering campaign efforts. His remarks were clearly addressed to them and to his broader circle of supporters across the US and of course in India: it was, in effect, a political campaign speech conducted on foreign soil. It inspired the audience, which was overwhelmingly BJP in orientation, and showcased the kind of crowds an Indian leader can command in the US. But though it was an Indian-American celebration of India in America, it received very little traction in the mainstream American media.

For all the razzmatazz, its relevance to Mr Modi's overall trip, however, was debateable. Perhaps it might have served to remind his critics in the US government how popular he is and that he should not be trifled with, but they knew that already. Perhaps, by having 41 US Congressmen waiting on stage for his arrival, he was signalling to Indian-Americans that he embodied their own increased political clout in this country, which they should not shy away from using in defence of the motherland. But at bottom it was a self-indulgent love-fest for a leader who never seems to tire of reaffirming his larger-than-life heroic status in the public eye.

Mr Modi will soon leave the US to return to India. But the sub-text of his New York peregrinations is amply clear, and he wants us all to know it: Prime Minister Modi has arrived, and the rest of the world had better pay attention.